Different Strategies of Stratospheric Aerosol Injection Would Significantly Affect Climate Extreme Mitigation

Stratospheric aerosol injection (SAI) has been proposed as a potential supplement to mitigate some climate impacts of anthropogenic warming. Using Community Earth System Model ensemble simulation results, we analyze the response of temperature and precipitation extremes to two different SAI strategies: one injects SO2 at the equator to stabilize global mean temperature and the other injects SO2 at multiple locations to stabilize global mean temperature as well as the interhemispheric and equator‐to‐pole temperature gradients. Our analysis shows that in the late 21st century, compared with the present‐day climate, both equatorial and multi‐location injection lead to reduced hot extremes in the tropics, corresponding to overcooling of the mean climate state. In mid‐to‐high latitude regions, in comparison to the present‐day climate, substantial decreases in cold extremes are observed under both equatorial and multi‐location injection, corresponding to residual winter warming of the mean climate state. Both equatorial and multi‐location injection reduce precipitation extremes in the tropics below the present‐day level, associated with the decrease in mean precipitation. Overall, for most regions, temperature and precipitation extremes show reduced change in response to multi‐location injection than to equatorial injection, corresponding to reduced mean climate change for multi‐location injection. In comparison with equatorial injection, in response to multi‐location injection, most land regions experience fewer years with significant change in cold extremes from the present‐day level, and most tropical regions experience fewer years with significant change in hot extremes. The design of SAI strategies to mitigate anthropogenic climate extremes merits further study.


Introduction
Continued greenhouse gas (GHG) emissions caused by human activities have induced anthropogenic climate change since the pre-industrial era (Eyring et al., 2021).Anthropogenic climate change contributes to an enhanced frequency, intensity, and duration of some weather and climate extremes (e.g., heat/cold waves, heavy rainfall/ snowfall, droughts, hurricanes) across the world (NASEM, 2016;Seneviratne et al., 2021).Extreme climate events pose great risks to human society and natural ecosystem, and it is a global challenge to reduce the anthropogenic warming effects on extreme events.Achieving the 2°C or 1.5°C warming target set forth in the Paris Agreement requires substantial reduction in CO 2 emissions and reaching net negative emissions during the latter half of this century (IPCC, 2021).Cutting GHG emissions solely based on nationally determined contributions may prove inadequate and overdue to avoid significant risks from climate change (IPCC, 2022;Rogelj et al., 2016;Rogelj et al., 2018;Sanderson et al., 2016).
Solar radiation modification (SRM), also termed solar geoengineering, is gaining increasing attention as a potential supplement to temporarily alleviate certain adverse effects of changing climate triggered by anthropogenic forcing (Caldeira et al., 2013;Irvine et al., 2016;Keith, 2000;Lee, Marotzke, et al., 2021).The idea of SRM is to deliberately reduce solar radiation reaching the Earth surface and slow down anthropogenic warming induced by GHG emissions.Various SRM strategies have been proposed, such as space mirror sunshading, stratospheric aerosol injection (SAI), marine cloud brightening, surface albedo alteration, as well as the longwave-based cirrus cloud thinning (Lee, Marotzke, et al., 2021;NASEM, 2021).
Numerous modeling studies have made efforts to examine the effects of SRM on various aspects of the Earth system, including temperature, the hydrologic cycle, large-scale ocean circulation, the cryosphere, and the carbon cycle (refer to Irvine et al. (2016), NASEM (2021), Lee, Marotzke, et al. (2021), and Duffey et al. (2023) for a review of relevant studies).Some previous studies examined the impact of SRM on climate extremes.For example, under the framework of the Geoengineering Model Intercomparison Project (GeoMIP) (Kravitz et al., 2013;Visioni & Kravitz et al., 2023), a few studies have explored changes in climate extremes in response to different SRM methods including solar dimming (Curry et al., 2014;Ji et al., 2018;Muthyala et al., 2018aMuthyala et al., , 2018b)), SAI (Aswathy et al., 2015;Ji et al., 2018;Wei et al., 2018), and marine cloud brightening (Aswathy et al., 2015;Kim and Shin, 2020).These results showed that these SRM methods can mitigate the changes in climate extremes induced by GHG emissions with various degrees, but different SRM methods would lead to heterogeneous impacts on regional climate extreme events.SAI is one of the most studied methods of SRM.By artificially injecting sulfate aerosol particles or their precursors into the stratosphere to form a sustained layer of additional stratospheric sulfate aerosols, SAI would scatter a portion of the incoming solar radiation, thereby cooling the Earth (Crutzen, 2006;IPCC, 2018;NASEM, 2021;Scott et al., 2015).Earlier SAI modeling studies injected SO 2 into the lower stratosphere at the equator, often with the goal of stabilizing global mean surface temperature (e.g., Robock et al., 2008;G3 and G4 simulations in GeoMIP (Kravitz et al., 2013;Visioni & Kravitz et al., 2023)).However, a pronounced uneven temperature distribution is simulated in response to equatorial injection, with substantial overcooling in the tropics and residual warming in the high latitudes (Kravitz et al., 2013(Kravitz et al., , 2019;;Tilmes et al., 2017).In addition, any uneven cooling between the Northern and the Southern hemispheres would shift the meridional temperature gradient and tropical precipitation patterns (Crook et al., 2015;Haywood et al., 2013).
Recent climate modeling studies have attempted to examine the climate effects of different SAI deployment strategies, including the latitude (e.g., Bednarz et al., 2022;Tilmes et al., 2017), magnitude (e.g., Kleinschmitt et al., 2018;Niemeier and Timmreck, 2015;Visioni & Bednarz et al., 2023), altitude (e.g., Lee et al., 2023;Tilmes, Richteret & Mills et al., 2018), and timing (e.g., Lee, MacMartin, et al., 2021;Visioni et al., 2020) of SO 2 injection.Tilmes, Richter and Kravitz et al. (2018) described a 20-member Stratospheric Aerosol Geoengineering Large Ensemble project (referred to as GLENS) with SO 2 injection at four latitudes.This strategy involves a feedback-control algorithm (MacMartin et al., 2014) to adjust injection rate at each location to concurrently offset changes in global annual mean temperature, the interhemispheric and the equator-to-pole temperature gradients under Representative Concentration Pathway 8.5 (RCP8.5)(Kravitz et al., 2017;Tilmes, Richter & Kravitz et al., 2018).This scenario may not be representative of likely future emissions pathways (Burgess et al., 2020;UNEP, 2021), but was used to provide a high signal-to-noise ratio for improving scientific understanding of the effects of SAI.Some studies have investigated the effect of SAI on climate extremes based on GLENS outputs, including heatwaves and floods (Barnes et al., 2022;Tan et al., 2023;Tye et al., 2022), as well as regional droughts (Abiodun et al., 2021;Alamou et al., 2022;Odoulami et al., 2020).Tye et al. (2022) found that SAI could potentially mitigate certain extreme temperature and precipitation hazards caused by global warming, but the spatial patterns of climate extremes under SAI by the end of this century in this scenario would significantly deviate from the present-day state.Barnes et al. (2022) employed a machine learning method to show that the Earth's Future 10.1029/2023EF004364 impact of SAI on extreme temperature and precipitation could be robustly detected under GLENS within 1-15 years from the start of SO 2 injection relative to the case without SAI.Abiodun et al. (2021) found that SAI implementation through GLENS strategy has the potential to decrease the upper limit of drought stress over Africa, but increase the lower limit.
In this study, we build on previous work by exploring the climate extreme response to multi-location SO 2 injection (GLENS) and equatorial SO 2 injection.A few studies have compared the mean climate response to GLENS and equatorial SO 2 injection, including surface temperature, stratospheric circulation, the quasi-biennial oscillation, and the Hadley circulation intensity (Cheng et al., 2022;Kravitz et al., 2019).Compared with the relevant studies mentioned above, here we focus on the change in temperature and precipitation extremes with the aim to better understand climate extreme response to different SAI deployment strategies, thereby addressing an important gap in current studies.

