Map Calculus in GIS a proposal and demonstration(20)

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

practical implications (Fisher, 1997). In a Map Calculus-enabled GIS, the notion of resolution is meaningless, as the function can compute the values continuously across space. This removes the limitations on precision that are inherent in raster

representations – a function-based layer can be displayed at any required precision. For example, if the user zooms in to an area of 10x10 centimetres, the function is calculated on tiny cells, and thus provides a precise presentation which is impractical in a raster-based representation. It is wrong, of course, to claim that this makes function-based layers more accurate in all cases, although in some it will provide better accuracy. For example, when calculating absolute minima/maxima, or when calculating the average value of a field within a defined polygon, as Map Calculus-enabled GIS can calculate the value on the basis of an integral. On the other hand, there are classes of spatial functions that have some internal resolution. This is the case in raster implementation of Kernel Density Estimator function, where there is a link between the bandwidth and meaningful cell size. In such cases Map Calculus-enabled GIS can limit the spatial resolution that is displayed to the user, thus making this aspect explicit. For such classes of functions, Map Calculus-enabled GIS can store the spatial resolutions explicitly and use it when a function-based layer interacts with other layers.

As for function-based layers, they have several advantages. First, the presentation is clearer – throughout the life cycle of the layer, the user can interrogate it and view the function that was used to define it as well as its values and parameters. This explicit presentation makes the nature of the layer clearer to the user and removes ambiguities that exist with raster layers where the function and the parameters that created it are usually implicit or, at best, stored in a separated file if the user maintains a highly

organised log. This aspect is directly linked to the second advantage of function-based layers – the integrated metadata and model lineage. Due to the interconnectedness of function-based layers and the way in which high-order layers rely on lower level ones, the relationships amongst layers are stored as a practical requirement of GIS management functionality. Within the area of raster-based models, a decade passed between the suggestion of a graphical representation of the modelling process (Berry, 1993a) and its implementation in packages such as Idrisi , ArcView or Erdas Imagine (see Bruns & Egenhofer, 1997 for a review of Map Algebra interfaces). Even within these

implementations, there is no direct link between the model and the output layer and they mainly geared towards general documentation and process management. It must be noted, as Van Deursen (1995) demonstrated, that it is possible to provide a tighter link