Effective radiative forcing in the aerosol-climate model CAM5.3-MARC-ARG

We quantify the effective radiative forcing (ERF) of anthropogenic aerosols modelled by the aerosol-climate model CAM5.3-MARC-ARG. CAM5.3-MARC-ARG is a new configuration of the Community Atmosphere Model version 5.3 (CAM5.3) in which the default aerosol module has been replaced by the two-Moment, Multi-Modal, Mixing-state-resolving Aerosol model for Research of Climate (MARC). CAM5.3-MARC-ARG uses the default ARG aerosol activation scheme, consistent with the default configuration of CAM5.3. We compute differences between simulations using year-1850 aerosol emissions and simulations using year-2000 aerosol emissions in order to assess the radiative effects of anthropogenic aerosols. We compare the aerosol column burdens, cloud properties, and radiative effects produced by CAM5.3-MARC-ARG with those produced by the default configuration of CAM5.3, which uses the modal aerosol module with three log-normal modes (MAM3). Compared with MAM3, we find that MARC produces stronger cooling via the direct radiative effect, stronger cooling via the surface albedo radiative effect, and stronger warming via the cloud longwave radiative effect. The global mean cloud shortwave radiative effect is similar between MARC and MAM3, although the regional distributions differ. Overall, MARC produces a global mean net ERF of -1.75$\pm$0.04 W m$^{-2}$, which is stronger than the global mean net ERF of -1.57$\pm$0.04 W m$^{-2}$ produced by MAM3. The regional distribution of ERF also differs between MARC and MAM3, largely due to differences in the regional distribution of the cloud shortwave radiative effect. We conclude that the specific representation of aerosols in global climate models, including aerosol mixing state, has important implications for climate modelling.


The two-Moment, Multi-Modal, Mixing-state-resolving Aerosol model for Research of Climate (MARC)
The two-Moment, Multi-Modal, Mixing-state-resolving Aerosol model for Research of Climate (MARC), which is based on the aerosol microphysical scheme developed by Ekman et al. (2004Ekman et al. ( , 2006 and Kim et al. (2008), simulates the evolution of mixtures of aerosol species. Previous versions of MARC have been used both in cloud-resolving model simulations (Ekman et al., 2004(Ekman et al., , 2006(Ekman et al., , 2007Engström et al., 2008;Wang, 2005aWang, , 2005b and in global climate model simulations (Ekman et al., 2012;Kim et al., 2008Kim et al., , 2014. Recently, an updated version of MARC has been coupled to CAM5.3 within CESM1.2.2 . In contrast to MAM, MARC tracks the number concentrations and mass concentrations of both externally-mixed and internally-mixed aerosol modes with assumed lognormal size distributions. The externally-mixed modes include three pure sulfate modes (nucleation, Aitken, and accumulation), pure organic carbon, and pure black carbon. The internallymixed modes include mixed organic carbon plus sulfate and mixed black carbon plus sulfate. In the mixed organic carbon plus sulfate mode, it is assumed that the organic carbon and sulfate are mixed homogeneously within each particle; in the mixed black carbon plus sulfate mode, it is assumed that each particle contains a black carbon core surrounded by a sulfate shell. Sea salt and mineral dust are represented using sectional single-moment schemes, each with four size bins (Albani et al., 2014;Mahowald et al., 2006;Scanza et al., 2015).
Sea salt emissions follow the default scheme used by MAM , based on simulated wind speed and sea surface temperature. Dust emissions follow the tuning of Albani et al. (Albani et al., 2014), based on simulated wind speed and soil properties, including soil moisture and vegetation cover. Emissions of sulfur dioxide, dimethyl sulfide, primary sulfate aerosol, organic carbon aerosol, black carbon aerosol, and volatile organic compounds (such as isoprene and monoterpene) are prescribed.
The aerosol removal processes represented by MARC -including nucleation scavenging by both stratiform and
The three simulations using year-2000 emissions, referred to as the "year-2000 simulations", facilitate comparison of aerosol fields and cloud fields; the two simulations using year-1850 emissions, referred to as the "year-1850 simulations", further facilitate analysis of the aerosol radiative effects produced by MAM3 and MARC. There is no MAM7 simulation using year-1850 aerosol emissions, due to a lack of year-1850 emissions files for MAM7. The only difference between the year-2000 simulations and the year-1850 simulations is the aerosol (including aerosol precursor) emissions. In the figures and discussion of results, "2000-1850" and "! " both refer to differences between the year-2000 simulation and the year-1850 simulation for a given aerosol module (e.g. MARC_2000-MARC_1850).
The prescribed emissions for both MAM and MARC follow the default MAM emissions files, described in the Supplement of Liu et al. (2012), based on Lamarque et al. (2010). This differs from , who used different emissions of organic carbon aerosol, black carbon aerosol, and volatile organic compounds. In this study, we deliberately use identical emissions for MAM and MARC so that the influence of emissions inventories can be minimised when the results are compared.
For the MAM simulations, the aerosol emissions from some sources follow a vertical profile . For the MARC simulations, sulfur emissions follow the same vertical profile as for MAM; but all organic carbon, black carbon, and volatile organic compounds are emitted at the surface. 2.5% of the sulfur dioxide is emitted as primary sulfate. Mineral dust and sea salt emissions are not prescribed, being calculated "online". Each simulation is run for 32 years, and the first two years are excluded as spin-up. Hence, a period of 30 years is analysed.

