## 3 Results
### Results of Model Fitting and Validation  
We fitted the LMEM PM\({}_{2.5}\) estimation model for each year using the two different daily PM\({}_{2.5}\) data sets--the PM\({}_{2.5}\) 24 h average (Model-I) and the PM\({}_{2.5}\) period average (Model-II)--and 1 km MAIAC AOT. Figure 1(a) shows the model fitting performance statistics (R\({}^{2}\), Intercept, Slope, RMSPE, and MPE) at each site, with site-specific R\({}^{2}\) ranging from 0.72 to 0.97, Slope from 0.75 to 1.1, RMSPE from 11.50 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\) to 47.08 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\), and MPE from 7.17 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\) to 28.93 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\) for Model-I; and R\({}^{2}\) ranging from 0.70 to 0.96, Slope from 0.78 to 1.2, RMSPE from 15.28 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\) to 40.81 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\), and MPE from 8.56 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\) to 22.80 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\) for Model-II. The median values of R\({}^{2}\) and Slope for Model-I are higher than those for Model-II, and its Model-I's RMSPE values are lower.  
The model fitting performance for each year can be seen in Figure 2(a) and Table 1: the year-specific R\({}^{2}\) of Model-I ranges from 0.90 to 0.94 and is 0.90 for the whole study period, while the year-specific R\({}^{2}\) of Model-II ranges from 0.91 to 0.93 and is 0.92 for the whole study period. Therefore, both Model-I and Model-II have high R\({}^{2}\) values (more than 0.90), demonstrating that both the PM\({}_{2.5}\) 24 h average and the PM\({}_{2.5}\) period average between 10:00 a.m. and 2:00 p.m. can be used to fit the estimation model with high estimation performance. However, the other model fitting statistics indicate that Model-I performs slightly better than Model-II. In addition, model cross validation performance statistics are shown in Figure 1(b) for each site, and in Figure 2(b) and Table 1 for each year: Figure 1(b) shows that the site-specific R\({}^{2}\) for both Model-I and Model-II decreases, while RMSPE and MPE increase from model  
Figure 2: Boxplot statistics of the estimation performance at each site for R\({}^{2}\), Intercept, Slope, RMSPE (\(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\)), and MPE (\(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\)): (**a**) Model fitting; (**b**) Model validation. Here, ’I’ denotes models using the PM\({}_{2.5}\) 24 h average, and ’II’ denotes models using the PM\({}_{2.5}\) period average.  
fitting to model validation with small differences. The yearly model cross validation results shown in Figure 3b and Table 1 indicate that the year-specific R\({}^{2}\) of Model-I ranges from 0.87 to 0.93 and is 0.90 for the whole study period, while the year-specific R\({}^{2}\) of Model-II ranges from 0.89 to 0.92 and is 0.90 for the whole study period. Overall, although both Model-I and Model-II have good estimation performance with high R\({}^{2}\) values, Model-I is relatively better as it has lower RMSPE and MPE values.  
We fitted the model for each year and estimated the daily PM\({}_{2.5}\) concentrations for the period from 2013 through 2017. The annual mean PM\({}_{2.5}\) concentrations and five-year (2013-2017) mean PM\({}_{2.5}\) concentrations were generated for different seasons (warm and cold) and for specific urban areas (the whole urban area and the central city area) using estimated daily PM\({}_{2.5}\) concentrations in order to reveal the spatiotemporal variations of PM\({}_{2.5}\) levels.  
Figure 3: Scatterplots between estimated and measured PM\({}_{2.5}\) levels for each year: (**a**) Model fitting; (**b**) Model cross validation. The red solid line represents the regression line and the green dashed line is the 1:1 line with slope of 1.0; 'I’ denotes models using the PM\({}_{2.5}\) 24 h average, and ‘II’ denotes models using the PM\({}_{2.5}\) period average.