Future changes in isoprene-epoxydiol-derived secondary organic aerosol (IEPOX-SOA) under the shared socioeconomic pathways: the importance of explicit chemistry

Secondary organic aerosol (SOA) is a dominant contributor of fine particulate matter in the atmosphere, but the complexity of SOA formation chemistry hinders the accurate representation of SOA in models. Volatility-based SOA parameterizations have been adopted in many recent chemistry modeling studies and have shown a reasonable performance compared to observations. However, assumptions made in these empirical parameterizations can lead to substantial errors when applied to future climatic conditions as they do not include the mechanistic understanding of processes but are rather fitted to laboratory studies of SOA formation. This is particularly the case for SOA derived from isoprene epoxydiols (IEPOX-SOA), for which we have a higher level of understanding of the fundamental processes than is currently parameterized in most models. We predict future SOA concentrations using an explicit mechanism, and compare the predictions with the empirical 1 https://doi.org/10.5194/acp-2020-543 Preprint. Discussion started: 3 July 2020 c © Author(s) 2020. CC BY 4.0 License.


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parameterization based on the volatility basis set (VBS) approach. We then use the Community Earth System Model 2 (CESM2.1.0) with detailed isoprene chemistry and reactive uptake processes for the middle and end of the 21st century under four Shared Socioeconomic Pathways (SSPs): SSP1-2.6, . With the explicit chemical mechanism, we find that IEPOX-SOA is predicted to increase on average under all future SSP scenarios, however with some variability in the results depending on regions and the scenario chosen. Isoprene emission is the main driver of IEPOX-SOA changes in the future climate, but IEPOX-SOA yield from isoprene emission also changes by up to 50% depending on the SSP scenario, in particular due to different sulfur emissions. We conduct sensitivity simulations with and without CO 2 inhibition of isoprene emissions that is highly uncertain, which results in a factor of two differences in the predicted IEPOX-SOA global burden, especially for the high-CO 2 scenarios (SSP3-7.0 and SSP5-8.5). Aerosol pH also plays a critical role in the IEPOX-SOA formation rate, requiring accurate calculation of aerosol pH in chemistry models. On the other hand, isoprene SOA calculated with the VBS scheme predicts nearly constant SOA yield from isoprene emission across all SSP scenarios, as a result, it mostly follows isoprene emissions regardless of region and scenario. This is because the VBS scheme does not consider heterogeneous chemistry, in other words, there is no dependency on aerosol properties. The discrepancy between the explicit mechanism and VBS parameterization in this study is likely to occur for other SOA components as well, which may also have dependencies that cannot be captured by VBS parameterizations. This study highlights the need for more explicit chemistry, or for parameterizations that capture the dependence on key physico-chemical drivers when predicting SOA concentrations for climate studies.