Diagnosis of radiative effects
Pairs of prescribed-SST simulations, with differing aerosol emissions, facilitate diagnosis of anthropogenic aerosol ERF via the "radiative flux perturbation" approach (Haywood et al., 2009). When "clean-sky" radiation diagnostics are available, the ERF can be decomposed into contributions from different radiative effects (Ghan, 2013). (We use the term "radiative forcing" only when referring to ERF, defined as the radiative flux perturbation between a simulation using year-1850 emissions and a simulation using year-2000 emissions; we use the term "radiative effect" more generally.) The shortwave effective radiative forcing (! ) can be decomposed as follows: where ! refers to the 2000-1850 difference, ! is the direct radiative effect, ! is the clean-sky shortwave cloud radiative effect, and ! is the 2000-1850 surface albedo radiative effect. These components are defined as follows: where ! is the net shortwave flux at top-of-atmosphere (TOA), ! is the clean-sky net shortwave flux at TOA, and ! is the clean-sky clear-sky net shortwave flux at TOA. ("Clear-sky" refers to a hypothetical situation where clouds do not interact with radiation; "clean-sky" refers to a hypothetical situation where aerosols do not directly interact with radiation.) The longwave effective radiative forcing (! ) is calculated as follows: where ! is the net longwave flux at TOA, ! is the clear-sky net longwave flux at TOA, and ! is the longwave cloud radiative effect. Eq. (6) assumes that aerosols and surface albedo changes do not influence the longwave flux at TOA, so that ! .
The net effective radiative forcing (! ) is simply the sum of ! and ! : All the quantities mentioned in Eqs.
We also consider absorption by aerosols in the atmosphere (! ), defined as follows: where ! is the net shortwave flux at the earth's surface, and ! is the clean-sky net shortwave flux at the earth's surface.

Results
We focus on model output fields relating to different components of the ERF, taking each component in turn: the direct radiative effect, the cloud radiative effect, and the surface albedo radiative effect. When discussing each of these components, we also discuss related model field; for example, in the section discussing the direct radiative effect we also consider other fields related to direct aerosol-radiation interactions. But first, to provide context for the discussion of the radiative effects, we examine the aerosol column burdens.

Aerosol column burdens
An aerosol column burden, also referred to as a loading, reveals the total mass of a given aerosol species in an atmospheric column. The advantage of column burdens is that they are relatively simple to understand, facilitating comparison between the different aerosol modules. However, when comparing the column burdens, it is important to remember that information about aerosol size distribution and aerosol mixing state is hidden. Information about the vertical distribution is also hidden, because the burdens are integrated throughout the atmospheric column.   Oceania. For both MAM3 and MARC, global mean ! accounts for more than half of global mean year-2000 ! , indicating that anthropogenic sulfur emissions are responsible for more than half of the global burden of sulfate aerosol. unchanged so these species are unlikely to contribute to ! .   S8e, f) likely also influence ! , because precipitation efficiently removes sea salt aerosol from the atmosphere.

