Data Assimilation of AOD and Estimation of Surface Particulate Matters over the Arctic

: In this study, more accurate information on the levels of aerosol optical depth (AOD) was calculated from the assimilation of the modeled AOD based on the optimal interpolation method. Additionally, more realistic levels of surface particulate matters over the Arctic were estimated using the assimilated AOD based on the linear relationship between the particulate matters and AODs. In comparison to the MODIS observation, the assimilated AOD was much improved compared with the modeled AOD (e.g., increase in correlation coefﬁcients from − 0.15–0.26 to 0.17–0.76 over the Arctic). The newly inferred monthly averages of PM 10 and PM 2.5 for April–September 2008 were 2.18–3.70 µ g m − 3 and 0.85–1.68 µ g m − 3 over the Arctic, respectively. These corresponded to an increase of 140–180%, compared with the modeled PMs. In comparison to in-situ observation, the inferred PMs showed better performances than those from the simulations, particularly at Hyytiala station. Therefore, combining the model simulation and data assimilation provided more accurate concentrations of AOD, PM 10 , and PM 2.5 than those only calculated from the model simulations.


Introduction
The Arctic haze composed of sulfate, black carbon, organic matter transported from the mid-latitude industrial regions of Europe, Russia, and Asia has influences on perturbation of the radiation balance between the surface and the top-of-atmosphere over the Arctic [1][2][3][4][5][6]. First, the transported haze particles warm or cool the atmosphere by scattering or absorbing sunlight, which is the direct effect of aerosol [6,7]. Second, it interacts with clouds to produce more and smaller droplets, leading to more warmth, which are indirect effects of aerosol [8][9][10]. Third, when haze particles deposit into the snow or ice, they absorb more sunlight by reducing the surface albedo [11].
Prediction (NCEP) data [53,54]. The WRF simulation was configured with the following physical options shown in Table 1. As a 3D-CTM, Community Multi-scale Air Quality (CMAQ) v5.1 model was employed to simulate the levels of air pollutants over the Arctic for the year 2008 [61]. We decided on 2008 as the target year because many modeling and observation studies were conducted as part of POLARCAT-IPY, aiming at improving understanding of Arctic pollution and its impact on climate during International Polar Year (IPY) in 2007 and 2008 [62]. From a meteorological perspective, it is unusual for the Arctic weather in 2008, which showed an abnormally cold winter in Greenland, especially with an intense melt season [63]. The modeling domain centered on Svalbard was configured with 18 km × 18 km horizontal grid spacing and vertical resolution of 17 layers from surface to 80 hPa, covering the Arctic Ocean, Greenland Sea, Barents Sea, Norwegian Sea, Greenland, Queen Elizabeth Island, and some parts of Norway, Sweden, Finland, and Russia ( Figure 1a). We employed the SAPRC-07 mechanism and AERO6 module for the gas-phase chemistry and aerosol (thermo) dynamics, respectively (Table 1). Information on boundary conditions for atmospheric gases and aerosols were taken from the output simulated by the Model for Ozone and Related Chemical Tracers, version 4 (MOZART-4) model (http://www.acom.ucar.edu/ wrf-chem/mozart.shtml) [64].
The anthropogenic emissions of gaseous and particulate species were obtained from the Monitoring Atmospheric Composition and Climate and megacity Zoom for the Environment projects (MACCity), which has a 0.5 • resolved database compiled for the year 2008 [65]. For PM 10 and PM 2.5 , the anthropogenic emissions were taken into account from the Evaluating the Climate and Air Quality Impacts of Short-lived Pollutants (ECLIPSE) v4a emission inventories based on the CLE scenario [66]. Furthermore, to consider biogenic and biomass burning emissions, we used the 0.5 • resolved Model of Emissions of Gases and Aerosols from Nature-Monitoring Atmospheric Composition and Climate (MEGAN-MACC) and Global Fire Emissions Database v3 (GFED3) emission inventories, respectively [67,68]. All emissions were downloaded from the ECCAD archive (https://eccad3.sedoo.fr/). Figure 1 presented the annual emission fluxes of SO 2 , NO x , EC, OC, PM 10 , and PM 2.5 used in the CMAQ model simulations. High emission fluxes were found over Finland and Russia in the study domain. Despite relatively fewer amounts of emissions, the ship-emitted pollutants were considered in the emission inventory. The emissions can be seen along the coastal lines of Norway and Iceland.  10 , and (f) PM 2.5 for the CMAQ simulations over the Arctic. The red triangles ( ) in the panel of (a) represent the locations of five AERONET stations of Thule, Hornsund, Andenes, Hyytiala, and Kuopio.

