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Prediction of particle pollution through spatio-temporal multivariate geostatistical analysis: spatial special issue

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Abstract

Vehicular traffic, industrial activity and street dust are important sources of atmospheric particles, which cause pollution and serious health problems, including respiratory illness. Hence, techniques for analyzing and modeling the spatio-temporal behavior of particulate matter (PM), in the recent statistical literature, represent an essential support for environmental and human health protection. In this paper, air pollution from particles with diameters smaller than 10 \({\rm \mu}\)m and related meteorological variables, such as temperature and wind speed, measured during November 2009 in the south of Apulian region (Lecce, Brindisi, and Taranto districts) are studied. A thorough multivariate geostatistical analysis is proposed, where different tools for testing the symmetry assumption of the spatio-temporal linear coregionalization model (ST-LCM) are considered, as well as a recent fitting procedure of the ST-LCM, based on the simultaneous diagonalization of symmetric real-valued matrix variograms, is adopted and two non-separable classes of variogram models, the product–sum and Gneiting classes, are fitted to the basic components. The most significant aspects of this study are (a) the quantitative assessment of the assumption of symmetry of the ST-LCM, (b) the use of different non-separable spatio-temporal models for fitting the basic components of a ST-LCM and, more importantly, (c) the application of the spatio-temporal multivariate geostatistical analysis to predict particle pollution in one of the most polluted geographical area. Prediction maps for particle pollution levels with the corresponding validation results are given.

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References

  • Apanasovich, T.V., Genton, M.G.: Cross-covariance functions for multivariate random fields based on latent dimensions. Biometrika 97, 15–30 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Bevilacqua, M., Gaetan, C., Mateu, J., Porcu, M.: Estimating space and space-time covariance functions for large data sets: a weighted composite likelihood approach. J. Am. Statist. Assoc. 107(497), 268–280 (2012)

    Article  MathSciNet  Google Scholar 

  • Calder, C.A.: A dynamic process convolution approach to modeling ambient particulate matter concentrations. Environmetrics 19(1), 39–48 (2008)

    Article  MathSciNet  Google Scholar 

  • Cardoso, J.F., Souloumiac, A.: Jacobi angles for simultaneous diagonalization. SIAM J. Mat. Anal. Appl. 17, 161–164 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Choi, J., Fuentes, M., Reich, B.J., Davis, J.M.: Multivariate spatial-temporal modeling and prediction of speciated fine particles. J. Statist. Theory Practice 3(2), 407–418 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Cressie, N., Huang, H.: Classes of nonseparable, spatial-temporal stationary covariance functions. J. Am. Statist. Assoc. 94(448), 1330–1340 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  • Cocchi, D., Greco, F.P., Trivisano, C.: Displaced calibration of PM10 measurements using spatio-temporal models. Statistica. 66, 127–138 (2006)

    MathSciNet  MATH  Google Scholar 

  • Cocchi, D., Greco, F.P., Trivisano, C.: Hierarchical space-time modelling of PM10 pollution. Atmospheric Environment. 41, 532–541 (2007)

    Article  Google Scholar 

  • De Iaco, S., Myers, D.E., Posa, D.: Space-time analysis using a general product-sum model. Statist. and Probab. Lett. 52(1), 21–28 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  • De Iaco, S., Myers, D.E., Posa, D.: The linear coregionalization model and the product-sum space-time variogram. Math. Geol. 35(1), 25–38 (2003)

    Article  MathSciNet  Google Scholar 

  • De Iaco, S., Palma, M., Posa, D.: Modeling and prediction of multivariate space-time random fields. Comput. Statist. and Data Anal. 48, 525–547 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  • De Iaco, S., Myers, D.E., Palma, M., Posa, D.: FORTRAN programs for space-time multivariate modeling and prediction. Comput. & Geosc. 36(5), 636–646 (2010)

    Article  Google Scholar 

  • De Iaco, S., Myers, D.E., Posa, D.: Strict positive definiteness of a product of covariance functions. Commun. Stat. Theory Methods 40(24), 4400–4408 (2011a)

  • De Iaco, S., Myers, D.E., Posa, D.: On strict positive definiteness of product and product-sum covariance models. J. Stat. Plan Infer. 141, 1132–1140 (2011b)

  • De Iaco, S., Maggio, M., Palma, M., Posa, D.: Towards an automatic procedure for modeling multivariate space-time data. Comput. & Geosc. 41, 1–11 (2012)

    Article  Google Scholar 

  • Deutsch, C.V., Journel, A.G.: GSLib: Geostatistical Software Library and User’s Guide. Oxford Univ. Press, New York (1998)

    Google Scholar 

  • Dimitrakopoulos, R., Luo, X.: Spatiotemporal modeling: covariance and ordinary kriging systems. Geostatistics for the next century, Ed. Dimitrakopoulos, R., Kluwer Academic Publishers, 88–93 (1994)

  • Fassò, A., Finazzi, F.: Maximum likelihood estimation of the dynamic coregionalization model with heterotopic data. Environmentrics 22, 735–748 (2011)