Description of GLENS and GEQ Simulations
The simulations analyzed in this study are conducted with the state-of-the-art Community Earth System Model (CESM) version 1 (CESM1, Hurrell et al., 2013) incorporating the Whole Atmosphere Community Climate Model (WACCM) as its atmospheric component (CESM1(WACCM)).WACCM has 70 vertical layers from the Earth's surface up to 140 km altitude, with a horizontal resolution of 0.9°latitude by 1.25°longitude.The atmospheric component is fully coupled to land (the Community Land Model version 4.5 (CLM4.5))(Oleson et al., 2017), ocean (the Parallel Ocean Program (POP2)) (Danabasoglu et al., 2012), and sea ice (Los Alamos Sea Ice Model (CICE4)) (Holland, 2013) components.The model also incorporates a modal aerosol module (MAM3) (the three-mode version of the MAM3) (Liu et al., 2012) to handle the aerosol microphysics, which is interactively coupled to chemistry and radiation processes.The detailed features and evaluation of CESM1(WACCM) are described by Mills et al. (2017), except that the land component used here is CLM4.5 instead of CLM4.0 as noted by Tilmes, Richter and Kravitz et al. (2018).It has been validated that CESM1(WACCM) can reasonably reproduce the observed present-day climatological trends and variabilities of both troposphere and stratosphere including surface temperature, tropospheric temperature and wind, the quasi-biennial oscillation, as well as stratospheric ozone column and water vapor concentration (Mills et al., 2017).Also, the model-simulated radiative forcing from volcanic aerosol following the June 1991 Pinatubo eruption agrees well with satellite observations (Mills et al., 2017).These validations show that the model is suited for conducting stratospheric sulfate aerosol geoengineering experiments.CESM1(WACCM) is used for the GLENS project (Tilmes, Richter, Kravitz, et al., 2018) that employs a strategic SAI approach to meet specific climate goals under the Representative Concentration Pathway 8.5 (RCP8.5),which represent a future world with intensive GHG emissions (Meinshausen et al., 2011).A 20-member ensemble is performed under RCP8.5 over the time period of 2010-2030.The first three ensemble members from RCP8.5 simulations are extended until the end of this century.The 20-member SAI ensemble simulations start in 2020 by branching from each of the 20 RCP8.5 simulations and extend until 2099.In SAI simulations, sulfur dioxide (SO 2 ) is injected at more than 5 km above the annual mean tropopause at four locations: 15°N, 15°S, 30°N, and 30°S, all at 180°longitude.A feedback-control algorithm is employed in SAI simulations that annually adjusts the SO 2 injection rate at each of the four locations to simultaneously maintain three temperature targets at 2010-2030 mean states: the global mean surface air temperature (T 0 ), the interhemispheric temperature gradient (T 1 ), and the equator-to-pole temperature gradient (T 2 ) (the detailed description of the algorithm can be found in Kravitz et al. (2017) andMacMartin et al. (2017)).In this study, the 20-member ensemble mean of RCP8.5 simulations during 2010-2030 is referred to as the baseline condition.To examine the climate response to SAI, we use the SAI simulations output averaged over 2075-2095.During this period, SAI provides roughly 4°C of global-mean cooling relative to the RCP8.5 simulation without SAI.CESM(WACCM) is also used to conducted three ensemble SAI simulations under RCP8.5 between 2020 and 2099 in which SO 2 is injected at the equator (Kravitz et al., 2019).For the equatorial injection, referred to as GEQ here, SO 2 is injected at approximately 5 km above the annual mean tropopause at the equator (also at 180°l ongitude).A feedback algorithm is employed in GEQ simulations to adjust SO 2 injection rate every year with the temperature target of maintaining T 0 at 2010-2030 average level (Kravitz et al., 2019).The effect of different SAI Earth's Future 10.1029/2023EF004364 strategies on global climate can be examined by comparing climate response between GLENS and GEQ simulations.

