Effect of aerosol sub-grid variability on aerosol optical depth and cloud condensation nuclei: Implications for global aerosol modelling

A fundamental limitation of grid-based models is their inability to resolve variability on scales smaller than a grid box. Past research has shown that significant aerosol variability exists on scales smaller than these grid-boxes,which can lead to discrepancies in simulated aerosol climate effects between high and low resolution models. This study investigates the impact of neglecting subgrid variability in present-day global microphysical aerosol models on aerosol optical depth (AOD) 5 and cloud condensation nuclei (CCN). We introduce a novel technique to isolate the effect of aerosol variability from other sources of model variability by varying the resolution of aerosol and trace gas fields while maintaining a constant resolution in the rest of the model. We compare WRF-Chem runs in which aerosol and gases are simulated at 80 km and again at 10 km resolutions; in both simulations the other model components, such as meteorology and dynamics, 10 are kept at the 10 km baseline resolution. We find that AOD is underestimated by 13% and CCN is overestimated by 27% when aerosol and gases are simulated at 80 km resolution compared to 10 km. Processes most affected by neglecting aerosol sub-grid variability are gas-phase chemistry and aerosol uptake of water through aerosol/gas equilibrium reactions. The inherent non-linearities in these processes result in large changes in aerosol properties when aerosol and gaseous species 15 are artificially mixed over large spatial scales. These changes in aerosol and gas concentrations are exaggerated by convective transport, which transports these altered concentrations to altitudes where their effect is more pronounced. These results demonstrate that aerosol variability can have a large impact on simulating aerosol climate effects, even when meteorology and dynamics are held constant. Future aerosol model development should focus on accounting for the effect of sub-grid 20 variability on these processes at global scales in order to improve model predictions of the aerosol effect on climate. 1 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-360, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 23 June 2016 c © Author(s) 2016. CC-BY 3.0 License.


Introduction
Aerosols are known to have a significant effect on the earth's climate through their interactions with radiation and clouds. Aerosols interact with incoming solar radiation by scattering and absorption, 25 resulting a net cooling of the Earth (Boucher et al., 2013). Absorption can also cause a number of rapid adjustments to the climate system through local heating of the atmosphere (Koch and Del Genio, 2010). Aerosols interact with clouds by serving as cloud condensation nuclei (CCN) and/or ice nuclei (IN). The number of CCN can affect cloud radiative properties thereby altering cloud albedo (Twomey, 1974). Additionally, aerosols acting as CCN are hypothesized to affect precipitation ef-30 ficiency, cloud lifetime, and cloud thickness, although these interactions are complex and uncertain (Albrecht, 1989;Rosenfeld et al., 2008). The total effective radiative forcing due to aerosols including both radiation and cloud interactions is estimated to be -0.9 (-1.9 to -0.1) W m −2 (Boucher et al., 2013), which counteracts approximately one-third of the positive radiative forcing caused by greenhouse gases. Aerosols continue to contribute the largest uncertainty to estimates of the Earth's 35 energy budget (Boucher et al., 2013).
Prediction of the aerosol effect on climate depends on the ability of global climate models (GCM) to accurately estimate aerosol concentrations and their microphysical properties. However, a fundamental limitation of grid-based GCMs is their inability to capture spatial variations smaller than the size of their grid boxes, which typically range from 100 -400 km for aerosol climate simulations.

