Reduced effective radiative forcing from cloud-aerosol interactions (ERFaci) with improved treatment of early aerosol growth in an Earth System Model

Historically, aerosols of anthropogenic origin have offset some of the warming from increased atmospheric greenhouse gas concentrations. The strength of this negative aerosol forcing is, however, highly uncertain – especially the part originating from cloud-aerosol interactions. An important part of this uncertainty originates from our lack of knowledge about the pre-industrial aerosols and how many of these would have acted as cloud condensation nuclei (CCN). In order to simulate CCN concentrations in models, we must adequately model secondary aerosols, including new particle formation (NPF) and 5 early growth, which contributes with a large part of atmospheric CCN. In this study, we investigate the effective radiative forcing (ERF) from cloud–aerosol interactions (ERFaci) with an improved treatment of early particle growth, presented in Blichner et al. (2020). We compare the improved scheme to the default scheme, OsloAero, both part of the atmospheric component of the Norwegian Earth System Model v2 (NorESM2). The improved scheme, OsloAeroSec, includes a sectional scheme that treats the growth of the particles from 5–39.6 nm which thereafter inputs the particles to the smallest mode in the pre-existing, 10 modal aerosol scheme. The default scheme parameterizes the growth of particles from nucleation and up to the smallest mode, a process that can take several hours. The explicit treatment of the early growth in OsloAeroSec on the other hand, captures the changes in atmospheric condition during this growth time both in terms of air mass mixing, transport and condensation and coagulation. We find that the ERFaci with the sectional scheme is −1.16 Wm−2, which is 0.13 Wm−2 weaker compared to the default 15 scheme. This reduction originates from OsloAeroSec producing more particles than the default scheme in pristine, low-aerosolconcentration areas and less NPF particles in high-aerosol areas. We find, perhaps surprisingly, that NPF inhibits cloud droplet activation in polluted/high-aerosol-concentration regions because the NPF particles increase the condensation sink and reduces the growth of the larger particles which may otherwise activate. This means that in these high-aerosol regions, the model with lowest NPF – OsloAeroSec – will have highest cloud droplet activation and thus more reflective clouds. In pristine/low aerosol 20 regions however, NPF enhances cloud droplet activation, because the NPF particles themselves tend to activate. Lastly, we find that sulphate emissions in the present day simulations increase the hygroscopicity of the secondary aerosols compared to the pre-industrial simulations. This makes NPF particles more relevant for cloud droplet activation in the present day than the pre-industrial atmosphere, because the increased hygroscopicity means they can activate at smaller sizes. 1 https://doi.org/10.5194/acp-2021-151 Preprint. Discussion started: 29 March 2021 c © Author(s) 2021. CC BY 4.0 License.


Introduction
The aerosol scheme contains three condensing tracers, H 2 SO 4 , and two organic species, namely SOAG LV and SOAG SV .

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The H 2 SO 4 is produced through oxidation, or emitted directly into the atmosphere. The two organic tracers are produced through oxidation of monoterpene and isoprene, where each reaction has a certain yield of SOAG LV and SOAG SV . The reactions of isoprene with OH, O 3 and NO 3 all yield 5 percent SOAG SV , while monoterpene + OH and monoterpene + NO 3 yield 15 % SOAG SV . Finally, monoterpene reacting with monoterpene + O 3 yields 15 % SOAG LV , thus being the only reaction yielding SOAG LV .

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During condensation these are all treated as non-volatile, but we separate between SOAG LV and SOAG SV because only SOAG LV is considered low-volatile enough to contribute to NPF. In fact only 50 % of the SOAG LV in each time step is assumed to be low enough volatility to contribute to nucleation, and we will refer to this fraction of the SOAG LV as ELVOC.
New particle formation is parameterized by using an intermediate concentration of H 2 SO 4 and ELVOC in each time step to calculate a nucleation rate followed by a calculation of how many particles survive the growth up to the background mode 150 keeping the particles from NPF (23.6 nm in number median diameter).
The nucleation rate is calculated using Vehkamäki et al. (2002) for binary sulfuric acid-water nucleation and equation 18 from Paasonen et al. (2010) to represent boundary layer nucleation.
This survival of particles from nucleation at d nuc ≈ 2 nm, the NPF mode is parameterized (number median diameter d mode = 23.6 nm) by Lehtinen et al. (2007): where J dmode is the formation rate at d mode , d nuc is the diameter of the nucleated particle, CoagS(d nuc ) is the coagulation sink of the particles [h −1 ], GR is the growth rate [nmh −1 ] of the particle (from H 2 SO 4 and ELVOC, calculated using eq.21 from Kerminen and Kulmala (2002)) and γ is a function of d form and d nuc : − 1 , m = −1.6.

OsloAeroSec
We have implemented a sectional scheme for modelling the growth of particles from nucleation up to the mode which keeps the NPF particles in NorESM (number median diameter 23.6 nm) . The scheme is described in detail in Blichner et al. (2020). The scheme contains five bin sizes set according to a discrete geometric distribution (Jacobson, 2005, sec.13.3) and two condensing vapors: H 2 SO 4 and SOAG LV . The condensation of these species is treated as non-volatile and 165 after condensation, the particles are "grown" (moved) to adjacent bins according to a quasi-stationary structure (Jacobson, 1997(Jacobson, , 2005. Coagulation is accounted for both between particles in the sectional scheme and with particles in the modal scheme. When two particles in the sectional scheme coagulate, this contributes to grow the particles, while if they coagulate with particles in the modal scheme, their mass is added to a process tracer in OsloAero (see Blichner et al. (2020) for more details).

