Statistical Methods & Applications

, Volume 25, Issue 1, pp 107–124 | Cite as

Spatial–temporal modellization of the \(\hbox {NO}_{2}\) concentration data through geostatistical tools

  • Raquel Menezes
  • Helena Piairo
  • Pilar García-Soidán
  • Inês Sousa
Original Paper


The nitrogen dioxide is a primary pollutant, regarded for the estimation of the air quality index, whose excessive presence may cause significant environmental and health problems. In the current work, we suggest characterizing the evolution of \(\hbox {NO}_{2}\) levels, by using geostatistical approaches that deal with both the space and time coordinates. To develop our proposal, a first exploratory analysis was carried out on daily values of the target variable, daily measured in Portugal from 2004 to 2012, which led to identify three influential covariates (type of site, environment and month of measurement). In a second step, appropriate geostatistical tools were applied to model the trend and the space–time variability, thus enabling us to use the kriging techniques for prediction, without requiring data from a dense monitoring network. This methodology has valuable applications, as it can provide accurate assessment of the nitrogen dioxide concentrations at sites where either data have been lost or there is no monitoring station nearby.


\(\hbox {NO}_{2}\) Geostatistics Time series analysis Space–time analysis 


  1. Bivand R, Pebesma E, Gómez-Rubio V (2008) Applied spatial data analysis with R. Springer, New YorkMATHGoogle Scholar
  2. Bogaert P (1996) Comparison of kriging techniques in a space–time context. Math Geol 28:73–86CrossRefMathSciNetMATHGoogle Scholar
  3. Bruno F, Guttorp P, Sampson P, Cocchi D (2009) A simple non-separable, non-stationary spatiotemporal model for ozone. Environ Ecol Stat 16:515–529CrossRefMathSciNetGoogle Scholar
  4. Calculli C, Fasso A, Finazzi F, Pollice A, Turnone A (2015) Maximum likelihood estimation of the multivariate hidden dynamic geostatistical model with application to air quality in Apulia, Italy. Environmetrics 26:406–417CrossRefMathSciNetGoogle Scholar
  5. Cameletti M, Ignaccolo R, Bande S (2011) Comparing spatio–temporal models for particulate matter in piemonte. Environmetrics 22:985–996CrossRefMathSciNetGoogle Scholar
  6. Carslaw DC (2005) Evidence of an increasing no2/nox emissions ratio from road traffic emissions. Atmos Environ 39:4793–4802CrossRefGoogle Scholar
  7. Cressie N (1990) The origins of kriging. Math Geol 22:239–252CrossRefMathSciNetMATHGoogle Scholar
  8. Cressie N, Huang H (1999) Classes of nonseparable, spatio–temporal stationary covariance functions. J Am Stat Assoc 94:1330–1340CrossRefMathSciNetMATHGoogle Scholar
  9. Cressie N, Wikle C (2011) Statistics for spatio–temporal data. Wiley, New YorkMATHGoogle Scholar
  10. De Cesare L, Myers D, Posa D (2001) Estimating and modeling space–time correlation structures. Stat Probab Lett 51:9–14CrossRefMATHGoogle Scholar
  11. De Gruijter J, Brus D, Bierkens M, Knotters M (2006) Sampling for natural resource monitoring. Springer, GermanyCrossRefGoogle Scholar
  12. De Iaco S, Posa D (2012) Predicting spatio–temporal random fields: some computational aspects. Comput Geosci 41:12–24CrossRefGoogle Scholar
  13. Dimitrakopoulos R, Luo X (1994) Spatiotemporal modeling: covariances and ordinary kriging systems. In: Dimitrakopoulos R (ed) Geostatistics for the next century. Kluwer Academic Publishers, Dordrecht, pp 88–93CrossRefGoogle Scholar
  14. Dimitrakopoulos R, Luo X (1997) Spatiotemporal modeling: covariances and ordinary kriging systems. In: Baafi E, Scofield N (eds) Geostatistics Wollongong’96. Kluwer Academic Publishers, Dordrecht, pp 138–149Google Scholar
