Geostatistical modeling using the Gneiting's family of space-time covariance functions

Alexandre Sousa da SILVA[1]

Paulo Justiniano RIBEIRO JR[2]


§     ABSTRACT: The specification of space-time covariance functions is one of the possible strategies to model processes observed at different locations and time points. Such functions can define separable and non-separable processes and must fulfill the condition of positive-definiteness. Among the strategies to obtain such valid functions are the ones by Cressie and Huang based on inverse transforms of spectral representations and Gneiting, which allow constructions directly on the measurement domain. The former is based on the idea of obtaining valid functions in a space of increased dimension from valid functions on the primary dimension and requires operations in the frequency domain. Alternatively, the latter combines increasing monotone functions avoiding the inversion of spectral representations. There are still few reports of usage and comparisons of the strategies. This work follows Gneiting's proposal with different values for the space-time interaction parameter. Separable and non-separable models were investigated for the analysis of a real data set on soil water storage within a citrus field. The implementation on the R package RandomFields was used, with methodology and computational implementation being reviewed. For the data considered here the separable model provided a satisfactory fit, based on maximum likelihood estimation.

§     KEYWORDS: Covariance functions; geostatistics; space-time models, random fields; RandomFields Package.

[1]Departamento de Ciências Exatas, Escola Superior de Agricultura Luiz de Queiroz, Universidade de São Paulo – ESALQ/USP, CEP 13418-900, Piracicaba, SP, Brasil.  E-mail:

[2]Laboratório de Estatística e Geoinformação, Universidade Federal do Paraná – UFPR, CEP 81531-990, Curitiba, PR, Brasil. E-mail: