Surface warming and wetting due to methane’s long-wave radiative effects muted by short-wave absorption

Although greenhouse gases absorb primarily long-wave radiation, they also absorb short-wave radiation. Recent studies have highlighted the importance of methane short-wave absorption, which enhances its stratospherically adjusted radiative forcing by up to ~ 15%. The corresponding climate impacts, however, have been only indirectly evaluated and thus remain largely unquantified. Here we present a systematic, unambiguous analysis using one model and separate simulations with and without methane short-wave absorption. We find that methane short-wave absorption counteracts ~30% of the surface warming associated with its long-wave radiative effects. An even larger impact occurs for precipitation as methane short-wave absorption offsets ~60% of the precipitation increase relative to its long-wave radiative effects. The methane short-wave-induced cooling is due largely to cloud rapid adjustments, including increased low-level clouds, which enhance the reflection of incoming short-wave radiation, and decreased high-level clouds, which enhance outgoing long-wave radiation. The cloud responses, in turn, are related to the profile of atmospheric solar heating and corresponding changes in temperature and relative humidity. Despite our findings, methane remains a potent contributor to global warming, and efforts to reduce methane emissions are vital for keeping global warming well below 2 °C above preindustrial values. Climate simulations suggest that the contribution of methane to climate warming and wetting due to absorption of long-wave radiation is partially counteracted by short-wave absorption.

The atmospheric concentration of methane (CH 4 ) has increased by about a factor of 2.4 since preindustrial times (from ~0.75 to 1.8 parts per million by volume (ppm)), resulting in an effective radiative forcing (ERF; Methods) of 0.496 ± 0.099 W m −2 (from 1850 to 2019) 1 , with similar estimates based on the stratospherically adjusted radiative forcing (SARF; Methods) [2][3][4] . Due to methane's potency as a greenhouse gas (its global warming potential is 27.9 times that of CO 2 on a 100 yr time horizon 5 ), its relatively short lifetime (~1 decade) and chemical reactions in the atmosphere (for example, tropospheric ozone production), considerable interest exists in targeting CH 4 emissions to mitigate climate change and to improve air quality 4,6-13 . Article https://doi.org/10.1038/s41561-023-01144-z Under fSST experiments, CH 4 radiative effects can induce an ERF, which includes both the IRF and ADJs (change in state in response to IRF, but excluding changes in sea surface temperatures). Rapid adjustments can be LW adjustments (for example, tropospheric and stratospheric temperatures), SW adjustments (surface albedo) or both SW and LW adjustments (clouds). The coupled ocean-atmosphere experiments quantify the total climate response, including the IRF, ADJs and the slow, surface-temperature-mediated effects. Figure 1 shows the global mean change in near-surface air temperature and precipitation in coupled ocean-atmosphere CESM2 simulations, which is the total response (including IRF, adjustments and surface-temperature-mediated feedbacks) to increases in atmospheric methane concentrations, including 2×CH 4 , 5×CH 4 and 10×CH 4 relative to preindustrial (see also Extended Data Figs. 1 and 2). For all three perturbations, CH 4LW -which represents the total climate response to methane LW IRF, adjustments and feedbacks-yields an increase in near-surface air temperature and precipitation (warming and 'wetting'). Significant global mean warming of 0.09, 0.68 and 1.24 K occurs for 2×CH 4LW , 5×CH 4LW and 10×CH 4LW ; similarly, global wetting of 0.001 (not significant at the 90% confidence level), 0.035 and 0.063 mm d −1 occurs (corresponding precipitation changes are 0.04, 1.2 and 2.1%). Interestingly, CH 4LW+SW -which represents the total climate response to methane LW + SW IRF, adjustments and feedbacks-yields muted warming and wetting (except for 2×CH 4LW+SW ). This is due to SW effects (including the IRF, adjustments and feedbacks), where significant global cooling occurs for 5×CH 4SW and 10×CH 4SW at −0.23 and −0.39 K. Similarly, a significant decrease in global mean precipitation occurs under these two methane perturbations at −0.021 and −0.039 mm d −1 (−0.7 and −1.3%). Most of the precipitation decrease occurs over tropical oceans (for example, Extended Data Fig. 2c).

