Sensitivity of aerosol optical properties to the aerosol size distribution over central Europe and the Mediterranean Basin

Aerosol size distribution is, among others, a key property of atmospheric aerosols when trying to establish the uncertainties related to aerosol-radiation (ARI) and aerosol-clouds (ACI) interactions. These interactions ultimately depend on the size distribution through optical properties as aerosol optical depth (AOD) or cloud microphysical properties. Hence, the main objective of this work is to study the impact of the representation of aerosol size distribution on aerosol optical properties over Central Europe, and particularly over the Mediterranean Basin during a summertime aerosol episode. To fulfill 5 this objective, a sensitivity test has been carried out using the WRF-Chem on-line model. The test consisted on modifying the parameters which define a log-normal size distribution (the geometric diameter, from now on DG, and the standard deviation, SG) by 10, 20 and 50 %. Results reveal that the reduction in the SG of the accumulation mode leads to the largest impacts in the AOD representation due to a transfer of particles from the accumulation mode to the coarse mode. A reduction in the DG of the accumulation mode has also an influence on AOD representation since particles in this mode are assumed to be smaller. 10 In addition, an increase in the DG of the coarse mode produces a redistribution through the total size distribution by relocating particles from the finer modes to the coarse.

and Transport model aerosol scheme (Ginoux et al., 2001;Chin et al., 2002, GOCART;); Fast-J (Wild et al., 2000) for the photolysis; dry deposition is estimated by Wesely (1989) and wet deposition is also calculated with grid-scale wet deposition. 90 Anthropogenic emissions were provided by the Emissions Database for Global Research-Task Force on Hemispheric Transport of Air Pollution (EDGAR-HTAP) project (http://edgar.jrc.ec.europa.eu/htap.php; Janssens-Maenhout et al., 2012). Biomass burning emission data have been estimated from the Integrated monitoring and modelling system for wild-land fires (IS4FIRES; Sofiev et al., 2009;Soares et al., 2015). Both have been adapted to chemical species in WRF-Chem following Andreae and Merlet (2001) and Wiedinmyer et al. (2011); and plume rise calculation was on-line estimated by WRF-Chem. Biogenic emis-95 sions are on-line coupled with WRF-Chem by using the Model of Emissions of Gases and Aerosol from Nature (MEGAN; Guenther et al., 2006). Finally, dust (Ginoux et al., 2001) and sea salt GOCART (Chin et al., 2002) emissions were on-line estimated by WRF-Chem.
The target domain covers central Europe and the Mediterranean Basin with a resolution of ∼ 0.15 • (∼16.7 km, Figure 1), but this domain was run using nested domains in order to capture the total desert dust contribution from the Sahara Desert. For 100 that purpose, a parent domain covering the main areas of desert dust emissions (located around 15 • N) was used. The other domains were built by one-way nesting with a nesting ratio of 1:3 with respect to its larger domain. Thus, the parent domain has a spatial resolution of 1.32 • (150 km) and the second of 0.44 • ∼ 50 km. Vertical resolution presents 48 uneven layers establishing the top of the atmosphere at 50 hPa and the highest resolution at the bottom.
As mentioned above, the aerosol scheme used is GOCART (Ginoux et al., 2001;Chin et al., 2002), which includes a bulk 105 approach. This is a simple and cheap computational approach. The selection of this scheme is conditioned by the fact that WRF-Chem version 3.9.1.1 only allows the simulation of desert dust and sea salt with this GOCART scheme.
The aerosol optical properties module in WRF-Chem calculates optical properties from species estimated by the GOCART scheme. These properties depend on size and number distribution, composition and aerosol water. For a bulk approach as GOCART, bulk mass and number is converted into an assumed log-normal modal distribution, then dividing the mass into 110 sections or bins ("i"). The parameters which define this log-normal distribution are the modified variables for the sensitivity test. Then the aerosol optical calculation follows the process described in Barnard et al. (2010). For each bin and each chemical specie ("j"), mass is converted to volume. Summing over all the species volume and assuming spherical particles, a diameter (D) is assigned to each bin. Therefore, the aerosol size distribution is defined by the number and the associated diameter for each bin. Aerosol water content depends on relative humidity (RH) and the hygroscopicity factor of each species in the 115 aerosol composition. Refractive indices are averaged, by Maxwell-Garnett approximation (Bohren and Huffman, 2007), among the compositions for each section in which mass has been divided. All particles within a size range are assumed to have the same composition, although their relative fraction can differ among size ranges. Finally, an approximate version of the Mie solution (Ackerman and Toon, 1981) is used to estimated the absorption efficiency (Q a,i ), the scattering efficiency (Q s,i ) and the asymmetry parameter (g i ). Optical properties are computed by summing over the size distribution. The equation bellow 120 shows the example for the estimation of the scattering coefficient (σ s ):

