The Accuracy of Spatial Databases The Accuracy of Spatial Databases Edited by Michael Goodchild and Sucharita Gopal National Center for Geographic Information & Analysis University of California Santa Barbara, CA 93106 Taylor & Francis London · New York · Philadelphia UK Taylor & Francis Ltd, 4 John Street, London WC1N 2ET USA Taylor & Francis Inc, 1900 Frost Road, Suite 101, Bristol, PA 19007 This edition published in the Taylor & Francis e-Library, 2005. ªTo purchase your own copy of this or any of Taylor & Francis or Routledge's collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.º Copyright © Taylor & Francis Ltd 1989 Reprinted 1992, 1994 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, electrostatic, magnetic tape, mechanical, photocopying, recording or otherwise, without prior permission of the publishers. British Library Cataloguing in Publication Data Goodchild, Michael F The accuracy of spatial databases. 1. Geography. Information systems. Machine-readable files I. Title 910'.28'5574 ISBN 0-203-49023-1 Master e-book ISBN ISBN 0-203-79847-3 (Adobe eReader Format) ISBN 0-85066-847-6 (Print Edition) Library of Congress Cataloguing in Publication Data is available Contents List of figures vi List of tables viii Preface ix Contributors xiii Section I 1 1. Error modeling for the map overlay operation 2 Howard Veregin Section II 12 2. Modeling error in overlaid categorical maps 13 Nicholas R.Chrisman 3. User considerations in landscape characterization 23 Stephen J.Walsh 4. Knowledge-based approaches to determining and correcting areas of unreliability in geographic 29 databases Peter F.Fisher 5. Observations and comments on the generation and treatment of error in digital GIS data 36 Giulio MaffiniMichael ArnoWolfgang Bitterlich 6. Developing confidence limits on errors of suitability analyses in geographical information systems 45 Weldon A.Lodwick Section III 52 7. Distance calculations and errors in geographic databases 53 Daniel A.Griffith 8. Inclusion of accuracy data in a feature based, object-oriented data model 59 Stephen C.Guptill 9. Accuracy and bias issues in surface representation 64 David Theobald 10. Modeling error in objects and fields 70 Michael F.Goodchild 11. Frame independent spatial analysis 75 Waldo R.Tobler Section IV 80 12. Modelling locational uncertainty via hierarchical tesselation 81 Geoffrey Dutton v 13. Minimum cross-entropy convex decompositions of pixel-indexed stochastic matrices: a geographic 92 application of the Ising model Paul B.Slater 14. The traditional and modern look at Tissot's indicatrix 101 Piotr H.Laskowski Section V 113 15. Real data and real problems: dealing with large spatial databases 114 David BrusegardGary Menger 16. The small number problem and the accuracy of spatial databases 121 Susan Kennedy 17. Demand point approximations for location problems 128 Rajan Batta 18. Modeling reliability on statistical surfaces by polygon filtering 136 Adrian Herzog Section VI 143 19. Scale-independent spatial analysis 144 A.Stewart Fotheringham 20. The effect of data aggregation on a Poisson model of Canadian migration 150 Carl G.AmrheinRobin Flowerdew 21. Statistical methods for inference between incompatible zonal systems 156 Robin FlowerdewMick Green 22. Statistical effect of spatial data transformations: a proposed general framework 162 Guiseppe Arbia Section VII 170 23. Learning to live with errors in spatial databases 171 Stan Openshaw Subject index 181 Author index 190 List of figures 1.1 A hierarchy of needs for modeling error in CIS operations 3 1.2 Map overlay for categorical data 4 1.3 Map overlay for numerical data 5 1.4 Detection of spurious polygons (source: Goodchild 1978) 5 1.5 An error model for subtraction 7 1.6 An error model for the AND operator 8 1.7 Composite map accuracy for the AND operator 9 1.8 An error model for the OR operator 9 1.9 Composite map accuracy for the OR operator 10 2.1 Arbitrary collection units 14 2.2 Categorical coverages 15 2.3 Slivers: the classic form of overlay error 17 2.4 Another case of overlay error 17 2.5 Transitional intermediaries between pure position error and attribute error 18 2.6 Scale adds a dimension to the transition 18 5.1 The error issue 36 5.2 Digitizing trials approach 38 5.3 Examples of entities digitized 38 5.4 Results of digitizing trials 39 5.5 Continuous entities trials 39 5.6 What does error mean? 40 5.7 Within 100 meters of road 40 5.8 Areas with slope greater than 15% 41 5.9 Within drainage basin 28 41 5.10 Selected area 41 5.11 Error bounds used for case study 42 5.12 Probability of selected class 43 11.1 Density as a function of resolution 76 11.2 Computing migration before and after aggregation 77 11.3 Migration in Austria 78 11.4 Migration patterns computed at three levels of spatial resolution 78 11.5 Migration patterns computed at three levels of spatial resolution 79 12.1 Modelling locational uncertainty via hierarchical tesselation 83 12.2 Development of quaternary triangular mesh at level 3 on a basic octahedron 84 12.3 QTM facet breakdown numbering 85 12.4 First-order QTM tesselation of a sphere and octahedron 86 12.5 Second order QTM code sequencing 86 12.6 Pattern of least significant digits of QTM codes 86 12.7 Arrangement of QTM attractors across one octant at level 5 87 12.8 Octa and first level QTM attractor numerology 88 14.1 An infinitesimal unit circle on the ellipsoid, and Tissot's indicatrix on the map surface. 