Methane SW versus LW total climate responses
The decrease in precipitation is consistent with atmospheric energetic constraints-in the global mean, the primary balance is between net atmospheric radiative cooling and condensational heating from precipitation 16,[24][25][26] . As atmospheric SW absorption increases, net radiative cooling decreases, which is consistent with a decrease in Recent studies [14][15][16][17] have highlighted the importance of CH 4 short-wave (SW) absorption at near-infrared wavelengths-which is lacking in many climate models 1 -resulting in up to an ~15% increase in its SARF compared with the long-wave (LW) SARF 19 . A more recent study 20 found a smaller increase in SARF, at 7%, which was attributed, in part, to the inclusion of CH 4 absorption of solar mid-infrared radiation in the 7.6-μm-band spectral region. The reduced forcing is because this spectral region impacts mainly stratospheric absorption. CH 4 SW absorption has regional 'hotspots', including near bright surfaces (for example, deserts) and above clouds (for example, oceanic stratus cloud decks) 21 . Such bright regions enhance the upward reflection of sunlight, which in turn enhances top-of-the-atmosphere (TOA) and tropopause CH 4 SW instantaneous radiative forcing (IRF). Considerable uncertainty exists, however, as this forcing depends on several quantities, including the cloud radiative effect, CH 4 vertical profile 20 and surface albedo specification 20 . In particular, large spatial gradients in the SW forcing are caused by near-infrared surface albedo 21 .
These studies focus largely on how CH 4 SW absorption impacts its radiative forcing, with some also addressing the corresponding rapid adjustments (ADJs, surface-temperature-independent responses). For example, CO 2 and CH 4 (with SW absorption) fixed sea surface temperatures (SST) and slab ocean simulations were compared to show that ADJs associated with CH 4 SW radiative effects act to mute precipitation increases 16 due to enhanced warming of the upper troposphere and lower stratosphere (UTLS). Methane SW ADJs were also investigated in Precipitation Driver and Response Model Intercomparison Project (PDRMIP) 22 simulations. Models that lack CH 4 SW absorption yield a positive overall ADJ (acting to increase net energy into the climate system), whereas models that include CH 4 SW absorption yield a negative overall ADJ (acting to increase net energy out of the climate system) 18 . This difference is due to a more negative tropospheric temperature adjustment and negative as opposed to positive stratospheric and cloud adjustments in models that include CH 4 SW absorption. These negative adjustments, in turn, are consistent with stronger UTLS warming, which promotes enhanced outgoing LW radiation to space and high-level cloud reductions, which further promote enhanced outgoing LW radiation. Although other model differences (for example, cloud parameterizations and CH 4 vertical profile) may impact this result, the implication is that CH 4 SW absorption may not lead to additional surface warming.
Although the importance of CH 4 SW absorption has been recognized, a comprehensive (and systematic) analysis of how it impacts the climate system remains to be conducted. In this study, we perform experiments to rigorously assess CH 4 SW radiative impacts on the climate system, including ADJs, surface-temperature-mediated feedbacks and the overall climate response.

Results
A suite of idealized methane-only time-slice perturbation simulations (Table 1 and Methods) are conducted with the National Center for Atmospheric Research Community Earth System Model version 2.1.3 (CESM2) 23 . CESM2 includes the newest model components, including the Community Atmosphere Model version 6 (CAM6). Unlike many climate models 18 , CAM6 includes CH 4 SW absorption in the near-infrared bands except the mid-infrared band in its radiative transfer parameterization. For each methane perturbation (2×, 5× and 10× preindustrial atmospheric CH 4 concentrations) considered and ocean boundary condition (fixed climatological sea surface temperatures, fSST, versus coupled ocean), we conduct pairs of identical experiments, one that includes CH 4 LW + SW radiative effects and one that lacks CH 4 SW radiative effects (Table 1). This allows quantification of the response signals (relative to preindustrial CH 4 ) to CH 4 LW + SW, LW and SW radiative effects, abbreviated as CH 4LW+SW , CH 4LW and CH 4SW , respectively. Under radiative transfer experiments (Methods), CH 4 radiative effects include the IRF only (the initial perturbation to the radiation balance).  (Fig. 1a,b). Figure 1c shows the corresponding near-surface air temperature response, decomposed into CH 4LW+SW , CH 4LW and CH 4SW . We find global warming of 0.17 K in response to present-day CH 4 (relative to preindustrial); this is decomposed into warming of 0.20 K from CH 4LW and −0.04 K (cooling) from CH 4SW . Our estimate of 0.17 K for CH 4LW+SW is less than that given in the newest IPCC report (based on 2019 relative to 1750 and a two-layer emulator) at 0.28 K, with a 5-95% range of 0.19 to 0.39 K (ref. 1 ) (discussed in Supplementary Note 1). For global mean precipitation (Fig. 1d), precipitation increases of 0.16% and 0.31% occur for CH 4LW+SW and CH 4LW , respectively; a precipitation decrease of −0.15% occurs under CH 4SW . The apparent hydrological sensitivities (defined as the change in precipitation divided by the change in surface temperature) 27 are 0.97, 1.51 and 4.30% K −1 for CH 4LW+SW , CH 4LW and CH 4SW , respectively ( Fig. 1e; discussed in Supplementary Note 2). Our decomposition helps to explain the larger apparent hydrological sensitivity to methane found in PDRMIP models (many of which lack CH 4 SW radiative effects; discussed in Supplementary Note 2).