Description of Remote-Sensed Observations
The mission of the MODIS instrument equipped on the NASA Earth Observation System (EOS) platforms of Terra and Aqua satellites is to capture the vertical columnar aerosol loading and aerosol properties such as AOD, Angström exponent, and single scattering albedo over the cloud-and snow-free land and ocean. The MODIS/Terra observes the atmosphere with a descending orbit, passing over the equator at about 10:30 local sun time while the MODIS/Aqua flies northward across the equator at about 13:30 local sun time. In particular, the vertically-integrated aerosol extinction (i.e., AOD, τ MODIS ) observed by the MODIS sensor has been used to evaluate the performance of 3D-CTM and conduct the data assimilation of the model-calculated AODs [69][70][71]. For such purpose of study, we obtained the daily level 2 AOD of Terra satellite (MOD04_L2) from the NASA LAADS (https://ladsweb.modaps.eosdis.nasa.gov/search/). The AOD products were retrieved at a wavelength of 550 nm through the NASA Collection 6 algorithm (C6). Although, latest product via the C6.1 algorithm were released, there is no change in the combined dataset between the C6 and C6.1 collections [72]. The C6 includes three retrieval algorithms, which are (i) Dark Target (DT) over vegetated/dark-soiled land retrieved in the visible wavelength [73,74], (ii) Deep Blue (DB) over the brighter surface in the visible wavelength (e.g., deserts) [75], and (iii) DT over water surface in the visible and longer wavelength [74,76]. The expected uncertainty of AOD was reported to be ± (0.05 ± 15%) over land and (0.04 ± 10%, −0.02 ± 10%) over the ocean [74]. Levy et al. also reported that in comparison with AERONET-retrieved AODs (τ AERONET ), 69.4% of τ MODIS fall within expected error [74]. In this study, to use more gap-filled data set, we used a merged AOD product combining the DT with DB over ocean and land, which is "AOD_550_Dark_Target_Deep_Blue_Combined" data with a spatial resolution of 10 km × 10 km at the nadir (and 48 km × 20 km near the swath edge) and the temporal resolution of 5 min [74,77]. In the analysis, only pixels recommended quality assurance, good and very good flag (QA = 2 and 3) were used [77]. The MODIS-retrieved AOD (τ MODIS ) were re-gridded to a model grid of 18 km × 18 km on a daily basis. Figure S1 shows a spatiotemporal map of the monthly availability of data for the entire domain, using the merged AOD product. As expected, there were large numbers of missing pixels over the Arctic Ocean and Greenland because of high surface albedo due to sea ice and snow cover. The low data availability over the Arctic Ocean region greatly varies from season to season. On the other hand, higher than 30% of data availability was found frequently over some parts of the Greenland Sea, Barents Sea, and the Norwegian Sea. The results indicate that data integration (or assimilation) between model-calculated and satellite-observed AODs is needed for the regions showing high surface albedo such as the Arctic to address the defects of each model estimation and satellite observation and to maximize their advantages.
The AOD product retrieved from the C6 algorithm has been validated with the AERONET-observed AOD (τ AERONET ), which is a global network of ground-based sun/skyphotometers [78]. The sun-photometers measures the sun radiances at the eight typical channels of 340, 380, 440, 500, 675, 870, 1020, and 1640 nm. The sun-photometers-measured AODs are regarded as truth because the ground observations are not affected by surface reflectivity. Thus, in the study, we employed the available AERONET AOD data at five monitoring sites (Hornsund, Thule, Andenes, Kuopio, and Hyytiala stations) to evaluate the CMAQ-calculated, MODIS-retrieved, and assimilated-AODs over the Arctic. As shown in Figure 1a, the Thule, Hornsund, and Andenes stations are adjacent to the coast, so the AODs in the areas is easily affected by sea salt particles. On the other hand, the Kuopio and Hyytiala stations are located in the inner parts of Finland, which the air quality is affected by anthropogenic sources. The level 2.0 product of AOD obtained from the AERONET archive (https://aeronet.gsfc.nasa.gov) is cloud-screened, quality-controlled, processed via version 3.0 algorithm [79]. Here, AOD at 550 nm was selected as the same as τ MODIS and calculated by Equations (1) and (2): where, λ and λ 0 represent wavelengths at 550 nm and 500 nm, respectively. The Angström exponent (α) was calculated from the 870 nm (λ 1 ) and 440 nm (λ 2 ) channels [80]. Figure 2 showed the seasonal scatter plots and statistical analysis between τ AERONET and τ MODIS over the 5 AERONET stations. For synchronization with the AERONET observation, the MODIS data were collected within at most 10 km and 30 min in the spatial and temporal differences.