Total black carbon aerosol burden
However, it should be noted that the 2000-1850 differences in ! , surface wind speed, and precipitation rate are both relatively small and often statistically insignificant across most of the world. If an interactive dynamical ocean were to be used, allowing SSTs to respond to the anthropogenic aerosol ERF, it is likely that we would find much larger 2000-1850 differences in surface wind speed, precipitation rate, and ! . play a role. As we noted above when discussing the sea salt burden, if an interactive dynamical ocean were to be used, it is likely that we would find much larger 2000-1850 differences in surface wind speed, precipitation rate, and ! .

Aerosol optical depth
Aerosols scatter and absorb shortwave radiation, leading to extinction of incoming solar radiation. Before considering the direct radiative effect, we first look at aerosol optical depth (! ), a measure of the total extinction due to aerosols in an atmospheric column.   have also previously noted that the ! for MARC is generally lower than that retrieved from the MODerate Resolution Imaging Spectroradiometer (MODIS; Collection 5.1); but it should be noted that differences in spatial-temporal sampling (Schutgens et al., 2017(Schutgens et al., , 2016 have not been accounted for.
The differences between the aerosol burdens for MAM3 and MARC, discussed above, are insufficient to explain the differences in year-2000 ! . Hence it is likely that differences in the optical properties of the MARC aerosols and the MAM3 aerosols are responsible for the fact that MARC generally produces lower values of ! .

Direct radiative effect
Figure 7a-c shows the direct radiative effect (! ) for the year-2000 simulations. ! reveals the influence of direct interactions between radiation and aerosols on the net shortwave flux at TOA (Eq. (3)). Aerosols that scatter shortwave radiation efficiently, such as sulfate, generally contribute to negative values of ! , indicating a cooling effect on the climate system; aerosols that absorb shortwave radiation, such as black carbon, generally contribute to positive values of ! , indicating a warming effect on the climate system. Other factors, such as the presence of clouds, the vertical distribution of aerosols relative to clouds, and the albedo of the earth's surface, also play a role in determining ! (Stier et al., 2007). Due to these factors -especially the differing impact of scattering and absorbing aerosols and

Absorption by aerosols in the atmosphere
Figure 8a-c shows the absorption of shortwave radiation by aerosols in the atmosphere (! ; Eq. (8) 3.3 Aerosol-cloud interactions and the cloud radiative effects

Cloud condensation nuclei concentration
Many aerosol particles have the potential to become the cloud condensation nuclei (CCN) on which water vapour condenses to form cloud droplets. Figure 9a- When we look in more detail at the regional distribution of year-2000 ! for MAM3, and compare this to the column burden results, we notice that locations with high ! have either high ! or high ! . This suggests that, for MAM3, the organic carbon aerosol -internally-mixed with other species with high hygroscopicitycontributes to efficient CCN, consistent with two previous MAM3-based studies that found that organic carbon emissions from wildfires can exert a strong influence on clouds (Grandey et al., 2016a;Jiang et al., 2016).
In contrast, for MARC, the regional distribution of year-2000 ! closely resembles that of ! but does not resemble that of ! . This suggests that, for MARC, the organic carbon aerosol -much of which remains in a pure organic carbon aerosol mode with very low hygroscopicity -is not an efficient source of CCN.
If we look at the results for ! , the 2000-1850 difference in ! (Figs. 9d-f, S1d-f, and S2d-f), similar deductions about sulfate aerosol and organic carbon aerosol can be made as were made above. For MAM3, the regional distribution of ! reveals that changes in the availability of CCN are associated with both ! and ! . For MARC, the regional distribution of ! is associated with ! , but is not closely associated with ! . For both MAM and MARC, ! is generally positive, revealing increasing availability of CCN between year-1850 and year-2000. The absolute increase is smaller for MARC than for MAM.
It is important to note that these ! results are for a fixed supersaturation of 0.1%; but as pointed out by Rothenberg et al. "all aerosol [particles] are potentially CCN, given an updraft sufficient enough in strength to drive a highenough supersaturation such that they grow large enough to activate" . Furthermore, the number of CCN that are actually activated is influenced by competition for water vapour among various types of aerosol particles, which depends on the details of the aerosol population including size distribution and mixing state. When aerosol particles with a lower hygroscopicity rise alongside aerosol particles with a higher hygroscopicity in a rising air parcel, the latter would normally be activated first at a supersaturation that is much lower than the one required for the former to become activated; the consequent condensation of water vapour to support the diffusive growth of the newly formed cloud particles would effectively lower the saturation level of the air parcel and further reduce the chance for the lower hygroscopicity aerosol particles to be activated Wang, 2016, 2017). In other words, ! at a fixed supersaturation is not necessarily a good indicator of the number of CCN that are actually activated, because activation depends on specific environmental conditions and the details of the aerosol population present. In an aerosol model such as MAM3 that includes only internally-mixed modes, the hygroscopicity of a given mode is derived by volume weighting through all the included aerosol species and is therefore not very sensitive to changes in the chemical composition of the mode. In contrast, MARC explicitly handles mixing state and thus hygroscopicity of each individual type of aerosol.

