The land-based natural emissions analysed here are dust, BVOCs and wetland methane (Table 3).

Dust emissions are parameterised as a function of surface wind speeds or wind stress, and account for the amount of bare soil, soil type and aridity (Ackerley et al., 2012; Collins et al., 2011; Evan et al., 2014; Fiedler et al., 2016; Huneeus et al., 2011; Shao et al., 2011; Zender et al., 2004). There is a variation between the models in the sizes considered, whether binned or modal, and the optical properties of the dust particles (Kok et al., 2018; Xie et al., 2018). Table S1 lists the parameterisations for desert-dust aerosol for the contributing models and the simulated dust–aerosol sizes.

BVOC emissions are parameterised as a function of vegetation type and cover, and also temperature and photosynthesis rates (gross primary productivity) (Guenther et al., 1995; Pacifico et al., 2011; Sporre et al., 2019; Unger, 2014). Some parameterisations also include dependence on CO2 concentrations (Pacifico et al., 2012). Models differ in the speciation of the VOCs emitted but typically include isoprene and monoterpenes, with different emission parameterisations for different species. The ability of VOCs to form secondary organic aerosol is typically parameterised as a fixed yield (Mulcahy et al., 2020). For further details, see Table S1 in the Supplement and references therein.

The ocean emissions analysed here are sea salt, DMS and primary organic aerosols (Table 4).

The air–sea exchange processes for these emissions are parameterised as a function of wind speed and sometimes temperature (Gong, 2003; Jaeglé et al., 2011).

Changes in DMS emissions can be initiated by various factors such as changes in temperature, insolation, depth of the ocean-mixed layer, sea ice extent, wind strength, nutrient recycling or shift in marine ecosystems (Heinze et al., 2019). The DMS fluxes into the atmosphere are prescribed in some models (CNRM-ESM2-1, GFDL-ESM4, MIROC6, CESM2-WACCM) and calculated interactively from ocean biogeochemistry in others (UKESM1, NorESM2). Further details on the current generation of marine biogeochemical models, including the representation of DMS emission scheme, can be found in Séférian et al. (2020). Oceanic organic aerosol emissions are also wind-speed dependent and in addition depend on chlorophyll concentrations generated either from interactive biogeochemistry or observation-based chlorophyll concentrations in models without ocean biogeochemistry components.

The models with tropospheric chemistry (UKESM1, GFDL-ESM4, CESM2-WACCM, GISS-E2-1) all include parameterisations of the emission of nitrogen oxides (NOx) from lightning, related to the height of the convective cloud top (Price et al., 1997; Price and Rind, 1992). The lightning frequency depends strongly on the convective cloud-top height, and the ratio of cloud-to-cloud vs. cloud-to-ground lightning depends on the cold cloud thickness (from 0 ∘C to the cloud top). The precise implementation of lighting emissions and their height profile varies between the models.

The 2xdust perturbation is applied by scaling the parameterisation in the emission scheme. Since changing dust emissions will affect the boundary layer meteorology, the net effect is not an exact doubling of the emissions (Table 6). Four of the six models in AerChemMIP have a negative radiative forcing for doubled dust (Figs. 1a, S2–S4, Table 6). The models all agree on a negative ERF over the oceans close to the source regions. They differ in the sign of the ERF over the deserts themselves, with most (four out of six) showing a positive longwave ERF (Fig. S4). The shortwave ERF is more variable (Fig. S3) and is also affected by any changes in low cloud amount. For CNRM-ESM2-1 and UKESM1, this positive ERF over the deserts outweighs the oceanic negative ERF. The ERF for GFDL-ESM4 is not significantly different from zero. UKESM1 has by far the largest dust emissions (and change from doubling) because it includes particles that are emitted and deposited in the same time step. CNRM-ESM2-1 also includes large particles (up to 20 µm). These models, however, have similar changes in dust AOD compared to the other models, and hence the magnitude of the forcing efficiency per change in AOD (Table 6) is not out of line with the others. MIROC6 has the strongest forcing even with the lowest emissions and smallest change in AOD, thus giving it the largest forcing efficiency per AOD.

