The first set of simulations considered in this study, first presented in , was conducted using the National Center for Atmospheric Research (NCAR) Community Earth System Model version 2 (CESM2) with the Whole Atmosphere Community Climate Model version 6 as its atmospheric component (CESM2(WACCM6)) . The atmospheric component (WACCM) has a 1.25∘ longitude by 0.9∘ latitude resolution and 70 vertical levels with a model top at 140 km. The tropospheric physics are the same as in the lower top configuration, the Community Atmosphere Model version 6 (CAM6). CESM2(WACCM6) uses prognostic aerosols represented using the Modal Aerosol Model version 4 (MAM4) and also includes a comprehensive chemistry module with interactive tropospheric, stratospheric, mesospheric, and lower-thermospheric (TSMLT) chemistry with 228 prognostic chemical species, described in detail in . Finally, the ocean model is based on the Parallel Ocean Program version 2 (POP2; ).

The second set of simulations presented in this article used the UK Earth System Model UKESM1.0 . UKESM1 consists of the physical atmosphere–land–ocean–sea ice model HadGEM3-GC3.1 and uses the Met Office Unified Model (UM) as its atmospheric component, which has a 1.875∘ longitude by 1.25∘ latitude resolution and 85 vertical levels with a model top at ∼85 km. The model includes the United Kingdom Chemistry and Aerosol (UKCA) chemistry model , with troposphere–stratosphere chemistry and coupling to a multi-species modal aerosol scheme . For a more complete description of the UKESM1 model configuration used in the SAI scenarios the reader is referred to the GeoMIP study of .

The reference simulations use the SSP2-4.5 scenario, which follows on from the Representative Concentration Pathway 4.5 (RCP4.5) scenario and is considered a “middle-of-the-road” intermediate mitigation scenario , which is arguably close to our projected emission trajectory . The reference SSP2-4.5 simulations begin in 2015 and run until 2100. The CESM2 ensemble comprises 10 members, and the UKESM1 ensemble comprises 5. The SAI simulations branch from SSP2-4.5 beginning in 2035 and run until 2070.

The stratospheric aerosol injection (SAI) simulations are part of a set of different solar climate intervention (SCI) implementation scenarios collectively called “Assessing Responses and Impacts of Solar climate intervention of the Earth system”, or “ARISE”, and the SAI simulations are denoted “ARISE-SAI”. Following and , we begin SAI in 2035 with the target of maintaining global-mean surface temperatures at 1.5 K above pre-industrial levels. Hence, this simulation set is called ARISE-SAI-1.5; other ARISE-SAI simulations are planned with different temperature targets and start dates. The stratospheric aerosol injection occurs at an altitude of 21.5 km at four locations: 15∘ N, 15∘ S, 30∘ N, and 30∘ S. The longitude of injection is 180∘ for both UKESM1 and CESM2. The control algorithm starts with a “best guess” (or feedforward) for the desired injection rates, which is then corrected by feedback. In this case, the initial guess is set to only apply injection at 15∘ N and 15∘ S to manage the global-mean surface temperature (T0). The control algorithm then (i) adjusts the total amount of injection across all four latitudes to maintain T0, (ii) adjusts the balance between Northern Hemisphere and Southern Hemisphere injection rates to maintain the hemispheric temperature difference (T1), and then (iii) adjusts the balance between 15∘ N/S and 30∘ N/S to maintain the Equator-to-pole temperature difference (T2). Importantly, the priority is chosen in that order; as the injection rate cannot be negative at any latitude, this introduces constraints on simultaneously meeting the multiple objectives . T1 and T2 are defined in Eq. (1) from . The integral and proportional control gains are 0.0183, 0.0753, and 0.3120 for T0, T1, and T2, respectively, for both CESM2 and UKESM1.