Experimental Design
In order to understand how sub-grid aerosol variability affects model predictions of aerosol fields, we modify the chemistry version of the Weather and Research Forecast model (WRF-Chem) (Grell et al., 2005) so that it is capable of simulating aerosol microphysical processes at a different resolution than the dynamical and meteorological processes. The purpose of this technique is to recreate 100 the artificial mixing of trace gas and aerosol properties that occurs in global climate models, while maintaining a constant resolution in the other fields within the model. This is accomplished by running the model at a specified high resolution and averaging the aerosol and trace gas fields online over a pre-defined, lower resolution grid. Figure 1 describes the process conceptually. The grid in Figure 1a represents the high resolution 105 aerosol and gas fields. To simulate these fields at a lower resolution than the rest of the model, we take the mean value of all of the high resolution grid cells residing within the corresponding low resolution grid cell and re-assign each of the high resolution cells to the mean value, as depicted in Figure 1b. This occurs after each aerosol process. This means that even though the aerosol and trace gas species are calculated on the high resolution grid, each fine grid cell within the coarse grid 110 cell has the same value. Therefore, from the model's perspective, the fields are equivalent to a low resolution grid similar to Figure 1c.
The modular structure of WRF-Chem allows for easy execution of this experimental design. In WRF-Chem, the aerosol and gas-phase processes occur within the "chemistry driver", which contains separate modules for each aerosol process. These modules include emissions, photolysis, dry 115 deposition, vertical mixing and wet deposition by convective transport, gas-phase chemistry, and aerosol microphysical processes. In our modified set-up, the aerosol and gaseous fields are averaged over the lower resolution grid before and after each module within the chemistry driver so that every time the aerosol and gaseous fields are modified, their concentrations are once again averaged over the low resolution grid. The averaged fields are then passed onto the rest of the model. This process 120 is repeated at every time step. As a result, the aerosol and gaseous species are effectively simulated at a lower resolution while allowing for interaction with the high resolution meteorology.
With this design, the resolution of the aerosol and gaseous fields can be varied by simply changing the number of high resolution grid points over which the fields are averaged. In this paper, we refer to these types of simulations as "aerosol averaged" (AA) runs. These aerosol averaged runs can then  (Shaw et al., 2008) are also calculated online and are proportional to 10-metre wind speed over salt water for sea-salt and over non-urban land surfaces with sparse vegetation for dust.

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We present the results in three sections. The first two sections explore the impact of aerosol subgrid variability on AOD at 600 nm and CCN at 0.5% supersaturation using the "aerosol averaged" technique. The third section presents results from the full resolution run at 80 km (FRA80) to demonstrate the difficulty in separating meteorological and aerosol effects in traditional model resolution studies.

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In all comparisons, the FRA10 simulation is taken as the "truth". The FRA10 simulation is intended to be representative of typical aerosol conditions in the specific environment of the simulation and is meant to capture most of the aerosol variability important for accurately depicting aerosols' microphysical evolution and effect on climate.
3.1 Effect of aerosol sub-grid variability on AOD 225 Figure 3 presents results of simulated AOD for the FRA10, AA40, AA80 and AA160 where we vary the resolution of aerosol and gaseous species from 10 km to 40 km, 80 km, and 160 km, respectively.
We calculated the differences by first coarse-graining the results from the high resolution simulation to the grid of the low resolution run to which it is being compared. This eliminates differences due to the inevitably smoother low resolution run not being able to capture the same degree of AOD is underestimated with respect to the high resolution run. Relative to FRA10, the negative bias in monthly averaged AOD increases from an average of -9.4%, to -13.1% to -15.8% as the aerosol resolution is decreased to 40 km, 80 km, and 160 km, respectively. We investigate the mechanisms behind this underestimation by exploring differences between the FRA10 and AA80 simulations. 235 We performed pattern correlation analysis between the hourly spatial differences in AOD in the FRA10 and AA80 simulations and the hourly spatial differences in a number of aerosol properties known to have an impact on AOD. The analysis revealed that differences in AOD between the FRA10 and AA80 simulations are highly correlated to differences in accumulation mode aerosol water content, with an average correlation of 0.97 over the entire time period. Accumulation mode nitrate and 240 ammonium also demonstrate high correlations, with averages of 0.84 and 0.82, respectively.
It is clear that uptake of water by accumulation mode aerosols plays an important role in the underestimation of AOD in the low aerosol resolution runs, as shown in Figure 4. Compared to Figure   3, we can see the strong relationship between the two properties, as confirmed by the correlation analysis.

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This is not surprising as many studies have shown that aerosol water content has a large impact on aerosol optical properties. Shinozuka et al. (2007) used aircraft measurements to show that the fraction of ambient AOD due to water uptake is 37 ± 15% over continental U.S.; the fraction is likely even higher over marine environments. Using a box model, Pilinis et al. (1995), found that in their simulations the most important process in determining aerosol direct radiative forcing is increase in 250 aerosol mass as a result of water uptake. In both the FRA10 and AA80 simulations aerosol water content makes up approximately two thirds of the total aerosol mass, making AOD highly sensitive to changes in water.

