Propagation of errors in spatial modelling with GIS

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Abstract
Methods are needed for monitoring the propagation of errors when spatial models are driven by quantitative data stored in raster geographical information systems. This paper demonstrates how the standard stochastic theory of error propagation can be extended and applied to continuously differentiable arithmetic operations (quantitative models) for manipulating gridded map data. The statistical methods have been programmed using the Taylor series expansion to approximate the models. Model inputs are (a) model coefficients and their standard errors and (b) maps of continuous variables and the associated prediction errors, which can be obtained by optimal interpolation from point data. The model output is a map that is accompanied by a map of prediction errors. The relative contributions of the errors in the inputs (model coefficients, maps of individual variables) can be determined and mapped separately allowing judgments to be made about subsequent survey optimization. The methods are illustrated by two case studies.