Prediction of PM concentrations at unsampled points using multiscale geographically and temporally weighted regression.

Numerous statistical models have established the relationship between ambient fine particulate matter (PM, with an aerodynamic diameter of less than 2.5 μm) and satellite aerosol optical depth (AOD) along with other meteorological/land-related covariates. However, all the models assumed that all covariates affect the PM concentration at the same scale, and none could provide a posterior uncertainty analysis at each regression point. Therefore, a multiscale geographically and temporally weighted regression (MGTWR) model was proposed by specifying a unique bandwidth for each covariate. However, the lack of a method for predicting values at unsampled points in the MGTWR model greatly restricts its corresponding application. Thus, this study developed a method for inferring unsampled points and used the posterior uncertainty assessment value to improve the model accuracy. With the aid of the high-resolution satellite multi-angle implementation of atmospheric correction (MAIAC) AOD product, daily PM concentrations with a 1 km × 1 km resolution were generated over the Beijing-Tianjin-Hebei region between 2013 and 2019. The coefficient of determination (R) and root mean square error (RMSE) of the fitted MGTWR results vary from 0.90 to 0.94 and from 10.66 to 25.11 μg/m, respectively. The sample-based and site-based cross-validation R and RMSE vary from 0.81 to 0.89 and from 14.40 to 34.43 μg/m respectively, demonstrating the effectiveness of the proposed inference method at unsampled points. With the uncertainty constraint, the sample-based and site-based validated MGTWR R results for all years are further improved by approximately 0.02-0.04, demonstrating the effectiveness of the posterior uncertainty assessment constraint method. These results suggest that the inference method proposed in this study is promising to overcome the defects of the MGTWR model in inferring the prediction values at unsampled points and could consequently enhance the wide applications of MGTWR modeling.