Investigation of aerosol water uptake in WRF-Chem
In WRF-Chem, the total aerosol water content is calculated using a program based on the Model 255 for an Aerosol Reacting System (MARS) described in Saxena et al. (1986), which determines the amount of water taken up by the complex of sulphate (SO 4 2-), nitrate (NO 3 -), and ammonium (NH 4 -) aerosol species. At thermodynamic equilibrium, the amount of water contained in these particles depends on temperature, relative humidity (RH), and aerosol amount and composition, the latter of which, in turn, depends on the concentrations of the gaseous precursors ammonia (NH 3 ), nitric 260 acid vapour (HNO 3 ), and sulphuric acid vapour (H 2 SO 4 ) (Seinfeld and Pandis, 2006). We explicitly designed this study so that temperature and relative humidity are identical in both the FRA10 and AA80 simulations; therefore, the changes in aerosol water content must be due to changes in aerosol amount and/or composition.
Although the RH fields are the same in the two runs, different aerosol types react differently at 265 particular levels of RH. Aerosols such as nitrate and ammonia exhibit deliquescent behaviour, with a deliquescent relative humidity (DRH) of approximately 60% (Saxena et al., 1986). Sulphuric acid, In the sulphate-ammonium-nitrate-water system, the relative amounts of these aerosols are deter-270 mined by competition between the following two thermodynamic equilibrium reactions (Seinfeld and Pandis, 2006): In this system, the first reaction dominates; ammonia preferentially neutralises sulphuric acid due to its low saturation vapour pressure and drives the reaction to the aerosol phase. Therefore, ammonium nitrate (NH 4 NO 3 ) is formed only when there is sufficient ammonia to neutralise the amount 280 of sulphate present, i.e. in areas of high concentrations of ammonia and/or low concentrations of sulphate. (NH 4 ) 2 SO 4 is the preferred form of sulphate, meaning that each mole of sulphate will remove two moles of ammonia from the gas phase. The system is therefore divided into two cases of interest: high-ammonia and low-ammonia.
In the low-ammonia case, there is insufficient NH 3 to neutralise the available sulphate. The sul-285 phate present will tend to drive the nitrate to the gas phase. The partial pressure of ammonia is low, resulting in zero or near-zero levels of ammonium nitrate.
In the high-ammonia case, there is excess ammonia so that the aerosol phase is largely neutralised.
The ammonia that does not react with sulphate will be available to react with nitric acid vapour to produce NH 4 NO 3 .