Radiative flux components
To understand the cause of the CH 4SW surface cooling in coupled simulations, we evaluate the radiative flux components (Methods)-including ERF, IRF and the ADJs-in the fSST experiments. Figure 2a shows the TOA radiative flux components in response to 10×CH 4LW+SW , 10×CH 4LW and 10×CH 4SW . The IRF is 2.08 W m −2 , with 10×CH 4LW and 10×CH 4SW both contributing positive values at 1.81 and 0.27 W m −2 , respectively. Thus, the 10×CH 4SW IRF increases the 10×CH 4LW IRF by 15% (13% for 5×CH 4 and 2×CH 4 ). A previous study found a similar 15% increase under a 750-1,800 ppb CH 4 perturbation 20 . A smaller increase of 6% was found at the tropopause 19 , but the partitioning of SW IRF and LW IRF at the tropopause will differ from the TOA 17 . We also note that the presence of clouds increases the 10×CH 4SW IRF from 0.20 W m −2 under clear-sky conditions to 0.27 W m −2 under all-sky conditions (a 35% increase; 5×CH 4SW and 2×CH 4SW yield 27% and 33% increases, respectively). The increased 16 ppm) and 10×CH 4 (7.11 ppm) from coupled simulations (which include the IRF, adjustments and feedbacks). Responses are decomposed into CH 4LW+SW , CH 4LW and CH 4SW . Also included are the least-squares regression lines (dotted). Solid circles represent a significant response at the 90% confidence level, based on a standard t test. The thin black vertical line shows the present-day CH 4 perturbation of 1.1 ppm. c-e, The estimated (from the regressions) present-day CH 4 climate responses for near-surface air temperature (c), precipitation (d) and apparent hydrological sensitivity (e). Except for e, the CH 4LW+SW bar is equal to the sum of the CH 4LW and CH 4SW bars. Error bars in c-e show the 1 s.d. uncertainty estimate of the regression slope, which is estimated from the three like-coloured data points (CAM6 methane simulations) in a and b. The error-bar centre is the regression-estimated response.
The 10×CH 4SW+LW and 10×CH 4LW ERFs are also positive, at 1.69 and 2.13 W m −2 , respectively, but the 10×CH 4SW ERF is negative, at −0.44 W m −2 . Thus, 10×CH 4SW acts to reduce the 10×CH 4LW ERF by 21%. The difference between ERF and IRF is due to ADJs; 10×CH 4SW+LW yields a negative ADJ, at −0.40 W m −2 , which is due to the 10×CH 4SW of −0.77 W m −2 (relative to the positive ADJ for 10×CH 4LW of 0.37 W m −2 ). Thus, 10×CH 4SW drives a strong negative ADJ, offsetting its smaller positive IRF (by a factor of ~3), leading to a negative ERF of −0.44 W m −2 . This 10×CH 4SW negative ERF is consistent with the corresponding decrease in near-surface air temperature previously discussed (Fig. 1). We note that some of the 10×CH 4SW adjustments are LW adjustments (discussed in 'ADJ decomposition').
Qualitatively similar results are obtained from 5×CH 4 and 2×CH 4 (Supplementary Note 3 and Extended Data Fig. 3). Atmospheric and surface radiation contributions to the TOA radiation (ERF) changes are discussed in Supplementary Note 4 (see also Supplementary Fig. 1).

