Prediction of AOD data by geographical and temporal weighted regression with nonlinear principal component analysis

Abstract

When predicting aerosol optical depth (AOD) values for geographical weighted regression (GWR) and geographical and temporal weighted regression (GTWR), the input variables are influenced by multiple collinearity. Additionally, too many input variables make the model computationally complex, and too few input variables can reduce the prediction accuracy. In this study, a nonlinear principal component analysis geographical weighted regression method (NLPCA-GWR) and a nonlinear principal component analysis geographical and temporal weighted regression method (NLPCA-GTWR) are proposed. The NLPCA-GWR and NLPCA-GTWR methods use nonlinear principal component analysis (NLPCA) to reduce the dimensionality of several related variables that influence the AOD and to obtain several comprehensive indicators. The obtained comprehensive indicators are used as dependent variables that are input into the GWR and GTWR models to predict AOD values. To test the effectiveness of the NLPCA-GWR and NLPCA-GTWR methods, this paper uses Beijing, Tianjin, and Hebei AOD data from April 2015; air quality data; meteorological data; and geospatial data as experimental data to model and compare the GWR and GTWR methods with the same number of input variables. The results show that the MAE, RMSE, AIC, R2, and $$ {R}_{\mathrm{j}}^2 $$ of the NLPCA-GWR method are 13.58%, 6.99%, 13.86%, 4.07%, and 3.96% higher, respectively, than those of the GWR method. Compared with the GTWR method, the NLPCA-GTWR method improved the MAE, RMSE, AIC, R2, and $$ {R}_{\mathrm{j}}^2 $$ by 6.53%, 2.91%, 2.17%, 1.14%, and 1.14%, respectively.