Abstract
We present an approach to estimate hourly grid-cell surface ozone concentrations based on observations from point monitoring sites in space, for comparison with grid-based results from the SARMAP photochemical air-quality model for a region of northern California. Statistical estimation is carried out on a transformed (square root) scale, followed by back-transforming to the original scale of ozone in parts per billion, adjusting for bias and variance. We estimate a spatially-varying diurnal mean structure and a non-separable space-time correlation structure on the transformed scale. Temporal pre-whitening is followed by modelling of a spatially non-stationary, diurnally-varying spatial correlation structure using a spatial deformation approach. Comparisons of SARMAP model results with the estimated grid-cell ozone levels are presented.
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Akima, H. (1978) A method of bivariate interpolation and smooth surface fitting for irregularly distributed data points. ACM Transactions on Mathematical Software, 4, 148-64.
Bennett, R.J. (1979) Spatial Time Services, Pion, London.
Blumenthal, D.L. (1993) Field program plan for the San Joaquin Valley air quality study (SJVAQS) and the atmospheric utility signatures, predictions and experiments (AUSPEX) program. Version 3, post-field revision. Report by Sonoma Technology, Inc. for the Valley Air Pollution Study Agency. STI-98020-1241-FR.
Box, G.E.P., Jenkins, G.M. and Reinsel, G.C. (1994) Time Series Analysis: Forecasting and Control 3rd ed., Prentice Hall.
Brown, P.J., Le, N.D. and Zidek, J.V. (1994) Multivariate spatial interpolation and exposure to air pollutants. Canadian Journal of Statistics, 22, 489-509.
Carroll, R.J., Chen, R., Li, T.H., Newton, H.J., Schmiediche, H., Wang, N. and George, E.L. (1997) Trends in ozone exposure in Harris County, Texas, Journal of the American Statistical Association, 92, 392-415 (with discussion).
Casado, L.S., Rouhani, S., Cardelino, C.A. and Ferrier, A.J. (1994) Geostatistical analysis and visualization of hourly ozone data. Atmospheric Environment, 28, 2105-18.
Cohn, S.E. and Parrish, D.F. (1991) The behavior of forecast error covariances for a Kalman filter in two dimensions. Monthly Weather Review, 119, 1757-85.
Cressie, N.A.C. (1993) Statistics for Spatial Data, rev., ed., Wiley-Interscience, John Wiley and Sons, Inc.
Cressie, N.A.C. (1997) Contribution to discussion of R.J. Carroll, R. Chen, T.H. Li, H.J. Newton, H. Schmiediche, N. Wang and E.I. George (1997): Trends in ozone exposure in Harris County, Texas. Journal of the American Statistical Association, 92, 411-3.
Dee, D.P. (1991) Simplification of the Kalman filter for meterological data assimilation. Quarterly Journal of the Royal Meteorological Society, 117, 365-84.
Goodall, C. and Mardia, K.V. (1994) Challenges in multivariate spatio-temporal modelling. Proceedings of the XVIIth International Biometric Conference, Hamilton, Ontario, Canada, 8-12 August 1994.
Guttorp, P., Le, N.D., Sampson, P.D. and Zidek, J.V. (1993a) Using entropy in the re-design of an environmental monitoring network. In Multivariate Environmental Statistics, G.P. Patil and C.R. Rao (eds), Elsevier Science Publishers. pp. 175-202.
Guttorp, P., Meiring, W., Newman, K. and Sampson, P.D. (1993b) A space-time model for acidic precipitation. Poster presentation at Joint Statistics Meetings, San Francisco.
Guttorp, P., Meiring, W. and Sampson, P.D. (1994) A space-time analysis of ground-level ozone data. Environmetrics, 5, 241-54.
Guttorp, P., Meiring, W. and Sampson, P.D. (1997) Contribution to discussion of R.J. Carroll, R. Chen, T.H. Li, H.J. Newton, H. Schmiediche, N. Wang and E.I. George (1997): Trends in ozone exposure in Harris County, Texas. Journal of the American Statistical Association, 92, 405-8.
Guttorp, P. and Sampson, P.D. (1994) Methods for estimating heterogeneous spatial covariance functions with environmental applications. In Handbook of Statistics XII: Environmental Statistics, G.P. Patil and C.R. Rao (eds), Elsevier/North Holland, New York. pp. 663-90.
