# Data Assimilation of AOD and Estimation of Surface Particulate Matters over the Arctic
## 4 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 (\(\tau_{CMAQ}\)) were highly underestimated, compared to the MODIS-retrieved AODs (\(\tau_{MODIS}\)), and the correlation between \(\tau_{CMMQ}\) and \(\tau_{MODIS}\) 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 (\(\tau_{Assim}\)) were spatially and temporally compared with the MODIS and AERONET observed AODs. In terms of daily variations, mean values, and statistical analysis, \(\tau_{Assim}\) were much more improved, compared with \(\tau_{CMAQ}\). The correlation coefficients were also improved from \(-\)0.15-0.26 to 0.17-0.76 over the Arctic. In the comparison with \(\tau_{MODIS}\), \(\tau_{Assim}\) showed better correlation coefficients (R = 0.46-0.82) than those (R = 0.19-0.41) of \(\tau_{CMAQ}\) 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 \(\mu\)g m\({}^{-3}\) (between 0.85 and 1.68 \(\mu\)g 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, 3.78,  
Figure 6: Temporal variations of the modeled (bright and dark green lines) and estimated (red and purple lines) PM\({}_{10}\) and PM\({}_{2.5}\) at (**a**) Thule, (**b**) Hyytiala, (**c**) Hornsund, (**d**) Kuopio, (**e**) Andenes, and (**f**) the North Pole. The RD (relative differences) of PM\({}_{10}\) and PM\({}_{2.5}\) were also calculated at each station from following equations of RD\({}_{\text{PM}10}\) = (PM\({}_{10,\text{CMAQw/OI}}\)-PM\({}_{10,\text{CMAQ}}\)) / PM\({}_{10,\text{CMAQ}}\) and RD\({}_{\text{PM}2.5}\) = (PM\({}_{2.5,\text{CMAQw/OI}}\)-PM\({}_{2.5,\text{CMAQ}}\)) / PM\({}_{2.5,\text{CMAQ}}\)). 6.37, 2.19, 7.99, 0.61 ug m\({}^{-3}\) (2.21, 3.09, 2.54, 1.79, 2.25, 0.41 ug m\({}^{-3}\)) at Thule, Hyytiala, Hornsund, Kuopio, Andenes, and the North Pole, respectively. 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].