ADJ decomposition
To further understand the ADJs and climate impacts of CH 4 SW absorption, Fig. 2b shows the decomposition of TOA ADJs (for 10×CH 4 ) into the tropospheric temperature, stratospheric temperature, surface temperature, water vapour, albedo and cloud adjustment (Methods). Clouds are the main driver of the relatively large negative 10×CH 4SW ADJ. The corresponding cloud adjustment is −0.58 W m −2 , which is 75% of the total ADJ. The stratospheric temperature adjustment also contributes, at −0.15 W m −2 , as does the tropospheric temperature adjustment, at −0.11 W m −2 . The water-vapour adjustment-at 0.10 W m −2 -acts to oppose these negative adjustments. The remaining ADJs, including surface temperature and albedo, are relatively small. Similar results are obtained for 5×CH 4 and 2×CH 4 (Extended Data Fig. 4).
The 10×CH 4SW cloud adjustment (Fig. 2b) is due to both SW radiation, at −0.42 W m −2 (Extended Data Fig. 4c), and LW radiation, at −0.16 W m −2 (Extended Data Fig. 4b). The corresponding 10×CH 4SW temperature and water-vapour adjustments are consistent with atmospheric warming (particularly in the UTLS; Fig. 3b), which leads to enhanced outgoing LW radiation (a negative LW adjustment; Extended Data Fig. 4b); the warming likewise increases water vapour (a greenhouse gas), which acts to decrease outgoing LW radiation (a positive LW adjustment; Extended Data Fig. 4b). Supplementary Note 5 discusses the decomposition of surface (and atmospheric) ADJs for 10×CH 4 (see also Supplementary Fig. 2).
Recent analyses 3,18 have shown similar results across different kernels [28][29][30] , including the Geophysical Fluid Dynamics Laboratory kernel used here. Nonetheless, we repeat our ADJ calculations with the CloudSat/CALIPSO 30 radiative kernel and find similar results (Supplementary Note 6 and Extended Data Fig. 5).

Understanding the cloud adjustment
The negative 10×CH 4SW cloud adjustment-including negative TOA SW and LW contributions-is consistent with the change in the global mean vertical profile of cloud cover (Fig. 3d, dashed line). This includes increased low-level cloud cover (peaking at 800 hPa) and enhanced reflection of SW radiation (a negative adjustment) but decreased high-level cloud cover (peaking at 100 hPa) and enhanced outgoing LW radiation (a negative adjustment). The change in the vertical profile of cloud cover is related to the change in relative humidity (RH), which increases below ~500 hPa but decreases aloft (Fig. 3c, dashed line). The corresponding correlation, r, from the surface up to the lower stratosphere (up to ~100 hPa) is 0.86, suggesting an increase (decrease) in RH is associated with more (fewer) clouds. The change in RH is consistent with the change in the vertical profile of temperature (r = −0.76; Fig. 3b, dashed line), which in turn is related to the atmospheric SW heating rate (r = 0.88; 3a dashed line). Thus, we suggest the 10×CH 4SW cloud response is driven ultimately by the atmospheric SW heating-rate profile, which decreases in the low/mid troposphere (below ~700 hPa) but increases aloft, peaking in the UTLS at 100 hPa. This is consistent with the traditionally defined aerosol-cloud semi-direct effect 31-34 , whereby solar heating (for example, from black carbon) increases atmospheric temperature and decreases RH, leading to cloud burn-off (with the opposite occurring in the lower troposphere). Atmospheric cooling below ~800 hPa and warming aloft also imply an increase in stability, which is also probably associated with the increase in low cloud cover. Similar responses occur under 5×CH 4 ( Supplementary  Fig. 3) and (although weaker) 2×CH 4 ( Supplementary Fig. 4).