The response of dust aerosols to abrupt-4xCO2 (Figs. 1b, S1) is substantially different across the model ensemble. Four models (CNRM-ESM2-1, MIROC6, GFDL-ESM4 and GISS-E2) show an increase in dust emission in a 4xCO2 climate due to increased aridity and near-surface wind speeds, whereas UKESM1 has a decrease in dust emissions with more CO2 due to increased fertilisation of the vegetation (hence less bare soil) paired with decreased near-surface winds. NorESM2 shows near-zero change. The spatial pattern of the opposing response of dust emission to 4xCO2 in the two most extreme models, UKESM1 and CNRM-ESM2-1, is consistent with the responses in near-surface wind speed to 4xCO2 (Fig. S5). These reflect larger increases in mean winds over regions where the mean emission amount is larger for 4xCO2 compared to the pre-industrial climatology. The increase or decrease in winds is also likely to be affected by changes in vegetation in semi-arid regions, e.g., the Sahel.

As well as affecting the emissions, changing climate can also affect the removal of dust through changes in both dry and wet deposition. In all models except UKESM1, the lifetime of dust increases (Table 6). The effect of an increase in lifetime can be seen by comparing the change in AOD. The modelled changes in dust AOD in the abrupt-4xCO2 experiment are a factor of 1.5–2 larger (for those models where lifetime increases) as would be expected assuming a linear scaling with emissions across all size ranges (“scaled AOD” in Table 6).

The climate feedback parameter for dust (α) is given by the product of the radiative efficiencies (ϕ) with the sensitivities to climate (γ). These vary from -0.012 to +0.0020 W m-2 K-1 with a multi-model mean of -0.0026±0.0048 W m-2 K-1, i.e. consistent with zero. Scaling with AOD change rather than emission change gives a slightly larger magnitude, with a range of -0.016 to +0.0048 W m-2 K-1 and a multi-model mean of -0.0040±0.0072 W m-2 K-1. Although some models obtain similar feedback terms, this is not necessarily for the same reason. For instance, GFDL-ESM4 and NorESM2 have small feedback terms. NorESM2-LM has a large ERF for doubled dust emissions but a small change in dust emission for 4xCO2, whereas GFDL-ESM4 has a large change in emissions but a small ERF.

Dust–aerosol feedback assessments are a relatively new area of research due to the large uncertainties of climate models in simulating dust aerosols with changes in atmospheric composition. For instance, the spread in model estimates for dust aerosol changes in the 21st century is the largest among wildfires, biogenic SOA and DMS sulfate (Carslaw et al., 2010). Predictions for future dust emission range from an increase (Woodward et al., 2005) to a decrease (Mahowald and Luo, 2003). The modelled feedbacks in Table 6 are smaller in magnitude compared to the theoretical model estimates of -0.04 to +0.02 W m-2 K-1 by Kok et al. (2018).

The model ranges in dust forcing and feedbacks are not surprising in light of past studies that highlight model differences in dust-emitting winds and dust–aerosol parameterisations that contribute to the model diversity in the dust–aerosol loading, optical properties and radiative effects (Ackerley et al., 2012; Evan et al., 2014; Huneeus et al., 2011; Shao et al., 2011; Zender et al., 2004). For instance, the parameterisation of the planetary boundary layer plays an important role in determining the dust loading, forcing and regional feedbacks on winds (Alizadeh Choobari et al., 2012). Influencing factors for regional differences in the dust radiative effects are the surface albedo and aerosol size distribution (Kok et al., 2018; Xie et al., 2018), whereas feedbacks on winds depend also on meteorological factors (Heinold et al., 2008). The substantial model differences in the dust emission response to 4xCO2 paired with corresponding differences in mean 10 m wind speed in this study suggest that also the dust feedback parameter critically relies on accurately simulating atmospheric dynamics. Modelling atmospheric circulation has been identified as a grand challenge in climate research (Bony et al., 2015). Currently, we have no estimate which of the dust feedbacks shown are the most plausible, because convective dust storms are missing in such models, but this dust storm type is believed to be important for north African dust emissions (Heinold et al., 2013). Moreover, natural aerosol–climate feedbacks are thought to depend on the anthropogenic aerosol burden and might therefore be both time-dependent and underestimated in the present-day polluted atmosphere (Spracklen and Rap, 2013). Taken together, we have low confidence in the feedback estimates for dust aerosols to increases in atmospheric concentrations of greenhouse gases.

