ABSTRACT
Many ecological data sets include not only a spatial but also a temporal component. Data may be collected in an agricultural field trial over a period of years in the same field. An uncultivated ecosystem may be monitored over an extended period of time. Both of these processes lead to spatiotemporal data sets. In this chapter, we discuss methods for dealing with data that contain both spatial and temporal components. The theory for spatiotemporal data is much less well developed than that for dealing with purely spatial or purely temporal data, and the contents of this chapter are somewhat ad hoc in nature. Perhaps unsurprisingly, this is also one of the most active areas of research, and one of the most dynamic, both in the development of the theory and in the development of analytical methods and software. The development of the theory took a major step forward with the publication of the book by Cressie and Wikle (2011). As Gräler et al. (2016) point out, however, the implementation of the theory has lagged behind. For this reason, the chapter consists of a diverse selection of methods that attempt to put some of the material discussed by Cressie and Wikle (2011) into the context of the data used in this book. Section 15.2 deals with spatiotemporal variograms and kriging, that is, the interpolation of spatial quantities in both space and time. Section 15.3 introduces the concept of spatiotemporal process models derived from physicochemical models for diffusion-reaction processes. Section 15.4 introduces discrete time approximations to spatiotemporal processes, sometimes called “state and transition models.” Finally, Section 15.5 describes a Bayesian approach to the analysis of spatiotemporal processes.