Atmospheric SW heating response profile
The global annual mean CH 4 instantaneous SW heating-rate response profile is not related to the vertical profile of the CH 4  Article https://doi.org/10.1038/s41561-023-01144-z which in CESM2/CAM6 has a uniform distribution in the troposphere (up to ~200 hPa) and then exponentially decreases aloft (Extended Data Fig. 6), consistent with chemical destruction of CH 4 above the tropopause. Instead, the instantaneous SW heating-rate response profile is related to overlap of the three CH 4 SW absorption bands with water vapour. Under clear-sky conditions, with water-vapour SW absorption in the three methane SW bands (Methods) turned off (using the Parallel Offline Radiative Transfer (PORT) model), the vertical profile of CH 4 SW instantaneous absorption is relatively uniform in the troposphere, peaking in the UTLS (Fig. 4a). Adding back the SW absorption by water vapour leads to the characteristic SW heating-rate response profile (as in Fig. 3a), with decreases in the lower troposphere and increases aloft, peaking in the UTLS. As expected, the 10×CH 4SW clear-sky IRF increases (from 0.20 to 0.40 W m −2 ) when the overlapping SW absorption by water vapour is turned off. Since water vapour is at its maximum in the lower troposphere, these SW absorption bands are already highly saturated in the lower atmosphere at preindustrial CH 4 concentrations, so perturbing methane does not lead to an increase in SW heating here. However, methane SW radiative effects enhance SW absorption aloft (increase in SW heating rate). This reduces the amount of solar radiation in these three bands that can be subsequently absorbed by water vapour in the lower troposphere, which results in the SW heating-rate decrease below ~700 hPa. Similar results are obtained under all-sky conditions (Fig. 4b).
The 10×CH 4SW IRF increases (from 0.27 to 0.43 W m −2 ) when the overlapping SW absorption by water vapour is turned off. Here, however, even with water-vapour SW absorption (in the three methane bands) tuned off, there is still a decrease in the instantaneous SW heating rate near 800 hPa. This appears to be related to clouds, which peak at about the same level. Extended Data Fig. 7 shows similar plots but based on three different latitude bands: the low latitudes (30° S-30° N); mid-latitudes (30° N-60° N and 30° S-60° S) and the high latitudes (60° N-90° N and 60° S-90° S). There are some differences relative to the global mean (Fig. 4), but the results are generally similar. For example, absorption by water vapour (in the three methane bands) is more important in the low latitudes (Extended Data Fig. 7e), consistent with the larger amount of water vapour (specific humidity) in the tropics. To summarize, methane SW instantaneous radiative effects result in a vertical redistribution of atmospheric SW heating, with enhanced SW heating aloft (maximizing in the UTLS) but decreased SW heating in the lower troposphere. This, in turn, leads to the corresponding cloud-cover changes (increased low-level but decreased high-level cloud cover) and negative cloud adjustment, through modification of atmospheric temperature and relative humidity. Figure 5 shows the radiative kernel decomposition applied to the coupled ocean-atmosphere simulations for 10×CH 4SW (5×CH 4SW and 2×CH 4SW are included in Supplementary Fig. 5). We also include the previously discussed ADJs ('fast' responses from the fSST runs) and the difference between the coupled and fSST decompositions (the surface-temperature-induced 'slow' feedbacks). Note that we do not In most cases, the slow feedback dominates the sign of the overall response, consistent with the climate system acting to restore TOA radiative equilibrium. For example, the slow tropospheric temperature feedback is positive at 1.14 W m −2 (which is offset to some extent by the water-vapour feedback at −0.62 W m −2 ). Both of these feedbacks are consistent with tropospheric cooling (Supplementary Fig. 6b).

Climate feedbacks under methane SW radiative effects
For clouds, however, the ADJ and the slow feedback are both negative, with a larger value for the ADJ, at −0.58 versus −0.37 W m −2 . Thus, the surface cooling in response to CH 4 SW radiative effects is due largely to cloud ADJs, but surface-temperature-induced cloud feedbacks also act to cool the planet.
The 10×CH 4SW cloud feedback is dominated by increases in low-level (and mid-level) clouds, with weaker decreases in high-level clouds ( Supplementary Fig. 6d and Supplementary Note 7). Similar results exist for 5×CH 4SW (Supplementary Fig. 7), but weaker results exist for 2×CH 4SW (Supplementary Fig. 8 and Supplementary Note 7).

Conclusions
Using targeted climate model simulations, we have shown that methane SW absorption and the associated ADJs act to reduce its ERF by ~20% and mute its warming and wetting effects in coupled simulations by up to 30% and 60%, respectively. Similar simulations with additional climate models are needed to understand the robustness of the results presented here-particularly since the CH 4 SW IRF is dependent on uncertain quantities, such as the cloud radiative effect 21 , the surface albedo 20,21 and the CH 4 vertical profile 20 . However, the indirect assessment of multiple models from PDRMIP CH 4 simulations supports our findings 18 . In fact, expanding on the results of ref. 18 , we find a 20% decrease in ERF, 45% less warming and 65% less wetting in models that include CH 4 SW absorption versus those that do not (Supplementary Note 8 and Extended Data Fig. 8).
Although the SW radiative effects associated with the present-day methane perturbation remain relatively small, they could be quite large by the end of the century-Shared Socioeconomic Pathway 3-7.0, which lacks climate policy and has 'weak' levels of air-quality control measures 7,35,36 , features end-of-century increases of CH 4 concentrations approaching 5× preindustrial (3.4 ppm). Overall, methane remains a potent contributor to global warming, and emissions reductions are a vital component of climate change mitigation policies and for continued pursuit of the climate goals laid out under the Paris Agreement.

Online content
Any methods, additional references, Nature Portfolio reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41561-023-01144-z. Also includes the climatological SH. b, Instantaneous atmospheric all-sky (with clouds) SW heating rate (QRS IRF; as in Fig. 3a) and the corresponding SW heating rate without water-vapour SW absorption (QRS IRF noH2Ov) in the same three near-infrared bands that methane absorbs in. Also includes the climatological cloud fraction (CLOUD).