Introduction
Secondary organic aerosol (SOA) contributes substantial mass fractions of submicron particle concentrations globally (Zhang et al., 2007) , but it is difficult to predict due to its complex sources and behavior in the atmosphere (Tsigaridis et al., 2014) . There are typically many thousands of organic species and reactions involved depending on the precursor hydrocarbon (Lannuque et al., 2018) , which necessitates the use of parameterizations in chemistry-climate SOA simulations. Over the last two decades, there has been much progress in understanding chemistry of SOA (Ziemann and Atkinson, 2012;Glasius and Goldstein, 2016;Shrivastava et al., 2017;Bianchi et al., 2019) , which has helped chemical transport models to develop more advanced SOA parameterizations (Hodzic et al., 2016;Tsimpidi et al., 2018;Schervish and Donahue, 2019) .
Parameterizations range from simplified empirical methods (Hodzic and Jimenez, 2011) to volatility basis set (VBS) approaches of various complexity (Donahue et al., 2006(Donahue et al., , 2012 which can calculate not only mass concentrations but also oxidation states (Tsimpidi et al., 2018) . A recent evaluation of global OA schemes reported that a simple parameterization showed similar performance compared to explicit chemistry and a complex parameterization scheme, in terms of bias and variability (Pai et al., 2019) . This can be explained by the fact that simple parameterizations are based on observational constraints from field campaigns (Hodzic and Jimenez, 2011;Kim et al., 2015) . However, even though two different SOA schemes simulated similar SOA concentrations in present-day atmospheric conditions, they can have different responses to not only preindustrial conditions (Tilmes et al., 2019) but also future emissions and climate changes and provide different performance in predicting future SOA concentrations, as discussed below.
In order to obtain realistic predictions of future SOA changes, all the variables affecting SOA concentrations should be considered. However, parameterizations inevitably omit some important processes, for example, the two-product or VBS approaches conventionally used in chemical transport models do not consider acid-catalyzed multiphase chemistry Zhang et al., 2018a) 90 95 100 105 and autoxidation (Bianchi et al., 2019;Schervish and Donahue, 2019) . Based on recent laboratory and theoretical studies, which provide a nearly complete gas-phase oxidation mechanism for isoprene and its major products (Wennberg et al., 2018, and references therein) , recent SOA models have started to employ explicit chemistry rather than relying on parameterization schemes, especially for isoprene SOA. As a result, state-of-the-art chemical transport models have started to use a hybrid approach to simulate SOA by using both parameterizations and explicit chemistry including heterogeneous reactions (Pye et al., 2013;Marais et al., 2016;Jo et al., 2019;Shrivastava et al., 2019;Zare et al., 2019;Hodzic et al., 2020) .
When it comes to climate modeling studies, generally simplified SOA parameterizations have been used (e.g. Sporre et al., 2019) . In the fifth phase of the Coupled Model Intercomparison Project (CMIP5), most models used a constant SOA yield without performing the oxidation of volatile organic compounds (VOCs) and gas-to-particle partitioning calculations (Tsigaridis and Kanakidou, 2018) .
Climate studies focusing on SOA employed more detailed schemes with initial oxidation of VOCs and dynamic gas-to-particle partitioning such as the two-product scheme (Heald et al., 2008;Liao et al., 2009;Wu et al., 2012;Cholakian et al., 2019a) and the VBS scheme (Megaritis et al., 2013;Pommier et al., 2018;Zhang et al., 2018b) . Recent studies used even more detailed processes such as SOA formation from highly oxygenated molecules (Zhu et al., 2019) and heterogeneous reactions (Lin et al., 2016) .
A few previous studies examined the effects of different SOA schemes on future SOA prediction. Cholakian et al. (2019b) showed that the complex VBS scheme shows a higher relative change of biogenic SOA between future and historical simulations than the two-product scheme. On the other hand, Day and Pandis (2015) reported that the inclusion of the volatility of primary particles and chemical aging processes in the VBS scheme does not increase its sensitivity to climate change.
However, these studies only compared different volatility-based parameterizations, not including explicit chemistry. As pointed out by Jo et al. (2019) , both the SIMPLE and VBS parameterizations in GEOS-Chem cannot capture the response to changes in NO x and SO 2 emissions predicted by the 115 120 125 130 explicit chemistry. This is critical because these emissions are expected to be substantially different in future climate/emissions scenarios (Feng et al., 2019a) . Lin et al. (2016) used the hybrid approach to simulate global SOA using both parameterizations and explicit chemistry. In their sensitivity simulation, they investigated the effects of aerosol acidity on present-day and future SOA concentrations by comparing two cases using the constant and the pH-dependent reactive uptake coefficient of isoprene epoxydiols (IEPOX), and they concluded that the global average SOA production rate changes very little. This result is contrary to the results by Marais et al. (2017) who concluded that isoprene SOA mass yields per unit isoprene oxidized decreased from 13% in 1991 to 3.5% in 2013 over the Southeast US. This could be because Lin et al. (2016) investigated aerosol pH effects only, while keeping other conditions the same (e.g. HO 2 /NO oxidation channel and aerosol surface area), whereas all the conditions were changed in Marais et al. (2017) . Furthermore, Lin et al. (2016) calculated the effects of acidity on total SOA, but most of SOA components were not affected by the acidity change except for IEPOX-SOA. Stadtler et al. (2018) also investigated the IEPOX-SOA sensitivity to variable aerosol pH compared to fixed pH, and found 58% differences between the two cases.
In this study, we investigate the future SOA change as predicted by the Community Earth System Model version 2.1.0 (CESM2.1.0) using explicit IEPOX-SOA chemistry, and compare it with the SOA predictions by the VBS parameterization recently implemented in the model (Tilmes et al., 2019) . We focus on IEPOX-SOA as we have a higher mechanistic understanding of the IEPOX-SOA formation compared to other SOA species, as well as IEPOX-SOA contributes a substantial mass fraction of SOA especially under low NO conditions (Hu et al., 2015) . The CESM model includes several updates such as an adjustment of isoprene emissions, detailed isoprene chemistry, NO x -dependent yields of the VBS, and the heterogeneous uptake of IEPOX. We evaluate the simulated IEPOX-SOA against aircraft campaign and surface network measurements. We then predict future IEPOX-SOA concentration changes for the mid and end of the 21st century under four shared socioeconomic pathways (SSPs) -SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 (O'Neill et al., 2016;Riahi et al., 2017) . We also conduct sensitivity simulations to examine the effects of CO 2 inhibition on isoprene change and IEPOX-SOA 5 https://doi.org/10.5194/acp-2020-543 Preprint. Discussion started: 3 July 2020 c Author(s) 2020. CC BY 4.0 License. 145 150 155 budget, and the effects of aerosol pH on IEPOX-SOA formation. Finally, we compare the explicit scheme and the VBS parameterization to investigate the differences between the two schemes in predicting future SOA concentrations.
We constrained sea surface temperatures and sea ice conditions from observations for present runs and from the Whole Atmosphere Community Climate Model version 6 (WACCM6) results for future runs.
The WACCM6 results used in this study were those of the CMIP phase 6  .
For present-day conditions, anthropogenic emissions are from the Community Emissions Data System (CEDS) (Hoesly et al., 2018) and biomass burning emissions from the inventory developed for CMIP6 (van Marle et al., 2017) . The SSPs were used for future climatic scenarios (Riahi et al., 2017) .
For the model evaluation in Sect. 3, we used a specified dynamics option (FCSD compset) to reduce uncertainties related to dynamic simulations in the atmospheric model (CAM6). The meteorological fields (temperature, wind, and surface fluxes) were nudged towards the Modern-Era Retrospective analysis for Research and Applications version 2 (MERRA2) (Gelaro et al., 2017) with a relaxation time of 50 hours.

