Abstract
Modeling of spatio-temporal processes is critical in many fields such as environmental sciences, meteorology, hydrology and reservoir engineering. The variogram is an important correlation measure in geostatistics and a useful tool for spatial or spatio-temporal modeling. Although many space-time covariance/variogram models are available, in practice,the generalized product-sum model is most widely used. The theoretical aspects of the generalized product-sum variogram model have been presented in other papers. However, the dissemination of software that brings the generalized product-sum variogram model to a wider group of users is undoubtedly desirable. In this paper, we describe an R routine for “spatio-temporal kriging” with hole effects, and appropriate space-time search neighborhoods. An application to ozone pollutants in an area of five counties of the US is presented. The experimental results show that the spatio-temporal random field provides more information than the purely spatial random field, because the accuracy of interpolation has been improved.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Christakos G, Vyas VM (1998) A composite space-time approach to studying zone distribution over eastern United States. Atmos Environ 32(16):2845–2857
Cressie N, Huang H (1999) Classes of nonseparable, spatio-temporal stationary covariance functions. J Am Stat Assoc 94(448):1330–1340
Cressie N, Wikle CK (2011) Statistics for spatio-temporal data. Wiley, New York
Deutsch CV, Journel AG (1998) GSLIB: geostatistical software library and user’s guide, 2nd edn. Oxford University Press, New York & Oxford, pp 63–94
De Cesare L, Myers DE, Posa D (1997) Geostatistics Wollongong’96. Kluwer Academic Publishers, Dordrecht, pp 1031–1042
De Cesare L, Myers DE, Posa D (2001a) Estimating and modeling space-time correlation structures. Stat Probablility Lett 51(1):9–14
De Cesare L, Myers DE, Posa D (2001b) Product-sum covariance for space-time modeling-an environmental application. Environmetrics:12
De Cesare L, Myers DE, Posa D (2002) Fortran programs for space-time modeling. Comput Geosci:28
De Iaco S, Myers DE, Posa D (2001) Space-time analysis using a general product-sum model. Stat Probablility Lett:21–28
De Iaco S, Myers D, Posa D (2002) Nonseparable space-time covariance models: some parametric families. Math Geol 34(1):23–41
De Iaco S, Myers DE, Posa D (2003) The linear coregionalization model and the product-sum space-time variogram. Math Geol 35(No.1):25–38
De Iaco S, Posa D (2012) Predicting spatio-temporal random fields: some computational aspects. Comput Geosci 41:12–24
De Iaco S, Posa D (2013) Positive and negative non-separability for spacectime covariance models. J Stat Plan Infer 143(2):378–391
De Iaco S, Maggio S, Palma M, Posa D (2012) Towards an automatic procedure for modeling multivariate spacectime data. Comput Geosci 41:1–11
De Iaco S, Posa D, Myers DE (2013) Characteristics of some classes of spacectime covariance functions. J Stat Plan Infer 143(11):2002–2015
Edzer P (2012) Spacetime:space-temporal data in r. J Stat Softw 51 (7)
Gneiting T (2002) Nonseparable, stationary covariance functions for space-time data. J Am Stat Assoc 97(458):590–600
Kyriakidis PC, Journel AG (1999) Geostatistical space-time models: a review. Math Geol 31(6):651–684
Ma C (2002) Spatio-temporal covariance functions generated by mixtures. Math Geol 34(8):965–975
Ma C (2003) Families of spatio-temporal stationary covariance models. J Stat Plan Infer 116:489–501
Oliver MA, Webster R (2007) Geostatistics for environmental scientists. John Wiley & Sons, Chichester
Oliver MA, Webster R (2014) A tutorial guide to geostatistics: computing and modelling variograms and kriging. Catena 113:56–69
Pyrcz MJ, Deutsch CV (2003) The whole story on the hole effect. In: Searston S (ed) Technical report, Association of Australasia, newsletter
Rouhani S, Myers DE (1990) Problem in space-time kriging of geohydrological data. Math Geol 22(5):611–623
Stein ML (2005) Space-time covariance functions. J Am Stat Assoc:469
Acknowledgments
Jointly supported by the State Key Program of National Natural Science of China (No. 41331175), the National Natural Science Foundation of China (No. 41171313), the Hubei Provincial Natural Science Foundation of China (No. 2014CFB725/ZRY2014000982), and the Suzhou Science and Technology Program of Applied Basic Research (No. SYG201319).
Author information
Authors and Affiliations
Corresponding authors
Additional information
Communicated by: H. A. Babaie
Rights and permissions
About this article
Cite this article
Xu, J., Shu, H. Spatio-temporal kriging based on the product-sum model: some computational aspects. Earth Sci Inform 8, 639–648 (2015). https://doi.org/10.1007/s12145-014-0195-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12145-014-0195-x