# Data Assimilation of AOD and Estimation of Surface Particulate Matters over the Arctic
## 3 Results and Discussions
### 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 \(PM_{10,\text{CMAQ(w/OI)}}\) and \(PM_{2,5,\text{CMAQ(w/OI)}}\), we used the Equations (11) and (12) because AOD is regarded as a proxy for concentrations of PMs in many studies [89; 90]. \[PM_{10,\text{CMAQ (w/OI)}}=\frac{PM_{10,\text{CMAQ}}}{\tau_{CMAQ}}\times\tau_{ CMAQ\text{ (w/OI)}} \tag{11}\]  
\[PM_{2,5,\text{CMAQ (w/OI)}}=\frac{PM_{2,5,\text{CMAQ}}}{\tau_{CMAQ}}\times\tau_{ CMAQ\text{ (w/OI)}} \tag{12}\]  
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 \(PM_{10,\text{CMAQ}}\) and \(PM_{2,5,\text{CMAQ}}\) were smaller than 1-2 ug 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 \(PM_{10,\text{CMAQ(w/OI)}}\) and \(PM_{2,5,\text{CMAQ(w/OI)}}\) inferred from the assimilated AODs were 3.50 (\(\pm\) 2.96) and 1.68 (\(\pm\) 1.38) ug 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 \(PM_{10,\text{CMAQ(w/OI)}}\) and \(PM_{2,5,\text{CMAQ(w/OI)}}\) over the entire domain were between 2.18 and 3.70 ug m\({}^{-3}\) and between 0.85 and 1.68 ug m\({}^{-3}\), respectively. The maximum values of \(PM_{10,\text{CMAQ(w/OI)}}\) and \(PM_{2,5,\text{CMAQ(w/OI)}}\) 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 \(PM_{s,\text{CMAQ(w/OI)}}\), 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 CMAQ-calculated PM\({}_{10}\) and PM\({}_{2,5}\) were almost flat, the inferred \(PM_{s,\text{CMAQ(w/OI)}}\) well represented the high concentrations of observation. Compared to the in-situ observation (i.e., black squares), the \(PM_{S,\text{CMAQ(w/OI)}}\) (i.e., red lines) inferred from the assimilation AODs showed better performance in the statistical point of view (see the M, MB, IOA, and S in the figure) than those from the CMAQ simulations (i.e., green lines), particularly at Hyytiala. The estimated average values of \(PM_{10,\text{CMAQ(w/OI)}}\) were 4.85 and 3.04 ug m\({}^{-3}\) at Hyytiala and Vindeln, respectively. Additionally, those of \(PM_{2,5,\text{CMAQ(w/OI)}}\) were estimated to be 3.85 and 4.35 ug m\({}^{-3}\) at Hyytiala and Virolahi, respectively.