Time series modeling of PM_2.5 concentrations with residual variance constraint in eastern mainland China during 2013–2017

Satellite-based mapping has been proven to be an effective method to reveal the spatiotemporal variations of PM_2.5 distributions. However, most satellite AOD (aerosol optical depth) statistical models suffer from unstable accuracy over long time spans. This study thus aims to propose an accurate and stable method for PM_2.5 concentration estimations in time series. Specifically, a three-step residual variance constraint method (RVCM) is developed to simulate PM_2.5 concentrations from January 2013 to December 2017 with the aid of AODs and other auxiliary data. Results show that the five-year fitting R² and cross-validation R² of RVCMs improved from 0.77 to 0.88 and 0.71 to 0.84, respectively, compared to those models without residual variance constraint (WO-RVCM). Additionally, RVCM demonstrated more stable performance on time series simulation of PM_2.5 concentrations than WO-RVCM, with the yearly fitting R² of 0.89, 0.88, 0.85, 0.87 and 0.88, and corresponding cross validation R² of 0.85, 0.84, 0.80, 0.82 and 0.83, respectively. Furthermore, accuracy verification of removed outliers in residual variance constraint modeling confirmed the credibility of RVCM in outliers' simulation compared to WO-RVCM models. Finally, RVCM-aided estimations of time series PM_2.5 concentrations and associated premature deaths in the study area (east and southeast mainland China) revealed their total decrease rates were 35.21% and 21.57%, and excellent air quality days increased from 7% to 35%. These findings suggest that residual variance constraint is effective and could be a reliable solution to providing time series AOD-PM_2.5 modeling with stable accuracy over long time spans.