## 1 Introduction  
PM\({}_{2.5}\) refers to atmospheric particulate matter (PM) with a diameter of less than 2.5 micrometers, which remains suspended for a longer time in the air. Numerous studies have demonstrated that exposure to PM\({}_{2.5}\) is associated with adverse health effects including respiratory and cardiovascular diseases [1; 2; 3]. In urban areas, PM\({}_{2.5}\) concentrations vary sharply over short distances caused by uneven distribution of emission sources, diffusion, and physicochemical transformations. While traditional ground-based monitoring measures PM\({}_{2.5}\) concentrations with high temporal resolution (e.g., daily and hourly), the monitoring sites are generally distributed sparsely and unevenly, lacking the spatial resolution necessary to analyze the fine-scale spatial variability of pollution; this variability is important for health impact assessment and is needed to characterize the heterogeneity of human exposure to PM\({}_{2.5}\), analyze its adverse health effects, and effectively prevent and control air pollution [4].  
Aerosol optical thickness (AOT), defined as the integrated extinction coefficient over a vertical column of atmosphere at an observation location, is a measure of the extinction of the solar beam by aerosol particles in the atmosphere. Satellite-derived AOT can be used to monitor urban air quality through adding synoptic and spatial distribution information to ground-based air quality data and modeling [5]. Different approaches have been employed to estimate surface PM\({}_{2.5}\) concentrations from AOT, with many efforts on developing linear regression models to effectively relate PM\({}_{2.5}\) and AOT [6; 7]. For example, meteorological data have been incorporated in a multiple regression analysis and improved the PM\({}_{2.5}\)-AOT correlation [8]; considering that spatial variation of pollution may introduce significant biases, a geographically weighted regression model (GWR) was developed to accommodate such spatial variations [9; 10; 11]; and local scaling factors obtained from a global chemical transport model (GEOS-Chem) were combined with AOT to estimate ground-level PM\({}_{2.5}\)[12]. Taking time-varying parameters into account, a statistical model was developed to calibrate 10 km MODIS AOT and predict daily PM\({}_{2.5}\) concentrations [13], and this model was further improved through adding meteorological data, land use, and pollution sources [14; 15; 16; 17; 18; 19; 20; 21; 22; 23], and applied in the Beijing area to estimate PM\({}_{2.5}\) spatial variations using Moderate Resolution Imaging Spectroradiometer (MODIS) AOT data products at 3 km resolution [24; 25].  
In this study, considering the attention paid to the linear mixed effect model (LMEM) developed by [PERSON] et al. [13] and its demonstrated effectiveness, we assessed the performance of the LMEM in heavily polluted urban areas. Specifically, the results of LMEM fitting with AOT at 1 km and 3 km resolutions and different PM\({}_{2.5}\) datasets were compared, the spatiotemporal trends of PM\({}_{2.5}\) pollution in Beijing from 2013 to 2017 were analyzed, and the effectiveness of government policies regarding air pollution mitigation in recent years was evaluated.