# Data Assimilation of AOD and Estimation of Surface Particulate Matters over the Arctic
## 3 Results and Discussions
### Simulated, Observed and Assimilated AODs over the Arctic
Nevertheless, \(\tau_{Assim}\) was still underestimated compared to \(\tau_{MODIS}\). In the second column of Figure S3, the white pixels of \(\tau_{MODIS}\) represent the areas indicating no available data due to cloud contamination or high surface reflectance. Figure 4 showed the daily-mean variations of \(\tau_{AERONET}\), \(\tau_{MODIS}\), \(\tau_{CMAQ}\), and \(\tau_{Assim}\) 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, \(\tau_{Assim}\) were improved, compared with \(\tau_{CMAQ}\). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Correlation Coefficient (R)** & **Thule** & **Hornsund** & **Andenes** & **Hyytiala** & **Kuopio** \\ \hline \(\tau\)_AERONET_ vs. \(\tau\)_MODIS_ & **0.52** & **0.82** & **0.75** & **0.91** & **0.69** \\ \(\tau\)_AERONET_ vs. \(\tau\)_CMAQ_ & 0.21 & 0.10 & 0.48 & 0.13 & 0.08 \\ \(\tau\)_AERONET_ vs. \(\tau\)_Assim_ & 0.03 & 0.57 & 0.53 & **0.65** & **0.49** \\ \(\tau\)_MODIS_ vs. \(\tau\)_CMAQ_ & 0.19 & 0.38 & 0.31 & 0.41 & 0.30 \\ \(\tau\)_MODIS_ vs. \(\tau\)_Assim_ & **0.46** & **0.82** & **0.76** & **0.65** & 0.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficients among AODs from AERONET, MODIS, model, and data assimilation at several AERONET stations. The MODIS sensor similarly captures the levels of AODs observed by AERONET at all stations. The correlation coefficients between \(\tau_{MODIS}\) and of \(\tau_{AERONET}\) were from 0.52 to 0.91 (Table 2). The monthly similarity was also discussed in Figure 2. The similarity between \(\tau_{AERONET}\) and \(\tau_{MODIS}\) 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., \(\tau_{MODIS}\) 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]. Figure 4: Daily mean variations of \(\tau_{AERONET}\) (black closed square), \(\tau_{MODIS}\) (blue open circles), \(\tau_{CMAQ}\) (green lines), and \(\tau_{Assim}\) (red lines) at several stations of (**a**) Thule, (**b**) Hornsund, (**c**) Andenes, (**d**) Hyytiala, and (**e**) Kuopio. Their mean values with standard deviations for April–September.