The case study selected here covers an extended episode between 4 and 9 July 2015. The synoptic overview of the meteorological conditions has been widely presented in . Nonetheless, a brief summary of the meteorological episode selected is presented here.

During this episode, the development of an omega-blocking situation takes place, with low pressures located over western England. The episode presents a high stability over the Mediterranean Basin with a high aerosol load, fire emissions in the target area, and a strong dust outbreak induced by the penetration of warm air and dust from northwestern Africa towards the western Mediterranean Basin and northern Europe . The weakening of this synoptic situation results in a cyclonic circulation of the air over the western Mediterranean see Fig. S1 in the Supplement;. The choice of this episode reveals the crucial role of aerosols from different sources over the Mediterranean Basin, whose forcing is even stronger during summertime.

The Weather Research Forecast model coupled with Chemistry (WRF-Chem; ) version 3.9.1.1 was used in this work. This fully coupled online model represents ARIs and ACIs by allowing the simultaneous treatment of meteorology, gas and aerosol emissions, transport, mixing, and chemical transformation.

As previously mentioned, the case study selected here relies on an extended episode evaluated in . The model setup for all the experiments is the same as for that contribution. However, a brief summary of the configuration and parameterizations is included in Table .

The target domain covers central Europe and the Mediterranean Basin with a resolution of ∼ 0.15∘ (∼ 16.7 km, Fig. ), but this target domain is the inner domain (D3) of a nested run that allows us to capture the total desert dust contribution from the Sahara (Fig. ). For 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 the 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 with the highest resolution at the bottom. The top of the atmosphere is set at 50 hPa.

Meteorological initial and boundary conditions for the outer domain were provided by the ERA-Interim reanalysis . The WRF-Chem option for idealized gases and the aerosol profile has been chosen for the chemical boundary conditions. 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; last access: 13 May 2019; ). Biomass burning emission data have been estimated from the Integrated Monitoring and Modeling System for Wildland Fires IS4FIRES;. Both have been adapted to chemical species in WRF-Chem following and . The plume rise calculation was estimated online by WRF-Chem. Biogenic emissions are coupled online with WRF-Chem by using the Model of Emissions of Gases and Aerosol from Nature MEGAN;. Finally, dust and sea salt GOCART emissions were estimated online by WRF-Chem.

The GOCART aerosol scheme in WRF-Chem does not allow a full coupling of aerosol–cloud interactions. For instance, convective wet scavenging (conv_tr_wetscav), in-cloud wet scavenging, and cloud chemistry are not available. However, in those simulations denoted as ACI, the Morrison microphysics (used in this contribution) acts as a double-moment scheme; meanwhile, in the rest of the simulations, it works as a single-moment microphysics scheme. This latter approach is unsuitable for assessing aerosol–cloud interactions because it does not include a prognostic treatment of droplet number. Hence, the ACI configuration allows a double-moment microphysics with greater flexibility when representing size distributions and hence microphysical process rates . When the double-moment scheme is activated, a prognostic droplet number concentration using gamma functions and mixing ratios of cloud ice, rain, snow, graupel and hail, cloud droplets, and water vapor is estimated . Finally, the interaction of cloud and solar radiation with the Morrison microphysics scheme is implemented in WRF-Chem . Therefore, the droplet number will affect both the droplet mean radius and the cloud optical depth calculated by the model.

The aerosol size distribution represents the number (N), mass (M), or volume (V) of particles as a function of diameter d;. Commonly, the aerosol size distribution is represented as a function of the logarithm of the diameter. Thus, the total number, mass, or volume of aerosol particles is the integral of the diameter over the size distribution function .

When the aerosol size distribution is modeled, three different approaches are commonly used : (1) the first is a bulk approach in which only the aerosol mass concentration is computed. A constant size distribution is assumed and there is not a representation of a mixing state. That leads to a simple and computationally cheap approach. (2) A more complex approach uses multiple superposed modes, which are typically represented by a lognormal distribution described by a fixed mean and variance. The accuracy of this approach lies in the correct choice of these two parameters. (3) Last is the most computationally expensive approach of sectional representation, which consists of discretizing the aerosol size distribution into n classes or bins by diameter, with the concentration of aerosols in each bin following the conservation equation, and then the number, mass, or volume in each bin is predicted.