All models show a strong negative forcing to double sea salt emissions (Figs. 2a, S7, Table 7), although the ERF for MIROC6 is considerably smaller than for the others. The emissions and mass loading for the CNRM-ESM2-1 model are approximately 20 times those of the other models, largely due to including a size bin up to 20 µm. This coarse bin contains a large mass but a lower number of particles, so the AOD change is similar to other models. All models show a similar forcing efficiency per AOD change. All models show an increase in sea salt emissions in the Southern Ocean in 4xCO2 (Figs. 2b, S6) due to increased wind speeds, with a general tendency for decreases elsewhere due to rising temperatures (Jaeglé et al., 2011). The global mean change in emissions is positive in all models except MIROC6 and GISS-E2-1 (where the lower-latitude decreases outweigh the high-latitude increases). For models showing an increased sea salt lifetime in a 4xCO2 climate, the modelled increase in AOD is larger than that expected from scaling the emissions change (“scaled AOD” in Table 7). Although emissions (and the mass burdens) of sea salt decrease in MIROC6 and GISS-E2-1, the AODs increase. The mean feedback is -0.027±0.032 W m-2 K-1 based on emissions and -0.049±0.050 W m-2 K-1 based on the increase in AOD. The signs are consistently negative, except for the emission-based feedbacks for MIROC6 and GISS-E2-1.

Four models ran the 2xDMS experiment. Interactive biogeochemistry or interactive DMS emissions are not a prerequisite for the 2xDMS experiment. However, interactive emissions are required to calculate a feedback α; hence, we exclude CNRM-ESM2-1 from Table 8. Two models include interactive ocean biogeochemistry (UKESM1 and NorESM2). The ERF for 2xDMS is negative for all three models that ran this experiment (Figs. 3a, S9, Table 8), though less strongly so for GISS-E2-1. UKESM1 and NorESM2 show a decrease in sulfur emissions in 4xCO2, where the tropical decrease more than compensates for the increase along the edge of the sea ice retreat, whereas GISS-E2-1 shows an increase in overall sulfur emissions. The multi-model mean is shown in Fig. 3b and the individual models in Fig. S8. The multi-model mean emission-based α is slightly positive but consistent with zero. In spite of decreased DMS emissions in UKESM1 and NorESM2, there is an increased sulfur mass in all models in the 4xCO2 simulation due to an increase in the sulfate lifetime of around 2 % K-1. Since this lifetime change applies to all sulfate, not just that from DMS, the radiative efficiency from 2xDMS will not necessarily apply, and we do not calculate an AOD or mass-based feedback, but note that it would be negative.

DMS is produced by marine biological activity in the ocean, and it is assumed to be the largest natural source of sulfur to the atmosphere. Up to now, there has been no comprehensive model effort to include all the important effects, and therefore the DMS emission strength change under climate change is still uncertain. The slightly positive mean here is in contrast to the -0.02 W m-2 K-1 feedback from AR5 (Ciais et al., 2013) based on results from only one model (HadGEM2-ES).

Modelling studies including ocean biogeochemistry have shown that under climate change, an increased stratification of the ocean at low and midlatitudes leads to a reduction in nutrients supply into the surface ocean and thus a reduction in DMS emissions, whereas at high latitudes, retreat of sea ice can lead to increased biological activity and increase in DMS production (Kloster et al., 2007). Previous models which include ocean biogeochemistry have shown a slight increase in DMS production and emission to the atmosphere in a warming climate (Bopp et al., 2004; Gabric et al., 2004; Gunson et al., 2006; Vallina et al., 2007).