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When the particles have grown to the volume median diameter of the NPF mode in OsloAero, the particle mass is moved to the NPF mode, thus conserving both volume and number. Finally, in this version of the model, we have also added improvements to the diurnal variation of the oxidant concentrations, described below.
2.3 Chemistry: changes to oxidant diurnal variation: 175 The oxidant concentration in CAM6-Nor are read from prescribed 3D monthly mean fields (Seland et al., 2020b) with a diurnal cycle superimposed on OH, HO 2 and NO 3 . In the case of OH, this is basically a step function based on before vs after sunrise, which in turn lead to a step function in the H 2 SO 4 concentration and an unrealistic NPF diurnal cycle. In OsloAeroSec, we therefore implemented a simple sine shape on the daily variation in OH, to improve the realism of NPF.
3 Simulation setup 180 All simulations are performed with NorESM2 release 2.0.1 with 1.9 • (latitude) × 2.5 • (longitude) resolution with 32 height levels from the surface to ∼2.2 hPa in hybrid sigma coordinates. The time step is 0.5 hour. We use a configuration with active atmosphere (CAM6-Nor, Seland et al., 2020b) and land component (CLM5-BGC, Lawrence et al., 2019), while sea ice and sea surface temperatures are read from file. We use the fixed SST method combined with nudging to estimate effective radiative forcing (ERF) from aerosol-cloud interaction, ERF aci , and ERF from aerosol-radiation interactions, ERF ari (Hansen et al.,185 2005; Forster et al., 2016). This means that we use prescribed SST and sea ice and perturb the anthropogenic aerosol emissions.
We use nudging against model produced meteorology to constrain the natural variability (Kooperman et al., 2012;Zhang et al., 2014;Forster et al., 2016), nudging the horizontal wind components (U,V) and surface pressure with a relaxation time of 6 hours (as described in Karset (2020, sec 4.1)). Only nudging U, V and surface pressure is preferable over nudging more variables (temperature, humidity, energy fluxes, surface drag etc), because it allows for rapid adjustments which should be 190 included in ERF aci . See Karset (2020, ch. 4.1) for discussion.
In addition, we use the method proposed by Karset et al. (2018) to estimate the effective radiative forcing, i.e. we use not only to the anthropogenic aerosol emissions but also the oxidants from the present day atmosphere.
To produce the meteorology, we first ran a 7 years simulation (plus 2 years discarded as spin up), MMET 1850 with the default 195 model, OsloAero def . This was done with standard CMIP6 pre-industrial (here meaning 1850) forcing and emissions.
Two simulations were performed with each model version: *PI Pre-industrial (1850) simulation nudged to MMET 1850 *PD Simulation with aerosol emissions and oxidant fields from "present day" (2014) nudged to pre-industrial meteorol- These are the simulations used to calculate the ERF and which are analyzed in the result section. Emissions of aerosol and precursors for both the present and pre-industrial are from Hoesly et al. (2018); van Marle et al. (2017). Oxidant fields are as described in Seland et al. (2020b), from Danabasoglu et al. (2020).

Terminology
Because we are comparing model versions with and without the sectional scheme, we will only discuss particle number concentrations of particles in the modal OsloAero part of the scheme, that is excluding the ones still in the sectional scheme. This gives us an apples-to-apples comparison with the original model version. We will use N a to refer to total aerosol concentration, excluding the particles in the sectional scheme, and N NPF for the subset of these particles originating from NPF. Furthermore,

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we use N d1,d2 to refer to the particles with a diameter larger than d 1 but smaller than d 2 . These definitions are summarized in Table 3.
We will use the term NPF efficiency or the efficiency of NPF to describe model to model differences in how many NPF particles are produced with the same emissions (PI or PD). If model version A and B are both run with the same setup (e.g. preindustrial emissions), and model A produces more NPF particles than model B, we will say that A has higher NPF efficiency 220 than B.
We use the Ghan (2013) method for calculating ERF aci and ERF ari , meaning that we output the net radiation at the top of the atmosphere, F , and in addition output calls to the radiation scheme with clean (no aerosols), F clean and clean and clear (no aerosol, no clouds), F clean,clear . Thus, the direct aerosol radiative effect is DIR Ghan = F − F clean and the cloud radiative effect

Results and discussion
We will start by presenting globally averaged ERF ari and ERF aci in the model versions, and how these relate to PI to PD changes in globally averaged aerosol and cloud properties (section 5.1). Next, in section 5.2, we present a series of hypothesis for the differences in ERF ari and ERF aci between the model versions, which we will use to analyze the results. In section 5.3, we discuss the PI to PD changes on a regional level, before discussing the PI and PD simulations separately in sections 5.4 and 5.5. We discuss all model versions where this is helpful for understand the results, but we otherwise focus on OsloAeroSec versus OsloAero def , because OsloAero def is the version used in CMIP6.