Results
First the effects of the sensitivity test on AOD representation are investigated. Afterwards, the magnitude of these effects is analyzed by using the Kolmogorov-Smirnov test. Once the most relevant cases have been established, the causes of these 125 changes are scrutinized. Regarding the differences of the sensitivity test, the modeling results are not very sensitive to the modification of the standard 140 deviation for the Aitken mode (L50_SGai and H50_SGai). Identical results are found for the variation of the geometric diameter of the Aitken mode (L50_DGai and H50_DGai). In these experiments there is not a clear pattern in the response of AOD to the modifications implemented; that is, positive and negative low changes (most of them above 0.05) are alternated in the space.

Effects on AOD representation
Some small areas display higher differences (around and above >0.1), in particular, close to the boundaries. When temporal and spatial differences are studied, these differences range between -0.03 and -0.01, which shows that there is not a clear impact As mentioned previously, for all of the experiments, higher changes (above 0.1) are found close to the south boundary. This could be caused by the fact that the main natural sources of emissions are located in this area.

Significance of AOD changes
This section elucidates the importance of AOD changes, in order to discriminate those experiments more sensitive to changes in 165 the parameters characterizing the size distribution, in order to disentangle the physico-chemical causes behind those changes.
For that reason, Figure  test. This test estimates the distance between the cumulative distribution function (represented by D) and how significant this difference is (represented by the p.value).
For all of the experiments (top and bottom; SG and DG; and 10, 20 and 50 %) the distance between the samples is statistically significant (p.value close to 0) because of the high number of samples (cells) in each experiment. As all the spatio-temporal values are taken for statistical purposes, the number of samples is over 1000000. However, the distance varies between each 175 experiment.
L50_SGac is the experiment with the highest distance (0.2277), meaning that this experiment presents the largest difference with respect to the base case. H50_DGco, with a distance of 0.1920, and L50_DGac, with 0.1648, are those with a noticeable difference (distance), but lower than for L50_SGac. H50_SGac, with a distance of 0.0891, also shows differences but not as important as for the former cases. The rest of the sensitivity cases present differences lower than 0.05; that is, differences are 180 small with respect to the base case, although statistically significant.
Similar results are found when the modification of 10 and 20 % are analyzed ( Figure 2). These cases exhibit distances lower than for the modification of 50 % but higher than 0.05. The distance is lower as the magnitude of the modification decreases. For example, the L10_SGac distance is 0.0863, the L20_SGac is 0.1814 and the L50_SGac is 0.2270. This behaviour is repeated in the rest of the experiments, but with distances lower than 0.05.

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These measured distances can be observed in the PDF shown in the corresponding Figures. The second panel in the first row portraits the PDF for L50_SGac, showing a much higher peak (peak of density higher than 10) than for the base case (peak of density lower than 8). Moreover, the upper tail reaches AOD values lower that 3 for the L50_SGac meanwhile the upper tail for the base case reaches AOD values lower than 5. The response for the modification of 20 and 10 % is similar. However, this latter shows larger AOD values in the upper tail and a peak of density lower (around 9).