Some more recent studies have included the impact of ocean acidification on ocean DMS production (Schwinger et al., 2017; Six et al., 2013). Both studies used a very similar description of the ocean biogeochemistry and extended it with an observationally based relation between ocean alkalinity and ocean DMS production. Assuming a medium sensitivity of the DMS production on pH, Six et al. (2013) found a global DMS emission decrease by 18 % in 2100 under the Special Report on Emissions Scenarios (SRES) A1B scenario, and Schwinger et al. (2017) found an emission reduction by 31 % in 2200 under the Representative Concentration Pathways (RCP) 8.5 scenario. In addition, recent work has provided evidence for major pathways in the oxidation of DMS in the atmosphere which are not included in any of these ESMs (Berndt et al., 2019; Wu et al., 2015).

Biogenic VOC emissions lead to both organic aerosol and ozone production (in those models with tropospheric chemistry). It is therefore necessary to distinguish the two in the ERFs in these models. The ozone stratospheric-temperature-adjusted radiative forcing (SARF) from the ozone changes is diagnosed offline (Sect. 2.1). This is subtracted from the ERF to give the ERF due to aerosols only as shown in Table 9 (ozone is the only non-aerosol forcing agent that varies). For NorESM2, there is no ozone change. The ERF before subtracting the ozone SARF is shown in Fig. 4. These estimated aerosol forcing changes are large (up to -0.69 W m-2). All the ERF-SARFO3 values are negative, apart from UKESM1, which has a large positive forcing from cloud changes (diagnosed from comparing all-sky and clear-sky diagnostics; not shown).

In terms of aerosol, there is an increase in OA mass and expected increase in AOD with a very similar spatial pattern when the emission of BVOCs is doubled. The patterns of BVOC increase for the 4xCO2 experiments are much more similar between models (Fig. S10) in terms of pattern and sign than for the previous species (dust, sea salt, DMS), although the magnitude is considerably lower for UKESM1. In the 4xCO2 experiments, these models also simulate an increase in primary organic aerosol emissions from the ocean which adds to the OA mass on top of the effect of BVOC emissions. The feedback factors are negative, apart from UKESM1, and are very strong in some models (NorESM2 with -0.28 W m-2 K-1).

The ozone SARF is diagnosed offline (Sect. 2.1) and shown in Table 10. For all except UKESM1, the magnitude of the ozone forcing is smaller than that for aerosols, leading to a net negative ERF from BVOCs. For UKESM1, the non-ozone forcing is positive (Sect. 4.1.4) and the ozone adds to this. The ozone SARF per Tg VOC emission is similar between the models with CESM2-WACCM slightly lower. The overall feedback is therefore dominated by the variation in the sensitivity of BVOC emissions to climate. This ranges from 0.005 W m-2 K-1 for UKESM1, which has the lowest BVOC increase with climate, to 0.014 W m-2 K-1 for CESM2-WACCM and GISS-ES-1, which have the strongest BVOC response to climate.

At the multi-model mean level, the cooling associated with an increase in organic aerosol (-0.04±0.04 W m-2 K-1 – for the four models with chemistry) dominates over the warming associated with an increase in O3 (0.011±0.004 W m-2 K-1), leaving an overall negative feedback.

Using multi-annual simulations of global aerosol, Scott et al. (2018) diagnosed a feedback from biogenic secondary organic aerosol of -0.06 W m-2 K-1 globally and -0.03 W m-2 K-1 when considering only extratropical regions. This global feedback value was composed of a direct aerosol radiative feedback of -0.048 W m-2 K-1 and an indirect aerosol (i.e., cloud albedo) feedback of -0.013 W m-2 K-1. Using observations from 11 sites, Paasonen et al. (2013) estimated an indirect aerosol feedback of -0.01 W m-2 K-1 due to biogenic secondary organic aerosol. The ability of models to account for changes in vegetation has a large effect on the feedback. Sporre et al. (2019) found that interactive vegetation enhanced BVOC emissions by 63 % relative to prescribed vegetation, producing more organic aerosol and an increase in (negative) aerosol forcing.

