External drift kriging of NOx concentrations with dispersion model output in a reduced air quality monitoring network

J. van de Kassteele, A. Stein, A.L.M. Dekkers, G.J.M. Velders

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26 Citations (Scopus)


In the mid nineteen eighties the Dutch NOx air quality monitoring network was reduced from 73 to 32 rural and city background stations, leading to higher spatial uncertainties. In this study, several other sources of information are being used to help reduce uncertainties in parameter estimation and spatial mapping. For parameter estimation, we used Bayesian inference. For mapping, we used kriging with external drift (KED) including secondary information from a dispersion model. The methods were applied to atmospheric NOx concentrations on rural and urban scales. We compared Bayesian estimation with restricted maximum likelihood estimation and KED with universal kriging. As a reference we also included ordinary least squares (OLS). Comparison of several parameter estimation and spatial interpolation methods was done by cross-validation. Bayesian analysis resulted in an error reduction of 10 to 20% as compared to restricted maximum likelihood, whereas KED resulted in an error reduction of 50% as compared to universal kriging. Where observations were sparse, the predictions were substantially improved by inclusion of the dispersion model output and by using available prior information. No major improvement was observed as compared to OLS, the cause presumably being that much good information is contained in the dispersion model output, so that no additional spatial residual random field is required to explain the data. In all, we conclude that reduction in the monitoring network could be compensated by modern geostatistical methods, and that a traditional simple statistical model is of an almost equal quality.
Original languageEnglish
Pages (from-to)321-339
JournalEnvironmental and Ecological Statistics
Issue number3
Publication statusPublished - 2009


  • digital elevation model
  • geostatistical methods
  • spatial interpolation
  • rainfall
  • prediction
  • regression

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