Radiative-forcing definitions
The IRF is the initial perturbation to Earth's radiation budget and does not account for ADJs. We diagnose IRF using the PORT model 37 , which isolates the Rapid Radiative Transfer Model for general circulation models (RRTMG) 38,39 radiative transfer computation from the CESM2-CAM6 model configuration (more details on RRTMG are presented in 'CESM2/CAM6 simulations'). PORT simulations are run for 16 months; the last 12 months are used to diagnose annual mean IRF. PORT is also used to verify our methodology to remove RRTMG CH 4 SW absorption (the SW IRF is zero in the CH EXP 4NOSW and PI EXP NOSW experiments, and the LW IRF is unchanged).
The ERF is defined as the net TOA radiative flux difference between the perturbed and base simulation, with climatological fixed SSTs and sea-ice distributions and no correction for land surface-temperature change 40 . We note that the contribution of land surface warming/ cooling to the ERF in our simulations is relatively small (<5% of the ERF; Supplementary Note 9). ERF can be decomposed into the sum of IRF and the ADJs.
The SARF is equal to the sum of the IRF and the stratospheric temperature adjustment. Thus, the difference between ERF and SARF is that ERF includes all adjustments, whereas SARF includes only the adjustment due to stratospheric temperature change 2,41,42 .

CESM2/CAM6 simulations
We conduct pairs of identical simulations, one that includes CH 4 LW+SW radiative effects (CH EXP 4 ) and one that lacks CH 4 SW radiative effects (CH EXP 4NOSW ; Table 1). The latter simulations are conducted by turning off CH 4 SW absorption in the three near-infrared bands-1.6-1.9 μm, 2.15-2.50 μm and 3.10-3.85 μm-in CAM6's radiative transfer parameterization (RRTMG). RRTMG does not include methane SW absorption in the mid-infrared band at 7.6 μm. The sign of the CH 4 SW IRF (at the tropopause) depends on the increased absorption in the troposphere since the downward SW flux at the tropopause is always decreased due to absorption in the stratosphere 19 . Including the 7.6 μm band primarily increases CH 4 SW absorption in the stratosphere 20 . This reduces the forcing from the downward irradiance, with negligible change to the forcing from the upward irradiance; that is, the tropopause SW IRF is reduced. Thus, if RRTMG included the 7.6 μm methane band, we would expect the CH 4 SW IRF at the TOA to increase due to the increase in stratospheric absorption. This, however, will result in a larger (negative) stratospheric temperature adjustment.
RRTMG is an accelerated and modified version of RRTM and uses the correlated k-distribution method to treat gas absorption 39 . RRTMG calculates irradiance and heating rate in broad spectral intervals while retaining a high level of accuracy relative to measurements and high-resolution line-by-line models. Sub-grid cloud characterization is treated in both the LW and SW spectral regions with the Monte Carlo Independent Column Approximation 43 using the maximum-random cloud overlap assumption. RRTMG divides the solar spectrum into 14 SW bands that extend over the spectral range from 0.2 μm to 12.2 μm. The infrared spectrum in RRTMG is divided into 16 LW bands that extend over the spectral range from 3.1 μm to 1000.0 μm.
Few studies have evaluated broadband radiative transfer codes against benchmark calculations, particularly for CH 4 SW IRF. This is in part because the radiation parameterization in many climate models lacks an explicit treatment of CH 4 SW absorption 14,18 . The 6-band SOCRATES SW spectral file configuration used in the Met Office Unified Model significantly underestimates CH 4 SW tropopause and surface IRF by around 45% compared with the 260-band configuration 20 . Similarly, RRTMG-the radiative transfer model used here-was recently found to underestimate CH 4 (and CO 2 ) SW IRF by 25-45% (ref. 44 ). This implies that there are opportunities for improvement in the parts of the spectrum where the absorption by these gases is weak but not zero. Thus, incorporating CH 4 SW absorption in more models' radiative transfer codes is only part of the solution-making sure their radiative transfer codes have a validated treatment of SW absorption by CH 4 (and other greenhouse gases) is also vital. We also note that N 2 O is not represented in the SW part of RRTMG.
The Community Land Model version 5 45 provides both the surface albedo, area-averaged for each atmospheric column, and the upward LW surface flux, which incorporates the surface emissivity, for input to the radiation. For the SW, the surface albedos are specified at every grid point at every time step. The albedos are partitioned into two wavebands (0.2-0.7 μm and 0.7-12.0 μm) for both direct and diffuse incident radiation 46 . Surface albedos for ocean surfaces, geographically varying land surfaces and sea-ice surfaces are distinguished. They depend on the solar zenith angle, the amount and optical properties of vegetation and the optical properties of snow and soil 45 .
Rapid adjustments-which can be SW or LW adjustments-are estimated by subtracting the preindustrial control (PI EXP ) fSST experiment from each perturbation fSST experiment. For example, to quantify the ADJs in response to a tenfold increase in preindustrial atmospheric methane concentration, we take the 10×CH 4 fSST simulation minus the preindustrial fSST simulation (10×CH EXP 4 − PI EXP ). This signal (10×CH 4LW+SW ) includes the methane LW+SW IRF and its impact on LW and SW adjustments under the fSST boundary condition (ERF = IRF + adjustments). ADJs due to CH 4  . Specific details on how the ADJs are estimated (via radiative kernels) are discussed in 'Calculation of ADJs'. A similar procedure is used to quantify the total climate impacts from the coupled ocean simulations, which include the IRF, adjustments and surface-temperature-mediated feedbacks.
We note that an alternative experimental design where methane LW radiative effects are removed could be implemented. As our goal is to understand the impacts of adding CH 4 SW absorption (which many models lack) to the LW forcing (which models already have), our experimental design is based on the all-but-one type of experimental design. Our simulations therefore target the inclusion of CH 4 SW absorption, allowing quantification of its associated ADJs and climate impacts. This is in contrast to the studies discussed, which evaluate CH 4 SW radiative effects either by contrasting CH 4 versus CO 2 (which lacks strong SW absorption) simulations 16 or by comparing models that include CH 4 SW absorption with models that do not 18 . In the latter, other model differences (for example, cloud parameterizations and CH 4 vertical profile) may be important.
All CESM2/CAM6 simulations are conducted with a 1.9° × 2.5° horizontal resolution and 32 vertical levels in the atmosphere. Fixed SST experiments are run for 32 years each, the last 30 of which are used to quantify ERF and the ADJs/fast responses. Coupled ocean simulations are run for 90 years each, starting from a pre-spun-up preindustrial control simulation in year 321. The last 40 years of the coupled experiments-when the net TOA radiative flux stabilizes-are used to quantify climate impacts. The surface-temperature-mediated slow response is calculated as the difference between coupled ocean and fSST experiments 47 . A 90-year coupled ocean simulation has not yet reached equilibrium, so we refer to these simulations as being in near equilibrium (computational cost restrictions prohibited longer integrations), similar to previous projects including PDRMIP 22,48 . Our CESM2/CAM6 simulations do not include interactive chemistry; we therefore do not address possible atmospheric chemistry implications (for example, changes in ozone and stratospheric water vapour) or changes in methane lifetime.