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Essentially, at very low ammonia concentrations, ammonium sulphate primarily constitutes the aerosol composition. As ammonia increases, ammonium nitrate becomes a significant aerosol constituent once sulphate has been neutralised. At this point, sulphate concentrations remain constant, and aerosol water content increases with increasing nitrate. In addition to these constraints, the existing aerosol will only take up water if the relative humidity is sufficiently high (i.e. greater than the 295 DRH) (Seinfeld and Pandis, 2006).
During the 28 day simulation, the mean aerosol water content in the AA80 run is 12.1% less than in the high resolution FRA10 run; this difference reaches up to 36% less in some regions ( Figure   4). We explore the aerosol and gaseous species within the equilibrium system in Figure 5, which shows the mean percent difference of the total column amounts of sulphate, nitrate, ammonia, and 300 nitric acid between the FRA10 and AA80 simulations. Overall, the changes are small in the column amounts of the various species with average percent differences of +4.7%, -2.6%, -6.6%, and +6.1% for sulphate, nitrate, ammonia and nitric acid, respectively. Ammonia and nitrate are both slightly underestimated in the AA80 run; however, the magnitude and spatial distribution of the differences 9 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-360, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 23 June 2016 c Author(s) 2016. CC-BY 3.0 License.
do not match the underestimation in aerosol water content. This is due to the fact that the aerosol 305 species do not take up water under all conditions (as discussed above), and so looking at mean column differences over the full duration of the simulation may miss important information.
In MARS, four main regimes are defined as follows: High RH and High fraction of Ammonia to sulphate (HRHA); High RH and Low Ammonia (HRLA); Low RH and High Ammonia (LRHA); and Low RH and Low Ammonia (LRLA). High RH refers to a humidity greater than or equal to 310 40%, whereas a low RH is less than 40%. A value of 40% was used to approximate the RH of crystallisation of ammonium nitrate and ammonium sulphate. A high fraction of ammonia to sulphate refers to a fraction greater than or equal to 2.0, whereas a low fraction is less than 1.0. The model includes regimes for mass fractions between 1.0 and 2.0; however, they are not included in this analysis due to their relatively infrequent occurrence during the simulation. Because nitrate can only 315 exist once there is sufficient ammonia to neutralise sulphate and can only absorb water at relative humidities above its DRH, the HRHA regime is the only regime in which nitrate can uptake water.
The amounts of each chemical species and the total water content within each of the regimes are compared in Table 3. LRHA is not included in the table because the aerosol water content is set to zero in this regime. This is due to the fact that although there may be sulphate and nitrate present, 320 there is insufficient humidity to transition them to their aqueous states. One point to note regarding the LRHA regime, however, is that the AA80 simulation spends approximately 12% of its time in this regime, compared to 8% for the FRA10. This may therefore be a small contributing factor to the underestimation in aerosol water in AA80.
Looking at the overall differences, we see similar behaviour as Figure 5 there is a large decrease 325 in aerosol water, with small changes in all other species. By exploring the different regimes, we can see that the chemical system spends most of its time within the HRHA and the LRLA regimes.
We also see that the average aerosol water content is lower in AA80 compared to FRA10 in all three regimes; however, the absolute values of the concentrations in the HRHA regime are orders of magnitude higher than in the other two regimes, indicating that the HRHA has the largest impact 330 on total aerosol water content. This is the high-humidity, ammonia-rich regime described above. In this regime both sulphate and nitrate aerosol can uptake water; this is the only regime in WRF-Chem in which nitrate aerosol can contribute to the total aerosol water content. In the HRHA regime, the AA80 simulation underestimates both sulphate and nitrate aerosol, however, the underestimation in nitrate is roughly 2 orders of magnitude larger than that of sulphate. Also note that even though there 335 is less ammonia in AA80, this does not impact the amount of time the system spends within the HRHA regime, meaning there is enough ammonia present to fully neutralise sulphate, but there is less leftover to form nitrate within the HRHA regime. Thus, although there is a small decrease in nitrate overall, the decrease is much larger under the conditions that are most favourable for nitrate to take up water. This leads to less aerosol water in the AA80 run. The vertical profiles of ammonia, accumulation mode nitrate, accumulation mode aerosol water content, and extinction from the FRA10 and AA80 simulations are shown in Figure 6. The vertical profiles of ammonia ( Figure 6a) reveal a ∼30% underestimation at the surface in the AA80 simulation, with very little differences at higher altitudes. The vertical profiles of nitrate ( Figure 6b), however, show differences in the vertical distribution of nitrate at altitudes up to 9 km with the AA80 345 simulation having more nitrate at the surface, significantly less nitrate in the boundary layer (BL) and more nitrate above the BL compared to the FRA10 simulation. While the difference in total nitrate concentration between the two simulations is small (less than 3%), the differences in the BL reach up to 20%. The boundary layer is characterised as having high relative humidity and lower temperatures than the surface, which are the conditions under which nitrate most readily absorbs 350 water. It is therefore this underestimation in BL nitrate that leads to an underestimation in aerosol water content (Figure 6c), and, ultimately, extinction ( Figure 6d). Aerosol water content is largely unaffected by the small increases in nitrate at the surface and above the BL because nitrate does not efficiently take up water under these conditions.
Although previous studies showed the importance of sub-grid RH variability (Haywood et al.,355 1997; Bian et al., 2009), in our case compositional variability is more important. This is easily shown by doing an experiment where only RH is averaged and not the aerosol. In that case, AOD is only 8.7% lower than in AA10 (rather than 13.1% lower when aerosol composition is varied).
Understanding the mechanism causing the underestimation of BL nitrate in the low resolution simulation is complicated by the fact that nitrate is part of a coupled equilibrium system. The question 360 remains: what factors contribute to the simulated changes in nitrate? While the complete explanation for the changes in nitrate is difficult to constrain unambiguously, the following sections explore a number of mechanisms that may contribute to these changes.

