## 3 Methodology
### Data Preprocessing  
The estimation accuracy of the merged AOD data largely depends on the quality of the input satellite-based AOD observations during the fusion process. To dispose of near-cloud contamination for AOD data with ensured reliability, the Himawari-8 AHI AOD retrievals after preliminary cloud screening (i.e., \(AOD_{ori}\)) further underwent strict quality control according to the AHI official L3 AOD algorithm [14]. For a center point \((x_{0},y_{0},t_{0})\), the spatiotemporal variability at neighboring locations \((x_{i},y_{i},t_{i})\) is quantified by the root mean square difference (RMSE) as follows:  
\[\sigma(\Delta L,\Delta t)=\sqrt{\frac{1}{N}\sum_{1}^{N}(AOD_{ori}(x_{i},y_{i},t _{i})-AOD_{ori}(x_{0},y_{0},t_{0}))^{2}} \tag{1}\]  
where \(N\) is the total number of valid pixels within the calculation domain, \(\Delta L=\left((x_{i}-x_{0})^{2}\right.\)\(+\)\((y_{i}-y_{0})^{2})^{1/2}\), and \(\Delta t=t_{i}-t_{0}\). Based on the corresponding AOD pairs at domain radius from 0 to 12.5 km and time ranges from 0 to 50 min, we establish the look-up-table (LUT) (seen in Supplementary Table S4) for \(\sigma(\Delta L,\Delta t)\). The estimated AOD at the center point, namely, \(AOD_{est}(x_{0},y_{0},t_{0})\), is interpolated from the AODs in a radius of 12.5 km and past of  
Figure 2: Flowchart of the AOD fusion by integrating LEO and GEO AOD products. (RMSD and PDF are the abbreviations of root-mean-square difference and probability density function, respectively).  
\(1\) h (except center point) with the inverse of their error variances as weights. It is expressed as follows:  
\[AOD_{est}(x_{0},y_{0},t_{0})=\sum_{i=1}^{N}\frac{\frac{1}{\sigma_{ori}(x_{i}y_{i },t_{i})^{2}}}{\sum_{i=1}^{N}\frac{1}{\sigma_{ori}(x_{i},y_{i},t_{i})^{2}}}AOD_{ ori}(x_{i},y_{i},t_{i}) \tag{2}\]  
According to the joint Equations (3) and (4), \(AOD_{pure}(x_{0},y_{0},t_{0})\), the initial AHI AOD for the fusion process, is obtained from the \(AOD_{ori}(x_{0},y_{0},t_{0})\) if \(AOD_{ori}(x_{0},y_{0},t_{0})\) is within 2.58 \(\sigma_{pure}(x_{0},y_{0},t_{0})\) (i.e., the upper limit of the 99% confidence interval) based on the estimation of \(AOD_{est}(x_{0},y_{0},t_{0})\); otherwise, \(AOD_{ori}(x_{0},y_{0},t_{0})\) largely deviated from \(AOD_{est}(x_{0},y_{0},t_{0})\) is assigned to be a missing value due to near-cloud contamination. The \(\sigma(x_{0},y_{0},t_{0})^{2}\) at the center point is estimated via applying quadratic fitting in space and time of \(\sigma(\Delta L,\Delta t)^{2}\).  
\[AOD_{pure}(x_{0},y_{0},t_{0})=\left\{\begin{array}{ll}AOD_{ori}(x_{0},y_{0}, t_{0})&\mbox{if }\ AOD_{ori}(x_{0},y_{0},t_{0})\ \leq\ AOD_{est}(x_{0},y_{0},t_{0})+2.58\sigma_{pure}(x_{0},y_{0},t_{0})\\ &\mbox{missing value else}\end{array}\right. \tag{3}\]  
\[\sigma_{pure}(x_{0},y_{0},t_{0})=\sqrt{\sigma(x_{0},y_{0},t_{0})^{2}+\sigma_{ est}(x_{0},y_{0},t_{0})^{2}} \tag{4}\]  
To match up other satellite-based AODs with Himawari-8 AHI AODs with a spatial resolution of 5 km, MODIS AOD, CALIOP AOD, and CALIOP cloud/aerosol identification flag are resampled into the same geographic girds as Himawari-8 AHI AOD using the cubic convolution interpolation method. Meanwhile, to compensate for the deficiency of CALIOP observations in spatial completeness, CALIOP datasets are expanded with a 40-km morphological buffer on both sides from the center of the original 5-km track based on inverse distance weighting (IDW) [51; 56]. Benefiting from the similar scanning time and advantage of CALIOP in distinguishing clouds from aerosols, the dilated CALIOP cloud/aerosol identification flag is used to further screen Aqua MODIS AOD retrievals affected by cloud contamination. Similar to the strategies in our previous study [24], the cloud/aerosol identification grid will be set as a cloud flag if there exists any cloud flag pixel in interpolation and dilatation calculation since the potential abnormal AOD values contaminated by clouds should be excluded as much as possible to avoid error propagation in subsequent data fusion and recovery.