Table Of ContentError Propagation in
Environmental Modelling
with GIS
Error Propagation in
Environmental Modelling
with GIS
GERARD B. M. HEUVELINK
University of Amsterdam
UK Taylor & Francis Ltd, 1 Gunpowder Square, London EC4A 3DE
USA Taylor & Francis Inc., 1900 Frost Road, Suite 101, Bristol, PA 19007
This edition published in the Taylor & Francis e-Library, 2008.
“To 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.”
Copyright © Gerard B. M. Heuvelink 1998
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 the prior permission of the
copyright owner.
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ISBN 0-203-01611-4 Master e-book ISBN
ISBN 0 7484 0743 X HB
ISBN 0 7484 0744 8 PB
Library of Congress Cataloging-Publication-Data are available
Contents
Series introduction vii
Foreword ix
Preface xiii
Glossary xv
List of symbols xvii
1 Introduction 1
1.1 Error sources in GIS data 4
1.2 The propagation of errors through GIS operations 5
1.3 Objectives of this study 5
2 Definition and identification of an error model for
quantitative spatial attributes 9
2.1 A first look at quantitative errors 9
2.2 Definition of the error model 10
2.3 Identification of the error model 13
2.3.1 Three models of spatial variation 14
2.3.2 Error identification under the three models
of spatial variation 16
2.4 Multivariate extension 20
2.5 Change of support issues 22
3 Identification of the error model: a case study 25
3.1 Mapping the mean highest water table in the Ooypolder 25
3.2 Comparison of mapping results for the three models of spatial
variation 29
3.3 Discussion and implications for error propagation analysis 31
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vi CONTENTS
4 Error propagation with local GIS operations: theory 33
4.1 Error propagation with point operations 34
4.2 Four techniques of error propagation 36
4.2.1 First order Taylor method 36
4.2.2 Second order Taylor method 38
4.2.3 Rosenblueth’s method 39
4.2.4 Monte Carlo method 40
4.2.5 Evaluation and comparison of the four error propagation
techniques 42
4.3 Error propagation with neighbourhood operations 45
4.4 Sources of error contributions 46
5 Error propagation with local GIS operations: applications 51
5.1 Predicted lead consumption in the Geul river valley 51
5.2 Slope and aspect of the Balazuc digital elevation model 56
5.3 Predicting soil moisture content with linear regression for the
Allier floodplain soils 60
5.4 Selection of suitable soils in the Lacombe agricultural research
station using Boolean and continuous classification 67
6 Error propagation with global GIS operations: the use
of multidimensional simulation 77
6.1 Monte Carlo method for global operations 78
6.2 Stochastic simulation of the input random field 78
6.3 An iterative method for simulating autoregressive random fields 80
6.4 Numerical experiments with iterative autoregressive simulation 84
7 Implementation of error propagation techniques in GIS 89
7.1 Starting points for adding error propagation functionality to
an existing GIS 89
7.2 The ADAM error propagation software tool 90
7.3 Running the Allier case study with ADAM 93
8 Summary and conclusions 97
8.1 Summary of research results: the list of nine research questions 97
8.2 Summary of research results: additional results 103
8.3 Towards a full grown error handling capability of GIS 105
References 109
Author index 121
Subject index 125
Series introduction
Welcome to the Research Monographs in Geographical Information Science.
The new RMGIS aim to provide a publication outlet of the highest quality for
research in GIS which is longer than would normally be acceptable for
publication in a journal. The series will include single and multiple author
research monographs, possibly based upon PhD theses and the like, and special
collections of thematic papers.
The need
We believe that there is a need, from the point of view both of readers (researchers
and practitioners) and of authors, for longer treatments of subjects related to
GIS than are widely available currently. We feel that the value of much research
is actually devalued by being broken up into separate articles for publication in
journals. At the same tune, we realise that many career decisions are based on
publication records, and that peer review plays an important part in that process.
Therefore a named editorial board has been appointed to support the series,
and advice will be sought from them on all submissions.
Successful submissions will focus on a single theme of interest to the GIS
community, and treat it in depth giving full proofs, methodological procedures
or code where appropriate to help the reader appreciate the utility of the work in
the monograph. No area of interest in GIS is excluded although material should
demonstrably advance thinking and understanding in spatial information
science. Theoretical, technical and application-oriented approaches are all
welcomed.
The medium
In the first instance the majority of monographs will be in the form of a traditional
textbook, but, in a changing world of publishing, we actively encourage
publication on CD-ROM, the placing of supporting material on web sites, or
publication of programs and of data. No form of dissemination is discounted,
vii
and prospective authors are invited to suggest whatever primary form of
publication and support material they think is appropriate.
The editorial board
The monograph series is supported by an editorial board. Every monograph
proposal is sent to all members of the board which includes Ralf Bill, Antonio
Camara, Joseph Ferreira, Pip Forer, Andrew Frank, Gail Kucera, Peter van
Oostrom and Enrico Puppo. These people have been invited for their experience
in the field, of monograph writing, and their geographic and subject diversity.
With particular monographs members may also be involved later in the process.
Future submissions
Anyone who is interested in preparing a research monograph should contact
either of the editors. Advice on how to proceed will be available from them, and
is treated on a case by case basis.
For now we hope that you will find this, the first in the series, a worthwhile
addition to your GIS bookshelf, and that you may be inspired to submit one too.
Series editors
PETER FISHER JONATHAN RAPER
Department of Geography, Department of Geography,
University of Leicester, Birkbeck College, 7–15 Gresse
Leicester LE1 7RH, UK Street,
Telephone (+44) (0) 116 252 3839. London W1P 1PA, UK
Fax (+44) (0)116 252 3854. Telephone (+44) (0) 171 631 6457.
Email [email protected] Fax (+44) (0) 171 631 6498.
Email [email protected]
viii
Foreword
It is a great honour to be asked to write this brief foreword to Gerard Heuvelink’s
monograph. As Gerard notes in his Preface, the monograph is the culmination of
a decade of work, and it brings together and extends results that have been
published in a number of forms over that period. Gerard has made an outstanding
contribution to the field over that period, and his work is far and away the best
and most comprehensive attempt to formalise and offer solutions to the difficult
problem of error propagation in GIS. Publication of this monograph is very
timely, as it makes all of this work accessible in one source, and brings it to the
attention of a wide and multidisciplinary audience in a format that is both
rigorous and relatively easy to implement.
Error propagation in GIS may appear to the uninitiated as an obscure, abstruse
topic within a relatively obscure field – so why is it so important, and why does
it deserve attention in the form of this monograph? Aren’t computers accurate,
and isn’t everything that emerges from them perfectly true? We have made great
progress in the past decade or so in extending computer applications into the
domain of the vague and imprecise, and computers are now used to help make
decisions under conditions of uncertainty; computers armed with tools such as
the World Wide Web are far from the exact number-crunchers that defined the
computing world of thirty years ago. But in the case of geographic information
the problem of unreasonable expectations is made worse by two additional
factors. First, uncertainty is endemic in geographic information, since it is
virtually impossible to record and represent the true complexity of the Earth’s
surface in digital form. But perhaps more important is the fact that the previous
technology – in this case, the paper map – was also guilty of an exaggerated
sense of its own precision. Somehow, we have grown used to the idea of precisely
drawn contours on topographic maps, and precise boundaries on soil maps,
even though we know on reflec tion or closer examination that their true accuracy
is much lower. Somehow we accept this pretence of accuracy, and have developed
a technology of geographic information systems that takes and analyses that
map information at face value, without questioning its true accuracy. We are
only now coming to realise that much of what passes for accurate analysis in
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