Investigating changes in nitrate: Impact of equilibrium system
In a previous study, Metzger et al. (2002) coupled a gas-aerosol equilibrium scheme to a global at-365 mospheric chemistry-transport model and tested the effect of decreasing the full model resolution from 10 • x 7.5 • to 2.5 • x 2.5 • on aerosol nitrate. They found that boundary layer nitrate concentrations were 30-80% lower in the low resolution run. They attributed these large differences to the fact that aerosol nitrate formation non-linearly depends on the concentrations of its precursor gases.
To test whether the changes in boundary layer nitrate concentrations in the current study are related 370 to changes in resolution of aerosol and gaseous species within the equilibrium system, we conduct an alternative AA80 simulation during which all aerosols and gases are averaged over the lower resolution grid except the species involved in the equilibrium, namely, sulphate aerosol, ammonium aerosol, ammonia, nitric acid, and nitrate aerosol. The results from this simulation show that the differences in aerosol water content between the FRA10 and the altered AA80 simulations virtually We conduct the tests at six different relative humidities (0.50, 0.60, 0.70, 0.80, 0.90, 0.95) and four different temperatures (275K, 280K, 285K, 290K). We change the input variability of each of the five aerosol/gaseous species from high to low one at a time, so that a total of 120 sensitivity tests are performed at each model level (5 aerosol/gaseous species x 6 relative humidities x 4 temperatures).

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An example of the results from one sensitivity test is shown in Figure 7. In this particular test, the input concentrations of ammonia are randomly sampled at a high variability (in blue) and at a low variability (in red). This plot highlights the non-linear relationship between many of the species and ammonia. Remember that the means of the high and low variability input ammonia distributions are identical, so that if the relationships were linear, there would be no difference in the mean equilib-410 rium concentrations. However, we can see that the mean concentration of nitric acid is lower in the low variability run, whereas the mean concentrations of nitrate, ammonium, and aerosol water are higher in the low variability run. There is also a small decrease in the mean equilibrium concentra- The results from all of the sensitivity tests are summarised in Figure 8 using surface concentrations (left column) and boundary layer concentrations (right column) as inputs to the equilibrium calcu- lations. The first row shows the effect of reducing the variability of each aerosol/gaseous species on ammonia. The y-axis represents the percent difference in the mean equilibrium concentrations of ammonia between the low variability and high variability runs (low -high). Each colour repre-420 sents a different species whose variability was altered, e.g. the blue dots represent the runs when the variability of input sulphate was reduced. Each different dot within the same colour represents a test performed at a unique relative humidity and temperature value with darker colours corresponding to higher relative humidities and larger dots corresponding to higher temperatures. The second row shows the same for nitrate, and the third row shows the same for aerosol water.
425 Figure 8a shows that reducing the variability of nitrate, ammonia, and ammonium all result in lower ammonia concentrations at the surface by 10-15%. In the boundary layer, we see much higher percent differences, which is a consequence of lower ammonia concentrations having a higher sensitivity to changes in aerosol and gas variability. Reducing sulphate variability again produces mixed responses in mean ammonia equilibrium concentrations, and the rest of the aerosol/gaseous species 430 result in lower ammonia concentrations by up to 30%.
Looking at the impact of aerosol and gas variability on nitrate (Figure 8b), we see the opposite trend as ammonia. At the surface, reducing the variability of nitrate, ammonia, and ammonium results in higher mean nitrate concentrations up to 20%. While most of the changes result in higher nitrate concentrations, we see decreases in nitrate of close to 10% when the variability of sulphate, 435 nitric acid, and nitrate is reduced at the lowest relative humidity and highest temperature. The boundary layer shows a much more variable picture. While there is no strict trend, we tend to see less nitrate in the low variability run at lower relative humidities and higher temperatures. Aerosol water content (third row) follows a similar trend to nitrate except that the percent differences in the boundary layer are smaller in magnitude.

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Relating these sensitivity test results back to the simulated changes in the WRF-Chem, there are a few key observations to note. Firstly, these tests highlight the complicated nature of this equilibrium system. By simply changing the degree of variability of one input parameter, large differences arise in equilibrium concentrations of all aerosol and gaseous species (expect sulphate) within the equilibrium. In an additional test during which we changed the degree of variability of two input parameters 445 (not shown), the relationships become significantly more scattered and less predictable. In the WRF-Chem simulations, the variability of all aerosol and gaseous species are changed simultaneously, which makes the subsequent impact on the equilibrium system difficult to predict.
Nevertheless, the sensitivity tests provide significant insight. The differences in the some of the sensitivity runs are of similar magnitude to the differences between the FRA10 and AA80 simula-

