Abstract
Data from remote-sensing platforms play an important role in monitoring environmental processes, such as the distribution of stratospheric ozone. Remote-sense data are typically spatial, temporal, and massive. Existing prediction methods such as kriging are computationally infeasible. The multi-resolution spatial model (MRSM) captures nonstationary spatial dependence and produces fast optimal estimates using a change-of-resolution Kalman filter. However, past data can provide valuable information about the current status of the process being investigated. In this article, we incorporate the temporal dependence into the process by developing a dynamic MRSM. An application of the dynamic MRSM to a month of daily total column ozone data is presented, and on a given day the results of posterior inference are compared to those for the spatial-only MRSM. It is apparent that there are advantages to using the dynamic MRSM in regions where data are missing, such as when a whole swath of satellite data is missing.
Similar content being viewed by others
References
Agresti A (1990) Categorical data analysis. Wiley, New York
Berliner LM, Wikle CK, Cressie N (2000) Long-lead prediction of Pacific SSTs via Bayesian dynamic modeling. J Clim 13:3953–3968
Brown PE, Karesen KF, Roberts GO, Tonellato S (2000) Blur-generated nonseparable space–time models. J R Stat Soc Ser B 62:847–860
Calder C, Holloman C, Higdon D (2002) Exploring space–time structure in ozone concentration using a dynamic process convolution model. In: Gatsonis C, Kass RE, Carriquiry A, Gelman A, Higdon D, Pauler DK, Verdinelli I (eds) Case studies in Bayesian statistics 6. Springer-Verlag, New York, pp 165–176
Cane MA, Kaplan A, Miller RN, Tang B, Hackert EC, Busalacchi AJ (1996) Mapping tropical Pacific sea level: data assimilation via reduced state space Kalman filter. J Geophys Res 101:22599–22617
Carroll R, Chen R, George E, Li T, Newton H, Schmiediche H, Wang N (1997) Ozone exposure and population density in Harris county, Texas (with discussion). J Am Stat Assoc 92:392–415
Chou KC, Willsky AS, Nikoukhah R (1994) Multiscale systems, Kalman filters, and Riccati equations. IEEE Trans Autom Control. 39:479–492
Cressie N (1993) Statistics for spatial data (revised edition). Wiley, New York
Cressie N (1994) Comment on “An approach to statistical spatial-temporal modeling of meteorological fields” by M.S. Handcock and J.R. Wallis. J Am Stat Assoc 89:379–382
Cressie N (2002) Variogram estimation. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics, vol 4. Wiley, New York, pp 2316–2321
Cressie N, Huang H-C (1999) Classes of nonseparable, spatio-temporal stationary covariance functions. J Am Stat Assoc 94:1330–1340
Cressie N, Wikle CK (2002) Space–time Kalman filter. In: El-Shaarawi AH, Piegorsch WW (eds) Encyclopedia of environmetrics, vol. 4. Wiley, New York, pp 2045–2049
de Iaco S, Myers DE, Posa D (2001) Space–time analysis using a general product-sum model. Stat Probab Lett 52:21–28
Gelfand AE, Ghosh S, Knight J, Sirmans C (1998) Spatio-temporal modeling of residual sales data. J Bus Econ Stat 16:312–321
Gelpke V, Künsch HR (2001) Estimation of motion from sequences of images. In: Moore M (ed) Spatial statistics: methodological aspects and applications. Springer lecture notes in statistics, vol 159. Springer-Verlag, New York, pp 141–167
Gneiting T (2002) Nonseparable, stationary covariance functions for space–time data. J Am Stat Assoc 97:590–600
Guttorp P, Sampson PD, Newman K (1992) Nonparametric estimation of spatial covariance with application to monitoring network evaluation. In: Walden A, Guttorp P (eds) Statistics in environmental and earth sciences. Edward Arnold, London, pp 39–51
