Propagation of errors in spatial modelling with GIS

One of the most powerful capabilities of GIS, particularly for the earth and environmental sciences, is that it permits the derivation of new attributes from attributes already held in the GIS database. For example, elevation data in the form of a digital elevation model (DEM) can be used to derive maps of gradient and aspect (Hutchinson and Gallant, Chapter 9); or digital maps of soil type and gradient can be combined with information about soil fertility and moisture supply to yield maps of suitability for growing maize (Burrough 1986). The many basic types of function used for derivations of this kind are often provided as standard functions or operations in many GIS, under the name of ‘map algebra’ (Burrough 1986; Tomlin 1990). In practice, many GIS operations are used in sequence in order to compute an attribute that is the result of a (computational) model. For instance, the channel flow at the outlet of a watershed can be computed after the relevant hydrological processes have been translated into mathematical equations, thus after reality has been approximated by a suitable computational model. Using GIS for the evaluation of computational models is identified here by the term spatial modelling within GIS. To date, most work on spatial modelling with GIS has been concentrated on the business of deriving computational models that operate on spatial data, on the building of large spatial databases, and on linking computational models with the GIS. However, there is an important additional aspect that has long received too little attention. This concerns the issue of data quality and how errors in spatial attributes propagate through GIS operations.