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A similar behaviour is exhibited by the H50_DGco and the L50_DGac cases; but in this latter the upper tail reaches AOD values up to 3. However, the PDF of this experiment does not respond analogously to other quantitative modifications (10 and 20 %). H50_SGac is noticeable because its peak of density reaches values up to 9 and its upper tail up to 3; however, its distance is much lower (>0.1) than for the previously mentioned cases and decreases as the modification does.
In order to disentangle the causes for the results found in the sensitivity tests, the next section focuses in those cases where 195 the distance in the Kolmogorov-Smirnov test with respect to the base case is > 0.1. These are L50_SGac, L50_DGac and H50_DGco. Regarding other modifications, only the L20_SGac (see Figure 2 in Supplementary Material) shows a distance higher than 0.1. The L10_SGac difference is not higher than 0.1 (because of the limited modification of 10 %) but the distance is the highest for this range of modifications, with a value of 0.09. Finally, the experiment increasing the geometric diameter of the coarse mode (H50_DGco) produces a different response.

Disentangling the causes of AOD variations due to size distribution
Albeit this experiment presents lower values (up to -0.25) for the PM-ratio over most of the target domain (hence highlighting 215 the increase in the predominance of coarse particles), AOD is also lower in particular over central Europe.
In order to understand these changes, Figure 4 exhibits the total number concentration of particles at 1000 hPa in the Aitken+accumulation (summed) and coarse modes and the relative differences between the different experiments and the base case for the sensitivity tests modifying the parameters by 50 %. Figure 5 is similar to Figure 4 but for total mass concentration. Aloft particles (750 hPa in Figure 5), and sensitivities (20 % in Figure 7 and 12 and 10 % in Figure 9 and 14) as well 220 as non-relative differences (Figures 6, 8, 10, 11, 13 and 15) are available for both total number and mass concentration in the Supplementary Material.
The experiment reducing the standard deviation in the accumulation mode (L50_SGacc) and its lower modifications, L20_SGac and L10_SGac, show a similar response that becomes stronger the larger the modification is. Because of that, only L50_SGacc is analyzed in this contribution as it is representative of changes in SGacc. This experiment leads to a reduction in the total 225 number concentrations (up to -80 % for the Aitken and accumulation modes and -60 % of the base case for the coarse particles) 9 https://doi.org/10.5194/gmd-2020-68 Preprint. Discussion started: 28 April 2020 c Author(s) 2020. CC BY 4.0 License. and total mass (up to -60 % of the base case for the Aitken and the accumulation modes and -40 % for the coarse mode) over the European continent for all the modes. However, a reduction in the total number concentration is found over the Mediter-   12 https://doi.org/10.5194/gmd-2020-68 Preprint. Discussion started: 28 April 2020 c Author(s) 2020. CC BY 4.0 License.
These changes could be attributed to a narrowed distribution in the accumulation mode. This leads to an increase in the 235 number (and mass) of particles in the coarse mode. This increase presents two different scenarios: (1) Over the central Mediterranean Sea, where fine particles dominate, the number of particles in the coarse mode increases and now this type of particles dominates, resulting in an increase of AOD since particles become larger. (2) Over the European continent, where coarse particles come predominantly from the Saharan desert dust outbreak, two aspects have to be highlighted: on one hand, particles are removed from the accumulation mode due to a narrowed size distribution; and on the other hand, an increase in the total 240 number concentration is expected, but this increase favors deposition and finally results in a reduction (smaller than for the accumulation mode) of the total number concentration also in the coarse mode. This preferential removal during atmospheric transport of coarse particles was previously observed by Maring et al. (2003). This reduction does not result in a significantly different PM-ratio because fine particles and coarse particles are removed, but it leads to a decrease in AOD due to a reduction in total mass concentration (see Figure 5).

