## 4 Discussion
Our overall RMSPE of 21.67 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) from model cross validation is higher than those in studies on areas in the United States (<9.0 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\)) [9; 13; 14; 15; 16; 17; 35; 36; 37], but much lower than other results over the whole of China (32.98 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\)), which might be mainly due to the much denser ground monitoring sites in our study area. Our method has a slightly higher overall RMSPE than do those studies in the same study area (Beijing) using the coarser 3 km spatial resolution for PM\({}_{2.5}\) estimation by [PERSON] (16.04 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\)) [24] and [PERSON] (17.85 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\)) [25], but with higher R\({}^{2}\). This is possibly due to the smoothing effect of satellite data at coarser resolutions, representing more coverage for air quality conditions. The higher RMSPE in Beijing than in the United States is more likely due to the higher PM\({}_{2.5}\) levels in Beijing ranging from 3.0 to 773.6 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\), which is up to 10 or more times those in the United States, and the larger variations in the PM\({}_{2.5}\) levels may possibly be overlooked due to the missing satellite AOT values. Another possible reason is that the correlation of PM\({}_{2.5}\)-AOT was negative instead of positive under heavy pollution conditions, causing the dense aerosol layer (high AOT) with low PM\({}_{2.5}\) levels or much lower PBLH (low AOT) with high PM\({}_{2.5}\) levels to occur in northern China [38]. The model also may underestimate the PM\({}_{2.5}\) concentrations at the high PM\({}_{2.5}\) levels shown in Figure 6. Furthermore, the air pollution sources and location of the monitoring sites may also causing high RMSPE values [13]. The annual mean PM\({}_{2.5}\) concentrations decreased to 48.56 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) from 63.93 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) (~24.04%) over the whole Beijing area and to 55.90 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) from 81.56 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) (~31.46%) for the downtown area from 2013 to 2017, showing that the air quality has been dramatically improved since 2013. The annual mean PM\({}_{2.5}\) concentrations averaged from all monitoring sites decreased to 55.73 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) from 79.84 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) (~30.20%) over the whole Beijing area and to 57.63 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) from 85.63 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) (~32.70%) for the downtown area from 2013 to 2017. The trends in the annual mean PM\({}_{2.5}\) concentrations revealed by our model estimation and by the ground measurements are consistent, indicating that the PM\({}_{2.5}\) levels have really been lowered from 2013 to 2017. While the PM\({}_{2.5}\) concentrations across Beijing remain high, substantial improvements have occurred in recent years due to government policies and mitigation measures implemented to improve air quality. In September 2013, the Chinese government released the \"Plan of Action for Preventing and Controlling of Atmospheric Pollution\" [39] promoting ten control measures, including restriction on the number of vehicles in megacities, reducing coal combustion, and promoting the use of clean energy such as water, gas, geothermal energy, wind power, solar energy, and bioenergy. The Plan also set the goal for Beijing to reduce its annual mean PM\({}_{2.5}\) concentration to 60 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\mathrm{m}^{3}\) by 2017.