As expected from Figure S1, the synchronized hourly dataset were small (N = 139 during the periods of April-September 2008) because the MODIS data-set was filtered due to the high surface albedo. The overall correlation coefficients (Index of Agreement) were 0.73 (0.81) and were good, particularly for April and August 2008. From the analysis, the slopes between τ AERONET and τ MODIS were smaller, in particular in warm seasons, which indicates that the MODIS AOD was possibly underestimated. Therefore, the underestimated τ MODIS would affect the surface PM 10 and PM 2.5 estimations from the assimilated AOD. In the study, AERONET AODs (τ AERONET ) were also used to determine the free parameter for the data assimilation. The details were discussed later in Section 2.3.

CMAQ-Derived and Assimilated AODs
The radiant energy is attenuated in the atmosphere by aerosol scattering and absorption. The attenuation is expressed by the extinction coefficient (σ ext = σ sct + σ abs , unit: Mm −1 ), which depends on the particulate composition with respect to particle size [81].
With consideration of all modeled particulate species, the CMAQ-derived AOD was calculated by integrating the aerosol extinction coefficient vertically from the surface to the top-of-atmosphere: where, ∆z i and N are layer thickness at each layer and 17 layers, respectively. The AOD was calculated using the extinction coefficients estimated from the empirical "reconstructed mass-extinction method" as following Equations (4) and (5). We used the formula of Pitchford et al. [82] instead of the original Interagency Monitoring of PROtected Visual Environments (IMPROVE) extinction equation because of the possibly significant contributions of sea salt to extinction over the oceans [82,83]. Light scattering by sea salt aerosol was not considered in the original IMPROVE formula. Additionally, our domain covers a wide range of ocean, as shown in Figure 1.
where, f s (RH) denotes the hygroscopic growth factor for ammonium sulfate, ammonium nitrate, and sea salt as a function of relative humidity (RH, %). Specifically, f s (RH) is classified into f F (RH), f L (RH), and f SS (RH) for fine, large, and sea salt particles, respectively. The f s (RH) is also function of coefficients of the a 1 and a 2 in Equation (5), which are 0.4175 and 1.2312 for fine aerosol (F), 0.2381 and 1.3276 for large aerosol (L), and 0.2913 and 2.3308 for sea salt (SS). The reference relative humidity (b 1 ) is 37% for fine and coarse aerosol and 46% for sea salt. C s represents the concentrations of species (s), which are organic mass (OM), element carbon (EC), sea salt (SS), coarse mass (CORS), and soil-derived mass (SOIL), respectively. α S,dry is the dry mass extinction coefficients (m 2 g −1 ) of the species (s). Here, we used the constant values of α S,dry for ammonium sulfate, ammonium nitrate, sea salt, and organic mass calculated from the Mie theory at 550 nm under the dry condition [82]. Many investigators have used the data assimilation technique by combing modeling and observations to produce an optimal estimated AOD of the evolving state of the system [38,42,84]. We performed the data assimilation every hourly using the OI (optimal interpolation) method expressed as the following Equations (6)- (9). For the data assimilation, the MODIS data were collected every hour within a 30 min in time differences.
The τ', τ m , and τ o represent hourly assimilated, model-calculated, and MODIS-observed AODs, respectively. H is the linear observation operator allowing the calculation of the model equivalents in observation location. K denotes the Kalman gain matrix combining the error covariance matrix for the modeled (B) and observed (O) fields.
2l xy 2 (9) where, f o and f m represent fractional error coefficients in the observed and modeled τ, respectively. ε o and ε m are minimum error in the observed and modeled τ, respectively. d x and d y are horizontal grid resolution (i.e., d x = d y = 18 km in this study). l xy is the horizontal correlation length for errors in the modeled τ. In the sensitivity test, the best free parameters of f o , f m , ε o , and ε m on a monthly basis were determined by minimizing a statistical parameter of χ 2 defined in Equation (10). This approach was introduced in the study of Park et al. [42]. The best values from the sensitivity test were summarized in Table S2.
