Encyclopedia of GIS

Living Edition
| Editors: Shashi Shekhar, Hui Xiong, Xun Zhou

Space-Time Geostatistics

  • Gerard B. M. Heuvelink
  • Edzer Pebesma
  • Benedikt Gräler
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-23519-6_1647-1

Definition

Space-time geostatistics is concerned with the statistical modeling of environmental variables that vary in space as well as in time. It is an extension of conventional geostatistics, which only considers spatial variation. Common geostatistical concepts, such as the variogram, kriging, stochastic simulation, and sampling design optimization, have a natural extension in the space-time domain, although extra effort is required to model the joint variation in space and time effectively and realistically. The space-time variogram will have spatial and temporal components which may be very different because variation in space is not the same as variation in time. Space-time kriging takes these differences into account and yields optimal predictions at any point in the space-time domain of interest. The interpolation results can be displayed as a series or animations of spatial maps over time or as time series of predictions at as many spatial points as desired.

Space-time...

Keywords

Spatiotemporal Data Spatiotemporal Covariance Kriging With External Drift Sample Variogram Variogram Estimation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. Bakar KS, Sahu SK (2015) spTimer: spatio-temporal bayesian modelling using R. J Stat Softw 63:1–32CrossRefGoogle Scholar
  2. Bardossy A, Pegram GGS (2009) Copula based multisite model for daily precipitation simulation. Hydrol Earth Syst Sci 13:2299–2314CrossRefGoogle Scholar
  3. Brus DJ, Heuvelink GBM (2007) Optimization of sample patterns for universal kriging of environmental variables. Geoderma 138:86–95CrossRefGoogle Scholar
  4. Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, HobokenMATHGoogle Scholar
  5. De Cesare L, Myers DE, Posa D (2001) Estimating and modeling space-time correlation structures. Stat Probab Lett 51:9–14MathSciNetCrossRefMATHGoogle Scholar
  6. De Cesare L, Myers DE, Posa D (2001) Product-sum covariance for space-time modeling: an environmental application. Environmetrics 12:11–23CrossRefGoogle Scholar
  7. Erhardt TM, Czado C, Schepsmeier U (2015) R-vine models for spatial time series with an application to daily mean temperature. Biometrics 71:323–332MathSciNetCrossRefMATHGoogle Scholar
  8. Fuentes M, Chen L, Davis JM (2008) A class of nonseparable and nonstationary spatial temporal covariance functions. Environmetrics 19:487–507MathSciNetCrossRefGoogle Scholar
  9. Gasch CK, Hengl T, Gräler B, Meyer H, Magney TS, Brown DJ (2015) Spatio-temporal interpolation of soil water, temperature, and electrical conductivity in 3D+T: The Cook Agronomy Farm data set. Spat Stat 14:70–90MathSciNetCrossRefGoogle Scholar
  10. Gething PW, Noor AM, Goodman CA, Gikandi PW, Hay SI, Sharif SK, Atkinson PM, Snow RW (2007) Information for decision making from imperfect national data: tracking major changes in health care use in kenya using geostatistics. BMC Med 5:37CrossRefGoogle Scholar
  11. Gneiting T (2002) Nonseparable, stationary covariance functions for space-time data. J Am Stat Assoc 97:590–600MathSciNetCrossRefMATHGoogle Scholar
  12. Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New YorkGoogle Scholar
  13. Gräler B (2014) Modelling skewed spatial random fields through the spatial vine copula. Spat Stat 10:87–102MathSciNetCrossRefGoogle Scholar
  14. Gräler B, Pebesma E, Heuvelink GBM (2016, in review) Spatio-temporal interpolation using gstat. R JournalGoogle Scholar
  15. Heuvelink GBM, Griffith DA (2010) Space-time geostatistics for geography: a case study of radiation monitoring across parts of Germany. Geogr Anal 42:161–179CrossRefGoogle Scholar
  16. Heuvelink GBM, van Egmond FM (2010) Space-time geostatistics for precision agriculture: a case study of NDVI mappping for a dutch potato field. In: Oliver MA (ed) Geostatistical applications for precision agriculture. Springer, Dordrecht/New York, pp 117–137CrossRefGoogle Scholar
  17. Johannesson G, Cressie N, Huang H-C (2007) Dynamic multi-resolution spatial models. Environ Ecol Stat 14:5–25MathSciNetCrossRefGoogle Scholar
  18. Jost G, Heuvelink GBM, Papritz A (2005) Analysing the space-time distribution of soil water storage of a forest ecosystem using spatio-temporal kriging. Geoderma 128:258–273CrossRefGoogle Scholar
  19. Kilibarda M, Hengl T, Heuvelink GBM, Gräler B, Pebesma E, Perčec Tadić M, Bajat B (2014) Spatio-temporal interpolation of daily temperatures for global land areas at 1 km resolution. J Geophys Res Atmos 119:2294–2313Google Scholar
  20. Kyriakidis PC, Journel AG (1999) Geostatistical space-time models: a review. Math Geol 31:651–684MathSciNetCrossRefMATHGoogle Scholar
  21. Lindgren F, Rue H, Lindstrőm J (2011) An explicit link between gaussian random fields and gaussian markov random fields: the stochastic partial differential equation approach. J R Stat Soc B 73:423–498MathSciNetCrossRefMATHGoogle Scholar
  22. Mugglin AS, Cressie N, Gemmell I (2002) Hierarchical statistical modelling of influenza epidemic dynamics in space and time. Stat Med 21:2703–2721CrossRefGoogle Scholar
  23. Pebesma E (2012) spacetime: spatio-temporal data in R. J Stat Softw 51:1–30CrossRefGoogle Scholar
  24. Pebesma EJ (2004) Multivariable geostatistics in S: the gstat package. Comput Geosci 30:683–691CrossRefGoogle Scholar
  25. Porcu E, Gregori P, Mateu J (2006) Nonseparable stationary anisotropic space–time covariance functions. Stoch Environ Res Risk Assess 21:113–122MathSciNetCrossRefGoogle Scholar
  26. R Core Team (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, ViennaGoogle Scholar
  27. Schlather M, Malinowski A, Menck PJ, Oesting M, Strokorb K (2015) Analysis, simulation and prediction of multivariate random fields with package randomfields. J Stat Softw 63:1–25CrossRefGoogle Scholar
  28. Sigrist F, Künsch HR, Stahel WA (2015) Spate: an R package for spatio-temporal modeling with a stochastic advection-diffusion process. J Stat Softw 63:1–23CrossRefGoogle Scholar
  29. Snepvangers JJJC, Heuvelink GBM, Huisman JA (2003) Soil water content interpolation using spatio-temporal kriging with external drift. Geoderma 112:253–271CrossRefGoogle Scholar
  30. Stein A, Kocks CG, Zadoks JC, Frinking HD, Ruissen MA, Myers DE (1994) A geostatistical analysis of the spatio-temporal development of downy mildew epidemics in cabbage. Ecol Epidemiol 84:1227–1239Google Scholar
  31. Stein ML (2005) Space-time covariance functions. J Am Stat Assoc 100:310–321MathSciNetCrossRefMATHGoogle Scholar
  32. Torabi M Spatiotemporal modeling of odds of disease. Environmetrics 25:341–350 (2014)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Gerard B. M. Heuvelink
    • 1
  • Edzer Pebesma
    • 2
  • Benedikt Gräler
    • 3
  1. 1.Environmental Sciences GroupWageningen UniversityWageningenNetherlands
  2. 2.Institute for GeoinformaticsUniversity of MünsterMünsterGermany
  3. 3.Institute of HydrologyRuhr University BochumBochumGermany