Gas-phase chemistry of isoprene
Because the isoprene SOA yield strongly depends on the gas-phase chemistry, we used the MOZART-TS2 (Model of Ozone And Related chemical Tracers, Troposphere-Stratosphere V2) detailed isoprene chemical mechanism recently developed by Schwantes et al. (2020) . The MOZART-TS2 chemical mechanism includes more comprehensive and updated both isoprene and terpene chemistry, but for computational efficiency, we only implemented the new isoprene chemistry. The updates for isoprene chemistry added 39 new compounds and 139 reactions on top of the MOZART-TS1 chemistry  , and includes updates to isoprene hydroxy hydroperoxide (ISOPOOH) and IEPOX chemistry relevant to this work. These updates were applied to all simulations in this work.

Heterogenous IEPOX reactive uptake
We implemented the heterogeneous uptake of IEPOX based on the work by Jo et al. (2019) . We used the resistor model equation (Anttila et al., 2006;Gaston et al., 2014b) to calculate the reactive uptake coefficient of IEPOX ( IEPOX ). The equation needs several parameters such as Henry's law constant and Aerosol pH was calculated online for each mode by the MOSAIC module (Zaveri et al., 2008) , as implemented in CESM by Zaveri et al. (2020) and Lu et al. (2020). In addition, we modified MOSAIC to calculate submicron (Aitken and accumulation modes) aerosol pH without sea salt following Jo et al.
(2019) based on previous studies showing that sea salt aerosols were dominantly externally mixed with submicron sulfate-nitrate-ammonium rather than internally mixed (Guo et al., 2016;Bondy et al., 2018;Murphy et al., 2019) . We note that sea salt was calculated in the model but excluded only for pH calculation. Removing sea salt resulted in substantially lower pH (more acidic aerosol) over the ocean, and a better agreement with the observationally-constrained pH values by Nault et al. (2020). The effects of sea salt on global aerosol pH and IEPOX-SOA formation are discussed in Sect. 4.2. It is worth noting that the submicron aerosol nitrate burden predicted by MAM4-MOSAIC is about 50% of MAM7-MOSAIC (Lu et al., 2020;Zaveri et al., 2020), due to the different treatments of sub-micron sea salt and dust between MAM7 (Liu et al., 2012) and MAM4 (Liu et al., 2016) , while the super-micron aerosol nitrate burdens are close. Nitrate aerosol affects pH and in turn, IEPOX-SOA formation, and pH also strongly affects nitrate aerosol formation. MAM4-MOSAIC has been found to predict similar nitrate levels compared to the observed nitrate aerosol concentrations over the US and East Asia (Lu et al., 2020), but additional studies will be needed to evaluate the nitrate simulation in other regions.
The effects of organic coatings have been often neglected in previous studies using the explicit chemistry for IEPOX-SOA (Lin et al., 2016;Marais et al., 2016;Budisulistiorini et al., 2017;Stadtler et al., 2018;Shrivastava et al., 2019) , although it can reduce IEPOX-SOA formation rate by up to ~30% (Zhang et al., 2018a;Schmedding et al., 2019b) . We considered the organic coating effect by assuming inorganic-core and organic-shell mixture, as described in detail in Jo et al. (2019) .
The SOA yield of IEPOX reactive uptake was assumed to be 100% and IEPOX-SOA was treated as non-volatile in the model. This is consistent with other previous modeling studies  215 220 225 230 Budisulistiorini et al., 2017;Stadtler et al., 2018;Schmedding et al., 2019b) , based on field studies which showed that ambient IEPOX-SOA has very low volatility Lopez-Hilfiker et al., 2016;Riva et al., 2019) . A recent chamber-based study by D'Ambro et al. (2019) confirmed the low-volatility of IEPOX-SOA, and suggested that the semivolatile products measured by some techniques in ambient IEPOX-SOA mostly resulted from thermal decomposition in those methods. On the other hand, they reported that the semi-volatile 2-methyltetrols that are also formed can evaporate after IEPOX reactive uptake, and can be lost to gas-phase reactions with OH and dry/wet deposition, resulting in an IEPOX-SOA yield lower than unity. However, the evaporation is completed within one hour, and thus is not inconsistent with the very low volatility characteristics of ambient IEPOX-SOA.
D'Ambro et al. (2019) also pointed out that the measured IEPOX is an order of magnitude or more higher than often used in models. We conducted sensitivity tests to investigate these uncertain parameters on model evaluation results in Sect. 3.

