This paper provides a new representation for fields (continuous surfaces) in Geographical Information Systems (GIS), based on the notion of spatial functions and their combinations. Following Tomlin’s (1990) Map Algebra, the term “Map Calculus” is used

between dynamic models and a standard raster-based GIS environment. PCRaster and its modelling language combine the information about the layer with the steps that created it. Within the framework of Map Calculus-enabled GIS, the model and the layer definition are tightly linked and thus maintained more rigorously.

Finally, the visualisation of Map Calculus-enabled GIS is more explicit. As detailed above, the proposed visualisation algorithm is tightly linked to the computer’s display properties and no generalisation occurs. In comparison, when a 10,000x10,000 cell raster is displayed in a common GIS, the system performs unsupervised and undocumented generalisations in order to fit the raster to the pixels on the screen. Although most users are satisfied with the performance of this generalisation, the proposed method is more straightforward and avoids such distortions.

When considering the two representations, special attention must be paid to analytical and visual resolutions. Analytical resolution is the resolution that is used during the analysis process as the computer calculates the raster or performs operations on a raster layer, while visual resolution is being used when displaying a raster layer on the

computer’s screen. With Map Calculus-enabled GIS, the concept of resolution becomes mainly a visual one, and the system can instruct the computer how to visualise various functions according to limitations or instructions that are integral to the specific

operation, as in the case of specific bandwidth in interpolations. When performing map-algebra operations with function-based layers, the analytical resolution does not change or alter. However, when operating on a raster layer, the issue of analytical resolution is highly important, as in the case of operating on two raster layers when each is defined with different cell resolution.

Finally, the issue of efficiency and computational complexity must be considered. At first, it seems clear that Map Calculus-enabled GIS are inherently more computationally intensive than traditional GIS. While this is true with regard to real time calculations, a closer examination of traditional representations demonstrates their batch processing origins and a certain wastage of computer resources. For the following analysis, a modern raster-based spatial analysis project is used (Thurstain-Goodwin & Unwin, 2000). This project relies on a composite model whereby multiple interpolated rasters, created using the KDE algorithm, are normalised and combined to create an integrated layer which is the outcome of the whole model. Within the resulting raster the user defines a specific threshold and the areas containing values that are higher than this threshold receive