Environmental and Ecological Statistics

, Volume 18, Issue 1, pp 185-207

First online:

A fast Bayesian method for updating and forecasting hourly ozone levels

  • Sujit K. SahuAffiliated withSchool of Mathematics, University of Southampton Email author 
  • , Stan YipAffiliated withExeter Climate Systems, University of Exeter
  • , David M. HollandAffiliated withU.S. Environmental Protection Agency, National Exposure Research Laboratory

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A Bayesian hierarchical space-time model is proposed by combining information from real-time ambient AIRNow air monitoring data, and output from a computer simulation model known as the Community Multi-scale Air Quality (Eta-CMAQ) forecast model. A model validation analysis shows that the model predicted maps are more accurate than the maps based solely on the Eta-CMAQ forecast data for a 2 week test period. These out-of sample spatial predictions and temporal forecasts also outperform those from regression models with independent Gaussian errors. The method is fully Bayesian and is able to instantly update the map for the current hour (upon receiving monitor data for the current hour) and forecast the map for several hours ahead. In particular, the 8 h average map which is the average of the past 4 h, current hour and 3 h ahead is instantly obtained at the current hour. Based on our validation, the exact Bayesian method is preferable to more complex models in a real-time updating and forecasting environment.


Bayesian inference Eta-CMAQ model Space-time forecasting Hierarchical model Separable models Spatial interpolation