Climate Extreme Indices
Here we use a set of climate extreme indices developed by the Expert Team on Climate Change Detection and Indices group (hereafter abbreviated as ETCCDIs) (Klein Tank et al., 2009;Zhang et al., 2011).The specific names, definitions and units of ETCCDIs used in this study are listed in Table 1.ETCCDIs provide standardized metrics for quantifying extreme events across different regions and time periods.They have been widely used to monitor and assess the occurrence of climate extremes based on observational data set and climate model output (e.g., Sillmann, Kharin, Zhang, et al., 2013;Sillmann, Kharin, Zwiers, et al., 2013;Aswathy et al., 2015;Ji et al., 2018;Tye et al., 2022).
The ETCCDIs can be roughly divided into three categories based on the determination of thresholds beyond which conditions are considered extremes (Sillmann, Kharin, Zhang, et al., 2013;Tye et al., 2022): (a) fixed indices including the annual maximum and minimum values and spell duration; (b) threshold indices that count the number of days when a fixed threshold of temperature or precipitation is exceeded; (c) percentile-based threshold indices that describe the exceedance frequency of temperature or precipitation above or below a threshold, which is defined as a certain percentile derived from a reference period (namely 2010-2030 baseline period here).These indices are correlated with extreme climate events.For example, the annual warmest temperature (TXx), the frequency of annual warm days (TX90p), and the number of summer days (SU) are related to hot extremes; the annual coldest temperature (TNn), the frequency of annual cold nights (TN10p), and the number of frost days (FD) are related to cold extremes; the greatest 5-day precipitation amount (Rx5day) and the annual total precipitation for days with daily precipitation above 95th percentile (R95pTOT) could represent some of extreme heavy precipitation events, and the number of consecutive dry days (CDD) could be a rough indicator for drought conditions (Frich et al., 2002).These selected indices, as outlined in Table 1, would provide some insights into the projected changes in temperature and precipitation extremes in response to RCP8.5, GLENS and GEQ scenarios.

Regional Analysis
For the regional division, we adopt the land regional division method following the Special Report on Managing the Risks of Extreme Events and Disasters to Advance Climate Change Adaptation (referred to as the IPCC SREX report) (IPCC, 2012).The distribution and abbreviations of the respective regions are shown in Figure S1 of Supporting Information S1.We also use the population data of year 2020 provided by the Gridded Population of

