Imprecision and Spatial Uncertainty
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acterize known uncertainties. Vagueness, imprecision, and inaccuracy all imply specific conceptual frameworks, ranging from fuzzy and rough sets to traditional theories of scientific measurement error, and whether or not it is implied that some true value exists in the real world that can be compared to the value stored in the database.
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Imprecision and Spatial Uncertainty M ICHAEL F. G OODCHILD Department of Geography, University of California Santa Barbara, Santa Barbara, CA, USA Synonyms Quality, spatial data; Accuracy, spatial; Accuracy, map; Error propagation Definition Spatial uncertainty is defined as the difference between the contents of a spatial database and the corresponding phenomena in the real world. Because all contents of spatial databases are representations of the real world, it is inevitable that differences will exist between them and the real phenomena that they purport to represent. Spatial databases are compiled by processes that include approximation, measurement error, and generalization through the omission of detail. Many spatial databases are based on definitions of terms, classes, and values that are vague, such that two observers may interpret them in different ways. All of these effects fall under the general term of spatial uncertainty, since they leave the user of a spatial database uncertain about what will be found in the real world. Numerous other terms are partially synonymous with spatial uncertainty. Data quality is often used in the context of metadata, and describes the measures and assessments that are intended by data producers to char-
Historical Background Very early interest in these topics can be found in the literature of stochastic geometry (Kendall, 1961), which applies concepts of probability theory to geometric structures. An early paper by Frolov and Maling (1969) analyzed the uncertainties present in finite-resolution raster representations, and derived confidence limits on measures such as area, motivated in part by the common practice of estimating measures of irregular patches by counting grid cells. Maling’s analysis established connections between the spatial resolution of the overlaid raster of cells and confidence limits on area estimates. Maling’s book (Maling, 1989) was a seminal venture into the application of statistical methods to maps, and helped to stimulate interest in the topic of spatial uncertainty. The growth of geographic information systems (GIS) provided the final impetus, and led to the first research initiative of the new US National Center for Geographic Information and Analysis in 1988, on the topic of accuracy in spatial databases (Goodchild and Gopal, 1989). The notion that spatial databases could be treated through the application of classical theories of measurement error soon
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