Aerosol number 235
In general, the sectional scheme produces more particles than the original scheme in very pristine environments, while producing fewer in areas with high aerosol concentrations . This is reflected in the globally averaged profiles of NPF particles, N NPF , for each model version shown in Fig. 2. In the PD simulations, OsloAeroSec mostly has lower N NPF concentrations than the other model versions, surpassing OsloAero imp only above ∼ 650 hPa. However, in the cleaner PI atmosphere, OsloAeroSec has N NPF concentrations closer to, or even higher, than the other two schemes. OsloAeroSec has 240 higher N NPF concentrations above ∼ 850 hPa and ∼ 700 hPa compared to OsloAero imp and OsloAero def , respectively. Close to the surface, where aerosol concentrations in general are higher, OsloAeroSec has lower N NPF that the other two models, even in the PI simulation.
As we shall explain more in depth later, these changes in NPF in clean remote versus higher aerosol concentration areas, are important for ERF aci because the NPF particles are more likely to activate in pristine regions, while may even act to suppress 245 activation in the more polluted regions.
Furthermore, note that even though OsloAero imp is the same as OsloAeroSec, excluding the sectional scheme, the profile is qualitatively different: OsloAeroSec has fewer particles close to the ground and much more further up in the PI atmosphere, see section 5.6.

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The globally averaged ERF aci is significantly influenced by the introduction of the sectional scheme, as is seen in Fig. 3 showing total, shortwave and longwave components of ERF aci , and ERF ari . ERF aci in OsloAeroSec is significantly (p< 0.01) lower than both OsloAero def and OsloAero imp , using a two-tailed paired Student's t-test on the globally averaged monthly output. The ERF aci is 0.13 Wm −2 weaker in OsloAeroSec compared to OsloAero def . The ERF aci with OsloAero imp and OsloAero def is roughly the same (difference of 0.01 Wm −2 ). Also, the total radiative effect from aerosols, ERF aci+ari , is 255 lower ∼0.1 Wm −2 in OsloAeroSec compared to both OsloAero def and OsloAero imp . One can further see in Fig. 3, that the difference in the ERF aci between the OsloAeroSec and OsloAero def is completely caused by difference in the SW forcing.
Moreover, even though OsloAero imp has roughly the same ERF aci as OsloAero def (not significantly different with p< 0.05) it has a significant strengthening (p< 0.01) of the forcing in both the SW and LW component that ends up cancelling each other out in the total forcing. Lastly, the direct effective aerosol forcing, ERF ari , is also shown in Fig. 3 and the direct effect 260 is slightly closer to zero with OsloAeroSec than OsloAero def and OsloAero imp (∼-0.03 Wm −2 smaller than OsloAero def and OsloAero imp , significant with p< 0.01). It may seem surprising that both OsloAero def and OsloAero imp have positive ERF ari . Note that we are using Ghan (2013) to calculate ERF ari and that other methods may give a slightly different result. Smith et al. (2020) show comparisons of different estimates of the ERF ari for CMIP6 models and find similar values to ours for NorESM with the Ghan (2013) method, while e.g. the approximate partial radiative perturbation (APRP) method while the 265 APRP method gave a negative ERF ari for the same simulations. The difference between OsloAeroSec and the default model likely originates from OsloAeroSec producing fewer particles than OsloAero def in the PD simulation and thus allowing the remaining particles to grow larger and thus scatter radiation more efficiently .
As discussed in the introduction, ERF aci depends both on the increase in CCN between PI and PD and on the number of CCN in the PI base state. The less CCN there is in the base state, the larger the impact of a given increase in CCN will be, 270 because the clouds are more susceptible. As OsloAeroSec has much lower particle number concentrations than OsloAero def in the PI, we might expect OsloAeroSec to have a less CCN/CDNC and weaker (less negative) NCRE Ghan in the PI. In this case OsloAeroSec would have clouds that are more susceptible to change from PI to PD, than OsloAero def . The opposite is in fact the case, as can be seen in Fig. 4 which relates the column burden of N NPF particle mass (which, due to the technical setup of OsloAero, is proportional to the number) to the net cloud radiative effect (NCRE Ghan ). While the column burden of N NPF is 275 lower in OsloAeroSec compared to OsloAero def , the NCRE Ghan is stronger (more negative). On the other hand, OsloAero imp has the lowest column burden of N NPF and the weakest NCRE Ghan , and thus follows the logic that a "cleaner" atmosphere ERF aci ERF aci, SW ERF aci, LW ERF ari OsloAero def OsloAero imp OsloAeroSec Figure 3. Globally averaged effective radiative forcings (ERF) from aerosols. ERFaci is the ERF from aerosol-cloud interaction, ERFaci,SW and ERFaci,LW are the short wave and long wave component of ERFaci and ERFari is the ERF from aerosol radiation interaction alone.
All are computed in accordance with Ghan (2013). The circles are the the averages for each individual year in the 5 year simulations and the gray bar indicates the 95% confidence interval of the mean.
gives a less negative (weaker) NCRE Ghan . In the PD simulations, OsloAeroSec has the lowest column burden of N NPF of all the models and approximately the same NCRE Ghan as OsloAero def , while OsloAero imp has a less negative NCRE Ghan than the other two. Since ERF aci = NCRE Ghan PD -NCRE Ghan PI , it is clear from Fig. 4, that most of the difference between 280 the schemes originate in different NCRE Ghan in the PI simulations; −0.15 and −0.24 Wm −2 compared to OsloAero def and OsloAero imp , respectively. The difference in the PD simulations partially compensate this but is considerably smaller; −0.02 and −0.1 Wm −2 compared to OsloAero def and OsloAero imp , respectively. Furthermore and maybe surprisingly, this plot shows that the change in NCRE Ghan per change in column burden N NPF (i.e., the slope of the line in Fig. 4), is much more negative for OsloAeroSec than for the other two model versions.