Calculation of ADJs
The ADJs (for example, clouds, water vapour and temperature) in the climatological fixed SST experiments are estimated using the Nature Geoscience Article https://doi.org/10.1038/s41561-023-01144-z radiative kernel method 3,18,28,30,42 . Radiative kernels represent the radiative impacts from small perturbations in a state variable (for example, temperature, water vapour and surface albedo). Subsequently, ADJs can be computed by multiplication of the kernel with the response of the state variable. We use the Python-based radiative kernel toolkit (downloaded from ref. 49 ) and the Geophysical Fluid Dynamics Laboratory radiative kernel 49 .
We use the same radiative kernel procedure to calculate the unnormalized (we do not divide by the change in global mean surface temperature) feedbacks. Specifically, surface-temperature-induced feedbacks are estimated by subtracting the ADJs (from fixed SST experiments) from the corresponding radiative kernel decomposition applied to the coupled experiments. Unnormalized feedbacks facilitate comparison with the ADJs.
ERF can be decomposed as ERF = IRF + ADJ TT + ADJ ST + ADJ TS + ADJ WV + ADJ α + ADJ C + ϵ, where ADJ TT is the tropospheric temperature adjustment, ADJ ST is the stratospheric temperature adjustment, ADJ TS is the surface-temperature adjustment, ADJ WV is the water-vapour adjustment, ADJ α is the albedo adjustment, ADJ C is the cloud adjustment and ϵ is the radiative kernel error. Individual ADJs are estimated as ADJ x = δR δx dx, where δR δx is the radiative kernel and dx is the response of state variable x as simulated by CESM2/CAM6. Kernels are four-dimensional (latitude, longitude, pressure and month) fields for atmospheric temperature and specific humidity and threedimensional (latitude, longitude and month) fields for surface temperature and surface albedo. Two sets of kernels are used: clear-sky kernels, where the fluxes are calculated without clouds, and allsky kernels.
As the radiative effect of clouds depends on several variables (fraction, ice and liquid-water content, droplet effective radius and so on), several approaches have been used to estimate cloud adjustments 18,50 . Here we estimate cloud adjustments using the kernel difference method 18 , which involves a cloud-masking correction of cloud radiative-forcing diagnostics using the kernel-derived non-cloud adjustments and IRF according to ADJ C = (ERF − ERF cs ) − (IRF − IRF cs ) − ∑ x=[T, TS, WV, α] (ADJ x − ADJ x,cs ), where subscript 'cs' refers to clear-sky quantities. Thus, the kernel difference method relies on the difference of all-sky and clear-sky kernel decompositions. See ref. 18 for additional details.
The total ADJ is estimated as the sum of individual ADJs from the radiative kernel decomposition. Since we estimate IRF using PORT for all of our methane simulations, this can be used to estimate the radiative kernel error (ϵ) as ϵ = ERF − IRF − ∑ x=[T, TS, WV, α, C] (ADJ x ). For example, the 10×CH 4LW+SW ERF and IRF are 1.69 and 2.08 W m −2 , yielding an ERF − IRF difference of −0.39 W m −2 . The sum of the individual ADJs from the kernel decomposition is −0.40 W m −2 . Thus, the radiative kernel error for 10×CH 4LW+SW is 0.01 W m −2 . Similar results hold for 5×CH 4LW+SW and 2×CH 4LW+SW , where ϵ is 0.03 W m −2 and −0.02 W m −2 , respectively. Relative to the corresponding ERFs, these errors are <1.0%, 3.1% and 5.7%, respectively. As ref. 18 lacked an estimate of the IRF (which we estimate using PORT), they estimated ϵ under select situations (where the SW or LW IRF is known to be zero). In these situations, they found that the residual term is small, being "6%, 12% and 2% of the ERF for 10×BC LW, 3×CH 4 SW and 2%Solar LW in magnitude, respectively. The larger multimodel residual in the 3×CH 4 SW case is biased by a large relative residual in the HadGEM2 model, whereas residuals in the other four models analysed are close to 0." Thus, our radiative kernel errors are relatively small, and comparable to those estimated from select PDRMIP simulations 18 .
We note that methane IRF has an approximate square root dependency on concentration 5,51 . PDRMIP 3×CH 4 simulations yield a 3×CH 4 IRF of 1.1 ± 0.24 W m −2 , but nearly all of the PDRMIP models used year 2000 as the base year. This perturbation is thus similar to 5-6× preindustrial CH 4 (our 5×CH 4 IRF is 1.18 W m −2 , with 0.14 W m −2 due to SW radiative effects).

