Bayesian autoregressive spatiotemporal model of PM₁₀ concentrations across Peninsular Malaysia

Abstract

Rapid industrialization and haze episodes in Malaysia ensure pollution remains a public health challenge. Atmospheric pollutants such as PM₁₀ are typically variable in space and time. The increased vigilance of policy makers in monitoring pollutant levels has led to vast amounts of spatiotemporal data available for modelling and inference. The aim of this study is to model and predict the spatiotemporal daily PM₁₀ levels across Peninsular Malaysia. A hierarchical autoregressive spatiotemporal model is applied to daily PM₁₀ concentration levels from thirty-four monitoring stations in Peninsular Malaysia during January to December 2011. The model set in a three stage Bayesian hierarchical structure comprises data, process and parameter levels. The posterior estimates suggest moderate spatial correlation with effective range 157 km and a short term persistence of PM₁₀ in atmosphere with temporal correlation parameter 0.78. Spatial predictions and temporal forecasts of the PM₁₀ concentrations follow from the posterior and predictive distributions of the model parameters. Spatial predictions at the hold-out sites and one-step ahead PM₁₀ forecasts are obtained. The predictions and forecasts are validated by computing the RMSE, MAE, R² and MASE. For the spatial predictions and temporal forecasting, our results indicate a reasonable RMSE of 10.71 and 7.56, respectively for the spatiotemporal model compared to RMSE of 15.18 and 12.96, respectively from a simple linear regression model. Furthermore, the coverage probability of the 95% forecast intervals is 92.4% implying reasonable forecast results. We also present prediction maps of the one-step ahead forecasts for selected day at fine spatial scale.