The values for the temperature targets T0, T1, and T2 are based on the 2020–2039 mean of the SSP2-4.5 simulations for CESM2 (288.64, 0.8768, and -5.89 K, respectively) and on the 2014–2033 mean for UKESM1 (288.06, 0.54, and -6.05 K, respectively). The target period for CESM2 was chosen as representative of when the climate might reach 1.5 K ; this is not based on the ensemble of the CESM2 SSP2-4.5 scenarios but on a combination of observational temperature trend extrapolations and estimates from climate models (the median estimate for crossing that threshold from CMIP6 models is 2028, but with a large uncertainty; ). From 2020–2039, CESM2 reaches 1.58 K above its pre-industrial level (287.06 K), and it reaches 1.5 K above pre-industrial from 2016–2035. The target period for UKESM1 was chosen based on the UKESM1 historical simulations as the 20-year period over which the global-mean surface temperature value exceeds UKESM1’s pre-industrial value by 1.5 K. In what follows, comparisons will be made relative to each model's own reference period.

Figure 1 shows the global-mean near-surface air temperature (T0), inter-hemispheric temperature gradient (T1), and the Equator-to-pole temperature gradient (T2) for all simulations of the reference scenario (SSP2-4.5 in red) and the ARISE-SAI-1.5 scenario (blue). In CESM2, neither the inter-hemispheric temperature gradient nor the Equator-to-pole gradient changes much in the reference SSP2-4.5 scenario runs; hence the difference between ARISE-SAI-1.5 and SSP2-4.5 simulations for these metrics is small. UKESM1 ARISE-SAI-1.5 simulations, on the other hand, only reach the global-mean and inter-hemispheric temperature gradient targets by around 2045. In addition, while the increase in Equator-to-pole temperature gradient is smaller in the ARISE-SAI-1.5 simulations compared to the SSP2-4.5 simulations, it does not reach the relevant T2 target. This was also the case for the Geoengineering Large Ensemble Project using CESM1 , though the discrepancy from the T2 target was smaller.

In the first simulation, which used this multi-target strategy in CESM1(WACCM) , the required injection rates were roughly hemispherically symmetric. Subsequently, there was a land model change in CESM1(WACCM), and more injection was needed in the Northern Hemisphere than Southern Hemisphere in order to maintain the inter-hemispheric temperature difference T1 . However, in CESM2(WACCM), the same control algorithm required more injection in the Southern Hemisphere to satisfy T1 . There are three contributors to this difference : the fast cloud adjustment to CO2 in CESM2 results in decreased cloud cover over the Southern Hemisphere, requiring more aerosols from SAI to compensate; the North Atlantic warming hole (which has been linked to a reduction in the Atlantic Meridional Overturning Circulation, AMOC; increased heat transport out of the North Atlantic; and a poleward shift in westerly winds as a response to external forcings; ) means the Northern Hemisphere needs fewer aerosols from SAI; and the decrease in tropospheric aerosol pollution in SSP2-4.5 (primarily in the Northern Hemisphere) is smaller in CESM2 than in CESM1 (due to a change from RCP8.5 to SSP2-4.5), which results in less need for Northern Hemisphere mitigation from SAI. The fast cloud adjustment to CO2 is expected to be different in other climate models . However as shown in , separating the fast adjustment from the surface-temperature-dependent response requires further idealised experiments, which are beyond the scope of the present study. The baseline scenario (SSP2-4.5) is the same for both models; nonetheless, the response to the same aerosol forcing and short-lived greenhouse gas forcing might be different between the two models . The North Atlantic warming hole, however, is not present in UKESM1 (Fig. 4) and is expected to be different for other climate models (further discussed in Sect. 3.4). These differences result in a difference in the distribution of injection rates that are required to satisfy the temperature objectives.