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These changes could also be ascribed to modifications in atmospheric transport patterns caused by the ARI and ACI (taken into account in the simulations), which could alter atmospheric dynamics. However, changes in the sea level pressure (SLP, see Figure 16 in the Supplementary Material), a proxy for changes in the atmospheric transport patterns, are negligible when compared to other works that attribute changes in AOD to modifications in atmospheric dynamics (e.g. Palacios-Peña et al., 2019b). Finally, the sensitivity experiment increasing the geometric diameter of the coarse mode (H50_DGco) leads to a general reduction of AOD, which in this case is associated to a reduction in PM-ratio. When the total number concentration is evaluated, the sum of Aitken and accumulation mode exhibits a reduction up to -60 % with respect to the base case over most of the domain. However, for the coarse mode the total number concentration remains roughly constant. Thus, the reduction in AOD 260 comes from the decrease in the total number concentration in the Aitken and accumulation modes. It should be highlighted that while in the coarse mode the total number concentration remains roughly constant, the total mass concentration increases (>80 % with respect to the base case over located areas) likely because particles with a higher diameter are considered. Similar results were found by Porter and Clarke (1997), whose data demonstrated that both the accumulation and coarse mode aerosol gradually shifted to larger diameters as the aerosol mass increased. Regarding the mass and number reduction in the Aitken and 265 accumulation modes, this comes from a redistribution through the total size distribution caused by the increase in the coarse diameter, which produces a relocation of number and mass particles from the finer modes to the coarser.

Discussion: uncertainties in DG and SG regarding observations
A question arising from the results presented so far relies not only on which modification presents the highest sensitivity for modifying AOD, but also how the modifications implemented in the GOCART aerosol scheme (which assumes the fixed size 270 distribution defined in Table 1 for each experiment) compare with observations. In this sense, this section tries to bring some light on the relationship between our findings and observed aerosol size distributions available in the scientific literature. To cope with that, Table 3 summarizes observed DG and SG found through a comprehensive review.  Table 3 is representative of the large uncertainty existing the characterizing the different modes of aerosol distribution. These values have been derived from a wide range of environments and over various locations worldwide. Regarding the geometric 275 diameter, none of the works reviewed displays a three-mode size distribution analogous to the parameters used in GOCART (base case).
However, some similarities can be found. Regarding the smallest particles, the GOCART model represents an only mode (Aitken), whose values are similar to those modes called by Covert et al. (1996) ultrafine; or by Mäkelä et al. (2000) or Rissler et al. (2006) nucleation. Vakkari et al. (2013) found similar but higher values for a ultrafine/nucleation mode. Thus, our 280 experiment in which DG increases (H10, H20 and H50_DGai) will represent better this mode. However, even the H50_DGai experiment displays lower values (0.015) than those found by Tunved et al. (2003) (0.0294 and 0.0308) in the boundary layer over the Scandinavian Peninsula. So GOCART model seems to be underestimating the DG for the Aitken mode over the target domain, and the H50_DGai could contribute to enhance the skills of the modeling results.
These values are slightly smaller or in the range of the mode named in the GOCART model as accumulation. Again, the cases in which DG for the accumulation mode is increased will improve the representation of this mode. Moreover, the decrease in the DG for the accumulation mode is one of the cases with noticeable differences for AOD. Thus, special attention should be paid for a correct definition of this mode.
290 Finally, our model considers a coarse mode with a DG of 1µm. Again, this value is underestimated because the literature reviewed (Table 3) found coarse mode DG with values higher than 2 (maximum value of 1.5 in our H50 experiment) and up to 30. Thus, particles in our model are modelled smaller than those observed. Moreover, the increase of the DG in the coarse mode is one of the case in which AOD shows noticeable differences. Marinescu et al. (2019) found a mode number 4 with DG lower but close to the coarse mode in out simulations. Henceforth, increasing the DG in the coarse mode in GOCART model 295 could contribute to improve the results of AOD in our simulations.
Values taken by SG in our base case are similar to those reported by Whitby (1978). However, observed SG are highly uncertain. Most of these works found SG values lower than those used in our base case for all of the modes, ultrafine/nucleation, which correspond with our Aitken; Aitken and accumulation, which are represented by our accumulation and coarse modes. Tunved et al. (2003) observed SG values similar to the ones used for the Aitken mode in the base case (1.70), both in winter 300 and summer in the boundary layer over the Scandinavian Peninsula. However, this value is underestimated in comparison with the measurement carried out by Rissler et al. (2006); Vakkari et al. (2013) and Marinescu et al. (2019). Whitby et al. (1972) is the only work in which SG value is higher than 2 for the accumulation mode. The rest of works reported lower values than the value used by GOCART in the base case. Probably because of that, the reduction in this parameter is the case which shows a higher influence in AOD representation (for all the experiments 10, 20 and 50%). As also 305 happened for the accumulation mode, the SG in the base case for the coarse mode is highly overpredicted by the model when comparing its value with observations available in the literature.