Hóst, G., Omre, H. and Switzer, P. (1995) Spatial interpolation errors for monitoring data. Journal of the American Statistical Association, 90, 853-61.
Huang, H.-C. and Cressie, N.A.C. (1996) Spatio-temporal prediction of snow water equivalent using the Kalman filter. Computational Statistics and Data Analysis, 22, 159-75.
Jones, R.H. (1980) Maximum likelihood fitting of ARMA models to time series with missing observations. Technometrics, 22, 389-95.
Journel, A.G. and Huijbregts, C.J. (1978) Mining Geostatistics, Academic Press, New York.
Kendall, M. and Ord, J.K. (1990) Time Series, Oxford University Press.
Künsch, H.R. (1989) The jackknife and the bootstrap for general stationary observations. Annals of Statistics, 17, 1217-41.
Meiring, W. (1995) Estimation of heterogeneous space-time covariance. Ph.D. thesis, University of Washington.
Meiring, W., Monestiez, P., Sampson, P.D. and Guttorp, P. (1997) Developments in the modelling of nonstationary spatial covariance structure from space-time monitoring data. In Geostatistics Wollongong '96, vol. 1, E.Y. Baafi and N. Schofield (eds), Kluwer Academic Publishers. pp. 162-73.
National Research Council (1991) Rethinking the Ozone Problem in Urban and Regional Air Pollution, National Academy Press, Washington, D.C.
Oehlert, G.W. (1993) Regional trends in sulphate wet deposition. Journal of the American Statistical Association, 88, 390-9.
Rouhani, S. and Wackernagel, H. (1990) Multivariate geostatistical approach to space-time data analysis. Water Resources Research, 26, 585-91.
Sampson, P.D. and Guttorp, P. (1992) Nonparametric estimation of nonstationary spatial covariance structure. Journal of the American Statistical Association, 87, 108-19.
Sampson, P.D., Guttorp, P. and Meiring, W. (1994) Spatio-temporal analysis of regional ozone data for operational evaluation of an air quality model. 1994 Proceedings of the Section on Statistics and the Environment, American Statistical Association, American Statistical Association, Alexandria. pp. 46-55.
Smith, T.B. (1994) Ozone episode forecasting in the San Joaquin Valley. In Planning and Managing Air Quality Modeling and Measurement Studies: A Perspecitve through SJVAQS/AUSPEX, P.A. Solomon and T.A. Silver (eds), Lewis Publishers/Pacific Gas and Electric Company, Chelsea, MI pp. 507-27.
Solomon, P.A., and Silver, T.A. (eds) (1994) Planning and Managing Air Quality Modeling and Measurement Studies: A Perspective through SJVAQS/AUSPEX. Lewis Publishers/Pacific Gas and Electric Company, Chelsea, MI.
Statistical Sciences Inc. (1991) Splus Reference Manual, vol. 1.
Tiao, G.C. and Grupe, M.R. (1980) Hidden periodic autoregressive-moving average models in time series data. Biometrika, 67, 365-73.
Wahba, G. (1990) Spline Models for Observational Data Society for Industrial and Applied Mathematics, Philadelphia.
Wikle, C.K., Berliner, L.M. and Cressie, N.A.C. (1997) Hierarchical bayesian space-time models. Preprint No. 97-13, Statistical Laboratory, Iowa State University.
Wikle, C.K. and Cressie, N.A.C. (1996) A spatially descriptive, temporally dynamic statistical model with applications to atmospheric processes. In Spatio-temporal statistical models with applications to atmospheric processes, Ph.D. dissertation by C.K. Wikle, Dept. of Statistics, Dept. of Geological and Atmospheric Sciences, Iowa State University, Ames, IA. pp. 118-82.
Wikle, C.K. and Cressie, N.A.C. (1997) A dimension-reduction approach to space-time Kalman filtering. Preprint No. 97-24, Statistical Laboratory, Iowa State University.
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Meiring, W., Sampson, P.D. & Guttorp, P. Space-time estimation of grid-cell hourly ozone levels for assessment of a deterministic model. Environmental and Ecological Statistics 5, 197–222 (1998). https://doi.org/10.1023/A:1009663518685
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DOI: https://doi.org/10.1023/A:1009663518685