A comparison of injection rates between UKESM1 and CESM2 chosen by the controller is given in Fig. 2. While CESM2 has a linear increase in injection rates, UKESM1 has a large initial increase followed by a slower increase in the injection rate. This is caused by having the same 2035 start date for both sets of simulations: by 2035, the global-mean temperature in UKESM1 already exceeds its target temperature (defined as the 2014–2033 period); hence it requires a large initial increase in injection. The target period for CESM2 however is 2020–2039; hence by 2035 the temperature has not exceeded its target by much, making the initial increase in injection rates much smoother. Since the initial guess is set to only apply injection at 15∘ N and 15∘ S to manage the global-mean surface temperature (T0), the algorithm preferentially injects at those latitudes in the initial decade for UKESM1. Then, the majority of the injection happens at 30∘ N and 30∘ S. However, after 2055, there is a marked increase in injection at 15∘ N, while the injections at 30∘ N and 30∘ S stabilise. In CESM2, 82 % of the injection occurs in the Southern Hemisphere by 2070, whereas in UKESM1 it is only 27 %.

In UKESM1, the temperature responses to injection at 15∘ N only and 30∘ N only are quite similar, in contrast with CESM2 . Thus the influence matrix between injection rates and changes in T0, T1, and T2 is almost singular; therefore small changes in what the controller needs to respond to can result in large changes in the controller-defined injection rates, as observed after 2055 in these simulations. In an effort to correct for an increasing error in meeting the T1 objective caused by continued Arctic warming and slight Southern Hemisphere cooling after 2050, the controller increases the fraction of injection at 15∘ N. However, redistributing the injection rates is unable to significantly change T1, resulting in further increases in the fraction injection at 15∘ N. Therefore the set of injection latitudes chosen in CESM2 during initial studies to simultaneously meet these temperature objectives might not necessarily work in other climate models and may need to be adjusted to ensure that the set of injection latitudes yield distinct influences on the zonal-mean temperature response. It is worth noting that the decrease in the Equator-to-pole temperature gradient from the increase in greenhouse gases is still moderated by using SAI (Figs. 1e and 4e, f).

Figure 3 compares the increase in stratospheric aerosols in the first (2035–2054, top) and last (2050–2069, bottom) 2 decades of the simulations between UKESM1 (left) and CESM2 (right) relative to their respective reference periods. The aerosol distributions are consistent with the injection rates (Fig. 2). In UKESM1, there is a higher concentration of aerosols in the Northern Hemisphere from 2050–2069, which is consistent with the increase in injection at 15∘ N. In CESM2, the aerosols are mostly in the Southern Hemisphere, which is consistent with the majority of the injection occurring at 15∘ S.

In previous work , the output of single-latitude injection simulations was compared. Notably, the sulfate lifetime and increase in SO4 burden are approximately 50 % higher for CESM2 than for UKESM1 for a given constant SO2 injection, though this depends somewhat on the latitude of injection. This reduced lifetime is compensated by the total injection being approximately 50 % greater in UKESM1 than in CESM2 (Fig. 2). Hence, the total SO4 burden increase is similar by 2050–2069 in the two models (6.2 TgS for UKESM1 and 6.8 TgS for CESM2). Figure 3e and f show the increase in aerosol optical depth (AOD) for both models; the global-mean increases are 0.20 for UKESM1 and 0.12 for CESM2, with 31 % of the increase in the Northern Hemisphere for CESM2 and 57 % for UKESM1. Again, this is consistent with , who found that the normalised SO4 increase per 0.1 AOD is approximately 50 % larger for CESM2 than for UKESM1. Finally, this agrees with the larger effective radius of aerosols in CESM2 relative to UKESM1 , as for the same mass, smaller particles are generally more reflective and hence lead to a higher optical depth.