104 17.1 Illustration for Theorem 1 130 17.2 Numerical example 131 17.3 Illustration for partial dominance of a region 133 17.4 Illustration of dominance result in theorem 133 18.1 Raw data 140 18.2 Filtered data (5 iterations) 140 21.1 Hypothetical example to illustrate method 158 vii 21.2 Districts and parliamentary constituencies in Lancashire, 1983 160 23.1 Discreteness in point data distribution 175 23.2 A fuzzy geodemographic system 177 List of tables 4.1 Examples of measurements of errors in soil maps 31 6.1 Area-class tabulations 41 6.1 The suitability process 45 8.1 Domain of attribute values for the attribute ªoperational statusº 60 8.2 The encoding of attribute values for a feature instance 61 8.3 Example of attributes of attribute values 61 8.4 Describing accuracy of nonlocational attributes 61 8.5 Locational attributes of spatial objects 62 8.6 Locational accuracy attributes and attribute values 62 8.7 Misclassification matrix of land versus water for the lake/pond feature 62 8.8 Misclassification matrix of lakes versus reservoirs for the lake/pond feature 62 12.1 Planetary octahedral triangular quadtrees statistics for 1 to 24 hierarchical levels 84 13.1 Input binomial parameters 94 13.2 Dual binomial parameters 94 13.3 Interpixel correlation matrix 95 13.4 Statistics for inverse temperature 96 13.5 Comparison of dual binomial (ª1º) param eters 96 14.1 The analogies and the differences between the singular value analysis and Tissot's indicatrix 102 17.1 Allocations for the example in figure 2 130 20.1 Proportion of deviance explained (130 region model) 152 20.2 Proportion of deviance explained (65 region model) 153 20.3 r-square statistic for the 130 region models 153 20.4 r-square statistic for the 65 region models 153 20.5 Mean regression coefficients: constant 153 20.5 Mean regression coefficients: destination population 153 20.5 Mean regression coefficients: distance term 153 22.1 Some examples of spatial data transformations 166 Preface In December, 1988 a group of over 50 people drawn from universities, the GIS industry and data dissemination agencies met at La Casa de Maria in Montecito, California to discuss accuracy problems in spatial data. The meeting was convened by the new National Center for Geographic Information and Analysis (NCGIA) to lay out a research agenda in this area for the Center for the following two years. This volume is an edited collection of the position papers presented at that meeting. The NCGIA was announced by the National Science Foundation on 19th August 1988, and awarded to a consortium of universities led by the University of California at Santa Barbara, and including the State University of New York at Buffalo and the University of Maine at Orono. Its published research plan (NCGIA, 1989) outlines a program aimed at the systematic removal of perceived impediments to the adoption and use of GIS technology, particularly in the social sciences. The Center's research program consists of a series of initiatives in certain key problem areas, 12 of which are planned to begin in the first three years of the Center's operation. Each initiative begins with a meeting of specialists to lay out the detailed agenda, and proceeds with research distributed over the three sites of the Center. The Montecito meeting was the first of these specialist meetings, to lay out the agenda for the first initiative, on the Accuracy of Spatial Data. As Ronald Abler noted in his description of the processes leading to the establishment of the NCGIA, ªTwo GIS capabilities that excite enthusiasm among potential users are the ability to change map scales and the ability to overlay maps at random. Both capabilities are indeed exceedingly useful; they constitute much of the comparative advantage GIS holds over spatial analysis based on analogue maps. Both capabilities may also mislead decision makers who are unaware of the imprecision inherent in all cartography and who are untutored in the ways errors compound when map scales are changed or when maps are merged.º (Abler, 1987 p. 305). Peter Burrough introduces his chapter ªData Quality, Errors and Natural Variationº by identi fying: ªa false lure (in) the attractive, high quality cartographic products that cartographers, and now computer graphics specialists, provide for their colleagues in environmental survey and resource analysis¼Many soil scientists and geographers know from field experience that carefully drawn boundaries and contour lines on maps are elegant misrepresentations of changes that are often gradual, vague or fuzzy. People have been so conditioned to seeing the variation of the earth's surface portrayed either by the stepped functions of choropleth maps or by smoothly varying mathematical surfaces that they find it difficult to conceive that reality is otherwise.º (Burrough, 1986 p. 103). If the burgeoning GIS industry is indeed being driven by false perceptions of data accuracy, then the truth will be devastating: even the simplest products will be suspect. The best insurance at this point is surely to sensitize the GIS user community to the accuracy issue, and to develop tools which allow spatial data handling systems to be used in ways which are sensitive to error. Map accuracy is a relatively minor issue in cartography, and map users are rarely aware of the problem. So why does digital spatial data handling raise issues of error and accuracy, when conventional map use does not? The following seven points establish the basis and objectives of the research initiative. 1. The precision of GIS processing is effectively infinite. The typical vector-based GIS allocates 8 decimal digits of precision to each of its coordinates, and many allocate 16. The precision of processing is normally dictated by the precision of input, so one would expect line intersection points, for example, to be computed with at least the precision of input coordinates. However such levels of precision are much higher than the accuracy of typical GIS data. On a topographic map of 100cm by 100cm, 8 digits of precision would resolve