Linking a GIS to a spatially distributed, physically-based environmental model offers many advantages. However, the implementation of such linkages is generally problematic. Many problems arise because the relationship between the reality being represented by the mathematical model and the data model used to organize the spatial data in the GIS has not been rigorously defined. In particular, while many environmental models are based on theories that assume continuity and incorporate physical fields as independent variables, current GISs can only represent continuous phenomena in a variety of discrete data models. This document develops and outlines a strategy in which field variables are used to enable modelers to work directly with the spatial data as spatially continuous phenomena.

Several outcomes from the use of this strategy are explored. Modelers can express their spatial data needs as representations of reality, rather than as elements of a GIS database, and a GIS-independent language for model development results. By providing a formal linkage between the various models of spatial phenomena, a mechanism is created for the explicit expression of transformation rules between the models of spatial data stored and manipulated by GIS. The incorporation of field variables allows several operations (such as determining integrals, slope and aspect) and reserved variables (such as latitude and longitude) which are commonly used in environmental models to be defined. While scalar fields are the focus of this document, consideration of the potential for the definition of vector fields and related operations (such as divergence and gradient) using this strategy is also included.