Figure 4 shows the near-surface air temperature change for SSP2-4.5 and ARISE-SAI-1.5 between the 2050–2069 and the reference periods for UKESM1 and CESM2. Panel e shows the zonal-mean temperature change for both models and scenarios, and panel f shows the zonal-mean surface temperature cooling from SAI compared to the same period of the SSP2-4.5 simulation. The most notable difference between models is the large Arctic amplification in UKESM1 compared to CESM2 (a ratio of 3.6 for UKESM1 compared to 2.1 for CESM2 when defined as warming northward of 70∘ N relative to the global mean). The coupled nature of the Arctic climate makes it difficult to quantify the role of individual mechanisms in the Arctic-amplified warming, which were reviewed in and . The uncertainty in the sea ice feedback would be reduced in a world with SAI as the sea ice would be restored. However, the uncertainties in cloud response to CO2 and aerosol–cloud interactions would be at least as important. The Arctic warming in UKESM1 in the ARISE-SAI-1.5 scenario happens mostly in winter, with no warming in summer; this is in contrast to CESM2, which has no seasonality of Arctic temperature change (Fig. A1). The total Arctic warming in UKESM1 under ARISE-SAI-1.5 is equivalent to the warming of CESM2 under SSP2-4.5 (Fig. 4e). Moreover, the cooling from SAI is much more Arctic-amplified in UKESM1 (Fig. 4f), even though the T2 target was not reached in that model. The latitudinal pattern of the AOD increase (roughly hemispherically symmetric for UKESM1 and Southern-Hemisphere-amplified for CESM2) is poorly correlated with the pattern of cooling (Arctic-amplified for both models). This indicates that the pattern of surface cooling is dominated by the model’s climate feedbacks rather than the pattern of the direct radiative forcing from aerosol scattering. This will also have an impact on the distribution of SO2 injection: until the amount of future Arctic warming is further constrained, it will be hard to determine which injection strategy will maintain T1 and T2.

Another notable difference is the North Atlantic warming hole, which is present in CESM2 but not in UKESM1. The North Atlantic warming hole has been associated with oceanic heat transport processes (slowdown in the Atlantic Meridional Overturning Circulation, AMOC, and increased heat transport out of the North Atlantic), but it is also linked to a poleward shift in westerly winds as a response to external forcings , and all CMIP6 models show a decline in AMOC in SSP2-4.5, including UKESM1 and CESM2 . Figure A2 shows the AMOC for one ensemble member for UKESM1 and for the 10 ensemble members for CESM2: both models show a decline in AMOC in SSP2-4.5 (≈25 % for UKESM1 and ≈28 % for CESM2) and a smaller decline in AMOC in ARISE-SAI-1.5 (≈18 % for UKESM1 and ≈24 % for CESM2). Thus it is unclear what drives the difference in North Atlantic temperature change between these two models, though this affects the pattern of temperature change outside of the area as the controller optimises for T0, T1, and T2.

Figure 5a and b show the time series of global-mean precipitation for all simulations, and Fig. 5c and d show the annual-mean temperature change as a function of the percentage change in annual-mean precipitation for both models and scenarios relative to their respective reference period for the global mean and the tropics only (between 30∘ N and 30∘ S). The effects of SAI on precipitation and other hydrological variables (reviewed in ) are very uncertain. The reduction in precipitation as a consequence of SAI is consistent with previous work and is also consistent with observations of a spin-down in the hydrological cycle subsequent to the volcanic eruption of Pinatubo in 1991 .

The hydrological sensitivity is commonly defined as a change in precipitation for a given change in surface temperature. We find good agreement in the hydrological sensitivity simulated under SSP2-4.5 for CESM2 and UKESM1. In contrast, in ARISE-SAI-1.5, the hydrological sensitivity is higher in UKESM1 than in CESM2: when the surface temperature is returned to that of the reference period, there is a ≈0.5 % reduction in precipitation in CESM2 and a ≈1.2 % reduction in UKESM1. This apparent difference in the hydrological sensitivity may be due to the difference in the pattern of cooling. UKESM1 undercools the Arctic and overcools the tropics, and the change in global-mean precipitation is strongly influenced by tropical surface temperatures. Figure 5d reproduces the analysis of Fig. 5c focused on the tropics and shows a more consistent slope between temperature and precipitation changes between both models.

