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Download Error propagation in environmental modelling with GIS by Gerard B.M. Heuvelink PDF

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By Gerard B.M. Heuvelink

GIS clients and execs are conscious that the accuracy of GIS effects can't be naively in accordance with the standard of the graphical output. info kept in a GIS can have been accrued or measured, labeled, generalised, interpreted or anticipated, and in all situations this enables the advent of errors.; With the processing of translation of this knowledge into the GIS itself additional propagation or amplification or mistakes additionally happen. it's crucial that GIS execs comprehend those concerns systematically in the event that they are to construct ever extra exact systems.; during this publication the authors decade of research into those difficulties is introduced into concentration with an account of the improvement, software and implementation of mistakes propagation concepts to be used in environmental modelling with GIS. Its goal is to supply a technique for dealing with blunders and mistake propagation.

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One attractive method for generating realisations from a multivariate Gaussian distribution uses the Cholesky decomposition of the covariance matrix (Johnson, 1987; Ripley, 1987). ERROR PROPAGATION WITH LOCAL GIS OPERATIONS: THEORY 41 Accuracy of the Monte Carlo method Let the outcomes of N times running operation g(·) with the error-perturbed inputs be ui, i = 1, …, N. 17) The sample mean and sample variance are both unbiased and consistent estimators of ζ and τ2. Their variances are (Lewis and Orav, 1989, p.

4), it follows that negative error correlations must prevail. In fact, this result is quite conceivable, because when the error for sand is positive (when the real sand content is larger than the map value), then either silt or clay or both must make up for this, by taking on a lower value. Another example of correlated errors is taken from soil pollution by heavy metals, such as is the case in the river Geul valley, in the south of the Netherlands (Leenaers, 1991). Consider the concentration of lead and cadmium in the soil, maps of which are obtained from interpolating point observations.

Admittedly there always remains some subjectivity in the choice of a model of spatial variation (Matheron, 1989). However, given that the choice of model has such a profound influence on the resulting map and its error, one would like to avoid subjective decisions as much as possible. Perhaps a test such as proposed by Kitanidis (1997) may assist in reaching the ‘optimal’ model in a more objective fashion. CHAPTER FOUR Error propagation with local GIS operations: theory The purpose of this chapter is to trace the propagation of errors for one class of GIS operations, which have been identified in the first chapter by the name of local operations.

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