  15. Fernández-Casal R, González-Manteiga W, Febrero-Bande M (2003) Flexible spatio–temporal stationary variogram models. Stat Comput 13:127–136CrossRefMathSciNetGoogle Scholar
  16. Fox J (2008) Applied regression analysis and generalized linear models. SAGE Publications, Thousand OaksGoogle Scholar
  17. Gneiting T, Genton MG, Guttorp P (2007) Statistical methods for spatio–temporal systems. Chapman and Hall, CambridgeGoogle Scholar
  18. Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New YorkGoogle Scholar
  19. Grice S, Stedman J, Kent A, Hobson M, Norris J, Abbott J, Cooke S (2009) Recent trends and projections of primary no2 emissions in europe. Atmos Environ 43:2154–2167CrossRefGoogle Scholar
  20. Heuvelink G, Griffith D (2010) Space-time geostatistics for geography: a case study of radiation monitoring across parts of Germany. Geogr Anal 42:161–179CrossRefGoogle Scholar
  21. Host G, Omre H, Switzer P (1995) Spatial interpolation errors for monitoring data. J Am Stat Assoc 90:853–861MathSciNetGoogle Scholar
  22. Isaaks E, Srivastava R (1989) An introduction to applied geostatistics. Oxford University Press, New YorkGoogle Scholar
  23. Kyriakidis P, Journel A (1999) Geostatistical space–time models: a review. Math Geol 31:651–684CrossRefMathSciNetMATHGoogle Scholar
  24. Lewne M, Cyrys J, Meliefste K, Hoek G, Brauer M, Fischer P, Gehring U, Heinrich J, Brunekreef B, Bellander T (2004) Spatial variation in nitrogen dioxide in three European areas. Sci Total Environ 332:217–230CrossRefGoogle Scholar
  25. Lindley S, Walsh T (2005) Inter-comparison of interpolated background nitrogen dioxide concentrations across greater manchester, uk. Atmos Environ 39:2709–2724CrossRefGoogle Scholar
  26. Myers D (2004) Estimating and modeling space-time variograms. In: McRoberts R (ed) Proceedings of the joint meeting of TIES-2004 and ACCURACY-2004Google Scholar
  27. Porcu E, Mateu J, Saura F (2008) New classes of covariance and spectral density functions for spatio–temporal modelling. Stoch Environ Res Risk Assess 22:65–79CrossRefMathSciNetMATHGoogle Scholar
  28. R Team D (2010) R: a language and environment for statistical computing. R Foundation for Statistical ComputingGoogle Scholar
  29. Rodriguez-Iturbe I, Mejía J (1974) The design of rainfall networks in time and space. Water Resour Res 10:713–728CrossRefGoogle Scholar
  30. Rouhani S, Hall T (1989) Space–time kriging of groundwater data. In: Armstrong M (ed) Geostatistics. Kluwer Academic Publishers, Dordrecht, pp 639–651CrossRefGoogle Scholar
  31. Saiz-Lopez A, Adame J, Notario A, Poblete J, Bolívar J, Albaladejo J (2009) Year-round observations of no, no2, o3, so2 and toluene. Water Air Soil Pollut 200:277–288CrossRefGoogle Scholar
  32. Shaddick G, Yan H, Salway R, Vienneau D, Kounali D, Briggs D (2013) Large-scale bayesian spatial modelling of air pollution for policy support. J Appl Stat 40:777–794CrossRefMathSciNetGoogle Scholar
  33. Stedman J, Goodwin J, King K, Murrells T, Bush T (2001) An empirical model for predicting urban roadside nitrogen dioxide concentrations in UK. Atmos Environ 35:1451–1463CrossRefGoogle Scholar
  34. Stein M (2005) Space-time covariance functions. J Am Stat Assoc 469:310–320CrossRefGoogle Scholar
  35. Stone M (1974) Cross-validatory choice and assessment of statistical predictions. J R Stat Soc B 36:111–133MATHGoogle Scholar
  36. WHO (2003) Health aspects of air pollution with particulate matter, ozone and nitrogen dioxide. World Health Organization, GermanyGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Raquel Menezes
    • 1
  • Helena Piairo
    • 1
  • Pilar García-Soidán
    • 2
  • Inês Sousa
    • 1
  1. 1.Centre of MathematicsUniversity of MinhoGuimarãesPortugal
  2. 2.Department of Statistics and O.R.University of VigoPontevedraSpain

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