N is the number of available data set from the AERONET stations.

Simulated, Observed and Assimilated AODs over the Arctic
The CMAQ-calculated AOD (τ CMAQ or τ m ) were compared to those from the MODIS observations (τ MODIS or τ o ) to evaluate the performances of the model simulations over the Arctic. As shown in Figure 3 (i.e., green dots), the modeling performance was insufficient in terms of the correlation coefficients and slopes. There were almost no correlations between τ CMAQ and τ MODIS , showing the low values of −0.15-0.26 for all months. In addition, the slopes are under a bias towards the x-axis. There are several uncertain issues of emission fluxes, chemistry transport model simulation, and AOD calculations. Among them, such large underestimations could be primarily related to the highly uncertain bottom-up emission fluxes over the Arctic. In Figure S2, we compared the emission fluxes of SO 2 , NO x , BC, OC, PM 10 , and PM 2.5 from the several emission inventories over the regions (70 • N-90 • N; 60 • W-60 • E) including Greenland Sea, Barents Sea, and the Norwegian Sea. The most emissions over the areas can be attributed to the shipping activities. The oceanic regions were selected because the MODIS observed data were distributed mainly over the ocean due to high surface albedo over the Greenland and Arctic Ocean. As shown in Figure S2, the ECLIPSE inventory had the smallest values in their emission fluxes. Additionally, the emission fluxes were considerably different by emission inventory. The emission inventories (ECLIPSE and MACCity) used in the simulations were marked as an asterisk in Figure S2. For example, unlike the little amounts of PM 10 for the ECLIPSE inventory, the emission fluxes werẽ 3 Gg yr −1 for both EDGARv4.2 and HTAPv2 and~10 Gg yr -1 for EDGARv4.3.2. Such a comparison was also as similar as for PM 2.5 . For the species of BC and OC, the MACCity inventory showed relatively small emissions fluxes. In addition to anthropogenic sources, natural sea salt particles generated from the sea surface, particularly in coastal regions, have an enhanced contribution to the concentrations of particle matters over the ocean [85]. However, the estimations in the sea salt emissions are afflicted with several uncertain time-varying information on surf zone, wind speed, sea surface friction velocity, salinity, sea surface temperature, and dry sea salt particle size [86,87]. Figure 3 also shows the monthly scatter plots between the assimilated (τ' or τ Assim ) and MODIS-retrieved AODs (τ MODIS ) and their statistical values over the entire domain (see the red dots). Compared to the statistical analyses between τ CMAQ and τ MODIS , those between τ Assim and τ MODIS was much improved. For example, the correlation coefficients were improved from −0.15-0.26 to 0.17-0.76. However, there were still low correlations, particularly in June and July. Additionally, the slopes between τ Assim and τ MODIS were close to 1:1 lines (S = 0.38-0.82), indicating the elevated AOD through the data assimilation. Such improvement can be visually seen from the spatial distributions of the τ CMAQ , τ MODIS , and τ Assim in Figure S3.
The MODIS observed data produce a complete 2-dimensional set of AOD when assimilated into the CMAQ-calculated AOD. Thus, τ Assim are much improved, compared with τ CMAQ , particularly over Greenland Sea, Norwegian Sea, and the Barents Sea as shown in Figure S3. Nevertheless, τ Assim was still underestimated compared to τ MODIS . In the second column of Figure S3, the white pixels of τ MODIS represent the areas indicating no available data due to cloud contamination or high surface reflectance. Figure 4 showed the daily-mean variations of τ AERONET , τ MODIS , τ CMAQ , and τ Assim and their mean values at the AERONET stations of Thule, Hornsund, Andenes, Hyytiala, and Kuopio for 2008. In addition, the correlation coefficients among the AODs from AERONET, MODIS, CMAQ, and assimilation were calculated in Table 2 (see the bold numbers for the statically significant correlation coefficients in Table 2). In terms of daily variations, mean values, and statistical analysis, τ Assim were improved, compared with τ CMAQ .  The MODIS sensor similarly captures the levels of AODs observed by AERONET at all stations. The correlation coefficients between τ MODIS and of τ AERONET were from 0.52 to 0.91 ( Table 2). The monthly similarity was also discussed in Figure 2. The similarity between τ AERONET and τ MODIS had a positive effect on the performance of data assimilation, which indicates that the accuracy of MODIS observations is primarily crucial in data assimilation. Thus, the AODs assimilated by the OI technique produced similar levels and daily-variations in AOD from the MODIS and AERONET observations, compared to the model-calculated AOD. Additionally, the analysis increments from the data assimilation system were still generated in some selected periods, although there were no sufficiently available data of MODIS AODs (e.g., τ MODIS in March, April, and May at Hornsund station). The results are because the MODIS AODs observed in the adjacent areas provide a positive effect on the data assimilation. However, as shown in Figure 4, the effect of the data assimilation was insignificant since there were few available data of MODIS observation; in particular, in February, March, October, and November. Overall, from the analysis, we found that the combination between the CMAQ model and data assimilation based on OI method provided more accurate atmospheric levels and spatial distributions of AODs than those only calculated from the CMAQ simulations [88].