Isoprene emission adjustment
Isoprene emission changes are one of the main driving factors of IEPOX-SOA change in the future climate (Sect. 5). MEGAN v2.1 has been considered as the most reliable biogenic emission algorithm and used in many chemistry models (e.g. all models that participated in the intercomparison study by Hodzic et al. (2020) used MEGAN). However, there are still many uncertainties in calculating isoprene emissions in models, especially for tropical forests which are less understood than their temperate and boreal counterparts due to great heterogeneity and many forest subtypes at scales of hundreds of meters (Batista et al., 2019) . For example, ter Steege et al. (2013) reported that Amazonia harbors ~16,000 different tree species, and Silk et al. (2015) showed that there are 40,000-53,000 tree species in the tropics, in contrast to only 124 across temperate Europe. Furthermore, there have been fewer emission studies over Tropics (< 20%) compared to their contribution to global biogenic VOC emissions (75%) (Guenther, 2013) .
Satellite-based top-down studies have reported that chemistry models with the MEGAN v2.1 algorithm tend to overestimate isoprene emissions over the Tropics (Worden et al., 2019) including the In order to calculate the isoprene emissions as realistically as possible, especially for the Tropics, we used two constraints. First, we compared the simulated global isoprene emissions by CESM2.1.0/MEGANv2.1 (PFT-based emission factors, MODIS-based leaf area index (LAI)) with isoprene top-down estimates using HCHO from the Ozone Monitoring Instrument (OMI) (Bauwens et al., 2016) . As discussed above, the model overestimated isoprene emissions especially for the Tropics (Sect. S1 and Figs. S1 and S2 in the Supplement). Second, we evaluated the modeled isoprene concentrations against aircraft measurements over the Amazon, which also suggested an overestimation (see Sect. 3.2 for details). To reduce discrepancies found in both of these comparisons, we reduced isoprene emission factors for tropical PFTs (broadleaf evergreen tropical tree and broadleaf deciduous tropical tree) by a factor of 2. The resulting isoprene emissions were comparable to OMI-based isoprene emission estimates in terms of the annual global total value, although there were still some regional differences (Figs. S1 and S2). For example, the base model overestimated OMI-based isoprene emissions over the Amazon by a factor of 3-4. Because satellite-based top-down emissions also have uncertainties in the inversion process (e.g., a priori source uncertainty), and the aircraft comparison of ambient isoprene over the Amazon (Sect. 3.2) only supported reducing isoprene emissions by a factor of 2, we considered that reducing isoprene emissions by a factor of 3-4 would have been excessive.
The CO 2 inhibition effect on isoprene emissions becomes important at high CO 2 concentrations under future climatic conditions, which can solely offset isoprene emission increase associated with the future temperature increase (Tai et al., 2013) . Controlled chamber experiments revealed isoprene emissions are lower at elevated CO 2 conditions (Wilkinson et al., 2009;Possell and Hewitt, 2011) , and MEGANv2.1 includes the CO 2 inhibition effect in the isoprene emission calculation (Guenther et al., 2012) . However, the quantitative effects of CO 2 inhibition on isoprene emission are still difficult to predict, likely due to the onset of complex feedback and feedforward biochemical mechanisms and interactive effects (Sharkey and Monson, 2017;Feng et al., 2019b) . Bauwens et al. (2018) also reported the large uncertainty associated with CO 2 inhibition calculations by using two distinct CO 2 inhibition parameterizations. Therefore, we conducted future simulations without CO 2 inhibition effects as a base case, and we additionally carried out simulations with CO 2 effects to estimate the robustness of our conclusions with regard to CO 2 effects. We note that the CO 2 inhibition effect is included in MEGANv2.1 in CESM as a default (Guenther et al., 2012) .