A lognormal approach is typically employed in chemistry transport models for aerosol size distribution, since this approach fits the observed aerosol size distribution reasonably well and its mathematical form is convenient for dealing with the moment distribution. In this approach, all of the moment distributions are lognormal and present the same geometric mean diameter and geometric standard deviation, parameters that determine the lognormal distribution . One of the most common lognormal size distributions used is that described in Eq. , which has also been employed in this contribution. Equation () represents the zeroth moment of the particle size distribution, where dp is the particle diameter, σg is the standard deviation of the distribution, and Fm0 is the number concentration as diameter dgN (number median diameter). 1dndln⁡dp=Fm02πln⁡σg×exp-(lndp-lndg0)22(lnσg)2

GOCART includes a bulk approach for black carbon (BC), organic carbon (OC), and sulfate, as well as a sectional scheme for mineral dust and sea salt using brittle fragmentation theory, 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 module of aerosol optical properties 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 such as GOCART, bulk mass and number are converted into an assumed lognormal modal distribution, followed by dividing the mass into sections or bins (“i”). The parameters that define this lognormal distribution are the modified variables for the sensitivity test. Then the aerosol optical calculation follows the process described in . For each bin and each chemical species (“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 the relative humidity (RH) and the hygroscopicity factor of each species in the aerosol composition. Refractive indices are averaged by the Maxwell Garnett approximation among the compositions for each section into 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 is used to estimate the absorption efficiency (Qa,i), the scattering efficiency (Qs,i), and the asymmetry parameter (gi). Optical properties are computed by summing over the size distribution. Equation () shows an example for the estimation of the scattering coefficient (σs). 2σs=∑i=18binsNiQs,iπDi22

Figure  shows the AOD at 550 nm simulated by the base case (top row) and the differences between each of the experiments vs. the base case. This figure only exhibits the results for the modification of 50 %, but the rest of the experiments are shown in Fig. S3. The reason to show only the 50 % experiment is the qualitatively similar spatial pattern of changes found for each experiment when modifying the parameters by 10 %, 20 %, and 50 %. Overall, the difference lies in the quantitatively larger changes in the latter experiment.

As previously mentioned, the experiments consist of the modification of the geometric diameter (DG) and the standard deviation (SG) of the aerosol size distribution by 10 %, 20 % and 50%. Taking this consideration into account, the experiments have been named to indicate the sign of the modification (L for a reduction or low and H for an increase or high), the percentage (10, 20, or 50), the variable of the size distribution modified (SG for the standard deviation and DG for the geometric diameter), and the mode in which the modification has been implemented (“ai” for Aitken, “ac” for accumulation, and “co” for coarse). Thus, the acronym for an experiment follows the this pattern: (L|H)(10|20|50)_(SG|DG)(ai|ac|co). For example, L50_SGai indicates a 50 % reduction (L) of the standard deviation (SG) in the Aitken mode (ai).

The top row in Fig.  displays the hourly mean of AOD for the base case, averaged for the entire target period (from 4 to 9 July). As established by , high AOD values over the western part of the Mediterranean Basin and central Europe were caused by a strong desert dust outbreak from the Sahara. The AOD at the eastern part of the Mediterranean has high values because the outbreak reached that area at the end of the period. evaluated this base case against observations from the Moderate Resolution Imaging Spectroradiometer (MODIS; and the instrument's onboard satellite) and the Aerosol Robotic Network (AERONET). The evaluation results (Fig. S2) evince negligible errors of the model over large areas but an underestimation of AOD over the north of Germany and the central and western Mediterranean (around -0.2 to -0.4). Despite this underestimation, the spatiotemporal mean bias error is -0.02 (when evaluated against both observational datasets, MODIS and AERONET), and the mean absolute errors are 0.16 (when assessed against MODIS) and 0.12 (when evaluated against AERONET). also pointed out that this underestimation over the central and western Mediterranean Basin turns into a larger overestimation when a coarser resolution is used due to a worsening of the representation of the dynamical patterns and thus the dust transport.