Estimations of Surface PMs from Assimilated AODs over the Arctic
Since the modeled AODs were highly underestimated (e.g., Figure 3 and Figure S3) due to the uncertain issues related to the emissions and boundary conditions, the low concentrations of PMs can be expected. Therefore, to estimate more realistic levels of PMs for the entire domain, the surface PMs were calculated using the assimilated AODs over the Arctic based on the linear relationship between the concentrations of PMs and AODs. For the estimations of PM 10,CMAQ(w/OI) and PM 2.5,CMAQ(w/OI) , we used the Equations (11) and (12) because AOD is regarded as a proxy for concentrations of PMs in many studies [89,90].
Figure 5a-d and Figure S4 presented the spatial distributions of monthly averaged PM 10 and PM 2.5 concentrations calculated from the CMAQ simulations and inferred from the linear Equations (11) and (12). In Figure 5a,c, the concentrations of modeled PM 10,CMAQ and PM 2.5,CMAQ were smaller than 1-2 µg m −3 and were spatially homogeneous over the Arctic. In addition, it was clearly shown that the concentrations were relatively high in southern parts of the domain due to the influences of aerosols transported from the boundary. On the other hand, the concentrations of PM 10 and PM 2.5 inferred from the elevated AODs via data assimilation (shown in Figures 3 and 4) increased by approximately 140-280% in April-September for the entire domain (refer to Table  S1). Monthly average PM 10,CMAQ(w/OI) and PM 2.5,CMAQ(w/OI) inferred from the assimilated AODs were 3.50 (± 2.96) and 1.68 (± 1.38) µg m −3 over the entire domain in May, as shown in Figure 5b,d. We summarized the monthly mean of PM 10 and PM 2.5 for April-September in Table S1. Monthly means of PM 10,CMAQ(w/OI) and PM 2.5,CMAQ(w/OI) over the entire domain were between 2.18 and 3.70 µg m −3 and between 0.85 and 1.68 µg m −3 , respectively. The maximum values of PM 10,CMAQ(w/OI) and PM 2.5,CMAQ(w/OI) were found along the coastline and over the Gulf of Bothnia, where the air quality is usually influenced by local air pollutants emitted from ships [91]. As shown in Figure 5b and Figure S3 for May, there can be a spatial inconsistency between the assimilated AOD and PMs, CMAQ(w/OI) , particularly over the Gulf of Bothnia (i.e., white circle in Figure 5b. Such inconsistency is related to the vertical profile of aerosols because while the AODs are quantitative values of aerosols integrated from the surface to the top of the atmosphere, the PMs are the concentrations at the surface level. For the validation, we compared the estimated PMs with in-situ observations. Figure 5e-h showed the daily mean variations of observed, simulated, and estimated PM 10 and PM 2.5 at Hyytiala, Vindeln, and Virolahi stations. While the temporal variations of the CMAQcalculated PM 10 Figure 6, the estimated values increased by ap-proximate 170-670% for all regions except the North Pole, compared to those from the CMAQ model simulations. The temporal variations of model-calculated PM 10 and PM 2.5 (colored as bright and dark green lines, respectively) remained flat. However, the estimated PM 10,CMAQ(w/OI) and PM 2.5,CMAQ(w/OI) (colored as red and purple lines, respectively) fluctuated considerably. In February, March, October, and November, the similar concentrations between the model-calculated PM S and the inferred PM S,CMAQ(w/OI) over Thule and Hornsund indicate that the effect of data assimilation is insignificant due to the absence of MODIS observed data originated from high surface reflectivity. As shown in Figure 6, there were two separate groups divided in terms of the ratio of PM 2.5 to PM 10 . The first group, having relatively low ratios, included Thule, Hornsund, and Andenes. Their ratios were 0.35, 0.35, and 0.30, respectively. These areas located near the coastal line have geographical conditions favorable for generating the coarse particle of sea salts. On the other hand, the second group, showing high ratios of PM 2.5 to PM 10 concentrations, were Hyytiala and Kuopio. The ratios were 0.80 and 0.77, respectively. These areas located in inland Finland are easily affected by anthropogenic sources. To confirm the origin of the air mass, we conducted the 5-day backward trajectory analysis for April-September using the HYSPLIT v5.0 [92]. From the trajectory analysis, we found that air masses at Hyytiala and Kuopio were mainly transported from Europe (39-47%) and the Arctic regions (38-46%) while those arriving at Thule, Hornsund, and Andenes were originated dominantly from the Arctic regions (81-92%).

