Error Propagation in Environmental Modelling

GIS users and professionals are aware that the accuracy of GIS results cannot be naively based on the quality of the graphical output. Data stored in a GIS will have been collected or measured, classified, generalised, interpreted or estimated, and in all cases this allows the introduction of errors.; With the processing of translation of this data into the GIS itself further propagation or amplification or errors also occur. It is essential that GIS professionals understand these issues systematically if they are to build ever more accurate systems.; In this book the authors decade of study into these problems is brought into focus with an account of the development, application and implementation of error propagation techniques for use in environmental modelling with GIS. Its purpose is to provide a methodology for handling error and error propagation.

Series introduction

vii

(2)

Foreword

ix

(4)

Preface

xiii

(2)

Glossary

xv

(2)

List of symbols

xvii

1 Introduction

1

(8)

1.1 Error sources in GIS data

4

(1)

1.2 The propagation of errors through GIS operations

5

(1)

1.3 Objectives of this study

5

(4)

2 Definition and identification of an error model for quantitative spatial attributes

9

(16)

2.1 A first look at quantitative errors

9

(1)

2.2 Definition of the error model

10

(3)

2.3 Identification of the error model

13

(7)

2.3.1 Three models of spatial variation

14

(2)

2.3.2 Error identification under the three models of spatial variation

16

(4)

2.4 Multivariate extension

20

(2)

2.5 Change of support issues

22

(3)

3 Identification of the error model: a case study

25

(8)

3.1 Mapping the mean highest water table in the Ooypolder

25

(4)

3.2 Comparison of mapping results for the three models of spatial variation

29

(2)

3.3 Discussion and implications for error propagation analysis

31

(2)

4 Error propagation with local GIS operations: theory

33

(18)

4.1 Error propagation with point operations

34

(2)

4.2 Four techniques of error propagation

36

(9)

4.2.1 First order Taylor method

36

(2)

4.2.2 Second order Taylor method

38

(1)

4.2.3 Rosenblueth's method

39

(1)

4.2.4 Monte Carlo method

40

(2)

4.2.5 Evaluation and comparison of the four error propagation techniques

42

(3)

4.3 Error propagation with neighbourhood operations

45

(1)

4.4 Sources of error contributions

46

(5)

5 Error propagation with local GIS operations: applications

51

(26)

5.1 Predicted lead consumption in the Geul river valley

51

(5)

5.2 Slope and aspect of the Balazuc digital elevation model

56

(4)

5.3 Predicting soil moisture content with linear regression for the Allier floodplain soils

60

(7)

5.4 Selection of suitable soils in the Lacombe agricultural research station using Boolean and continuous classification

67

(10)

6 Error propagation with global GIS operations: the use of multidimensional simulation

77

(12)

6.1 Monte Carlo method for global operations

78

(1)

6.2 Stochastic simulation of the input random field

78

(2)

6.3 An iterative method for simulating autoregressive random fields

80

(4)

6.4 Numerical experiments with iterative autoregressive simulation

84

(5)

7 Implementation of error propagation techniques in GIS

89

(8)

7.1 Starting points for adding error propagation functionality to an existing GIS

89

(1)

7.2 The ADAM error propagation software tool

90

(3)

7.3 Running the Allier case study with ADAM

93

(4)

8 Summary and conclusions

97

(12)

8.1 Summary of research results: the list of nine research questions

97

(6)

8.2 Summary of research results: additional results

103

(2)

8.3 Towards a full grown error handling capability of GIS

105

(4)

References

109

(12)

Author index

121

(4)

Subject index

125

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Error Propagation in Environmental Modelling with GIS

Summary

Table of Contents

Supplemental Materials