Map Calculus in GIS a proposal and demonstration(19)

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

integrated in different systems easily; they are non-volatile, and they have a clear spatial resolution. Functional representations are more precise; they contain their own metadata as well as model lineage explicitly, and directly associate the visualisation with the current display scale. Two aspects are more complex to compare: the issue of visual and

analytical resolution and the computational side of their implementations. In these topics, each implementation have some strengths in terms of efficiency and redundancy.

The first advantage of the raster representation is its generality, vividly demonstrated by Tomlin (1990). The same data structure, visualisation functionality, and storage mechanism is applicable to all forms of spatial analysis functions. Regardless of the complexity of the calculation, the output data structure and format is always the same. This makes the raster representation easy to manipulate and subsequent calculations, such as map-algebra operations, are not dependent on the functions that created the raster layers. As discussed earlier, a Map Calculus-enabled GIS must take into account the unique properties of the specific function during construction of the layer and during its visualisation and application. Yet, this is mainly an issue that is tackled during the programming of the GIS and not its use. Therefore, this aspect can be handled in a transparent way to the end-users and should not pose any difficulty or complexity for them.

Secondly, raster representations are non-volatile because they require the full

computation to be carried out only once. Once the calculation is completed, visualisation and manipulation of the layers is reduced to simple input-output (I/O) operations. This is probably the major drawback of function-based layers and possibly the reason that they were impractical until computer power had reached scales that made intensive computations possible and cheap. It must be noted that while it is impossible to

construct the function that created a raster from the raster itself, a user of Map Calculus-enabled GIS can create a raster at will and use this raster instead of the function.

Thirdly, in the process of creating raster layers the user is usually required to define the spatial resolution of the output layer. In some cases, this can be considered as an

advantage and forces the user to consider the nature of the spatial phenomena that the raster captures. Nevertheless, on many occasions the decision on raster resolution is arbitrary and, as higher resolutions lead to exponential growth in the size of the output raster, users tend to make concessions and choose the coarsest resolution that is relevant to their problem. Thus, the use of pixels as spatial units has significant theoretical and