Column-integrated cloud droplet number concentration
The availability of CCN influences cloud microphysics via the formation of cloud droplets. Figure 10a- : there appears to be no influence from organic carbon aerosol, consistent with the ! results discussed above; and the influence of sulfate aerosol appears weaker than for MAM. Interestingly, there is good agreement between MAM and MARC over the Southern Ocean: for both MAM and MARC, sea salt appears to have a substantial influence on year-2000 ! .
When we look at ! , the 2000-1850 difference in ! (Fig. 10d-f), we see that anthropogenic emissions generally drive increases in ! , as expected. The absolute increase is smaller for MARC than for MAM.

Grid-box cloud liquid and cloud ice water paths
In addition to influencing cloud microphysical properties (such as cloud droplet number concentration), the availability of CCN and ice nuclei influence cloud macrophysical properties (such as cloud water path). Figure 11a-c shows grid-box cloud liquid water path (! ) for the year-2000 simulations.
Year-2000 ! is highest in the tropics and midlatitudes. The regional distribution of year-2000 ! is similar to that of total cloud fractional coverage (Fig. S4a-c).  increases in ! over Europe, East Asia, Southeast Asia, South Asia, parts of Africa, and northern South America -the regional distribution of ! is similar to the regional distributions of ! and ! . MARC produces large increase in ! over the same regions, and additionally over Australia and North America. Overall, ! is larger for MARC than for MAM3, especially over the Northern Hemisphere mid-latitudes. For MARC, in comparison with MAM3, the relatively strong ! response contrasts with the relatively weak ! response and ! response.
Globally, for both MAM3 and MARC, the ! response is relatively weak (Fig. 12d-f). However, relatively large values of ! , both positive and negative, are found regionally. This regional response differs between MAM3 and MARC. For both MAM3 and MARC, it appears that decreases in ! correspond to increases in ! (Fig.   2e, f); but this relationship is likely spurious, because organic carbon aerosol does not directly influence ice processes in either aerosol module.  The same applies to ! , the 2000-1850 difference in ! (Fig. 13d-f), which is strongly negatively correlated with ! and ! : increases in ! and ! drive a stronger shortwave cloud cooling effect. For both MAM3 and MARC, the cooling effect of ! is strongest in the Northern Hemisphere, particularly regions with high anthropogenic sulfur emissions, especially East Asia, Southeast Asia, and South Asia. Compared with MAM3, MARC produces a slightly stronger ! response in the mid-latitudes and a slightly weaker ! response in the sub-tropics. Another difference between MAM3 and MARC is the land-ocean contrast: compared with MAM3, MARC often produces a slightly stronger ! response over land but a weaker ! response over ocean.

Shortwave cloud radiative effect
When globally averaged, the global mean for MARC ( W m -2 ) is very similar to that for MAM3 ( W m -2 ). Considering the differences between MAM3 and MARC, we find it somewhat surprising that the two aerosol modules produce such a similar global mean response, although we have noted differences in the regional distribution.

Longwave cloud radiative effect
The cooling effect of ! is partially offset by the warming effect of ! (Eq. (6)), the longwave cloud radiative effect which arises due to absorption of longwave thermal infrared radiation.