Handcock MS, Wallis JR (1994) An approach to statistical spatial-temporal modeling of meteorological fields. J Am Stat Assoc 89:368–378
Hartfield MI, Gunst RF (2003) Identification of model components for a class of continuous spatiotemporal models. J Agric Biol Environ Stat 8:105–121
Harville DA (1997) Matrix algebra from a statistician’s perspective. Springer-Verlag, New York
Haslett J, Raftery AE (1989) Space–time modeling with long-memory dependence: assessing ireland’s wind power resource. Appl Stat 38:1–21
Huang H-C (1997) Spatial modeling using graphical Markov models and wavelets. Ph.D. thesis, Department of Statistics, Iowa State University
Huang H-C, Cressie N (1996) Spatio-temporal prediction of snow water equivalent using the Kalman filter. Comput Stat Data Anal 22:159–175
Huang H-C, Cressie N (2001) Multiscale graphical modeling in space: applications to command and control. In: Moore M (ed) Spatial statistics: methodological aspects and some applications. Springer lecture notes in statistics, vol 159. Springer-Verlag, New York, pp 83–113
Huang H-C, Hsu N-J (2004) Modeling transport effects on ground-level ozone using a non-stationary space–time model. Environmetrics 15:251–268
Huang H-C, Cressie N, Gabrosek J (2002) Fast, resolution-consistent spatial prediction of global processes from satellite data. J Comput Graph Stat 11:63–88
Huerta G, Sanso B, Stroud JR (2004) A spatio-temporal model for Mexico City ozone levels. Appl Stat 53:231–248
Johannesson G (2003) Multi-resolution statistical modeling in space and time with application to remote sensing of the environment. Ph.D. thesis, Department of Statistics, The Ohio State University
Johannesson G, Cressie N (2004) Variance-covariance modeling and estimation for multi-resolution spatial models. In: Sanchez-Vila X, Carrera J, Gómez-Hernández J (eds) geoENV IV - geostatistics for environmental applications. Kluwer Academic Publishers, Dordrecht, Netherlands, pp 319–330
Jones RH, Zhang Y (1997) Models for continuous stationary space-time processes. In: Gregoire TG et al. (eds) Modelling longitudinal and spatially correlated data. Springer lecture notes in statistics, vol 122. Springer-Verlag, New York, pp 289–298
Kolaczyk ED, Huang H (2001) Multiscale statistical models for hierarchical spatial aggregation. Geogr Anal 33:95–118
Kyriakidis PC, Journel AG (1999) Geostatistical space-time models: a review. Math Geol 31:651–684
Mardia K, Goodall C, Redfern E, Alonso F (1998) The kriged Kalman filter (with discussion). Test 7:217–285
McCulloch CE, Searle SR (2001) Generalized, linear, and mixed models. Wiley, New York
Meiring W, Guttorp P, Sampson PD (1998) Space–time estimation of grid-cell hourly ozone levels for assessment of a deterministic model. Environ Ecol Stat 5:197–222
Stein M (2005) Space–time covariance functions. J Am Stat Assoc 100:310–321
Stroud JR, Müller P, Sansó, B (2001) Dynamic models for spatiotemporal data. J R Stat Soc Ser B 63:673–689
Wahba G (1990) Spline models for observational data. Society for Industrial and Applied Mathematics, Philadelphia, PA
Waller L, Carlin B, Xia H, Gelfand A (1997) Hierarchical spatio-temporal mapping of disease rates. J Am Stat Assoc 92:607–617
Wikle CK, Cressie N (1999) A dimension-reduced approach to space-time Kalman filtering. Biometrika 86:815–829
Wikle CK, Berliner M, Cressie N (1998) Hierarchical Bayesian space–time models. Environ Ecol Stat 5:117–154
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Johannesson, G., Cressie, N. & Huang, HC. Dynamic multi-resolution spatial models. Environ Ecol Stat 14, 5–25 (2007). https://doi.org/10.1007/s10651-006-0005-9
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10651-006-0005-9