NO x -dependent yield of VBS scheme
The VBS scheme (Hodzic et al., 2016) as implemented in CESM2.1.0 considers only low NO x conditions (Tilmes et al., 2019) . Because NO x levels in the future are predicted to change substantially (Feng et al., 2019a) , it is important to consider NO x -dependent yields to capture the response to HO 2 /NO ratio change in the future. We updated the VBS scheme to simulate high and low NO x pathways of SOA formation based on yields from Hodzic et al. (2016) . For example, for isoprene, the default scheme includes a reaction with OH forming the SOA precursor gas phase species (SOAG) for the 5 VBS bins: where SOAG0-4 represent gas-phase SOA species simulated by the VBS scheme, spanning saturation vapor concentrations from 0.01 µg m -3 to 100 µg m -3 at 300 K; α low,n is the SOA molar yield at low NO x conditions for the volatility bin n , with values 0.0031, 0.0035, 0.0003, 0.0271, and 0.0474, respectively; k is the reaction rate coefficient in cm 3 molecule -1 s -1 , and T is the temperature in K. To account for the high and low NOx conditions, we added two reactions to calculate the peroxy radical + HO 2 and peroxy radical + NO explicitly, as follows: Where α high,0-4 are 0.0003, 0.0003, 0.0073, 0.0057, and 0.0623, respectively. Isoprene, OH, HO 2 , and NO are not consumed by the VBS reactions to avoid duplication with the detailed gas-phase isoprene chemistry in Sect. 2.2.1. In other words, the VBS doesn't affect gas-chemistry in the model, so all simulations in Table 1 have the same gas-chemistry. The isoprene peroxy radical (ISOPO2VBS) is a non-transported tracer to reduce computational cost. It is reasonable as a typical lifetime of isoprene peroxy radicals in the atmosphere is less than a few minutes (Wennberg et al., 2018;Jo et al., 2019) .
The reaction rate constant of isoprene + OH reaction matches the isoprene gas-phase reaction (Schwantes et al., 2020) . Similar high NOx yields for SOA formed from terpenes, benzene, toluene and xylenes have been included in the mechanism.
3 Model evaluation

SEAC4RS
The Studies of Emissions, Atmospheric Composition, Clouds and Climate Coupling by Regional Surveys (SEAC 4 RS) campaign in August -September 2013 sampled the continental US troposphere with a heavy emphasis on the SE US and provided aircraft measurements of isoprene and its oxidation products Toon et al., 2016) . We evaluated the model against isoprene    polluted air masses from the data for evaluation: NO y > 1ppb, ozone > 20 ppb, and particle number > 1200 cm -3 for IOP1 and NO y > 1.3 ppb, ozone > 36 ppb, and particle number > 2240 cm -3 for IOP2. We applied these criteria to observations from the G-1 aircraft, by assuming that both the G-1 aircraft and the T3 surface site were affected by similar air masses. The G-1 aircraft mostly sampled the boundary layer (~75% data points below 1 km, see Fig. 2), and its flight tracks were close to the T3 site (Martin et   substantially overestimate observed concentrations. The data in Fig. 2 shows NMBs of 65% and 99% for isoprene during IOP1 (a) and IOP2 (b), respectively. The overestimations were higher for IEPOX-SOA, which were 430% during IOP1 (c) and 769% during IOP2(c). We attribute these overestimations to too high isoprene emissions as discussed in Sect. 2.2.3. A sensitivity simulation with the isoprene emissions from tropical trees decreased by 50% reduced model biases to -51% and -46% for isoprene during IOP1 and IOP2, respectively, and to 225% and 394% for IEPOX-SOA. A further reduction of isoprene emissions to 25% led to substantial underprediction of isoprene concentrations with biases of -84% during IOP1 and -77% during IOP2. Mean IEPOX-SOA concentrations were still overestimated (75% and 121%), with strong variability in biases according to altitude (Fig. 2d). Even the model with the lowest isoprene emissions overestimated IEPOX-SOA below 5 km, but it substantially underestimated IEPOX-SOA above 5 km (green line in Fig. 2d). One possible reason are inaccuracies in the convection scheme in the model, because the ACRIDICON-CHUVA period was strongly influenced by tropical deep convection (Schulz et al., 2018) . It is worth noting that the convection scheme in CAM6 (CLUBB; Cloud Layers Unified By Binormals) has shown improved performance for tropical deep convection over land compared to the previous convection schemes in CESM (Danabasoglu et al., 2020) , but it may still contribute to the observed differences. In terms of IEPOX-SOA concentrations above 5 km, NMBs were 181%, 6%, and -42% for the base, half, and quarter isoprene emission cases, respectively.
The higher model IEPOX-SOA bias against the ACRIDICON-CHUVA (121-769%) compared to the GoAmazon (75-430%) measurements can be explained by particle losses in the constant pressure inlet used by the HALO AMS. Mei et al. (2020) reported that there were particle losses in the constant pressure inlet used on the HALO AMS, by comparing G1 AMS and HALO AMS during coordinated flights. The differences between G1 and HALO AMS were up to a factor of two below 2 km (Fig. 11 in Mei et al. (2020) ). We further investigated the effects of IEPOX-SOA evaporation (Sect. 2.2.2) on the model performance, by using H * of 8.5 × 10 7 M atm -1 and the yield of 0.2 (IEPOX-SOA yield from IEPOX reactive uptake), especially for the model with the half isoprene emissions (Fig. S5). NMBs were 11% and 28% over all altitudes for IOP1 and IOP2, respectively. For the ACRIDICON-CHUVA campaign