Results
We first briefly discuss the model-simulated mean climate state before investigating the response of climate extremes.Related figures are shown in the supporting information.Relative to the baseline period (ensemble mean of RCP8.5 simulations during 2010-2030), a global mean warming of 4.1°C is simulated for the period of 2075-2095 under RCP8.5 with pronounced warming observed in the high latitudes (Figures S2 and S3 in Supporting Information S1).Meanwhile, annual mean precipitation increases by 7.9% but with large regional heterogeneity (Figure S3 in Supporting Information S1).In response to both GLENS and GEQ, global mean temperature is stabilized at the baseline level, while global mean precipitation is smaller than the baseline level (Figure S2 in Supporting Information S1).However, pronounced residual warming is observed in northern Eurasia and North America for both GLENS and GEQ.The residual warming is larger for GEQ than GLENS, and is larger over winter than summer (Figures S3 and S4 in Supporting Information S1).Relative to the baseline, annual mean precipitation decreases over large parts of the world, with the decrease much larger in GEQ compared to that of GLENS (Figure S3 in Supporting Information S1).
Next, we present time series and spatial patterns of changes in climate extremes under RCP8.5 as well as GLENS and GEQ simulations.All reported spatial changes are for the mean over period 2075-2095 relative to the mean of the baseline period (2010-2030).

Extreme Temperature Response
The time evolution of changes in area-weighted global mean extreme temperature indices (TNn, TXx, TN10p, TX90p, FD and SU) relative to the baseline for RCP8.5, GLENS, and GEQ simulations are shown in Figure 1.Under RCP8.5, substantial changes in a variety of temperature extremes are simulated.Averaged over years 2075-2095, the annual warmest day temperature (TXx) increases by 3.9°C relative to baseline, and the annual coldest night temperature (TNn) increases by 5.4°C.Summer days (SU, the annual count with daily maximum temperature above 25°C) increases by 40 days and (FD, the annual count with daily minimum temperature below 0°C) decreases by 21 days.The frequency of warm days (TX90p) increases by 42.7% and the frequency of cold nights (TN10p) decreases by 9.6% (Figure 1, Table S2 in Supporting Information S1).These projected changes in climate extremes are broadly in line with the results of previous studies (Collins et al., 2013;Seneviratne et al., 2021).Compared to the RCP8.5 scenario, GLENS and GEQ effectively maintain these global mean extreme temperature indices near present-day levels throughout this century (Figure 1, Table S2 in Supporting Information S1), indicating that both GLENS and GEQ can largely offset anthropogenic temperature extreme changes at the global scale.
Model simulated changes in the spatial distribution of temperature extremes are shown in Figure 2 and Figures S5-S7 of Supporting Information S1.Under RCP8.5, during the late 21st century, hot extremes increase over most land areas with an increased intensity, a higher frequency, and an extended duration as indicated by changes in TXx, TX90p, and SU.On the other hand, cold extremes diminish over most land areas in terms of intensity, frequency, and duration as indicated by changes in TNn, TN10p, and FD.Pronounced increases in TNn, TXx, and SU, and decreases in FD are observed over mid-to-high latitude regions in the Northern Hemisphere under RCP8.5 (Figures S5 and S6 in Supporting Information S1).
GLENS and GEQ substantially reduce RCP8.5-inducedchanges in temperature extremes over most regions (Figures S5-S7 in Supporting Information S1).In terms of hot extremes, both GLENS and GEQ reduce TXx, SU, and TX90p over large parts of land areas, but the extent of mitigation varies for different regions (Figures S5-S7 in Supporting Information S1).As shown in Figure 2, in large parts of the land regions of mid-to-high latitudes of the Northern Hemisphere and tropical region, both GLENS and GEQ reduce hot extremes below the baseline level.In mid-to-high latitudes, GLENS is more effective than GEQ in reducing TXx, SU, and TX90p.For example, in North America and northern Eurasia, relative to the baseline, TXx decreases by up to 3.7°C under GLENS and 2.6°C under GEQ.In terms of cold extremes, in the tropics, both GLENS and GEQ effectively stabilize TNn and FD at the baseline level.However, relative to the baseline, TN10p significantly increases under both GLENS and GEQ in the tropical regions, with the increase being more pronounced under GEQ (Figure 2).This is associated with tropical overcooling of the mean climate observed in GLENS and GEQ (Figure S4 in Supporting Information S1).In midto-high latitude regions, TNn under both GLENS and GEQ are notably larger than the baseline level, while FD and TN10p are significantly smaller than their baseline levels.In northern and central Europe, relative to the baseline, TNn increases by up to 9.2°C under GLENS and 14.5°C under GEQ; FD decreases by up to 20 days under GLENS and 40 days under GEQ; TN10p decreases by up to 4.6% under GLENS and 7.8% under GEQ.For comparison, in these regions under RCP8.5, TNn increases by up to 26.2°C, FD decreases by up to 85 days, and TN10p decreases by up to 9.7%.The substantial residual changes in cold extremes in mid-to-high latitude regions under both GLENS and GEQ are associated with the significant residual winter mean warming observed in these regions under GLENS and GEQ (Figure S4 in Supporting Information S1).This residual winter mean warming is also reported by previous studies (Banerjee et al., 2021;Jiang et al., 2019;Kravitz et al., 2019), which is associated with the fact that there is more sunlight to reflect in summer than winter, and SAI-induced stratospheric warming that causes the subsequent strengthening of the Northern Hemisphere polar vortex (Driscoll et al., 2012;  d-f) annual temperature minima (TNn), (g-i) annual count with daily maximum temperature >25°C (summer days, SU) (j-l) annual count with daily minimum temperature <0°C (frost days (m-o) annual frequency of warm days with daily maximum temperature above its 90th percentile from the baseline period (TX90p) (p-r) annual frequency of cold nights with daily minimum temperature below its 10th percentile from the baseline period (TN10p).Stippling indicates regions where changes are not statistically significant at the 95% confidence level using Welch's t-test.Thompson & Wallace, 2001).Also, the difference in the vertical structure of temperature change between CO 2 increase and insolation decrease is found to be an important reason for the residual warming at high latitudes (Henry & Merlis, 2020).
Since SAI aims to reduce warming by directly decreasing the incoming solar radiation reaching the Earth's surface, both GLENS and GEQ are more effective in diminishing extreme temperature during daytime than at nighttime.Also, both GLENS and GEQ are more effective in diminishing extreme temperature during summer than winter due to the greater amount of incoming solar radiation in summer (Figures 1a and 1b).In the mid-tohigh latitudes, relative to the baseline, GLENS and GEQ effectively reduce TXx, but TNn is still significantly increased under SAI.Also, GLENS and GEQ are more effective in stabilizing warm days (TX90p) than cold nights (TN10p) (Figure 2).

