## 2 Materials and Methods
### AOT Data Sets  
The major AOT data sets used in this study were the MAIAC AOT data sets, which are produced using a generic algorithm specifically developed for MODIS, performing aerosol retrievals and atmospheric correction over both vegetated surfaces and bright deserts at 1 km spatial resolution based on time series analysis and image processing [26,27]. The MAIAC algorithm also derives column water vapor (CWV), the surface reflectance (SR) bidirectional reflectance distribution function (BRDF),  
Figure 1: (**a**) Location of the study area (the red polygon on the map); (**b**) An elevation map (DEM—Digital Elevation Model) shows that the study area is surrounded by mountains in the west, north, and northeast; (**c**) The 24 h PM\({}_{2.5}\) average (ug/m\({}^{3}\)) for each site during 2013–2017, classified into six levels and represented by different colors; (**d**) The spatial distribution of average 1 km Multi-Angle Implementation of Atmospheric Correction (MAIAC) aerosol optical thickness (AOT) during 2013–2017, with white color denoting water areas. The boundaries of 16 Beijing districts are shown in black lines. and spectral regression coefficients (SRC). MAIAC collects 5 (over poles) to 16 (over equator) days of MODIS observations depending on locations on the Earth using a sliding window approach. These MODIS observations are then gridded to 1 km spatial resolution with specific projection coordinate systems. When the land surface conditions remain stable during a data collection period, the surface BRDF is retrieved using the regional background aerosol model. The 2.1 um MODIS band is used to retrieve AOT and surface reflectance over dark and moderately bright surfaces. Four or more low AOT days are used to calculate the SRC correlating surface reflectance in the blue and shortwave infrared bands. Once the SRC is obtained, the AOT is retrieved with the last MODIS observation. AOT retrieval is conducted with the regional background aerosol model in clear conditions, but with surface BRDF in hazy conditions. Aerosol Robotic Network (AERONET) [28] validation shows that the MAIAC and the MODIS Level-2 atmospheric aerosol product (MOD04 ) algorithms have similar accuracy over dark and vegetated surfaces and that MAIAC AOT generally improves in accuracy over brighter surfaces due to SRC retrieval and explicit BRDF factor characterization, as demonstrated for several U.S. West Coast AERONET sites [26]. MAIAC AOT data sets derived from Terra (at \(\sim\)10:30 a.m. local time) and Aqua (at \(\sim\)1:30 p.m. local time) were merged to improve its spatial coverage in urban areas [14]. For a given day, due to meteorological condition changes and other factors, the two MAIAC AOT measurements might vary slightly. When merging the AOT data for a given area and a given day, there are two possible cases regarding the availability of AOT data: (1) both MAIAC-Aqua AOT and MAIAC-Terra AOT are available, or (2) only one of the two MAIAC AOTs is available. In the second case, the missing AOT values were estimated through a regression model. As a result, the daily AOT average represents the average between 10:00 a.m. and 2:00 p.m. for each day. As the ratio of morning AOT and afternoon AOT varies by season, we reorganized all the AOT data sets into two seasons for each year: warm season (15 April-14 October) and cold season (15 October-14 April). For the missing AOT estimation, the R\({}^{2}\) values of the regression model in warm and cold seasons were 0.88 and 0.87 respectively, indicating a good regression-based AOT interpolation. For comparison purposes, MODIS Collection 6 Level 2 aerosol data products with 3 km spatial resolution (MOD-3K AOT) for 2014 were also collected. The algorithm for generating MOD-3K AOT is similar to the algorithm used in the previous 10 km AOT product, but the MOD-3K AOT algorithm averages 6 \(\times\) 6 pixels in a single retrieval box rather than 20 \(\times\) 20 pixels after cloud screening and other surface mask processes [29].