Spatio - temporal geostatistics using gstat

Since gstat package version 1.0-0, a dependency of gstat on the R package spacetime was introduced, allowing the code in gstat to exploit spatio-temporal data structures from that package. This vignette describes the possibilities and limitations of the package for spatio-temporal geostatistics. To understand some of the possibilities and limitations, some knowledge of the history of the software is needed. The original gstat software (Pebesma and Wesseling, 1998) was a standalone computer program written in around 25,000 lines of C code, and would do geostatistical modelling, prediction and simulation. The gstat R package (Pebesma, 2004) consisted mostly of an R interface to this C code, together with convenience functions to use R’s modelling interface (formula’s, see ?lm) and graphic capabilities (trellis graphics in package lattice to show cross variogram as matrix plots; interaction with variogram clouds using base plots). Starting 2003, a group of programmers developed a set of classes and methods for dealing with spatial data in R (points, lines, polygons, grids), which was supported by the publications of the well-known ASDAR book (Bivand et al. 2008; see also http://www.asdar-book.org/) and helped convergence in the user community, with in 2011 over 2000 subscribers on the r-sig-geo mailing list. Package gstat was one of the first packages that adopted and benefited from these classes. To realize a particular idea, writing code in C typically takes about 10-20 times as long as writing it in R. C code can be more efficient, gives more control over memory usage, but is also more error prone–mistakes in C code make an R session crash, something that is hard to do when writing R code. The original C code of gstat (Pebesma and Wesseling, 1998) provides all kriging varieties (universal, ordinary, simple; univariable, or multivariable as in cokriging) for twoor three-dimensional data. When the spatial domain is constrained to two dimensions (and this might cover over 99% of the use cases!), the third dimension might be used to represent time. As such, the metric variogram model, which allows for geometric anisotropy definition in three dimensions, can be used for spatio-temporal kriging. When defining the three-dimensional variogram as the sum of 2 or more nested variogram (summed)