Reasons for differences in ERF aci
From what we have seen so far, it is first of all clear that changes in the PI NCRE Ghan are dominating the difference in ERF aci between the models, i.e. the spread in modelled NCRE Ghan between the models is larger in PI than in PD. Secondly, we have  seen that at least in globally averaged properties, more efficient NPF, meaning more particles with the same emissions, does not necessarily lead to a stronger negative NCRE Ghan . To explain the somewhat unintuitive relationship between particle number 290 and NCRE Ghan , we must consider also their geographical distributions with respect to where the NPF particles are likely to activate in clouds and contribute to CDNC. In this section we first outline some important processes and then layout some hypothesis for the difference in NCRE Ghan with OsloAeroSec compared to the other versions. These will serve to ease the rest of the results and discussion.
The cloud droplet activation of particles and resulting CDNC depend on the following factors: 1) The maximum achieved 295 supersaturation (S max ) together with the hygroscopicity of the particles decide the activation diameter of each mode, 2) S max depends on the updraft velocity, but is also influenced by supersaturation adjustment due to the uptake of water vapor from large(r) particles which activate "early" during lifting, and finally, 3) the absolute number of particles in each mode which are larger than the activation diameter and thus activate.
Furthermore, note that the number of particles from NPF is strongly negatively correlated with the number median diameter 300 of the modes in the size distribution, both the NPF mode and the larger modes. This is because the total available surface area is larger when there are more NPF particles, which means the available condensate is distributed to more numerous, but smaller particles. This leads, as we will show, to NPF inhibiting cloud droplet activation in many regions in the model. Figure 5 illustrates the effect of changing the NPF efficiency on CDNC in two different environments. For simplicity, let us assume that we are comparing two models with different NPF efficiency; model A with high NPF efficiency and model B with 305 low NPF efficiency. As noted above, model A will have more numerous, but smaller, particles (A1 and A2 in Fig. 5), while model B will have fewer, but larger particles (B1 and B2 in Fig. 5). Furthermore, we will consider two different environments.
Environment 1 has a small activation diameter because, e.g. there are few large particles (no early activation) or the updraft is to activation in two different environments (1 and 2) and for two models; one model with high NPF efficiency (A) and one with low NPF efficiency (B). Let us first consider environment 1 (top panels): here the activation diameter is small (either due to strong updrafts, few large particles or high hygroscopicity) and particles all the way down to the mode holding the NPF particles (∼ Aitken mode) activate. In this environment model A will activate more particles than model B and have higher CDNC. Next let us consider environment 2 (bottom panels): here the activation diameter is large (due to weak updrafts, supersaturation adjustment due to larger particles or hygroscopicity) and only the largest particles activate. Here model B will activate more particles than model A because the size of the larger particles is what dominates.
strong (A1 and B1 in Fig. 5). Environment 2 has a large activation diameter because, e.g. it has high emissions of large primary particles which activate early and limit the maximum supersaturation (A2 and B2 in Fig. 5). In this simplification we assume 310 that the activation diameter does not change between model A and B. This is not strictly true, but a good assumption because the inter-model changes in S max (Fig. S15) and hygroscopicity (Fig. S20) are small and do not dominate the response in terms of CDNC.
cloud droplet activation and higher CDNC than model B (low NPF efficiency, B1). This is because a considerable fraction of the small NPF mode particles activate, and thus the decrease in the size of the larger particles does not matter.
Next we consider environment 2 where the activation diameter is large (e.g. a polluted area like China).This is illustrated by the two size distributions, A2 and B2, at the bottom of in Fig. 5. In this environment model A with high NPF efficiency (A2) will result in lower cloud droplet activation and lower CDNC than model B with a low NPF efficiency (B2). This is because 320 the change in the diameter of the larger particles is the only thing which is matters for activation, since the smaller particles will not activate anyways.
In this simplified thought example, we can say that in environment 1 (small activation diameter), NPF enhances cloud droplet activation while in environment 2 (large activation diameter), NPF inhibits cloud droplet activation.
With all this in mind, we can lay out some plausible hypothesis that might contribute to a weaker ERF aci in OsloAeroSec 325 compared to the other model versions:

