## 3 Results and Validation
### Validation  
Landsat8/OLI, Sentinel2/MSI and GF1/WFV from the US, ESA, and China, respectively, are selected for validation, since they have observations long enough and better radiometric capability. AOD values derived from Landsat/OLI, Sentinel2/MSI and GFI/WFV images at four AERONET sites with bright and stable surface are compared with ground-measured AOD from the corresponding AERONET sites and the four sites are Dalanzadgad, Fowlers_Gap, Mezaira, and Tamanrasset_INM (Table 2). In order to better validate the algorithm, all images from the three sensors since launched have been collected. The total number of collected images is 1531. For Landsat/OLI imagery, 723 images from 2013 to 2019 are retrieved for the four validation sites and only 136 corresponding measurements of AOD from AERONET are collected. The comparison between the retrieved AOD and the observed AOD is shown in the top left plot of Figure 6 and the statistics including the R\({}^{2}\) value, the mean of retrieved AOD, and the RMSE are 0.8929, 0.1138, and 0.0613, respectively, which shows that the retrieved AOD agrees very well with AERONET measurements. In addition, 87.5% of the discrepancy between the derived AOD and the measured AOD is less than 0.1, which is very low. For Sentinel2/MSI imagery, 733 images from 2015 to 2019 were retrieved for the four validation sites and only 276 corresponding measurements of AOD from AERONET were collected. The comparison between the retrieved AOD and the observed AOD is shown in the top right plot of Figure 6 and the statistics including the R\({}^{2}\) value, the mean of retrieved AOD, and the RMSE are 0.7372, 0.2313, \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameter** & **(a) and (b)** & **(c) and (d)** & **(e) and (f)** & **(g) and (h)** \\ \hline Image date & 31 May 2018 & 31 May 2018 & 19 February 2017 & 24 May 2018 \\ \hline View zenith angle (\({}^{\circ}\)) & 8.78 & 26.58 & 0 & 3.99 \\ Solar zenith angle (\({}^{\circ}\)) & 22.38 & 21.61 & 43.18 & 16.45 \\ Relative azimuth angle 1 (\({}^{\circ}\)) & 116.15 & 112.75 & 139.62 & 157.16 \\ Atmospheric model & Mid-latitude, summer summer summer & Mid-latitude, winter & Mid-latitude, summer summer \\ Aerosol model & Continental & Continental & Continental & Continental \\ AOD & 0.15 & 0.12 & 0.24 & 0.71 \\ Altitude (m) & 1569 & 1545 & 774 & 772 \\ Surface reflectance & 0.117 & 0.098 & 0.12 & 0.142 \\ Sensor & GF-1/WFV3 & GF-1/WFV4 & Landsat/OLI & Sentinel2B/MSI \\ \hline \hline \end{tabular} \({}^{1}\) Relative azimuth angle = absolute (solar azimuth-sensor azimuth line-of-sight).  
\end{table} 
Table 4: The parameters of images in Figure 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **(a) and (b)** & **(c) and (d)** & **(e) and (f)** & **(g) and (h)** & **(i) and (j)** \\ \hline Image date & 29 May 2015 & 1 December 2016 & 19 February 2017 & 23 March 2017 & 11 June 2017 \\ \hline View zenith angle (\({}^{\circ}\)) & 0 & 0 & 0 & 0 & 0 \\ Solar zenith angle (\({}^{\circ}\)) & 21.34 & 49.28 & 43.18 & 32.79 & 21.49 \\ Relative azimuth angle 1 (\({}^{\circ}\)) & 89.47 & 154.47 & 139.62 & 128.42 & 85.37 \\ Atmospheric model & Mid-latitude, summer winter & Mid-latitude, winter winter & Mid-latitude, summer summer summer \\ Aerosol model & Continental & Continental & Continental & Continental & Continental \\ AOD & 1.16 & 0.25 & 0.24 & 0.15 & 1.2 \\ Surface reflectance & 0.132 & 0.15 & 0.12 & 0.14 & 0.13 \\ \hline \hline \end{tabular} \({}^{1}\) Relative azimuth angle = absolute (solar azimuth-sensor azimuth line-of-sight).  
\end{table} 
Table 5: The parameters of images in Figure 5.  
and 0.1073, respectively, which shows that the retrieved AOD agrees also very well with AERONET measurements; 70.0% of the discrepancy between the derived AOD and the measured AOD is less than 0.1.