Prediction of High Resolution Spatial-Temporal Air Pollutant Map from Big Data Sources

In order to better understand the formation of air pollution and assess its influence on human beings, the acquisition of high resolution spatial-temporal air pollutant concentration map has always been an important research topic. Existing air-quality monitoring networks require potential improvement due to their limitations on data sources. In this paper, we take advantage of heterogeneous big data sources, including both direct measurements and various indirect data, to reconstruct a high resolution spatial-temporal air pollutant concentration map. Firstly, we predict a preliminary 3D high resolution air pollutant concentration map from measurements of both ground monitor stations and mobile stations equipped with sensors, as well as various meteorology and geography covariates. Our model is based on the Stochastic Partial Differential Equations (SPDE) approach and we use the Integrated Nested Laplace Approximation (INLA) algorithm as an alternative to the Markov Chain Monte Carlo (MCMC) methods to improve the computational efficiency. Next, in order to further improve the accuracy of the predicted concentration map, we model the issue as a convex and sparse optimization problem. In particular, we minimize the Total Variant along with constraints involving satellite observed low resolution air pollutant data and the aforementioned measurements from ground monitor stations and mobile platforms. We transform this optimization problem to a Second-Order Cone Program (SOCP) and solve it via the log-barrier method. Numerical simulations on real data show significant improvements of the reconstructed air pollutant concentration map.