The surface albedo radiative effect
In addition to interacting with radiation both directly and indirectly via clouds, aerosols can influence the earth's radiative energy balance via changes to the surface albedo. The surface albedo radiative effect (! ; Eq. (5)), "includes effects of both changes in snow albedo due to deposition of absorbing aerosol, and changes in snow cover induced by deposition and by the other aerosol forcing mechanisms" (Ghan, 2013). For both MAM and MARC, deposition of absorbing aerosol is enabled via the coupling between CAM5 and the land scheme in CESM; and "other aerosol forcing mechanisms" include aerosol-induced changes in precipitation rate. Aerosol-induced changes in column water vapor can also influence the calculation of ! , because ! is sensitive to near-infrared absorption by water vapour; but the contribution from such changes in column water vapour is small.
The ! response is associated with 2000-1850 changes in snow cover over both land and sea-ice ( Fig.   S10d-f): increases in snow cover lead to negative ! values, while decreases in snow cover lead to positive ! values. Changes in snow rate (Fig. S11d-f) likely play a major role, explaining much of the snow cover response.
Changes in black carbon deposition (Fig. S12d-f), contributing to changes in the mass of black carbon in the top layer of snow ( Fig. S13d-f), may also play a role. The mass of black carbon in the top layer of snow is much lower for MARC compared with MAM ( Fig. S13a-c); the 2000-1850 difference in the mass of black carbon in the top layer of snow is also much lower for MARC compared with MAM ( Fig. S13d-f).

Net effective radiative forcing
The net effective radiative forcing (! ) -the 2000-1850 difference in the net radiative flux at TOA (Eq. (7)) -is effectively the sum of the radiative effect components we discussed above. Figure 16 shows ! ; Table 1 summarises the global mean contribution from the different radiative effect components.
In general, the cloud shortwave component, ! , dominates, resulting in negative values of ! across much of the world. In particular, strongly negative values of ! , indicating a large cooling effect, are found near regions with substantial anthropogenic sulfur emissions. The cooling effect is far stronger in the Northern Hemisphere than it is in the Southern Hemisphere. If coupled atmosphere-ocean simulations were to be performed, allowing SSTs to respond, the large inter-hemispheric difference in ! would likely impact inter-hemispheric temperature gradients and hence rainfall patterns (Chiang and Friedman, 2012;Grandey et al., 2016b;Wang, 2015).
Across much of the globe, the net cooling effect of ! produced by MARC is similar to that produced by MAM. However, in the mid-latitudes, MARC produces a stronger net cooling effect, especially over North America, Europe, and northern Asia. Another difference is that MARC appears to exert more widespread cooling over land than MAM does, while the opposite appears to be the case over ocean. These differences in the regional distribution of ! are largely due to differences in the regional distribution of ! . As mentioned in the previous paragraph, rainfall patterns are sensitive to changes in surface temperature gradients. Therefore, if SSTs were allowed to respond to the forcing, the differences in the regional distribution of ! between MARC and MAM may drive differences in rainfall patterns.
When averaged globally, MAM3 produces a global mean of W m -2 ; MARC produces a stronger global mean of W m -2 . The produced by CAM5.3-MARC-ARG is particularly strong compared with many other global climate models (Shindell et al., 2013). However, the global mean ! may become weaker if the inter-annual variability in the wildfire emissions of organic carbon were to be carefully accounted for (Grandey et al., 2016a).

