Environmental and Ecological Statistics

, Volume 18, Issue 1, pp 185–207

A fast Bayesian method for updating and forecasting hourly ozone levels


DOI: 10.1007/s10651-009-0127-y

Cite this article as:
Sahu, S.K., Yip, S. & Holland, D.M. Environ Ecol Stat (2011) 18: 185. doi:10.1007/s10651-009-0127-y


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 inferenceEta-CMAQ modelSpace-time forecastingHierarchical modelSeparable modelsSpatial interpolation

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.School of MathematicsUniversity of SouthamptonSouthamptonUK
  2. 2.Exeter Climate SystemsUniversity of ExeterExeterUK
  3. 3.U.S. Environmental Protection AgencyNational Exposure Research LaboratoryResearch Triangle ParkUSA