Investigating changes in nitrate: Impact of convective transport
In aerosol simulations, nitrate-containing air in the boundary layer mixes with layers above and below. In the high resolution run, the mixing occurs as normal, with some nitrate-containing air being removed from the BL by mixing with adjacent layers. When nitrate concentrations are low or 460 depleted in the high resolution run, further removal of nitrate can only occur after it has been replenished by advection or emission/secondary production. In the AA80 run, the removal mechanism occurs at a high resolution but nitrate concentrations are spread over the low resolution grid box. In this scenario, the nitrate concentrations are continuously averaged and re-distributed over the large grid area so that the nitrate that has been removed from the BL by the high-resolution mixing is in-465 stantaneously replenished by the averaging over neighbouring grid boxes. It is therefore possible that more nitrate is being depleted from the BL in the low resolution run due to the continuous spreading of nitrate over areas where it has already been removed by convective transport.
We repeated the FRA10 and AA80 simulations but with convective transport turned off. Figure   9 demonstrates the effect of turning off convection on the vertical profiles of ammonia (a) and ac-470 cumulation mode nitrate (b). Ammonia shows very little difference from the original FRA10 and AA80 simulations, i.e. the underestimation of ammonia at the surface in AA80 persists when convective transport is turned off. On the other hand, the underestimation of nitrate in the BL in the original AA80 simulation disappears when convective transport is turned off and results in a higher overestimation at the surface. This agrees with results from the sensitivity tests in the previous sec-475 tion, which showed a tendency to simulate less ammonia and more nitrate at the surface at lower resolutions. Also, with the disappearance of the underestimation of BL nitrate, we no longer see an underestimation in the column amount of accumulation mode aerosol water (not shown).
At first glance, this appears to explain the differences in aerosol water content between the FRA10 and AA80 simulations. However, further investigation reveals a more complicated picture. Our re-480 sults show that although convective transport likely plays a role in the underestimation of nitrate in the BL, it does not explain the full story. To explore the impact of convective transport in more detail, we focus on a 5-day period from May 3 -7 during which there was a large convective rainfall event confined to one side of the domain (see the top panel in Figure 10). Figure 11 shows the differences in column aerosol water content between FRA10 and AA80 for this period with convective transport aerosol water content, this time confined to the lefthand side of the domain. This is to be expected as the relative humidity is much higher on this side of the domain during this time period, which also contributes to the large convective rainfall event. Once again, when convective transport is turned off, the underestimation in aerosol water largely disappears.

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However, if one examines the two sides of the domain separately, we see a different trend. Figure   10 shows It is likely that a combination of convective effects, which tend to cause underestimations in BL nitrate under conditions of high relative humidity, and non-linearities in the equilibrium system, which tend to cause decreases in BL nitrate under conditions of low relative humidity, lead to the differences in the FRA10 and AA80 simulations. to 27.3% to 36.0% as the aerosol resolution is decreased to 40 km, 80 km, and 160 km, respectively. 510 Figure 13 shows the mean spatial distribution of accumulation mode number concentration for the FRA10 simulation coarsened to the low resolution grid, the AA80 simulation, and the percent difference between them. The AA80 accumulation mode number concentration is also significantly overestimated compared to the high resolution run by an average of 27.4%. We can readily see that the overestimation in CCN is nearly equivalent in magnitude and spatial distribution to the overes- number concentration exists at all altitudes from 0 to 12 km, with the largest increase at the surface.
At altitudes above 2 km, the overestimation of aerosol number is due to the averaging of gaseous concentrations within the model. We perform an alternative AA80 simulation where only the aerosol fields are averaged over a lower resolution grid, and the gaseous fields remain on the original high resolution grid. In this case, the differences in accumulation mode number concentration at altitudes 530 above the surface largely disappear. Figure 15 shows the vertical profile of accumulation mode number concentration from FRA10 and the alternative AA80 simulation with high resolution gas fields.
One can see that the overestimation in the original AA80 run at altitudes greater than 2 km is significantly reduced. Accounting for the overestimation in the rate of nucleation, the overall bias reduces from +27.3% to +10.3%.

