GIS were originally designed for static analyses. The typical approach to spatial dynamic modeling of chemical fate and transport is that data are taken from GIS but processed through dedicated software. There are at least two remarkable exceptions to this approach: the dynamic GIS environment PCRaster and the modeling technique known as cellular automata. In this chapter we introduce the general idea behind these two cases. In addition, map algebra allows for directly including some limited time-dependent modeling of chemical fate and transport in the environment. Last but not least, the spatial capabilities of GIS can be exploited in a decoupled spatial/temporal modeling strategy as implemented in the MAPPE Global model, which is briefly discussed at the end of the chapter.
Map algebraic functions, neighborhood and other statistical operators, cost distances, and hydrologic functions in GIS are static operators; that is, an output map is computed as a function of input maps that are fixed in time. Dynamic cartographic modeling consists of computing an output map at a given time step, as a function of input at that time step, and the output map at the previous time step.
PCRaster  is a GIS designed to include functionalities beyond static operations, thanks to its unique capability of dynamic cartographic modeling:
In a dynamic model, for each timestep a series of […] operations is consecutively performed ...