Figure 6 shows the seasonal precipitation change (December, January, and February – DJF – and June, July, and August – JJA) for UKESM1 and CESM2 between 2050–2069 and their respective reference period for SSP2-4.5 and ARISE-SAI-1.5. The annual-mean changes may hide important seasonal differences, for example in the monsoon precipitation; hence we choose to show seasonal changes here. The shaded areas indicate where the difference is not statistically significant, as evaluated using a double-sided t test with p<0.05 considering all ensemble members and the 20 years as independent samples. We find large differences in the simulated precipitation responses to SAI between the two models. Importantly, large inter-model differences in the precipitation responses are also found for the SSP2-4.5 simulations without SAI. This is hardly surprising as it has long been known that climate models largely disagree on regional precipitation change (Box Ts.6 Fig. 1 in ). For example, in the Northern Hemisphere summer (JJA), there are important inter-model differences in key areas of high population and vulnerability such as Central Africa and South Asia. The uncertainty around precipitation changes in the climate with SAI is driven in part by the surface temperature change and in part by the direct effects of both increased greenhouse gases and stratospheric aerosols.

Figure 7 shows the zonal-mean change in precipitation over land for DJF and JJA and for all simulations. The shaded area shows the ensemble standard deviation at each latitude point, whereas the thick lines show the ensemble mean. This lets us analyse the intra-ensemble variability in precipitation response and the difference in precipitation response between models and scenarios. Outside of the tropics, both models broadly agree for both DJF and JJA and for both scenarios. However, there are important differences in precipitation over tropical land (also seen in Fig. 6). In the reference SSP2-4.5 simulations, the precipitation responses in JJA over land in the tropics are of opposite sign between UKESM1 and CESM2 (Fig. 7b). This is consistent with an increase in JJA T1 in the reference SSP2-4.5 simulations for UKESM1 and a decrease in JJA T1 for CESM2 (not shown), as the ITCZ generally migrates towards the warmer hemisphere. CESM2 has a larger standard deviation, which indicates a larger role for internal variability in its precipitation response. Finally, the precipitation changes over land under ARISE-SAI-1.5 are not larger than that under SSP2-4.5.

Figure 8 shows the different changes in projected extreme precipitation and reveals an interesting picture of the hydrological cycle under SAI. The change in the wettest pentad per year (annual maximum precipitation over 5 consecutive days; ) is statistically insignificant over most land areas in UKESM1. The main exception is over Pakistan and northern India, where projected increases in summer mean rainfall (Fig. 6g) may result from changes in the monsoon and correlate with projected increases in the wettest pentad. Projected decreases in dry spells (longest spell of consecutive days with <1 mm rain per year) also correlate with regions of projected increases in UKESM1 seasonal mean precipitation (e.g. Sahel region, eastern Brazil). While many of the projected changes in both the wettest pentad and dry spells are statistically insignificant, they do suggest a more muted hydrological cycle with fewer very heavy rain days and reduced persistence in wet and dry spells. As with mean precipitation, there are broad regions of agreement in the projected changes in the wettest pentad and dry spells between UKESM1 and CESM2 at higher latitudes. However, CESM2 projects significant increases in the wettest pentad further south and east than UKESM1, with the greatest changes over the Horn of Africa and India and Bangladesh. The projected increases in CESM2 correspond to regions with changes in seasonal mean precipitation (Fig. 6f, h) and may be related to a change in the simulated location of the Intertropical Convergence Zone and monsoon systems. Such changes are consistent with the projected increase in mean precipitation over the northern Indian Ocean and India and decrease south of the Equator. Differences between UKESM1 and CESM2 are also unsurprising given the known disagreements between regional precipitation changes. Projected decreases over the Amazon and Central Africa in CESM2 appear to be associated with changes in the persistence of wet and dry days, with significant decreases in the longest spells of wet days (not shown) and increases in dry spells. While the patterns of changes in extreme precipitation are also very different for UKESM1 and CESM2 under SSP2-4.5, their main similarity is that extreme precipitation is projected to increase in frequency and intensity everywhere at varying levels regardless of whether the region will otherwise be wetter or drier.