Pre-industrial to present day changes
We start by considering hypothesis 1, and how the PI to PD change looks on a regional level in OsloAeroSec versus OsloAero def . This is consistent with the major anthropogenic emission sources being located here. Over ocean regions in the Southern Hemisphere, there is even a small decrease in NPF particles many places. Comparing to OsloAero def (row 3) we see that OsloAeroSec has a smaller increase in N NPF from PI to PD, except in the South Pacific and over the Amazon. Especially high 350 pollution areas over land stand out as strongly negative. Note that the first column in Fig. S9 shows the same but for zonal averages, and underlines that ∆ PD-PI N NPF is higher in OsloAero def than OsloAeroSec all through the atmospheric column.
The second column shows the change in cloud droplet number concentration at cloud top (CDNC(CT)). Again the first row shows ∆ PD-PI CDNC(CT), which, as expected, shows an increase -in particular in the northern hemisphere. Comparing OsloAeroSec to OsloAero def (row 3) however, the first thing that stands out is that, somewhat surprisingly, ∆∆ PD-PI CDNC(CT) 355 is positive over polluted regions, meaning that the PI to PD increase in CDNC(CT) is stronger with OsloAeroSec than with OsloAero def , in spite of N NPF increasing less with OsloAeroSec. In other words, in these regions we are in the bottom panel of Fig. 5, where more particles are added with OsloAero def than OsloAeroSec, but fewer of these extra particles are activating into cloud droplets. Meanwhile, in more remote regions, like the North Pacific and the Arctic, we are in the top panel of Fig. 5 and CDNC(CT) increases less with OsloAeroSec than OsloAero def , following the more expected logic that a smaller increase 360 in particle number lead to a smaller increase in cloud droplets from PI to PD.
Finally, the last column shows the ERF aci . Here we see (first row, c), that the ERF aci is strongly negative over the North Pacific as well as over China and India. The difference in ERF aci between the models shows that the remote Pacific dominates in making ERF aci more strongly negative in OsloAero def than in OsloAeroSec. Even though the increase in CDNC(CT) from PI to PD is stronger in polluted regions with OsloAeroSec, these regions seem to have reached saturation with respect to 365 changing albedo and the ERF aci changes little between the model versions.
To summarize with regard to hypothesis 1: the change in particle number between PI and PD is indeed smaller with OsloAeroSec than the other model versions, but this can only explain the change in CDNC in remote regions (North Pacific, Siberia etc). Furthermore, as mentioned earlier, we need to consider the influence of the baseline aerosol state in PI, and not just the change between PI and PD.  OsloAeroSec almost everywhere in PI. However, as is seen in Fig. 8c, showing the zonally averaged difference, this decrease with OsloAeroSec is mostly confined to the near-surface areas. The decrease in N NPF with OsloAeroSec near the surface switches to an increase higher up in the atmosphere.

Cloud properties
OsloAeroSec has a higher cloud droplet number concentration at cloud top (CDNC(CT)) than OsloAero def in most of the PI 380 atmosphere, as can be seen in Fig. 9a. This is despite that OsloAeroSec has lower N NPF concentrations in most near-surface areas compared to OsloAero def . We must therefore investigate what happens to the size distribution, rather than just the absolute number. Figure 9c, e and g, shows the OsloAeroSec to OsloAero def difference in number concentrations of N 100 , Amazon area, where much lower concentrations of N 100 (and NPF efficiency) are associated with much higher concentrations of N 200 , but not N 150 . That the CDNC is higher here, tells us that the activation diameter here is probably usually between 390 150-200 nm. Additionally, the supersaturation is higher in OsloAeroSec due to fewer particles that compete for the water vapor (see figure S14), which has a small positive impact on the number of particles which activate.
To investigate further these relationships between changes in N d and CDNC in the PI simulations, we compute the correlation between ∆CDNC and ∆N d where ∆ signifies the difference between OsloAeroSec and OsloAero def . First we compute the correlation between ∆CDNC and ∆N NPF over time and longitude, shown in Fig. 10c. This reveals that close to the surface,

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∆CDNC and ∆N NPF are mostly negatively correlated indicating that these areas, NPF inhibits activation. In remote regions, like e.g. the Southern Ocean or high in the free troposphere, there is a positive correlation between ∆N NPF and ∆CDNC, indicating that here we are in a NPF enhanced activation regime and relevant parts of the NPF mode particles activate.  Table 4 for definitions) at different heights. These relationships for the PI simulations are shown in Fig. 11, column 1. If 400 ∆CDNC correlates clearly with the change in concentration of particles above some diameter d, N d , this indicates that these particle sizes are relevant for cloud droplet activation in the region. On the other hand if there is a negative correlation, this indicates that the particles are too small to activate.  OsloAeroSec and OsloAero def . Row 2-3: difference in average particle number concentration for particles larger than 100 nm (row 2), 150 nm (row 3) and 200 nm (row 4). The left column shows the difference for the pre-industrial atmosphere and the right column shows the difference for the present day atmosphere. The average particle concentrations are calculated by averaging up to 850 hPa and averaging by pressure difference. Dots are included in the plots to indicate where the difference between the two models is significant with a two-tailed paired Student's t-test with 95 % confidence interval. and we will discuss them further in the next section. In the PI simulations, however, the South Pacific shows a clear correlation with the larger particles (diameters larger than 150, 200 and 250), while in the North Pacific, the correlation is closer to zero or 410 insignificant.