The level of compensation between increased aerosol forcing and increased ozone is dependent on the model (here positive feedback for GFDL-ESM4, negative for UKESM1 and CESM2-WACCM). Unger (2014) found a positive feedback in NASA GISS ModelE2, whereas Scott et al. (2014) found a negative feedback in HadGEM2-ES.

Lightning NOx leads to ozone production and changes in methane lifetime. As for BVOCs (Sect. 4.2.1), ozone radiative kernels are used to quantify the ozone SARF. The ERF and SARFO3 agree for all models except UKESM1 (Table 11), suggesting that there is little effect on aerosols in these models. In UKESM1, NOx is known to increase the formation of new sulfate particles (O'Connor et al., 2020), partially offsetting the positive ozone forcing. The SARFO3 per Tg emission varies by a factor of 2 (0.023 to 0.048 W m2 (Tg(N) yr-1)-1) between the highest and lowest values.

The changes in lightning NOx emissions vary widely across the models, with three showing increases (UKESM1, CESM2-WACCM, GISS-E2-1) but a slight decrease in GFDL-ESM4. Although they all use variations on the cloud-top-height schemes (Sect. 3.2.3), the differences in how this is implemented and how the modelled clouds vary with climate change all affect the emission response. The feedback is positive for the three models with increased lightning (0.009 to 0.016 W m-2 K-1), based on the ozone changes, but slightly negative for GFDL-ESM4 (-0.001 W m-2 K-1). Including the aerosol response to lightning for UKESM1 would reduce its feedback to 0.005 W m-2 K-1, but this seems to be particular to this model.

The ESMs used in CMIP6 all use a cloud-top-height parameterisation of lightning. Such schemes have previously been found to increase lightning production in warmer climates, whereas more sophisticated schemes based on convective updraft mass flux or ice flux show decreases in lightning with temperature (Clark et al., 2017; Finney et al., 2016b, 2018). The result from the Atmospheric Chemistry and Climate Model Intercomparison (ACCMIP) of 0.44 Tg(N) yr-1 K-1 (Finney et al., 2016a) lies within the range of the models with increased lightning under 4xCO2 (0.27 to 0.61 Tg(N) yr-1 K-1).

BVOC and NOx emissions also affect the methane lifetime. Methane does not change in the AerChemMIP experimental setup, but the methane changes that would be expected if methane were allowed to evolve freely can be diagnosed from the change in methane lifetime. The methane lifetime to OH (troposphere and stratosphere) is diagnosed in the models. The losses to chlorine oxidation and soil uptake are assumed to be 11 and 30 Tg yr-1, respectively (Saunois et al., 2020). All models show an increase in methane lifetime with BVOC emissions (0.018–0.035 % (Tg(VOC)yr-1)-1 and a decrease due to lightning NOx emissions (-2.4 % to -6.8 % (Tg(VOC)yr-1)-1 (Table 12). From these, the expected lifetime changes with climate can be deduced from the changes in emissions with temperature. These lifetime changes are then converted to feedbacks using the radiative efficiency (including impacts on ozone and stratospheric water vapour) for methane lifetime changes in Sect. 2.2 (0.011 W m-2 %-1). The feedbacks range from 0.012 to 0.061 W m-2 K-1 for BVOCs and -0.042 to +0.001 W m-2 K-1 for lightning NOx, where the variability is mostly due to the different sensitivities of BVOC or lightning emissions to climate in the models. For BVOC, the methane lifetime feedback is larger than that due to ozone production, thus increasing the overall feedback. For lightning NOx, the methane lifetime feedback is of opposite sign to that from ozone production, with approximate compensation for UKESM1 and GFDL-ESM4 (net 0.002 and 0.000 W m-2 K-1, respectively) and an overall negative lightning feedback from CESM2-WACCM and GISS-E2-1 (-0.009 and -0.028 W m-2 K-1, respectively). For UKESM1, a feedback of -0.004 W m-2 K-1 could be added to the total lightning feedback to account for the increase in sulfate.

