Error propagation modelling in raster GIS: Overlay operations

Performing data manipulations on maps that possess error as a result of the process of data collection leads to error propagation. The errors that are present in maps are modified by such operations in ways that may undermine the purpose of analysis and lead to increased uncertainty in the validity of the conclusions that are drawn. This paper analyses how source map error propagates as a result of overlay operations. Geman and Geman's corruption model for individual source map error is used for the analysis which allows for attribute measurement error and location error that can then interact with the (true) source map geography. This paper reports theoretical results on the univariate overlay problem and then extends these results through simulation. Throughout a set of source maps and error processes are used with specified properties in order to examine in detail the interactions that can take place between the different elements of the source map structure and the error process. The paper uses ANOVA methods to quantify the contribution made by different components of the map and the measurement process to spatial (join count) and non-spatial (proportion of misclassified pixels and the Kappa index) descriptors of error. The paper concludes with a discussion of the usefulness of these results for managing error in spatial databases and for the development of automated uncertainty reporting.