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A simple spatio-temporal procedure for the prediction of air pollution levels
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A simple spatio-temporal procedure for the prediction of air pollution levels Jorge M. Mendes 1 and Kamil F. Turkman 2 * 1 Higher Institute of Statistics and Information Management, New University of Lisbon, Lisbon, Portugal 2 CEAUL Faculty of Sciences, University of Lisbon, Lisbon, Portugal Received 12 February 2001; Revised 3 September 2002; Accepted 3 October 2002 In this paper we study the spatio-temporal behaviour of air pollutants measured daily over the city of Lisbon, Portugal. Our specific aim is to predict air pollutant levels in time and space over a fine grid of locations based on observations from a small number of monitoring sites. Our suggested prediction procedure is based on the simple and intuitive idea of first making predictions in time at the monitoring sites and then extending these predictions in space to locations other than the monitoring sites using kriging methods. Copyright # 2002 John Wiley & Sons, Ltd. KEYWORDS: spatio-temporal models; kriging; multivariate time series 1. INTRODUCTION The city of Lisbon is the biggest urban area in Portugal. It is located by the estuary of the river Tagus at 38 °44' N, 9 °8' W. Its total area is 84 km 2 , corresponding to a population density of 7.272 inhabitants per km 2 . Owing to its location on the Atlantic coast and the north winds that often blow over the city, high concentrations of pollutants are rare. However, under adverse meteorological conditions, weak winds and thermic inversions, especially in autumn and winter, high concentrations of pollutants can occur. Cars and public transportation are the main source of atmospheric pollution in the city. Emissions from industrial facilities do not have a great influence, since over the last few years the main industries have been deactivated. At present the monitoring network is composed of eight monitoring stations, but there are plans to expand the network to 14 stations. Several pollutants are monitored over the network, such as carbon monoxide (CO), nitrogen oxides (NO and NO 2 ), sulphur dioxide (SO 2 ), nitrogen O 3 and particulate matter (PM 10 ). Owing to the relative importance of traffic emissions, three of these pollutants, CO, NO and NO 2 , are monitored at all eight stations. The spatial distribution of the network was set up by empirical guidelines. Because of the expected high pollutant concentration levels, locations with a high intensity of traffic and a high density of pedestrians were chosen, as well as the eastern residential areas of the city where, until some years ago, the major industries were concentrated. Figures 1 and 2 show the geographical distribution of the eight monitoring stations over a map of Lisbon. At each monitoring station, air samples are collected continuously. Several devices then analyse the sample, and the concentration level of each pollutant is determined based on optical characteristics of the air sample. Electrical signals are generated and converted to numerical values that are sent, by a phone line, to a central computer where the data are validated and processed. In this paper our objective is to study the spatio-temporal Figure 1. The air quality monitoring network in Lisbon. *Correspondence to: K. F. Turkman, DEIO, Faculdade de Ciencias, Bloco C2, Campo Grande, P-1749-016 Lisboa, Portugal. E-mail: [email protected] Contract/grant sponsor: Portuguese Science Foundation (FCT); Con- tract/grant number: PRAXIS/P/1001/98. Copyright # 2002 John Wiley & Sons, Ltd. JOURNAL OF CHEMOMETRICS J. Chemometrics 2002; 16: 623±632 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/cem.766
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Figure 3. Daily mean concentration (log-transformed) of NO2 in Lisbon from 1/1/94 to 31/12/98: (a)–(h) s1 (Olivais), s2
(Entrecampos), s3 (Beato), s4 (Chelas), s5 (Rua da Prata), s6 (Casal Ribeiro), s7 (Benfica) and s8 (Av. Liberdade).
Figure 4. Daily mean concentration (log-transformed) of NO2 in Lisbon from 1/1/94 to 31/12/98 after filling in missingobservations: (a)–(h) s1 (Olivais), s2 (Entrecampos), s3 (Beato), s4 (Chelas), s5 (Rua da Prata), s6 (Casal Ribeiro), s7
(Benfica) and s8 (Av. Liberdade).
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Figure 5. (a) Spatial configuration in G-plane: s1 (Olivais), s2 (Entrecampos), s3 (Beato),s4 (Chelas), s5 (Rua da Prata), s6 (Casal Ribeiro) and s8 (Av. Liberdade). (b) Spatialdispersion versus geographical interpoint distance.
Table I. Observed spatial dispersion for the seven air qualitymonitoring stations
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Figure 6. (a) Spatial configuration in D-plane: s1 (Olivais), s2 (Entrecampos), s3 (Beato),s4 (Chelas), s5 (Rua da Prata), s6 (Casal Ribeiro) and s8 (Av. Liberdade). (b) Spatialdispersion versus MSI distance. The curve represents the exponential semivariogramfitted to the MSI distance.
Table II. Estimated thin plate splines
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Figure 7. Selected area for modelling and prediction.
Figure 8. One-step-ahead spatio-temporal predictions for thewhole grid for t = 731.
Table III. One-step-ahead spatio-temporal predictions and actualvalues of daily mean concentration (log-transformed) of NO2 for
s1 (Olivais) and s5 (Rua da Prata)
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Figure 9. One-step-ahead spatio-temporal predictions, confidence intervalsand actual values of daily mean concentration (log-transformed) of NO2 for s1
(Olivais) and s5 (Rua da Prata).
Table IV. Summary of prediction results for leave-two-outvalidation
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