Table Of ContentThe 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
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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