Extreme Precipitation Response
Here we analyze the changes in a series of precipitation extreme indices with time evolution shown in Figure 3 and spatial distributions shown in Figure 4 and Figures S8-S10 in Supporting Information S1.Under RCP8.5, averaged over years 2075-2095, the global annual total wet-day precipitation (PRCPTOT) increases by 8% relative to the baseline, and the maximum 5-day total precipitation (Rx5day) increases by 18%.The annual total precipitation of very wet days (R95pTOT) and extremely wet days (R99pTOT) increases by 29% and 59%, respectively.The global mean annual amount of consecutive wet days (CWD) and CDD shows small changes during this century under RCP8.5 (Figure 3, Table S2 in Supporting Information S1).Under both GLENS and GEQ, the global mean precipitation extremes are generally projected to decrease relative to the baseline throughout the 21st century (Figure 3), in general consistent with the decrease in mean precipitation (Figure S2b in Supporting Information S1).As shown in Figure 3, the global mean changes in precipitation extremes under GLENS and GEQ are similar.However, significant differences are observed in the spatial distribution of changes in precipitation extremes between the two SAI ensembles.
Under RCP8.5, relative to the baseline, the intensity of heavy precipitation events represented by Rx5day, R95pTOT, and R99pTOT substantially increases over most land regions, especially in southern Asia, eastern Africa, and some coastal regions in North America and South America (Figures S8 and S9 in Supporting Information S1).This result is in line with previous findings that the monsoon rainfall will notably increase in response to GHG-induced warming (Lee, Marotzke, et al., 2021).The increase in the intensity of heavy precipitation contributes to the increase in annual total precipitation (PRCPTOT) over large parts of the land regions (Figures S8 and S9 in Supporting Information S1).On the other hand, some regions exhibit decreased PRCPTOT under RCP8.5 (e.g., Northeastern South America), which is associated with a shorter duration of wet spells (CWD) and a longer duration of dry spells (CDD) over these regions (Figures S8-S10 in Supporting Information S1).
Relative to RCP8.5, in general, both GLENS and GEQ decrease precipitation extremes in regions where these extremes increase under RCP8.5, and vice versa (Figures S8-S10 in Supporting Information S1).For example, RCP8.5 increases the intensity of heavy precipitation (indicated by increased Rx5day, R95pTOT, and R99pTOT) over most land regions while both GLENS and GEQ reduce the intensity of heavy precipitation on land regions worldwide.Meanwhile, over some regions of subtropical ocean, the intensity of heavy precipitation decreases under RCP8.5, and both GLENS and GEQ act to increase heavy precipitation relative to RCP8.5 (Figures S8 and S9 in Supporting Information S1).These projected changes in the pattern of precipitation extremes under GLENS and GEQ are in general consistent with the pattern of changes in annual mean precipitation: relative to the baseline, in regions where precipitation increases under RCP8.5, precipitation decreases under both GLENS and GEQ (wetget-drier); in regions where precipitation decreases under RCP8.5, precipitation increases under both GLENS and GEQ (dry-get-wetter) (Figure S3 in Supporting Information S1).This "wet-get-drier, dry-get-wetter" pattern of mean precipitation change is also reported by Simpson et al. (2019), which is associated with the fundamental difference between the effect of CO 2 forcing and solar forcing on the hydrological cycle (Bala et al., 2008;Kravitz et al., 2013;Tilmes et al., 2013) and aerosol-induced stratospheric heating and the subsequent dynamical responses.
Relative to the baseline, both GLENS and GEQ reduce PRCPTOT, Rx5day, R95pTOT, and R99pTOT over the tropical regions (Figure 4).This decrease in precipitation extremes under GLENS and GEQ is associated with the decreased annual mean precipitation observed in the tropics (Figure S3 in Supporting Information S1).Associated with more tropical overcooling, GEQ induces larger decreases in precipitation extremes over tropical land regions Earth's Future 10.1029/2023EF004364 than GLENS (Figure 4).The Hadley cell intensity is weakened more (exceeding 5%) in GEQ than that in GLENS during the boreal summer (Cheng et al., 2022), which further suppresses convection and reduces precipitation extremes.
Over the Northern Hemisphere subtropical land regions including the Sahel region in northern Africa, the southern Arabian Peninsula, and the India Peninsula, relative to the baseline, precipitation extremes increase in response to GEQ.In response to GLENS, overall, changes in precipitation extremes are small; over Northern Africa, CDD exhibits a significant decrease relative to the baseline (Figure 4).The intensified precipitation extremes under GEQ is associated with the increased annual mean precipitation under GEQ over the subtropical regions (Figure S3 in Supporting Information S1).In boreal summer, the location of the Intertropical Convergence Zone (ITCZ) shifts northward in response to GEQ and shifts southward slightly in response to GLENS (Cheng et al., 2022).The northward shift of ITCZ in GEQ could cause intensified monsoon precipitation in regions near the Tropic of Cancer, consequently resulting in the increased intensity of heavy rainfall and extended wet spells over these regions under GEQ.

