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Applications and Case Studies

Modeling and Regionalization of China’s PM2.5 Using Spatial-Functional Mixture Models

Pages 116-132 | Received 09 Apr 2019, Accepted 15 Apr 2020, Published online: 10 Jun 2020


Abstract–Severe air pollution affects billions of people around the world, particularly in developing countries such as China. Effective emission control policies rely primarily on a proper assessment of air pollutants and accurate spatial clustering outcomes. Unfortunately, emission patterns are difficult to observe as they are highly confounded by many meteorological and geographical factors. In this study, we propose a novel approach for modeling and clustering PM 2.5 concentrations across China. We model observed concentrations from monitoring stations as spatially dependent functional data and assume latent emission processes originate from a functional mixture model with each component as a spatio-temporal process. Cluster memberships of monitoring stations are modeled as a Markov random field, in which confounding effects are controlled through energy functions. The superior performance of our approach is demonstrated using extensive simulation studies. Our method is effective in dividing China and the Beijing-Tianjin-Hebei region into several regions based on PM 2.5 concentrations, suggesting that separate local emission control policies are needed. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Appendix C Supplementary Materials

Technical details: Implementation issues related to model selection, additional results for the Monte Carlo EM algorithm, model diagnostic results for the data analysis, and clustering results from other methods (PDF file).

Code: R code for simulation studies and data analysis (zip file).

Dataset: City-level daily PM2.5 concentrations of China’s entirety from January 2015 to December 2016, and station-level monthly PM2.5 concentrations from 73 stations in the BTH region from June 2013 to December 2016 (CSV file), the topographic information including the longitude and latitude for corresponding cities and stations (CSV file), and China’s elevation with 1km resolution (TIF file).


The authors are grateful for the detailed and constructive comments from an associate editor and three referees.

Additional information


The research was partially supported by the National Natural Science Foundation of China (Grant No. 11871485) and China’s National Key Research Special Program (Grant No. 2016YFC0207702).

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