The results of the sensitivity tests indicate that AOD is not very sensitive to the modification of the standard deviation of 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 perturbations of the test; that is, low positive and negative changes (most of them above 0.05) alternate spatially. Higher differences (around and above > 0.1) are found over some small areas close to the boundaries. Temporal and spatial differences range between -0.03 and -0.01, indicating that there is not a clear impact of the modification of size distribution for the Aitken mode on AOD levels.

Sensitivity experiments including modifications of the accumulation mode lead to larger spatial changes with a greater spatial extent when compared to sensitivity tests modifying the representation of the Aitken mode. The experiment wherein the standard deviation of the accumulation mode decreases (L50_SGac) is the experiment with the highest impact on AOD. Over most of the domain the change is limited to > 0.1. These changes are negative over central Europe and the Iberian Peninsula (for which AOD in the base case is > 0.3) and are positive over the eastern Mediterranean Basin. No significant patterns of change are visualized when increasing the standard deviation of the accumulation mode (H50_SGac), with changes in AOD under ± 0.05. With respect to the experiments modifying the geometric diameter, negative changes with a temporal and spatial mean of -0.04 are found when the DG decreases by 50 % (in general, the model considers particles in the accumulation mode to be smaller than in the base case). On the other hand, when DG increases, positive changes are widely observed (larger particles than in the base case). Despite this overall signal, positive and negative signals alternate spatially in both simulations.

Finally, when considering changes in the size distribution of the coarse mode, H50_DGco (geometric diameter increases by 50 %) is the experiment with the strongest response. Negative variations are found over large parts of the domain, with values up to -0.15 over smaller areas. However, when the DG decreases, the response oscillates between negative and positive values lower than 0.05. Analogously, the response to the modification of the standard deviation for the coarse mode does not show a clear pattern.

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 over this area.

This section focuses on elucidating and ranking the importance of AOD changes for the sensitivity experiments in order to select the experiments with the highest sensitivity. The physicochemical causes behind those changes for the selected experiments will be disentangled later in Sect. .

For that purpose, Fig.  displays the probability density function (PDF) of the values of AOD at 550 nm (for all cells and time steps in the model) simulated by the base case (solid black line) and each of the experiments (dashed red line). As in the previous section, this figure only exhibits the results for the modification of 50 %, but the results for the rest of the perturbations can be found in Fig. S4. The number in each panel represents the statistics obtained from the Kolmogorov–Smirnov test. Kolmogorov–Smirnov is a nonparametric test used for the evaluation of the statistical similarity of the distribution between two datasets. The test is based on the assumed similarity of the empirical cumulative distribution function (ECDF) between two random samples. The maximum distance between two ECDFs, normally named D, indicates how far the two distributions are. In this contribution, the distribution of each experiment (dashed red line) has been evaluated against the distribution of the base case (black line). The p values represent the probability of values as extreme as those obtained for samples coming from the same distribution. Low p values show a low probability of error when the null hypothesis is rejected and thus indicate that two samples do not come from the same distribution .

For all of the experiments 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 spatiotemporal values are taken for statistical purposes, the number of samples is over 1 000 000. However, the distance varies for each experiment.

L50_SGac is the experiment with the highest D (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 also experiments with a noticeable difference (D). 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 D values lower than 0.05; that is, differences are small with respect to the base case although statistically significant.

Similar results are found when the modifications of 10 % and 20 % are analyzed (Fig. S4). These cases exhibit D 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 behavior is repeated in the rest of the experiments but with D<0.05.

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

A similar behavior is exhibited by the H50_DGco and the L50_DGac experiments, but in the latter the upper tail reaches AOD > 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 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 perturbation in the sensitivity experiment does.