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To explain this behaviour we look at the rate of new particle production by nucleation. In the AA80 simulation, the nucleation rate is 25% higher in the upper troposphere than in the FRA10 simulation. A higher nucleation rate results in a higher concentration of Aitken mode particles in the upper troposphere, which leads to higher accumulation mode number concentration as there are more particles available to grow into the larger mode. These results are highlighted in Figures 14c   540 and d, which show the increase in nucleation rate and the corresponding increase in Aitken mode number concentrations above the surface, particularly between 6 and 9 km where the difference in nucleation rate is greatest.
The standard WRF-Chem nucleation scheme was used in these simulations. This scheme is a simple parameterisation of homogeneous nucleation in the sulphuric acid-water system (Kulmala 545 et al., 1998). Within this parameterisation, the nucleation rate depends non-linearly on temperature, relative humidity, and sulphuric acid vapour concentration. Because the meteorological parameters are identical in the full resolution and the aerosol averaged simulations, the non-linear dependence of the nucleation rate on sulphuric acid vapour concentration must be the source of the discrepancy between the FRA10 and AA80 simulations.

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The concentration of sulphuric acid vapour is determined by its chemical production and loss due to nucleation and condensation. Sulphuric acid vapour is produced by the reaction of the hydroxyl radical (OH) and sulphur dioxide gas (SO 2 ). Inspection of the changes in sulphuric acid vapour concentration between the FRA10 and AA80 runs shows very little difference; however, the concentration of OH is overestimated in the AA80 simulation by 15 -20% in the upper troposphere (shown 555 in Figure 16). Even though there is very little difference in overall concentration of sulphuric acid between the two runs, the overestimation in OH leads to an increased rate of oxidation of sulphur dioxide, causing an increase in the chemical production tendency of sulphuric acid by 26.8% at high 16 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-360, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 23 June 2016 c Author(s) 2016. CC-BY 3.0 License. altitudes in the AA80 run). The excess sulphuric acid produced is then subsequently used for new particle production and condensational growth in the upper troposphere, resulting in high aerosol 560 number concentrations at these altitudes.
Although OH chemistry in the upper troposphere involves a myriad of complex reactions, the concentration of OH has been found to largely depend on its primary production rate from ozone photolysis (Jaeglé et al., 2001). Ozone production is known to be dependent on its precursor concentrations in a non-linear manner, particularly NO x (NO + NO 2 ). Previous work has shown that ozone 565 production is relatively inefficient at high concentrations of NO x found in near-source areas compared with low concentrations typical of remote regions (Sillman et al., 1990). This non-linearity can therefore have a large impact on model-simulated ozone concentrations due to the artificial mixing of its precursor gases over large grid areas, resulting in excessive production of ozone and, consequently, higher hydroxide concentrations (Esler et al., 2004). In the AA80 simulation, the artificial 570 mixing of aerosols and trace gases is likely the cause of the higher rate of ozone production, which is up to 3.5 times greater than in the FRA10 simulation.
Convective transport also plays a role in the overestimation due to nucleation. This mechanism lofts gaseous species to altitudes above the boundary layer where ozone and hydroxide production is more efficient and where their lifetimes are longer. Turning off convective transport of aerosol and 575 gaseous species produces a similar result to the altered, no-gas-averaged AA80 simulation, reducing the overestimation of CCN from +27.3% to +10.7% (not shown).
Several previous studies have shown that ozone production is overestimated at lower model resolutions (e.g. Esler et al., 2004;Wild and Prather, 2006). This is due to the non-linear dependence of ozone production on its gaseous precursor concentrations, with most of the production occurring on 580 short time scales close to regions with high precursor emissions. Artificially diluting ozone and its precursor gases over a model grid box effectively increases the time scale over which its chemical production occurs. Also, artificial dilution of gas fields acts to exaggerate the importance of convection, enhancing the export of longer-lived gases to the mid-and upper troposphere where ozone production is more efficient.

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In summary, mixing of aerosol and gaseous fields over an 80 km grid results in an increase in ozone production, which is lofted to higher altitudes and leads to higher concentrations of OH in the upper troposphere. Enhanced OH concentrations result in faster oxidation of SO 2 , producing higher concentrations of sulphuric acid, which promotes the formation of new aerosol particles in the upper troposphere. Higher number concentrations at altitudes above 2 km lead to increased CCN. This 590 mechanism accounts for a significant portion of the total bias in CCN.
The overestimation in accumulation mode number at the surface is related to dry deposition processes. When both nucleation and aerosol/gas dry deposition processes are turned off, the difference between FRA10 and AA80 virtually disappears. The likely mechanism behind the overestimation due to dry deposition is that by simulating aerosols over a lower resolution grid than the underlying