Global surface AMS dataset
We evaluated the model against global IEPOX-SOA concentrations reported by Hu et al. (2015) , who quantified IEPOX-SOA by applying PMF to AMS measurements. They reported surface IEPOX-SOA concentrations averaged for each campaign period (from a month to a few months) as shown in Table   S1. Figure 3 shows the comparison of modeled versus observed IEPOX-SOA concentrations at the   Table S1. The southeast US, the Amazon, and urban regions are shown in blue, green, and red, respectively.   Table 1. One present (2010s) and two future (2050s and 2090s) simulations were conducted. In each set of simulations shown in Table 1, we simulated 10 years to account for interannual variability. The first 2 years were discarded as a spin-up period, and the remaining 8 years were used for the analysis. In addition to the future IEPOX-SOA changes, we investigated the effects of aerosol pH (Sect. 4.2) and CO 2 inhibition of isoprene emissions (Sect. 4.3) on IEPOX-SOA budgets. The westward continental outflow from the Amazon was enhanced under all SSP scenarios as shown in Figs. 4 and 5. This was due to longer lifetimes of isoprene and its products (Fig. 6), which resulted from lower OH concentrations in future conditions (Fig. S7). Increased OH consumption by higher isoprene and decreased OH production by less NO x (Fig. S8) led to lower OH concentrations.  The fate of the isoprene peroxy radical also changed, as the relative contribution of the reaction with NO and isomerization was quite different between the present and future conditions (Fig. 6). In present conditions, the reaction with NO (53% of the isoprene emission amount) was more dominant than the isomerization pathway (30%). However, it was reversed under the SSP5-8.5 scenario, with the flux of the isomerization pathway (39%) being higher than that of the reaction with NO (33%). There were two main causes: (1) isomerization rates increase with temperature (Bianchi et al., 2019) , and (2) the global mean NO x emissions decrease under all future SSP scenarios (Turnock et al., 2020) .

IEPOX-SOA changes
Interestingly, the fraction of isoprene emissions leading to ISOPOOH formation did not change much (62-67%), although the absolute amount was increased due to the isoprene emissions increase (Fig. S9).
The IEPOX formation rates from isoprene emissions were nearly constant (32-33%) for present and all SSP scenarios (SSP2-4.5 and SSP3-7.0 are not shown), due to compensating effects between factors discussed above.
The IEPOX-SOA yield from isoprene emissions varied from 5.6% (SSP1-2.6) to 8.6% (SSP3-7.0), although IEPOX/isoprene flux ratios were almost the same. Much of this difference is due to predicted changes in sulfate aerosol concentrations over the Amazon (Fig. S10). Higher sulfate concentrations over the Amazon not only increased the available surface area where IEPOX reactive uptake takes place but also enhanced aerosol acidity (reduced aerosol pH, Fig. S11), which led to a faster formation of IEPOX-SOA.
These findings show that IEPOX-SOA formation is nonlinear. Thus, the formation cannot be easily simplified as various processes are involved, such as isoprene emissions affecting OH consumption and thus the lifetime of other chemical species, NO and temperature affecting the fate of peroxy radicals, and aerosol surface area and pH affecting IEPOX reactive uptake. In the following section (Sect. 5), we present a comparison between the explicit chemistry and the VBS approach to investigate the ability of an empirical parameterization that is typical of those currently used in most models to simulate SOA under future climates.

Effects of aerosol pH on IEPOX-SOA formation
Here we discuss the effects of aerosol pH on IEPOX-SOA formation, by comparing EXP and EXP_SS simulations. Figure 7 shows IEPOX-SOA concentrations and ratios between future and present conditions simulated by EXP_SS which includes sea salt aerosols in the aerosol pH calculations. The predicted IEPOX-SOA levels were lower in the EXP_SS than in the EXP case, due to higher aerosol pH which hindered acid-catalyzed reactions of IEPOX (Gaston et al., 2014a) . Figure 8 illustrates that IEPOX-SOA formations were decreased by 25-37% in the EXP_SS simulation due to less acidic aerosols, even though emissions, chemistry, and deposition fluxes leading to IEPOX were almost the same compared to EXP. This result indicates that the correct treatment of inorganic aerosols and related thermodynamic calculations are critically needed for the accurate simulation of organic aerosols. The different pH treatments could also impact the nitrate formation, the accumulation mode nitrate burden was reduced by 19% in EXP_SS (14.8 GgN) compared to EXP (18.2 GgN).

Isoprene emission and IEPOX-SOA changes with CO 2 inhibition effects
As discussed in Sect. 2.2.3, the CO 2 inhibition effect on isoprene emissions is especially important for predicting future climate, but large uncertainties exist. We examined the predicted IEPOX-SOA concentrations with CO 2 inhibition (EXP_CO 2 ) and compared to the cases without CO 2 inhibition (EXP). Predicted global mean surface IEPOX-SOA concentrations in present and future (2090s) conditions are presented in Fig. 9 (a-e) along with relative changes in the future compared to the present conditions (f-i). While aerosol pH affected IEPOX-SOA in all the simulations including present conditions (Sect. 4.2), CO 2 inhibition played a critical role only in future simulations with higher CO 2 concentrations. As shown in Fig. 10, global isoprene emissions in EXP_CO2_2090 simulations were substantially lower than in EXP_2090 simulations (Fig. 6), especially for the SSP5-8.5 scenario with high CO 2 (53% decrease). Consequently, the annual IEPOX-SOA formation fluxes were also reduced, 24.7 Tg yr -1 (EXP_2090_CO2) from 55.0 Tg yr -1 (EXP_2090) for the SSP5-8.5 scenario. Global surface IEPOX-SOA concentrations were also decreased due to CO 2 inhibition across all SSP scenarios with higher relative changes for SSP3-7.0 and SSP5-8.5 (Fig. S12).    Figure 10. Same as Fig. 6 but for EXP_CO2 simulations (CO 2 inhibition effect is taken into account).