Summary hypothesis 3: Higher activation in the pre-industrial atmosphere
We do indeed see higher aerosol activation and higher CDNC with OsloAeroSec in the PI simulations. This is due to a combination of two things: 1) In pristine areas, NPF particles are likely to activate and lead to higher CDNC -i.e. NPF enhances activation. In these areas OsloAeroSec in general produces more NPF particles than OsloAero def and thus CDNC increases.

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2) In areas with higher aerosol number concentrations, NPF particles are unlikely to activate and NPF inhibits cloud droplet activation due to reducing the size of the larger particles. In these regions, OsloAeroSec in general produces less NPF particles than OsloAero def and thus CDNC increases.

5.5
The present day atmosphere: model to model differences We now move to consider differences in the PD simulations between OsloAeroSec and OsloAero def and will discuss the 420 hypothesis 4, "Lower activation in PD".
While with PI emissions, there are large regions, especially at higher altitudes where OsloAeroSec produced more NPF particles than the other model versions. With PD emissions, these areas shrink, as the atmosphere becomes less pristine overall. This is seen in Fig. 7d- OsloAeroSec produces fewer particles than the other model versions at most heights and latitudes, while the opposite is the case for the Southern Hemisphere. This is likely due to a combination of much higher emissions and more vertical mixing in the Northern than Southern Hemisphere. In other words, larger parts of the Northern Hemisphere pass into a pollution level regime where the sectional scheme produces fewer particles than the others.

Cloud properties
430 Figure 9b shows that the difference in CDNC(CT) between OsloAeroSec and OsloAero def in the PD simulations. The Southern Hemisphere resembles the difference in PI (Fig. 9a) with widespread increase in CDNC. In the middle-to high northern latitudes, on the other hand, CDNC is lower in OsloAeroSec than in OsloAero def , opposite of in the PI simulations. In these last pristine northern regions, more NPF particles in OsloAero def seem indeed to lead to higher CDNC than in OsloAeroSec.
Let us again consider the model to model difference in size distribution.  Fig. 5). This is because there are many large particles which activate early and act as a sink 440 for water vapor, thus reducing S max and increasing the activation diameter (see Fig. S14b). On the other hand, the decreases in CDNC in OsloAeroSec compared to OsloAero def in the PD northern high latitudes correspond better to the change in the smaller particles, N 100 and partially N 150 . This indicates that in these regions NPF enhances cloud droplet activation due to a smaller activation diameter (top panel in Fig. 5). Note that this is different in the PI and PD simulations: in the PD simulations, the CDNC goes down with OsloAeroSec in the northern high latitudes, in the PI it goes up. The reason for this is that the 445 activation diameter depends both on the maximum supersaturation and the hygroscopicity. The hygroscopicity of the particles almost doubles from the PI to the PD, due to increased sulphate emissions (see Fig. S20). The more hygroscopic particles in the PD simulations can then activate at smaller diameters (given the same S max ). The regions where CDNC is enhanced by NPF thus spreads in the pristine northern latitudes, favoring cloud droplet activation in OsloAero def over OsloAeroSec. Mark that the difference in hygroscopicity is large between the PI and PD simulations (again, see S20), but small (∼ 5%) between Let us again consider the correlations between ∆CDNC and N NPF , ∆N 50 , ∆N 100 , ∆N 150 , ∆N 200 and ∆N 250 for different regions, shown for the PD atmosphere in Fig. 10 and Fig. 11b, d, f and h.
Globally, the correlation of ∆CDNC with the change in larger particles is more pronounced in the PD than the PI simulations ( Fig. 11b and Fig. 10d), possibly indicating a stronger super saturation adjustment (reduced S max ) with more polluted PD emission conditions, leading to a higher activation diameter.

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Furthermore, we investigate the North and South Pacific separately in Figs. 11e-h, because these two show opposite sign in the PD simulations: in the North Pacific, OsloAeroSec has lower CDNC than OsloAero def , while in the South Pacific OsloAeroSec has higher CDNC (see Fig. S3b). In the South Pacific (e and f), the CDNC correlates best with the larger particles (diameter above 150 nm) in both PI and PD. In the North Pacific on the other hand, the correlation is not clear for any particle number in the PI (g) and slightly positive for the smaller particles sizes in PD (h). The likely cause for the difference 465 between the two cases is that 1) the South Pacific has higher concentrations of larger sea salt particles than the North Pacific (not shown), which can limit the maximum supersaturation and thus lead to a higher activation diameter, and 2) as mentioned above, the sulphate emissions are much higher in the PD Northern hemisphere, leading to more hygroscopic particles, and a lower activation diameter. In the South Pacific, we are therefore at the bottom panel of the sketch in Fig. 5, while in the North Pacific, we are more on the top panel. Note again that the hygroscopicity between the model versions with the same emissions 470 (either with PI or PD emissions) changes very little (Fig. S20), which is why we only discuss changes between the PI and PD.