Summary and conclusions
The specific representation of aerosols in global climate models, especially the representation of aerosol mixing state, has important implications for aerosol hygroscopicity, aerosol lifetime, aerosol column burdens, aerosol optical properties, and cloud condensation nuclei availability. For example, in addition to internally-mixed modes, MARC also includes a pure organic carbon aerosol mode and a pure black carbon aerosol mode both of which have very low hygroscopicity. The low hygroscopicity of these pure organic carbon and pure black carbon modes likely leads to increased aerosol lifetime compared with the internally-mixed modes. Therefore, far away from emissions sources, the column burdens of organic carbon aerosol and black carbon aerosol are higher for MARC compared with MAM3, which contains only internally-mixed aerosol modes.
Furthermore, the representation of aerosol mixing state, and the associated implications for hygroscopicity, strongly influences the ability of the aerosol particles to act as cloud condensation nuclei.
We have demonstrated that changing the aerosol module in CAM5.3 influences both the direct and indirect radiative effects of aerosols. Standard CAM5.3, which uses the MAM3 aerosol module, produces a global mean net ERF of W m -2 associated with the 2000-1850 difference in aerosol (including aerosol precursor) emissions; CAM5.3-MARC-ARG, which uses the MARC aerosol module, produces a stronger global mean net ERF of W m -2 , a particularly strong cooling effect compared with other climate models (Shindell et al., 2013). As summarised below, the difference in the global mean net ERF is primarily driven by differences in the direct radiative effect and the surface albedo radiative effect; but indirect radiative effects via clouds contribute to differences in the regional distribution of ERF produced by MAM3 and MARC.
By analysing the individual components of the net ERF, we have demonstrated that: 1. The global mean 2000-1850 direct radiative effect produced by MAM3 ( W m -2 ) is close to zero due to the warming effect of black carbon aerosol opposing the cooling effect of sulfate aerosol and organic carbon aerosol. In contrast, the 2000-1850 direct radiative effect produced by MARC is W m -2 , with the cooling effect of sulfate aerosol being larger than the warming effect of black carbon aerosol.
2. The global mean 2000-1850 shortwave cloud radiative effect produced by MARC ( W m -2 ) is very similar to that produced by MAM3 ( W m -2 ). However, the regional distribution differs: for MAM3, the cooling peaks in the Northern Hemisphere subtropics; while for MARC, the cooling peaks in the Northern Hemisphere mid-latitudes. The land-ocean contrast also differs: compared with MAM3, MARC often produces stronger cooling over land but weaker cooling over ocean. For both MAM3 and MARC, the 2000-1850 shortwave cloud radiative effect is closely associated with changes in liquid water path.
3. The global mean 2000-1850 longwave cloud radiative effect produced by MARC ( W m -2 ) is stronger than that produced by MAM3 ( W m -2 ). For both MAM3 and MARC, the 2000-1850 longwave cloud radiative effect is closely associated with changes in ice water path and high cloud cover.
4. The global mean 2000-1850 surface albedo radiative effect produced by MARC ( W m -2 ) is also stronger than that produced by MAM3 ( W m -2 ). The 2000-1850 surface albedo radiative effect is associated with changes in snow cover.
If climate simulations were to be performed using a coupled atmosphere-ocean configuration of CESM, these differences in the radiative effects produced by MAM3 and MARC would likely lead to differences in the climate response.
In particular, the differences in the regional distribution of the radiative effects would likely impact rainfall patterns (Wang, 2015).
In light of these results, we conclude that the specific representation of aerosols in global climate models has important implications for climate modelling. Important interrelated factors include the representation of aerosol mixing state, size distribution, and optical properties.

Appendix A: Computational performance
In order to assess the computational performance of MARC, in comparison with MAM, we have performed six timing simulations. The configuration of these simulations is described in the caption of Table S1.
Before looking at the results, it is worth noting that the default radiation diagnostics differ between MARC and MAM. As highlighted by Ghan (Ghan, 2013), in order to calculate the direct radiative effect of aerosols, a second radiation call is required in order to diagnose "clean-sky" fluxes -in this diagnostic clean-sky radiation call, interactions between aerosols and radiation are switched off. In MARC, these clean-sky fluxes are diagnosed by default. However, in MAM, these clean-sky fluxes are not diagnosed by default, although simulations can be configured to include the necessary diagnostics. The inclusion of the clean-sky diagnostics increases computational expense. Hence, in order to facilitate a fair comparison between MARC and MAM, we have performed two simulations for each aerosol module: one with clean-sky diagnostics switched on, and one with clean-sky diagnostics switched off.
The results from the timing simulations are shown in Table S1. When clean-sky diagnostics are switched off, as would ordinarily be the case for long climate-scale simulations, using MARC increases the computational cost by only 6%  condensation nuclei concentration (Figs. S1 and S2), cloud water path and fraction (Figs. S3-S7), total precipitation rate ( Fig. S8), wind speed (Fig. S9), snow cover and rate (Figs. S10 and S11), and black carbon deposition (Figs. S12 and S13). Table   Table S1: Results from the six timing simulations. Each of these simulations consists of "20-day model runs with restarts and history turned off" (CESM Software Engineering Group, 2015), repeated five times in order to assess variability. The repetition of each simulation allows the standard error to be calculated via calculation of the corrected sample standard deviation. For consistency, all runs have been submitted on the same day. For each run, 720 processors, spread across 20 nodes on Cheyenne