Describing dynamic modeling for landscapes with vector map algebra in GIS

A large class of applications that model physical processes use vector fields. This includes landscape processes that are naturally expressed using mathematics for two-dimensional vector fields. Geographical information systems (GIS) are a ubiquitous technology used not only for managing, analyzing and visualizing spatial data for landscapes, but also has the capability to perform landscape analysis and to compose models to address a wide range of problems. This paper proposes ways to extend data models in GIS to allow it to address an even wider range of problems that require the use of vector field representations and analysis operations. The paper describes a vector field data model, which relates well to the field data model commonly implemented in GIS using a raster data type, and demonstrates its application for landscape characterization and hydrological modeling in GIS. The main contribution of this paper is the definition of operations that are consistent with the theory for vector fields and may be implemented to manipulate rasters and multi-component rasters in GIS. The implementation describes a computational environment that supports writing models using primitive operations that are part of a vector map algebra (VMA) and for modeling dynamic changes to mapped landscapes over time.