Regional Differences in Extremes
In this section, we further assess the changes in regional temperature and precipitation extremes under different SAI strategies.We follow the IPCC SREX method to divide the global continents (except for the Antarctica) into 26 regions, and we also calculate the population for each region (detailed in Section 2.3, Figure S1 and Table S1 in Supporting Information S1).For each region, we calculate the number of years over the 76-year period (2020-2095) with a statistically significant change in a certain climate extreme index relative to the baseline (Figure 5).(d-f) maximum 5-day precipitation (Rx5day), (g-i) annual amount of precipitation with daily precipitation above its 95th percentile from the baseline period (R95pTOT), (j-l) annual amount of precipitation with daily precipitation above its 99th percentile from the baseline period (R99pTOT), (m-o) annual maximum length of wet spell (consecutive wet days, (p-r) annual maximum consecutive dry days.Stippling indicates regions where changes are not statistically significant at the 95% confidence level using Welch's ttest.
Relative to the baseline, under RCP8.5, all of the 26 regions experience a significant increase in hot extremes (as indicated by TXx, SU, and TX90p) for more than 40 years out of the total of 76 years; all regions experience a significant decrease in cold extremes (as indicated by TNn, FD, and TN10p) for more than 40 years (Figure S11 in Supporting Information S1).For comparison, only one region under GLENS and three regions under GEQ experience significant changes in hot extremes for more than 40 years; only two regions under GLENS and three regions under GEQ experience significant change in cold extremes for more than 40 years (Figure 5).Most regions experience more years with significant changes in cold extremes (mostly with decrease over mid-to-high latitudes and mostly with increase over low latitudes) under GEQ than GLENS, and most tropical regions experience more years with significant decrease in hot extremes under GEQ than GLENS.
For all cases, most regions experience fewer years with significant extreme precipitation change than that of temperature.This is not surprising given the fact that precipitation exhibits larger natural variability than temperature, making it harder to detect changes in precipitation (Fischer & Knutti, 2014;Hegerl et al., 2004).Under RCP8.5, eight out of 26 regions experience a significant increase in extreme precipitation (as indicated by Rx5day, R95pTOT, R99pTOT) for more than 20 years (Figure S11 in Supporting Information S1).For comparison, no region under GLENS and three regions under GEQ experience significant change in extreme precipitation for more than 20 years (Figure 5).Tropical regions including the Amazon basin (AMZ), northeast Brazil (NEB), and eastern Africa (EAF) experience more years with a significant decrease in the intensity of heavy precipitation under GEQ than GLENS.
We further assess the change in a set of percentile-based climate extreme indices for seven regions with a population exceeding 300 million (Figure 6, Figure S1 and Table S1 in Supporting Information S1).Under RCP8.5, over these densely populated regions, hot extremes significantly increase, cold extremes significantly decrease, and the amount of heavy precipitation generally increases relative to the baseline (Figure 6).Both GLENS and GEQ effectively mitigate change in climate extremes in these densely populated regions.Compared to GLENS, GEQ causes lower frequency of warm days (as indicated by TX90p) and higher frequency of cold nights (as indicated by TN10p) over the tropical populous regions of South Asia (SAS), Southeast Asia (SEA), Western Africa, and Eastern Africa (EAF), and lower frequency of cold nights over the Northern Hemisphere mid-to-high latitude populous regions of East Asia (EAS), Central Europe (CEU), Southern Europe and Mediterranean (MED) (Figures 6a and 6b).For precipitation extremes, in general, both GLENS and GEQ significantly decrease the intensity of heavy and extremely heavy precipitation (as indicated by R95pTOT and R99pTOT) over these densely populated regions (Figures 6c and 6d), especially over Asian monsoon regions of SAS, East Asia (EAS), and Southeast Asia (SEA).