Two models diagnosed changes in wetland emissions due to 4xCO2. Although the wetland emissions do not directly affect methane concentrations in the model, changes in emissions can be converted to concentration changes (Sect. 2.2). UKESM1 and CESM2-WACCM, both of which are models with interactive wetland emissions, show strong responses to climate change (Table 13), leading to a feedback of 0.16±0.03 W m-2 K-1.

Wetland emissions are more strongly sensitive to CO2 concentrations than to temperature or precipitation (Melton et al., 2013), so the values presented here are more likely to be “adjustments” to the CO2 rather than feedbacks and hence could be considered part of the CO2 ERF. We find emission increases following quadrupled levels of CO2 of 130 %–160 %. This compares with results from the Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP) of 20 %–160 % following an increase in CO2 of a factor of 2.8 (Melton et al., 2013). The CMIP6 simulation specifications do not include free-running methane concentrations; therefore, the effects of these increased wetland emissions will not be realised in any of the CMIP6 experiments. Outside CMIP6, ESMs are starting to include free-running methane (Ocko et al., 2018), so for these it will be important to understand the effects of changing CO2 and meteorology on wetland emissions.

As well as through changes in natural emissions, climate change can affect ozone burden and methane lifetime directly, as the production and loss reactions are sensitive to temperature and water vapour (Johnson et al., 2001). Here, we add the expected changes in ozone SARF and methane lifetime due to changes in BVOCs and lightning NOx from Sect. 4.2.1 and 4.2.2 and compare those to the changes diagnosed from the 4xCO2 experiments (Table 14). Since lightning NOx and BVOCs are the dominant climate-sensitive emissions of (non-methane) species affecting ozone and methane, the residual is then the direct effect of climate. UKESM1, GFDL-ESM4 and GISS-E2-1 all diagnosed ozone changes for the abrupt-4xCO2 experiment (Fig. S12). All three showed decreased tropospheric ozone and increased stratospheric ozone (apart from the tropical lower stratosphere) in the 4xCO2 climate. The ozone SARF (calculated using radiative kernels) is negative, whereas the expected change from lightning NOx and BVOCs would be positive; hence, the residual attributed to meteorological changes is negative.

For UKESM1, GFDL-ESM4 and GISS-E2-1, the meteorological changes decrease methane lifetime, leading to an overall decrease in lifetime for the 4xCO2. In CESM2-WACCM, the meteorological changes increase methane lifetime, adding to the strong increase from BVOC emissions. This is surprising since there is no known mechanism whereby temperature and humidity increases can increase the methane lifetime. This could be due to non-linearity, whereby the effect of increased VOCs on methane lifetime is larger than expected from scaling the 2xVOC experiment.

Combining the results from ozone and methane lifetime changes leads to overall feedbacks from temperature of -0.15, -0.14 and -0.08 for UKESM1, GFDL-ESM4 and GISS-E2-1.

The three models showing decreased methane lifetime are in approximate agreement with ACCMIP, which found a sensitivity of -3.4±1.4 % K-1 (Naik et al., 2013; Voulgarakis et al., 2013). ACCMIP found a variation in sign of the ozone feedback amongst models -0.024±0.027 W m-2 for a 1850–2000 change in climate. The ACCMIP models generally did not include stratospheric chemistry, so they either explicitly prescribed the cross-tropopause flux of ozone or imposed a climatology of ozone above the tropopause. The four CMIP6 models here all treat the chemistry seamlessly across the troposphere and stratosphere, so the impact of changes in stratosphere–troposphere exchange (STE) of ozone on the tropospheric column is likely to be different from ACCMIP.

Changes in the stratospheric ozone following a quadrupling of CO2 are driven by cooling temperatures in the stratosphere. This is likely to be due to temperature adjustments to the stratospheric CO2 concentrations and so part of the ERF for CO2 rather than a feedback. Feedbacks and adjustments cannot be distinguished with this experimental setup.