Summary hypothesis 4: Lower activation in the present day atmosphere
The discussion above shows that regionally, lower cloud droplet activation and CDNC with OsloAeroSec in the PD simulations, does indeed play a role in reducing the ERF aci in the pristine high northern latitudes and the North Pacific. Here the CDNC is lower with OsloAeroSec than OsloAero def and thus OsloAero def has a stronger negative cloud radiative effect in the PD 475 simulations. On the other hand, cloud droplet activation and CDNC in more polluted regions is higher with OsloAeroSec than OsloAero def (see Fig. 9b) in the PD simulations. This does, however, not have as big an impact on radiation (see e.g. Fig. S10) firstly because these areas are mostly continental and the cloud radiative effect is larger over dark ocean surfaces (e.g. the North Pacific) and secondly because the CDNC is already high in these regions with OsloAero def and thus the clouds are less susceptible to the increase to OsloAeroSec (see introduction for description of this effect). Furthermore, we have found that 480 hygroscopicity changes from PI to PD plays a role by reducing the activation diameter and making NPF particles more likely to activate in the PD simulations compared to the PI. This means that the areas where NPF enhances cloud droplet activation expands and thus there are larger areas where OsloAero def has higher CDNC than OsloAeroSec. Both these factors result in a lower CDNC in the high northern latitudes with OsloAeroSec, and a corresponding lower magnitude in NCRE Ghan .

Comparison to OsloAero imp
We have mostly focused on the comparison of OsloAeroSec to OsloAero def in the above section, but there are important points to take away from comparing OsloAeroSec to OsloAero imp as well. Note that OsloAero imp has the same updates to oxidants and nucleation rate as OsloAeroSec, but does not have the sectional scheme. Also, remember that OsloAero imp has much lower NPF efficiency than OsloAero def , but compared to OsloAeroSec it is more similar, but depends on the region. In general OsloAeroSec produces more NPF particles in pristine regions, while OsloAero imp produces more particles in regions 490 with higher aerosol concentrations.
When comparing only OsloAeroSec and OsloAero def , it is not possible to separate the effect that increased NPF efficiency in remote regions has from decreased NPF efficiency in high-aerosol regions with respect to the ERF aci . It is perhaps tempting to think that the reduction in NPF efficiency is alone responsible for the overall effect, and that the increase in NPF efficiency in remote regions is negligible. If so, any scheme which reduced NPF efficiency would have the same effect. The OsloAero imp 495 simulation however, represents exactly such another scheme which reduces the NPF efficiency compared to OsloAero def , with roughly the same amount as OsloAeroSec, though without the increases in NPF efficiency in remote regions. However, OsloAero imp does not weaken ERF aci like OsloAeroSec does, but rather slightly strengthens it. In essence, this shows that it is the combination of decreasing NPF efficiency in high aerosol regions and increasing NPF efficiency in low-aerosol regions which together gives the weakened ERF aci in OsloAeroSec.

Summary of hypothesis
We now summarize and relate the results back to the hypothesis presented in section 5.2.
1 Smaller ∆ PD-PI N a : While it is true that N a increases less from PI to PD with OsloAeroSec than OsloAero def (and OsloAero imp ), this can only explain the results in remote regions. Furthermore, OsloAero imp offers as a counter argument against this hypothesis: it also has a ∆ PD-PI N a than OsloAero def , but contrary to OsloAeroSec, OsloAero imp has a 505 stronger negative ERF aci than OsloAero def . In sum, this hypothesis does not explain well the differences in ERF aci .
2 Higher N a in PI: OsloAeroSec mostly produces fewer particles than OsloAero def in the PI simulations and this is thus only true in remote regions. This hypothesis can therefore not explain the resulting ERF aci .
3 Higher cloud droplet activation in PI: We found that OsloAeroSec has higher CDNC than the other model versions in the PI simulations both due to more efficient NPF in remote regions where NPF enhances cloud droplet activation (small 510 activation diameter) and due to less efficient NPF in regions where NPF inhibits cloud droplet activation (large activation diameter). In these last areas, OsloAeroSec indeed has a higher concentration of larger particles than OsloAero def and OsloAero imp , due to the condensate being distributed to fewer particles in OsloAeroSec. This hypothesis therefore explains well the part of the change in ERF aci originating from difference in NCRE Ghan in the PI simulations.
4 Lower cloud droplet activation in PD: We found this hypothesis to play an important role in the northern high latitudes, 515 especially the North Pacific, were sulphate emissions are high in the PD simulations. Due to higher hygroscopicity in the PD simulations compared to the PI, the NPF particles are more likely to activate (smaller activation diameter) and thus the number of particles (which is lower in OsloAeroSec) is more important than the particles sizes. This hypothesis therefore is important to explain the changes in the PD simulations.
Additionally, after the analysis of the results, we may add two more explanations: 520 5 Hygroscopicity: As explained for hypothesis 4 above, the change in hygroscopicity from PI to PD, results in larger areas in the northern pristine latitudes having a NPF enhanced cloud droplet activation regime in the PD simulations, compared to the PI. This results in stronger NCRE Ghan with OsloAero def than OsloAeroSec in the PD simulations which further leads to a stronger ERF aci in OsloAero def than OsloAeroSec.
6 Regional differences: The comparison with OsloAero def shows that regional differences in NPF matter significantly.

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For reasons discussed above, OsloAeroSec gives higher CDNC in the PI simulation in regions with susceptible clouds and large ERF aci , which dominates the global average.