590
Isoprene emission calculations by MEGANv2.1 are based on a simple mechanistic model that considers the major processes driving variations by using activity factors (Guenther et al., 2012) . We broke down activity factor changes under SSP1-2.6 ( Fig. S13) and SSP5-8.5 (Fig. S14) with respect to present conditions. The main driving factor in the isoprene emission increase was the response to temperature, although both LAI and light factors also contributed to the emission increase. On the other hand, CO 2 inhibition counteracted the temperature effect, surpassing it especially for the SSP5-8.5 scenario.
Isoprene emission changes due to CO 2 inhibition also affected chemistry. Lifetimes of IEPOX-SOA precursors were decreased drastically under the SSP5-8.5 scenario when CO 2 inhibition was included in the isoprene emission calculation (EXP_CO2, Fig. 10). This was due to higher OH concentrations in EXP_CO2, caused by less OH consumption by isoprene and its products (Fig. S15). The change increased as the forcing (CO 2 ) increased. It also affected the relative changes in IEPOX-SOA concentrations between future and present conditions, which has important implications for high forcing scenarios (SSP3-7.0 and SSP5-8.5).

Comparison with the VBS approach
In this section, we examined isoprene SOA and its future changes by the VBS approach (VBS case) and compared it against IEPOX-SOA by the explicit chemistry (EXP case). The VBS approach only simulates total isoprene SOA and does not separate IEPOX-SOA (Tilmes et al., 2019) . Because IEPOX-SOA is mostly formed by the isoprene + OH reaction pathway, here we only considered isoprene SOA formed via the isoprene + OH VBS reaction pathway. The VBS SOA from isoprene + O 3 and isoprene + NO 3 pathways were excluded in the analysis, although they were included in the model simulation. Hereafter, we refer to isoprene SOA as the VBS SOA from isoprene + OH pathway simulated by the VBS, in order to distinguish it from IEPOX-SOA simulated by the explicit chemistry. Figure 11 shows the VBS SOA and its change in the future. The VBS scheme captured global spatial patterns of isoprene SOA although absolute magnitudes were lower than IEPOX-SOA. VBS SOA was generally predicted to be increased under the future climate, which was also analogous to the IEPOX-SOA change (Fig. 5). However, the concentration changes in the future were regionally different. The model with the explicit chemistry predicted the IEPOX-SOA concentration decrease in the 2090s under the SSP1-2.6 scenario over mid-latitudes in the Northern Hemisphere, but the model with the VBS SOA predicted an increase. As a result, VBS SOA over the eastern US was lower than IEPOX-SOA in present conditions but higher in the 2090s under the SSP1-2.6 scenario, as shown in Fig. 12. This was because the explicit chemistry took into account aerosol surface area and pH that were less favorable for IEPOX-SOA formation under the SSP1-2.6 scenario, but the VBS does not consider aerosol properties in SOA formation (other than OA mass).
VBS SOA decreased over central Africa under the SSP3-7.0 scenario (Fig. 11h), which cannot be seen in the explicit chemistry (Fig. 5g). The SSP3-7.0 was the scenario with the highest NO x emissions among all SSP scenarios (Turnock et al., 2020) and NO x concentration was predicted to increase over central Africa (Fig. S8). The VBS SOA yields are lower in the high NO x pathway than in the low NO x pathway (Hodzic et al., 2016) , which resulted in the VBS SOA decrease over Africa. On the other hand, The NO x dependency considered in the VBS also applied to the explicit chemistry, but again, the explicit chemistry has other dependencies such as aerosol surface area and pH. The increase of sulfate aerosol concentration over Africa (Fig. S10) promoted IEPOX reactive uptake in the explicit chemistry, while the VBS SOA did not have this dependency. Figure 12 indicates that isoprene SOA was exceedingly low compared to IEPOX-SOA except for source regions. This result was consistent with Jo et al. (2019) , who used the GEOS-Chem chemical transport model (see Fig. 3c in their paper). The main reason was that IEPOX-SOA was nonvolatile but the VBS simulated most of the semi-volatile products as gas phase rather than aerosol phase especially for remote regions (Jo et al., 2019) . As a result, global tropospheric burdens of isoprene SOA were lower than those of IEPOX-SOA (e.g., 252 and 101 Gg for IEPOX-SOA and isoprene SOA in present conditions, respectively). reductions for the present, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios, respectively. The VBS SOA also showed a similar tendency as it followed isoprene emissions -2%, 8%, 27%, 39%, and 55% reductions for the present, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5 scenarios, respectively.
However, the VBS SOA did not have additional reductions by aerosol pH changes (16-33% reductions), due to a lack of aerosol pH dependency.
The isoprene emission was the main driving factor of IEPOX-SOA burden differences between the SSP scenarios, but Fig. 13 (right column) also showed that chemistry was important, which can change the SOA burden per unit isoprene emission up to 50% (SSP3-7.0 vs SSP1-2.6). However, the values were nearly constant when it comes to the VBS. This suggests that the detailed chemistry should be included for a more accurate SOA sensitivity in models.   We further investigated the SOA sensitivities against emissions in different model configurations, as depicted in Fig. 14. For each model configuration in Table 1, we calculated the regression slope and R 2 values between monthly gridded IEPOX-SOA (isoprene SOA) concentrations at the surface and isoprene emissions. Similar to the metric (burden/emission) in Fig. 13, the VBS showed a very narrow range of regression slopes. R 2 values of the VBS cases were higher than those of the explicit chemistry, which means isoprene SOA generally followed isoprene emissions with little non-linearity. Lower R 2 implies other dependencies in simulating SOA concentrations in addition to isoprene emissions.
Regression slopes of the models with sea salt in the aerosol pH calculation were lower, because of less acidic conditions. CO 2 inhibition also affected the regression slopes under the SSP3-7.0 and SSP5-8.5 scenarios. Higher isoprene emissions without CO 2 inhibition made longer lifetimes of IEPOX-SOA precursors (Sect 4.3) and resulted in more IEPOX-SOA in downwind regions. As a result, the regression slopes without CO 2 inhibition were lower than with CO 2 inhibition, due to less IEPOX-SOA concentrations above isoprene emission source regions. These effects were not apparent in the VBS models.