Statistical significance
Statistical significance of a climate response is calculated using a two-tailed pooled t test. An annual mean time series is calculated for both the perturbation experiment and the preindustrial base experiment (for example, at individual grid boxes or averaged globally), and their difference is taken. The null hypothesis of a zero difference is evaluated, with n 1 + n 2 − 2 degrees of freedom, where n 1 and n 2 are the number of years in the perturbation experiment and base (30 years for fSST experiments; 40 years for coupled ocean experiments). Here, the pooled variance, (n 1 −1)S 2 1 +(n 2 −1)S 2 2 n 1 +n 2 −2 , is used, where S 1 and S 2 are the sample variances. A similar procedure is used to quantify statistical significance of the radiative flux perturbations and rapid adjustments (for example, Fig. 2). These uncertainties are therefore relative to interannual variability and do not account for possible intermodel or kernel uncertainties (as in ref. 18 , using 10+ PDRMIP models). As we have only one year of data for the IRF, we evaluate its uncertainty relative to the preindustrial base experiment with fixed SSTs. Nearly all of our ADJs under 10×CH 4 are significant at the 90% confidence level (the lone exception is the surface-temperature adjustment under 10×CH 4SW ). Similar conclusions also hold for 5×CH 4 (Extended Data Fig. 4d). Under 2×CH 4 , however, most of the ADJs under 2×CH 4SW are not significant (Extended Data Fig. 4g), including the total ADJ. This is consistent with the relatively small 2×CH 4 SW IRF of 0.04 W m −2 .
We also find similar results using an alternative kernel (CloudSat/ CALIPSO; Extended Data Fig. 5), so our ADJ conclusions are robust across these two kernels. Finally, we note that the ADJs in PDRMIP models that include CH 4 SW absorption (under 3×CH 4 , which is a perturbation similar to our 5× preindustrial CH 4 ) are all significant at the 95% confidence level 18 , and this includes the intermodel and kernel uncertainty.