Summary and Conclusions
Among others, aerosol size distribution is a key property of atmospheric aerosols which largely determines their interaction with radiation and clouds. This occurs because optical properties (as AOD) are strongly dependent on aerosol size distribution.

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Moreover, this distribution holds a strong influence on ARI and the associated radiative forcing. Henceforth, the main objective of this work is to study the impact of the representation of aerosol size distribution on aerosol optical properties over central Europe, and particularly over the Mediterranean Basin during the summertime. The case study has been selected because the Mediterranean Basin presents an intense formation, accumulation and recirculation of aerosols from different sources intensified during this summer episode.

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In order to fulfill the objectives, a sensitivity test has been carried out in which the parameters which define a log-normal size distribution have been modified by ±10, 20 and 50 %.
The sensitivity test reveals that the modification (lowering) in the standard deviation of the accumulation mode (L_SGac) presents the highest sensitivity with respect to the AOD representation. This modification provokes a narrowed distribution in the accumulation mode which results in two different scenarios: (1) over those areas where fire particles predominate in the 320 base case, particles transfer from the accumulation to the coarse mode resulting in an increase of the total number and mass in the latter mode and an increase in AOD; and (2) over those areas where coarse particles dominate, particles are transferred from the accumulation to the coarse mode but this favors the removal of particles, reducing the total number and mass and hence the levels of AOD. This removal of particles of the coarse mode during atmospheric transport was previously observed by Maring et al. (2003).

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The reduction of the standard deviation of the accumulation mode is the only experiment in which all of the sensitivities tests run present important influences on AOD. Moreover, the response for all of the sensitivities is similar and increases as the modification becomes larger.
The rest of the sensitivity experiments only shows important differences for the modification of 50 % in the target parameters.
The experiment in which the diameter of the coarse mode is increased (H50_DGco) is the experiment with a higher influence on 330 AOD. For this experiment, a redistribution through the total size distribution occurs due to the increase in the coarse diameter, which produces a relocation of number and mass particles from the finer modes to the coarse. The other experiment with an important response to the sensitivity test is the case in which the diameter of the accumulation mode is decreased (L50_DGac).
In this case, the reduction observed in AOD could be attributed to the reduction in the diameter assumed by the log-normal distribution in the accumulation mode. Hence, although mass and number concentrations are similar, the model is assuming 335 that particles in the accumulation mode are smaller than in the base case and this results in a reduction of AOD.
The comparison of size distribution parameters (DG and SG) in our simulations and observations reveals that, generally, the base case underestimates the geometric diameter in all modes. This underestimation is even more noticeable for the coarse mode. Moreover, a mode is missed for the fine particles. While the model displays two modes (Aitken and accumulation) for particles lower than 1µm, observations indicate the presence of three modes (ultrafine/nucleation, Aitken and accumulation).

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The differences found in our experiments when DG is modified in the accumulation and coarse mode evince the need to carefully consider the definition in GOCART of the value of this parameter.
On the other hand, the modification in the standard deviation for the accumulation mode in our sensitivity experiments is one of the cases with a higher influence in AOD levels. This fact, together with the high uncertainty in the measurement of this parameter reported by observations, should be taken into account in order to improve the representation of size distribution in 345 aerosol models, in particular, in those that used a fix size distribution as GOCART.
This contribution identifies those cases where AOD exhibits a larger sensitivity to the target parameters. However, further experiments are needed in order to improve the representation of size distribution in models by using observational data (information for DG and SG from in-situ and remote sensing observations). Although a more accurate fixed size distribution could be defined, the use of any fixed has some limitations since aerosol size likely varies spatially/temporally as well. The 350 improvement in this representation will reduce the uncertainty associated to aerosol effects on climate, in particular to ARI.