Spatio-temporal modeling of PM_2.5 concentrations with missing data problem: a case study in Beijing, China

ABSTRACT

One of the major challenges in conducting epidemiological studies of air pollution and health is the difficulty of estimating the degree of exposure accurately. Fine particulate matter (PM_2.5) concentrations vary in space and time, which are difficult to estimate in rural, suburban and smaller urban areas due to the sparsity of the ground monitoring network. Satellite retrieved aerosol optical depth (AOD) has been increasingly used as a proxy of ground PM_2.5 observations, although it suffers from non-trivial missing data problems. To address these issues, we developed a multi-stage statistical model in which daily PM_2.5 concentrations can be obtained with complete spatial coverage. The model consists of three stages – an inverse probability weighting scheme to correct non-random missing patterns of AOD values, a spatio-temporal linear mixed effect model to account for the spatially and temporally varying PM_2.5-AOD relationships, and a gap-filling model based on the integrated nested Laplace approximation-stochastic partial differential equations (INLA-SPDE). Good model performance was achieved from out-of-sample validation as shown in R² of 0.93 and root mean square error of 9.64 μg/m³. The results indicated that the multi-stage PM_2.5 prediction model proposed in the present study yielded highly accurate predictions, while gaining computational efficiency from the INLA-SPDE.

KEYWORDS:

• Satellite aerosol optical depth (AOD)
• inverse probability weighting
• spatio-temporal linear mixed effect
• integrated nested Laplace approximation-stochastic partial differential equations (INLA-SPDE)

Acknowledgments

The authors would like to acknowledge Dr. Muhammad Bilal (Nanjing University of Information Science & Technology) and Dr. Bin Zou (Central South University) for providing merged AOD data and meteorological/land use data, respectively. We also thank the associated editor Dr. Bo Huang and three reviewers for insightful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

A sample dataset and exemplary scripts that support the findings of the present study are available in Zenodo at https://doi.org/10.5281/zenodo.3384304.

Additional information

Notes on contributors

Qiang Pu

Qiang Pu is a Ph.D. student in the department of Geography at the University at Buffalo, SUNY. His research interests lie in air pollution exposure modeling using GIS and geostatistic methods.

Eun-Hye Yoo

Eun-Hye Yoo is an associate professor in Geography at the University at Buffalo, SUNY, and works in the areas of applied geostatistics in air pollution and health, modeling human mobility using mobile phone data, and change of support problems.