Conclusions
Current climate models rely on parameterizations to predict SOA, due to complex non-linear chemistry affecting SOA formation. Thanks to recent progress in the mechanistic understanding of SOA formation from the combined laboratory, field, and modeling studies, chemistry models have started to include explicit SOA mechanisms for a few SOA species including IEPOX-SOA. Here, we implemented a detailed chemical mechanism to explicitly simulate IEPOX-SOA in CESM2.1.0. We investigated future IEPOX-SOA changes under four Tier 1 SSP scenarios, using the explicit chemical mechanism as well as the VBS parameterization.
IEPOX-SOA concentrations were generally predicted to be increased under the SSP scenarios.
Isoprene emission change was the primary factor driving IEPOX-SOA change. OH consumption by enhanced isoprene emissions increased lifetimes of IEPOX-SOA precursors, resulting in more 695 700 705 710 IEPOX-SOA in downwind regions. The CO 2 inhibition effect on isoprene emissions became highly influential for high forcing SSP scenarios (SSP3-7.0 and SSP5-8.5); more studies are needed to reduce the high uncertainty related to this effect in future conditions. Aerosol properties (surface area and pH) were an important factor affecting IEPOX-SOA. IEPOX-SOA concentrations were decreased over the Northern Hemisphere mid-latitudes especially under the SSP1-2.6. This was caused by the reduced sulfate aerosols compared to present conditions, and in turn the reduced aerosol surface area and acidity.
We further predicted isoprene SOA concentrations using the VBS scheme. The VBS scheme also simulated the overall increase of isoprene SOA in the future, mainly due to increased isoprene emissions. VBS SOA concentrations were decreased over central Africa under the SSP3-7.0. Increased NO x concentrations in this region reduced SOA yield, because SOA yields from the high-NO x pathway are lower than from the low-NO x pathway. A NO x dependency was also included in the explicit chemistry mechanism. However, the explicit chemistry further included other dependencies such as aerosol acidity, leading to the opposite trend -the explicit chemistry predicted the slight increase of IEPOX-SOA over central Africa. In terms of the global SOA burden to isoprene emission ratio, the explicit chemistry simulated 50% differences across different SSP scenarios, but the VBS scheme simulated nearly constant values.
The SOA parameterization involves assumptions, inevitably leaving out some chemistry. This can be negligible in simulating present conditions, but can become important under future climate with different emissions and meteorological conditions. Climate models have been improved in terms of resolution, thanks to the recent growth in computational power and parallel computing methods. In addition to the higher spatial and temporal resolution of climate models, the detailed explicit chemistry is also essential for the correct simulation of aerosols, and in turn, radiation and clouds in climate models. With the new development of measurements of the SOA formation mechanism from other compounds in the laboratory, the detailed explicit chemistry of SOA will be available. It would be recommended for climate models to use more comprehensive chemistry, or parameterizations with the Competing interests. The authors declare that they have no conflict of interest.