In order to disentangle the causes for the results found in the sensitivity tests, the next section focuses on those cases in which 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 (Fig. S4) 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.

Figure  displays the PM ratio for the base case at 1000 hPa and the corresponding differences between the experiment at 50 % and the base case. This statistical figure is estimated as the ratio between PM2.5 and PM10 and is a proxy for the predominance of fine or coarse particles in the air mass. High values of the PM ratio imply a higher proportion of fine particles (usually with an anthropogenic origin), while low values of the ratio point to the presence of coarse particles (natural origin).

The PM ratio of the base case (Fig. a) is close to zero in Africa because during this Saharan desert dust episode coarse particles (PM10) predominate over this area. When comparing the top row in Figs.  and , areas with high AOD levels match those areas with a null PM ratio due to the influence of desert dust. The high values of the ratio over the central Mediterranean Sea could be ascribed to the transport of dust particles. At the beginning of the episode, the dust outbreak reached the central Mediterranean (coarse particles from dust were modeled here), but as the episode developed, dust – and hence PM10 particles – moved eastwards and northwards, with the PM2.5 concentrations being higher over the Mediterranean Sea and the African coastline at the end of the target period.

For the selected cases, Fig.  shows an inverse behavior of the PM ratio with respect to AOD. The experiment decreasing the standard deviation in the representation of the accumulation mode (L50_SGac) presents a reduction up to -0.45 in the PM ratio (that is, coarse particles become predominant) over the eastern Mediterranean Basin, which matches the increase modeled for AOD. This behavior is also reproduced aloft (at 750 hPa, Fig. S5) and is consistent with the sensitivities of 20 % and 10 % (Fig. S6). However, for the other experiments the response is weaker.

The experiment decreasing the geometric diameter of the accumulation mode (L50_DGac) does not lead to large differences. This experiment shows a slight increase in the PM ratio (around 0.05) over the western Mediterranean and central Europe, which points to a slight increase in fine particles, and a limited decrease (around -0.05) in the PM ratio over Italy, Hungary, and Romania.

Finally, the experiment increasing the geometric diameter of the coarse mode (H50_DGco) produces a different response. Although this experiment presents lower values (up to -0.25) for the PM ratio over most of the target domain, hence highlighting the increase in the predominance of coarse particles, AOD is also lower (in particular over central Europe).

In order to understand these changes, Fig.  exhibits the total number concentration of particles at 1000 hPa in the Aitken+accumulation (summed) and coarse modes as well as the relative differences between the different experiments and the base case for the sensitivity tests modifying the parameters by 50 %. Figure  is similar to Fig.  but for total mass concentration. Aloft particles (750 hPa, Fig. S7), sensitivities (20 % and 10 %), and nonrelative differences are available for both total number and mass concentration in Figs. S8 to S17.

The experiments reducing the standard deviation in the accumulation mode (L50_SGacc) and its analogous 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 number concentrations (up to -80 % for the Aitken and accumulation modes and -60 % of the base case for the coarse particles) 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 Mediterranean and over eastern and western areas for the Aitken and accumulations modes. An increase is depicted over the central and western Mediterranean for the coarse mode (higher than 80 % with respect to the base case). This increase in the total number concentration of the coarse mode could explain the decrease estimated for the PM ratio and thus the increase in AOD as particles become larger. The reduction in both modes explains the observed decrease in AOD as the number and mass of particles decrease, which does not lead to modifications in the PM ratio because the total number concentration decreases in both modes.

These changes could be attributed to a narrowed distribution of the accumulation mode. This leads to an increase in the 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 this type of particle dominates, resulting in an increase in 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 the one hand, particles are removed from the accumulation mode due to a narrowed size distribution; on the other hand, an increase in the total number concentration is expected, but this increase favors deposition and finally also results in a reduction (smaller than for the accumulation mode) of the total number concentration in the coarse mode. This preferential removal during atmospheric transport of coarse particles was previously observed by . 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 Fig. ).

