# 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  
The CMAQ-calculated AOD (\(\tau_{CMAQ}\) or \(\tau_{m}\)) were compared to those from the MODIS observations (\(\tau_{MODIS}\) or \(\tau_{o}\)) 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 \(\tau_{CMAQ}\) and \(\tau_{MODIS}\), showing the low values of \(-0.15\)-\(0.26\) for all months. In addition, the slopes are under a bias towards the x-axis. Figure 3: Scatter plots and statistical analysis between \(\tau_{MODIS}\) and \(\tau_{CMAQ}\) and \(\tau_{ Assimilated}\) over the entire domain for (**a**) April, (**b**) May, (**c**) June, (**d**) July, (**e**) August, and (**f**) September 2008. The statistical analysis of R (correlation coefficient), IOA (index of agreement), MB (mean bias), NMB (normalized mean bias, %), S (slope), and N (number of data) was presented. 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 SO2, NOx, BC, OC, PM10, and PM25 from the several emission inventories over the regions (70\({}^{\circ}\) N-90\({}^{\circ}\) N; 60\({}^{\circ}\) W-60\({}^{\circ}\) 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 PM10 for the ECLIPSE inventory, the emission fluxes were \(\sim\)3 Gg yr\({}^{-1}\) for both EDGARv4.2 and HTAPv2 and \(\sim\)10 Gg yr\({}^{-1}\) for EDGARv4.3.2. Such a comparison was also as similar as for PM25. 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 (\(\tau\)' or \(\tau_{Assim}\)) and MODIS-retrieved AODs (\(\tau_{MODIS}\)) and their statistical values over the entire domain (see the red dots). Compared to the statistical analyses between \(\tau_{CMAQ}\) and \(\tau_{MODIS}\), those between \(\tau_{Assim}\) and \(\tau_{MODIS}\) 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 \(\tau_{Assim}\) and \(\tau_{MODIS}\) 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 \(\tau_{CMAQ}\), \(\tau_{MODIS}\), and \(\tau_{Assim}\) in Figure S3. The MODIS observed data produce a complete 2-dimensional set of AOD when assimilated into the CMAQ-calculated AOD. Thus, \(\tau_{Assim}\) are much improved, compared with \(\tau_{CMAQ}\), particularly over Greenland Sea, Norwegian Sea, and the Barents Sea as shown in Figure S3.