    Google Scholar 

  • Fuentes, M., Song, H.R., Ghosh, S.K., Holland, D.M., Davis, J.M.: Spatial association between speciated fine particles and mortality. Biometrics 62, 855–863 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  • Gelfand, A.E., Schmidt, A.M., Banerjee, S., Sirmans, C.F.: Nonstationary multivariate process modeling through spatially varying coregionalization. Sociedad de Estadystica e Investigacion Opertiva Test 13, 263–312 (2004)

    MathSciNet  MATH  Google Scholar 

  • Gneiting, T.: Nonseparable, stationary covariance functions for space-time data. J. of the Am. Statist. Assoc. 97(458), 590–600 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Gneiting, T., Kleiber, W., Schlather, M.: Matérn cross-covariance functions for multivariate random fields. J. of the Am. Statist. Assoc. 105(491), 1167–1177 (2010)

    Article  MathSciNet  Google Scholar 

  • Goovaerts, P.: Geostatistics for natural resources evaluation, Oxford University Press (1997)

  • Gregori, P., Porcu, E., Mateu, J., Sasvari, Z.: On potentially negative space time covariances obtained as sum of products of marginal ones. Ann. of the Inst. of Stat. Math. 60, 865–882 (2008)

    Google Scholar 

  • Kibria, B.M.G., Sun, L., Zidek, J.V., Bayesian, N.D.: spatial prediction of random space-time fields with application to mapping \(PM_{2.5}\) exposure. Journal of the American Statistical Association 97(457), 112–124 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Kolovos, A., Christakos, G., Hristopulos, D.T., Serre, M.L.: Methods for Generating Non-separable Spatiotemporal Covariance Models With Potential Environmental Applications. Adv. in Water Resour. 27(8), 815–830 (2004)

    Article  Google Scholar 

  • Li, B., Genton, M.G., Sherman, M.: Testing the covariance structure of multivariate random fields. Biometrika 95(4), 813–829 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  • Ma, C.: Spatio-temporal covariance functions generated by mixtures. Math. Geol. 34, 965–975 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  • Myers, D.E.: Pseudo-cross variograms, positive-definiteness and cokriging. Math. Geol. 23, 805–816 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  • Paciorek, C.J., Yanosky, J.D., Puett, R.C., Laden, F., Suh, H.H.: Practical large-scale spatio-temporal modeling of particulate matter concentrations. The Annals of Applied Statistics 3(1), 370–397 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Porcu, E., Mateu, J., Saura, F.: New classes of covariance and spectral density functions for spatio-temporal modelling. Stoch. Environ. Res. and Risk Assess. 22(Suppl. 1), 65–79 (2008)

    Google Scholar 

  • Porcu, E., Zastavnyi, V.: Characterization theorems for some classes of covariance functions associated to vector valued random fields. J. of Mult. Anal. 102, 1293–1301 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  • Sahu, S.K., Nicolis, O.: An evaluation of European air pollution regulations for particulate matter monitored from a heterogeneous network. Environmetrics 20(8), 943–961 (2008)

    MathSciNet  Google Scholar 

  • Silva, C., Pérez, P., Trier, A.: Statistical modelling and prediction of atmospheric pollution by particulate material: two nonparametric approaches. Environmetrics 12(2), 147–159 (2001)

    Google Scholar 

  • Stein, M.: Space-time covariance functions. J. of the Am. Statist. Assoc. 100, 310–321 (2005)

    Article  MATH  Google Scholar 

  • Sun, L., Zidek, J.V., Le, N.D., Ozkaynak, H.: Interpolating Vancouver’s daily ambient \(PM_{10}\) field. Environmetrics 11, 651–663 (2000)

    Article  Google Scholar 

  • Thiebaux, H.J., Morone, L.L., Wobus, R.L.: Global forecast error correlation. Part 1: isobaric wind and geopotential. Monthly Weather Review 118, 2117–2137 (1990)

    Article  Google Scholar 

  • Ver Hoef, J.M., Cressie, N.: Multivariable spatial prediction. Mathematical Geology 25, 219–240 (1993)

    Google Scholar 

  • Wackernagel, H.: Multivariate Geostatistics. An Introduction with Applications, 3rd edn. Springer, Berlin (2003)

  • Zhang, H.: Maximum-likelihood estimation for multivariate spatial linear coregionalization models. Environmetrics 18, 125–139 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the Editor and the reviewers, whose comments contribute to improve the present version of the paper. The authors thank Donald E. Myers for his useful suggestions on the use of simultaneous diagonalization. This research has been partially supported by the 5per1000 project (grant given to the authors by the University of Salento in 2011).

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Authors and Affiliations

  1. Facoltà di Economia, Dip.to di Scienze Economiche e Matematico-Statistiche, Complesso Ecotekne, Università del Salento, Via per Monteroni, 73100 , Lecce, Italy

    S. De Iaco, M. Palma & D. Posa

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  1. S. De Iaco
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  2. M. Palma
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  3. D. Posa
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Correspondence to S. De Iaco.

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De Iaco, S., Palma, M. & Posa, D. Prediction of particle pollution through spatio-temporal multivariate geostatistical analysis: spatial special issue. AStA Adv Stat Anal 97, 133–150 (2013). https://doi.org/10.1007/s10182-012-0199-0

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  • DOI: https://doi.org/10.1007/s10182-012-0199-0

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