Conclusion and Discussion
In this study, we use CESM ensemble simulations to explore the response of climate extremes to two deployment strategies of SAI: one injects SO 2 at the equator (GEQ) and the other injects SO 2 at multiple locations (GLENS).Our results show that both GLENS and GEQ substantially mitigate changes in temperature and precipitation extremes under the RCP8.5 scenario.In the tropics, both GEQ and GLENS reduce hot extremes below the baseline level with GEQ leading to a stronger reduction in hot extremes.In mid-to-high latitude regions, under both GEQ and GLENS, cold extremes are substantially reduced relative to the baseline with greater reduction for GEQ.This is associated with the pattern of the mean climate change.Relative to the baseline, both GLENS and GEQ cause overcooling in the tropics and residual winter warming in the mid-to-high latitude region; the overcooling and residual warming is more pronounced in GEQ than that of GLENS.Relative to RCP8.5, both GLENS and GEQ decrease the intensity of heavy precipitation over the tropical regions and increase the intensity of heavy precipitation over the subtropical regions, corresponding to a decrease in mean precipitation in the tropics and an increase in mean precipitation in the subtropics.Over most regions, GLENS induces a smaller change in precipitation extremes than GEQ.Overall, for most regions, relative to the baseline, both temperature and precipitation extremes show reduced change under GLENS as compared to GEQ.This is consistent with the fact that the mean climate under GLENS is closer to that of the baseline as compared to GEQ.
Previous studies have examined the response of climate extremes to different solar radiation modification (SRM) approaches.For example, under the framework of the GeoMIP, Aswathy et al. (2015) compared climate extremes response to equatorial SO 2 injection and marine cloud brightening; Ji et al. (2018) examined the response of climate extremes to equatorial SO 2 injection and solar dimming.Using GLENS outputs, some studies examined the response of climate extremes to SAI at global scale (e.g., Barnes et al., 2022;Tye et al., 2022) or regional scales (e.g., Abiodun et al., 2021;Alamou et al., 2022).These studies showed that SRM would be more effective in mitigating hot extremes over the tropical regions relative to the mid-to-high latitude regions and SRM reduces the intensity of precipitation extremes relative to the background warming scenarios.These studies also showed that in the mid-to-high latitudes, SRM cannot fully offset decreases in cold extremes induced by anthropogenic warming relative to the present-day state.The findings of these studies are in general consistent with our results.Here, by comparing temperature and precipitation extremes to the equatorial SO 2 injection and multi-location injection, we shed further insight into the climate extreme response to different strategies of SAI.
Our results are based on a set of simulations from a single model without considering bias correction.Here we focus on the change of climate extremes in response to SAI relative to the scenario without SAI.Thus, bias correction would affect reported values of climate extremes, but is not expected to affect our overall conclusion regarding the effect of SAI on climate extremes.The CESM1(WACCM) model employed in this study has some limitations, causing uncertainty in model results.One significant limitation is that the modal aerosol treatment uses fixed distribution widths for aerosol modes (Liu et al., 2012).Therefore, some of the critical nonlinearities linked to the growth of stratospheric sulfate aerosols may not be properly represented by the aerosol microphysics scheme, which would affect model-simulated size and spatial distribution of geoengineered aerosols (Kravitz et al., 2017;MacMartin et al., 2017).Also, the relatively coarse resolution of the model limits the model's ability to sufficiently capture the climate extreme-related processes.
This study is conducted under a high background CO 2 scenario of RCP8.5.It would be worthwhile to examine the effect of SAI on climate extremes under a lower CO 2 background scenario that might be more relevant to current policy scenario (Burgess et al., 2020;MacMartin et al., 2022).For example, a recently initiated SAI large ensemble (The Assessing Response and Impacts of Solar Climate Intervention on the Earth system with SAI (ARISE-SAI)) (Richter et al., 2022) employs the same feedback algorithm, injection locations, and controlled temperature dimensions in SO 2 injection as GLENS under a more moderate background warming scenario (the Shared Socioeconomic Pathway scenario of SSP2-4.5)(O'Neill et al., 2016).ARISE-SAI involves a series of simulations with different temperature targets.Richter et al. (2022) showed that ARISE-SAI-1.5 (maintaining global mean temperature, the interhemispheric and the equator-to-pole temperature gradients at the level consistent with 1.5°C mean warming above pre-industrial level) can effectively mitigate global warming and avoid the tropical overcooling observed in GLENS and GEQ.Also, the decrease in global mean precipitation under ARISE-SAI-1.5 is smaller than that under GLENS and GEQ (primarily because the amount of cooling is smaller).Irvine and Keith (2020) demonstrated that compared to the GLENS simulations that fully offset CO 2 warming, using a linearized scaling of GLENS to offset half warming can substantially mitigate changes in annual maximum temperature and precipitation and avoid some overcompensation problems associated with GLENS.It would be worthwhile to further examine climate extreme response to moderate CO 2 and SAI scenarios.
Changes of climate extremes would be more sensitive to external forcing than changes of the mean climate state (Hartmann et al., 2013;IPCC, 2012;Seneviratne et al., 2021), and shifts in climate extremes would pose significant impacts on human society and ecological environment (Alexander et al., 2006;Meehl et al., 2000;Seneviratne et al., 2021).Therefore, it merits further study to explore the climate extreme response, including compound climate extreme events, to different strategies of SAI deployment that vary in amount, timing, location, and altitude of injection under a multi-modeling comparison framework.
For comparison, relative to the baseline, TXx increases by up to 22.1°C in these regions under RCP8.5.In the tropics, GEQ causes a greater reduction in hot extremes.The different effects of GLENS and GEQ on hot extremes are associated with different responses in the mean climate.Relative to the Earth's Future 10.1029/2023EF004364 baseline climate, GEQ causes larger overcooling in the tropics and larger residual warming in the mid-to-high latitudes (Figure S4 in Supporting Information S1).