Summaries and Conclusions
In the study, we examined the spatial and temporal variations of aerosol optical depths and estimated the surface PM 10 and PM 2.5 concentrations over the Arctic. For the investigation, a 1-year simulation was carried out over the Arctic using the WRF-CMAQ model. The performances of the WRF-CMAQ simulations were then evaluated by comparison with MODIS-observed AODs. The model-calculated AODs (τ CMAQ ) were highly underestimated, compared to the MODIS-retrieved AODs (τ MODIS ), and the correlation between τ CMAQ and τ MODIS was low over the Arctic.
To produce optimal estimated AODs, we utilized data assimilation based on the optimal interpolation (OI) technique by combing the model-calculated and satellite-observed AODs. The assimilated AODs (τ Assim ) were spatially and temporally compared with the MODIS and AERONET observed AODs. In terms of daily variations, mean values, and statistical analysis, τ Assim were much more improved, compared with τ CMAQ . The correlation coefficients were also improved from −0.15-0.26 to 0.17-0.76 over the Arctic. In the comparison with τ MODIS , τ Assim showed better correlation coefficients (R = 0.46-0.82) than those (R = 0.19-0.41) of τ CMAQ at Thule, Hornsund, Andenes, and Hyytiala station. We also showed that the analysis increments from the data assimilation system were generated in some selected periods, although there were no sufficiently available data of MODIS AODs. Overall, combining the CMAQ model and satellite observation (based on the OI method) provided more accurate atmospheric concentrations and spatial distribution of AOD than those only calculated from the model simulation.
In this study, since the modeled quantities were highly underestimated, the surface PMs were calculated from the assimilated AODs and the linear relation between the model-calculated PMs and AODs to estimate more realistic levels of PMs over the Arctic. The monthly average of PM 10 (PM 2.5 ) inferred from the assimilated AODs was between 2.18 and 3.70 µg m −3 (between 0.85 and 1.68 µg m −3 ), which relatively increased by 140-280%. Compared to the in-situ observation, the PM 10 and PM 2.5 inferred from the assimilated AODs showed better performance in the statistical point of view than those from the CMAQ simulations, particularly at Hyytiala. The estimated surface concentrations of PM 10,CMAQ(w/OI) (PM 2.5,CMAQ(w/OI) ) averaged for April-September were 5. 88 Further fundamental improvement will be required, particularly in terms of the accuracy of ship emissions and boundary conditions for the Arctic simulations, although the MODIS data assimilated into the model-calculated AODs provided more accurate atmospheric levels of AOD and PMs in this study. In addition, the algorithm for AOD retrievals over some snow-covered regions (i.e., high surface reflectance) was recently developed by several investigators [93,94]. Moreover, the gap-filling technique based on artificial intelligence (AI) is nowadays a promising method [95,96]. Thus, it is expected that more accurate atmospheric levels of PMs can be available over the Arctic through the application of these studies.  Figure S3: Spatial distributions of the CMAQ model-estimated (first column), MODIS-observed (second column), and assimilated (third column) AODs over the Arctic from April 2008 to September 2008, Figure S4: Spatial distributions of monthly averaged PM 10 and PM 2.5 calculated from the CMAQ simulations and inferred from the linear relationship between PMs and assimilated AODs, Table S1: Monthly mean of PM 10 and PM 2.5 from the CMAQ simulation and linear estimation and their relative differences over the entire domain, Table S2: The optimized free parameters obtained from the sensitivity test.