Full resolution comparisons
As discussed in the introduction, a common method for investigating the impact of sub-grid variability on model predictions of the aerosol effect on climate is to vary a model's resolution and analyse 605 the resulting effect this has on aerosol fields. While this method can provide some insight into the differences in model behaviour at different grid spacings, it is limited in its ability to pinpoint the processes that contribute to these differences.
We highlight this difficulty by comparing results from the FRA10 and FRA80 simulations, where the full resolution of the model has been changed from 10 km to 80 km. Figures 17 and 18 show 610 mean AOD and CCN fields for each of these runs, respectively. Figure 17a shows AOD at 10 km resolution and Figure 17c at 80 km. The AOD fields from the higher resolution run are coarsened to the low resolution grid (Figure 17b) before taking the percent difference between the two runs ( Figure 17d). The changes in AOD due to varying the full model resolution are drastically different from the changes in AOD due to varying the resolution of the 615 aerosols only (Figure 3).
Decreasing the model resolution from 10 km to 80 km results in a 20 -40% underestimation of AOD over the English channel region, and a 20% overestimation in AOD in the northern regions of the domain. Further investigation reveals that the differences in AOD are again linked to changes in aerosol water content; however, the underlying mechanisms causing the changes in aerosol wa-620 ter are much less clear. Not only are there changes in aerosol composition, as seen in the "aerosol averaged" comparisons, there are also large changes in average daily relative humidity and temperature and other meteorological parameters, which further complicate the gas-aerosol thermodynamic equilibrium.
In fact, the amount of convective rainfall is more than 50% less in the FRA80 simulation compared 625 to FRA10. Since wet deposition and convective transport are important aerosol removal mechanisms this underestimation in rainfall likely masks many of the changes we observed due to aerosol variability.
The changes in CCN due to varying the full model resolution are also starkly different from the changes due to varying aerosol resolution only ( Figure 18). Whereas CCN was largely overesti- Additionally, while we were able to offer possible explanations to the changes seen in AOD and 640 CCN in the FRA80 simulation, the insight to these changes came from the previous analysis of the AA80 simulation, further highlighting the usefulness of isolating the effect of aerosol variability.

Conclusions
This study investigates the impact of subgrid variability, neglected in global microphysical aerosol models, on two important aerosol properties: aerosol optical depth and cloud condensation nuclei, The changes in AOD are linked to changes in accumulation mode aerosol water content, which is determined by the sulphate-nitrate-ammonium gas/particle partitioning equilibrium. In the AA80 simulation, nitrate aerosol concentrations in the boundary layer are approximately 20% less compared to the FRA10. Water uptake by nitrate is most efficient in the boundary layer, where relative 660 humidity is high and temperature is low relative to the surface; therefore, this underestimation of nitrate in the aerosol averaged runs leads to an underestimation of aerosol water. Box model tests of the nitrate equilibrium system demonstrate that neglecting variability of aerosol and gaseous species within the system has a highly non-linear effect on equilibrium concentrations. The underestimation of nitrate in the boundary layer is likely due to a combination of the response of the non-linear equilibrium system to changes in aerosol and gaseous variability and of convective transport, which removes more nitrate in the low resolution run.
Over the past decade, GCMs have been incorporating nitrate aerosol in direct radiative forcing calculations. In the AeroCom Phase II direct radiative forcing study, eight of the sixteen models currently use an equilibrium parameterisation for nitrate and aerosol water uptake, and two more are 670 in the process of incorporating them into their models (Myhre et al., 2013). The results presented in this paper indicate that accurate representation of aerosol radiative effects requires a realistic model of water uptake by aerosols, including sub-grid spatial variation in aerosol chemical composition.
While the variability in relative humidity is certainly an important factor in determining aerosol radiative forcing, we show that even when using identical resolution relative humidity, AOD is still 675 underestimated at GCM resolutions. These results suggest that at least some of this underestimation in AOD in previous studies is due to the impact of sub-grid variability of aerosol composition on water uptake as well as variability in RH. Similar results have been shown with modelling studies over the Netherlands, whose environment is characterised by its high concentrations of ammonia and nitric acid due to agricultural activity (Roelofs et al., 2010;Derksen et al., 2011).

680
The changes in CCN are linked to changes in accumulation mode number concentration, which is also overestimated by a similar degree. At the surface, the overestimation of CCN is related to differences in dry deposition processes over land and ocean when averaging aerosols over a lower resolution than the underlying terrain. At higher altitudes, the increase in accumulation mode number