Figure 1 .
Figure 1.Model-simulated time series of changes in global mean temperature extreme indices relative to the baseline (RCP8.5 2010-2030 ensemble mean) for RCP8.5 (red lines), GLENS (blue lines) and GEQ (black lines): (a) annual warmest day (TXx), (b) annual coldest night (TNn), (c) summer days (SU), (d) frost days, (e) frequency of warm days (TX90p), (f) frequency of cold nights (TN10p).The ensemble mean results are shown with the thick solid lines, and individual ensemble members are shown with the faint lines.

Figure 2 .
Figure 2. Model-simulated ensemble-mean spatial changes in temperature extreme indices relative to the baseline (RCP8.5 2010-2030 ensemble mean) for GLENS (2075-2095, left column), GEQ (2075-2095, middle column) and the difference between GEQ and GLENS (right column): (a-c) annual temperature maxima (TXx) (d-f) annual temperature minima (TNn),(g-i) annual count with daily maximum temperature >25°C (summer days, SU) (j-l) annual count with daily minimum temperature <0°C (frost days (m-o) annual frequency of warm days with daily maximum temperature above its 90th percentile from the baseline period (TX90p) (p-r) annual frequency of cold nights with daily minimum temperature below its 10th percentile from the baseline period (TN10p).Stippling indicates regions where changes are not statistically significant at the 95% confidence level using Welch's t-test.

Figure 3 .
Figure 3. Model-simulated time series of percentage changes in global mean precipitation extreme indices relative to the baseline (RCP8.5 2010-2030 ensemble mean) for RCP8.5 (red lines), GLENS (blue lines) and GEQ (black lines): (a) annual total precipitation in wet days (PCRPTOT), (b) maximum five-day precipitation (Rx5day), (c) precipitation of very wet days with daily precipitation >95th percentile from baseline (R95pTOT), (d) precipitation of extremely wet days with daily precipitation >99th percentile from baseline (R99pTOT), (e) maximum consecutive wet days, (f) maximum consecutive dry days.The ensemble mean results are shown with the thick solid lines, and individual ensemble members are shown with the faint lines.

Figure 4 .
Figure 4. Model-simulated ensemble-mean spatial changes in precipitation extreme indices relative to the baseline (RCP8.5 2010-2030 ensemble mean) for GLENS (2075-2095, left column), GEQ (2075-2095, middle column) and the difference between GEQ and GLENS (right column): (a-c) annual total rainfall (PCRPTOT),(d-f) maximum 5-day precipitation (Rx5day), (g-i) annual amount of precipitation with daily precipitation above its 95th percentile from the baseline period (R95pTOT), (j-l) annual amount of precipitation with daily precipitation above its 99th percentile from the baseline period (R99pTOT), (m-o) annual maximum length of wet spell (consecutive wet days, (p-r) annual maximum consecutive dry days.Stippling indicates regions where changes are not statistically significant at the 95% confidence level using Welch's ttest.

Figure 5 .
Figure 5.The number of years with significant changes in temperature and precipitation extremes for the IPCC SREX land regions under (a) GLENS, (b) GEQ, and (c) the difference between the two strategies relative to the baseline.The numbers represent the count of years when a certain extreme index becomes significantly different from its ensemble-mean value of the baseline (RCP8.5 2010-2030 mean) during the 76-year stratospheric aerosol injection implementation period (2020-2095).

Table 1 A
Subset of Climate Extreme Indices Defined by ETCCDI Used in This StudyIndices with percentile-based threshold are calculated using the percentile from the baseline period of 2010-2030 under RCP8.5 as a reference.World collection fourth version (GPWv4) (CIESIN, 2018) to calculate the total population of each region (TableS1in Supporting Information S1) to assess climate extreme response in densely inhabited regions. the