These changes could also be ascribed to modifications in atmospheric transport patterns caused by ARIs and ACIs (taken into account in the simulations), which could alter atmospheric dynamics. However, changes in the sea level pressure (SLP; see Fig. S18), 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.,.

For the experiment reducing the geometric diameter of the accumulation mode (L50_DGac), the PM ratio as well as the total number of particles (Fig. ) and mass (Fig. ) concentrations do not show remarkable differences with respect to the base case (< 20 %). Thus, the reduction observed in AOD can be attributed to the reduction in the diameter assumed by the lognormal distribution in the accumulation mode. Hence, although mass and number concentrations are similar, the model is assuming that particles in the accumulation mode are smaller than in the base case, leading to a lower AOD.

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 with a reduction in the PM ratio. The sum of Aitken and accumulation modes exhibits a reduction up to -60 % of the total number concentration 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 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 constant, the total mass concentration increases (> 80 % with respect to the base case over certain areas), likely because particles with a higher diameter are considered. Similar results were found by , whose data demonstrated that both accumulation- and coarse-mode particles gradually shifted to larger diameters as the aerosol mass increased. The reduction of mass and number in the Aitken and accumulation modes 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.

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 distribution defined in Table  for each experiment) compare with observations. In this sense, this section tries to shed some light on the relationship between the findings presented here and observed aerosol size distributions available in the scientific literature. To cope with that, Table  summarizes the observed DG and SG found through a comprehensive literature review and selecting those works using the same definition of the lognormal function as that described in Eq. ().

Table  is representative of the large uncertainty in characterizing the different modes of aerosol distributions. These values have been derived from a wide range of environments and over different locations worldwide. Regarding the geometric diameter, none of the works reviewed display 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 the only mode (Aitken) whose values are similar to those modes referred to by as ultrafine and and by as nucleation. found similar but higher values for an ultrafine–nucleation mode. Thus, experiments in which DG increases (H10, H20, and H50_DGai) will a priori represent better this mode. However, even the H50_DGai experiment displays lower values (0.015) than those found by (0.0294 and 0.0308) in the boundary layer over the Scandinavian Peninsula. So the GOCART model seems to be underestimating the DG for the Aitken mode over the target domain, and the H50_DGai could contribute to enhancing the skills of the modeling results.

The so-called Aitken mode by , , , , and shows a similar value as mode 2 in , , and . These values are slightly smaller than or in the range of the mode called accumulation and are expected to improve the representation of this mode. Moreover, the decrease in the DG for the accumulation mode is one of the cases with remarkable differences for AOD. Thus, special attention should be paid to a correct definition of this mode.

Finally, the model used in this contribution considers a coarse mode with DG 1 µm. Again, this value might be underestimated because the literature reviewed (Table ) found DG for the coarse mode with values higher than 2 µm (maximum value of 1.5 µm in our H50 experiment) and up to 30. Thus, particles in our model are modeled smaller than those generally observed. Moreover, the increase in the DG in the coarse mode is one of the cases in which AOD shows noticeable differences. found a mode 4 with DG lower than but close to the coarse mode in our simulations. Hence, increasing the DG in the coarse mode in the GOCART model could improve the results of AOD in our simulations.

Values of SG in our base case are similar to those reported by . However, observed SG values are highly uncertain. Most of these works found SG values lower than those used in our base case for all of the modes: (1) ultrafine–nucleation, which corresponds with our Aitken; and (2) Aitken and accumulation, which are represented by our accumulation and coarse modes. observed SG values similar to the ones used for the Aitken mode in the base case (1.70) in both winter and summer in the boundary layer over the Scandinavian Peninsula. However, this value is underestimated in comparison with the measurements carried out by , , and .

is the only work in which the SG value is higher than 2 for the accumulation mode. The rest of the works reported lower values than the value used by GOCART in the base case. Probably because of that, the reduction of this parameter is the case that shows a higher influence in AOD representation (for all the experiments 10 %, 20 %, and 50 %). As also 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.