Implications and discussion
The results in this paper go in line with previous work which shows both that the ERF aci is sensitive to the PI aerosol characteristics, e.g. Carslaw et al. (2013), and that changes the NPF parameterization can highly influence ERF aci (e.g. Gordon

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et al., 2016). However, the reduction in ERF aci found with OsloAeroSec in our simulations, is not a result of increased NPF in under PI conditions alone. Rather the increase in CDNC and NCRE Ghan in the PI simulation originates from increased NPF efficiency where the NPF enhances cloud droplet activation, and decreased NPF efficiency where NPF inhibits particle activation. Additionally, we find that the modelled increase in hygroscopicity from PI to PD from increased sulphate emissions, results in a lower activation diameter and thus that more of the NPF particles contribute to CDNC.

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The effect of NPF inhibition on cloud droplet activation, was also found by Sullivan et al. (2018), where they modelled the NPF effect on clouds over the mid-western USA using WRF-Chem v3.6.1 and using a 20 bin sectional aerosol scheme (Model for Simulating Aerosol Interactions and Chemistry, MOSAIC). As in this study, they find that the growth of the larger particles are inhibited by the increased condensation sink from the NPF particles. That fact that the same effect is seen in simulations with a completely differently structured aerosol model, shows it to be unlikely that this is an artifact of the OsloAero model.

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However, their study uses the same activation scheme, Abdul-Razzak and Ghan (2000), and we cannot exclude that this scheme for example overestimates the supersaturation adjustment effect.
As mentioned in the section 2, the sectional scheme, OsloAeroSec, has a higher contribution from organics to the growth from 5 nm than OsloAero def and OsloAero imp (only ELVOC in OsloAero). One could argue that the factor may be the driving factor of all these results, but in fact this is not the case. We did a test run where organics were treated in the same 545 way in OsloAeroSec as in OsloAero def and OsloAero imp and the result in terms on particle number changes very little (see and third row shows the difference OsloAeroimp minus OsloAeroSec (second row) and OsloAero def minusOsloAeroSec (third row). Dots are included in the plots to indicate where the difference between the two models is significant with a two-tailed paired Student's t-test with 95 % confidence interval.
Furthermore, note that we have not discussed CCN concentrations in this discussion. There are two reasons for this: Firstly, these are not yet available as standard output for CAM6-Nor. Secondly, the CCN concentrations at a given supersaturation matters only when this supersaturation is actually achieved, so focusing on CDNC gives a more complete picture which is 550 closer related to the actual climatic impact of the particles in question.
These results also illustrate the importance of adequately representing activation when investigating the effect of NPF on climate, and not simply considering CCN at fixed supersaturation as this will omit not only regional changes in updraft velocities, but also supersaturation adjustment by the aerosol population.

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In this study, we have shown that including a sectional scheme (OsloAeroSec) for the growth of particles from nucleation and up to the original modal scheme, reduces the estimated ERF aci by between 0.13-0.14 Wm −2 . The reduction originates from higher CDNC and NCRE Ghan in the PI simulation, together with a smaller increase from PI to PD. By comparing model versions with different NPF parameterization in the pre-industrial and present day atmosphere respectively, we find that NPF in fact inhibits cloud droplet activation in parts of the atmosphere and leads to lower CDNC, due to reducing the growth of 560 the larger, primary particles. The overall ERF aci therefore, depends on in which regions NPF is high/low both in the PI and in the PD simulations. The reduction in ERF aci with OsloAeroSec originates partly from higher NPF efficiency in PI areas where NPF enhances cloud droplet activation and lower NPF efficiency in PI areas where NPF inhibits cloud droplet activation.
Furthermore, we find that the increase in sulphate from the PI to the PD simulation increases the hygroscopicity of the particles and thus allows more NPF particles to activate. This expands the areas where NPF enhances cloud droplet activation in the PD 565 simulations which also contributes to a weaker ERF aci for OsloAeroSec than OsloAero def .
Roughly speaking, we can say that the results in ERF aci originate from OsloAeroSec is adding particles where the NPF particles are likely to act as CCN and removing them where they are unlikely to activate directly and rather act to diminish the size of the other particles.
Overall, this study shows that a more physical representation of the early growth of particles results in a lower ERF aci and 570 that adequately representing early growth on a regional scale is important when estimates of ERF aci .
Code and data availability. The model code of NorESM2, release 2.0.1, is available at https://doi.org/10.5281/zenodo.3760870 (Seland et al., 2020a). The code modifications in OsloAeroSec are available at https://doi.org/10.5281/zenodo.4265057 (Blichner, 2020), see Blichner et al. (2020) for details. The post-processing code and the data from the model simulations will be made available before publication Author contributions. SMB did the model code development and performed the simulations with NorESM. SMB did the data analysis 575 and wrote the manuscript. SMB, MKS and TKB contributed with discussions regarding the experimental design and data analysis. All contributors have contributed to the discussions regarding the manuscript.
Competing interests. There are no competing interests.
Acknowledgements. Many thanks to Dirk Oliviè and Alf Kirkevåg at Meteorologisk institutt for answering so many questions. Special thanks to Dirk Oliviè who let us use his simulations as initialization for simulations. Thanks to Diego Aliaga for helping to design the schematic in