Surface modeling : high accuracy and high speed methods

696 Pages·2011·19.13 MB·English

by  Tian-Xiang Yue

Surface Modeling
High Accuracy and
High Speed Methods
Applied Ecology
and Environmental Management
A SERIES
Series Editor
Sven E. Jørgensen
Copenhagen University, Denmark
Handbook of Ecological Indicators for Assessment of
Ecosystem Health, Second Edition
Sven E. Jørgensen, Fu-Liu Xu, and Robert Costanza
Surface Modeling: High Accuracy and High Speed Methods
Tian-Xiang Yue
ADDITIONAL VOLUMES IN PREPARATION
Surface Modeling
High Accuracy and
High Speed Methods
Tian-Xiang Yue
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2011 by Taylor and Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed in the United States of America on acid-free paper
10 9 8 7 6 5 4 3 2 1
International Standard Book Number-13: 978-1-4398-1759-9 (Ebook-PDF)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize to
copyright holders if permission to publish in this form has not been obtained. If any copyright material has
not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, transmit-
ted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter invented,
including photocopying, microfilming, and recording, or in any information storage or retrieval system,
without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the CCC,
a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used
only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
Contents
Preface ..................................................................................................................xvii
Acknowledgments ..............................................................................................xix
Section I Principles and Methods
1. Introduction .....................................................................................................3
1.1 Surface Modeling ..................................................................................3
1.2 Classical Methods .................................................................................7
1.2.1 Trend Surface Analysis ...........................................................7
1.2.2 Inverse Distance Weighted Method ......................................7
1.2.3 Triangulated Irregular Network ...........................................8
1.2.4 Kriging ......................................................................................8
1.2.5 Spline .......................................................................................10
1.3 Error and Multiscale Issues ...............................................................11
1.3.1 Error Issues .............................................................................11
1.3.2 Multiscale Issues ....................................................................12
1.4 Geographical Information Systems ..................................................14
1.4.1 Historical Development ........................................................14
1.4.2 Error Problem .........................................................................15
1.4.3 Multiscale Problem ................................................................16
1.4.4 Real-Time Problem .................................................................17
1.4.5 Direct Modeling Problem .....................................................18
References .......................................................................................................19
2. Basic Method of HASM ..............................................................................27
2.1 Introduction .........................................................................................27
2.2 Theoretical Formulation .....................................................................28
2.3 Optimum Formulation .......................................................................39
2.4 Iterative Formulation of HASM ........................................................43
2.5 Numerical Tests ...................................................................................48
2.5.1 Comparative Error Analyses ................................................48
2.5.2 Comparative Analysis of Simulating
Different Surfaces ..................................................................49
2.6 Discussion and Conclusions ..............................................................57
References .......................................................................................................63
3. Comparative Analyses of Various HASM Algorithms ........................65
3.1 Introduction .........................................................................................65
3.1.1 Algorithms ..............................................................................65
v
vi Contents
3.1.2 Preconditioning ......................................................................66
3.2 Direct Algorithms of HASM .............................................................67
3.2.1 Gaussian Elimination Algorithm of HASM
(HASM-GE) .............................................................................72
3.2.2 Square-Root Algorithm of HASM (HASM-SR) .................73
3.2.3 Numerical Test .......................................................................75
3.3 Iterative Formulation of HASM and Its Coefficient
Matrix Structure ..................................................................................76
3.3.1 Iterative Formulation of HASM ...........................................76
3.3.2 Coefficient Matrix Structure ................................................79
3.4 Gauss–Seidel Algorithm and Preconditioned
Gauss–Seidel Algorithm ....................................................................80
3.4.1 Gauss–Seidel Algorithm .......................................................80
3.4.1.1 Matrix Expression ..................................................81
3.4.1.2 Vector Expression ...................................................82
3.4.2 Preconditioned Gauss–Seidel Algorithm ...........................84
3.4.2.1 Matrix Expression ..................................................84
3.4.2.2 Vector Expression ...................................................85
3.4.3 Numerical Tests ......................................................................88
3.4.3.1 Comparison of HASM-PGS with Krylov
Subspace Algorithms .............................................88
3.4.3.2 Comparison of HASM-PGS with HASM-GS .....88
3.4.4.3 Effects of Initial Values on Convergence of
HASM-PGS ..............................................................90
3.5 Conjugate Gradient Algorithm and Preconditioned Conjugate
Gradient Algorithm ............................................................................91
3.5.1 Conjugate Gradient Algorithm ............................................91
3.5.2 Preconditioned Conjugate Gradient Algorithm ................94
3.5.3 Numerical Test .......................................................................95
3.6 Conclusions and Discussion ..............................................................97
References .......................................................................................................98
4. Adaptive Method of HASM .....................................................................103
4.1 Introduction .......................................................................................103
4.2 Test Area and Data Acquisition ......................................................104
4.3 Adaptive Method of HASM ............................................................106
4.3.1 Basic Formulation of HASM-AM ......................................106
4.3.2 Error Estimators and Error Indicators ..............................107
4.3.3 Adaptive Refinement ...........................................................109
4.4 Validation of HASM-AM .................................................................111
4.4.1 DEM Construction of Dongzhi Tableland ........................111
4.4.2 Testing Computational Efficiency .....................................114
4.5 Discussion and Conclusions ............................................................117
References .....................................................................................................119
Contents vii
5. Multigrid Method of HASM ....................................................................123
5.1 Introduction .......................................................................................123
5.2 Multigrid Method of HASM ...........................................................124
5.2.1 Multigrid ...............................................................................124
5.2.2 Numerical Tests ....................................................................125
5.3 Comparative Analysis of HASM-MG with OK ............................128
5.3.1 OK Method ...........................................................................128
5.3.2 Real-World Test ....................................................................128
5.4 Discussion and Conclusions ............................................................131
References .....................................................................................................133
6. Adjustment Computation of HASM .......................................................137
6.1 Adjustment Computation ................................................................137
6.1.1 Parametric Adjustment .......................................................137
6.1.2 Conditional Adjustment .....................................................140
6.1.3 Successive Conditional Adjustment ..................................142
6.1.4 Successive Independent Conditional
Adjustment ...........................................................................144
6.2 Adjustment Computation of HASM ..............................................146
6.3 Tests of Accuracy and Computing Speed ......................................153
6.3.1 Errors .....................................................................................154
6.3.1.1 Numerical Test ......................................................154
6.3.1.2 Real-World Test of Accuracy ...............................157
6.3.2 Real-World Test of Computing Speed ...............................160
6.4 Conclusions and Discussion ............................................................162
6.4.1 Conclusions ...........................................................................162
6.4.2 Discussion .............................................................................163
References .....................................................................................................164
7. Optimal Control Method of HASM .......................................................165
7.1 Introduction .......................................................................................165
7.2 HASM-OC ..........................................................................................167
7.2.1 Equality Constraint of HASM ............................................167
7.2.2 Inequality Constraint of HASM ........................................167
7.2.3 Determination of the Range of Elevation at the
Central Point of Every Lattice ............................................171
7.3 Validation of HASM-OC ..................................................................172
7.3.1 Numerical Test .....................................................................173
7.3.2 SRTM Test .............................................................................178
7.3.3 Real-World Test of Qian-Yan-Zhou in Jiangxi
Province of China ................................................................180
7.4 Conclusions and Discussion ............................................................185
References .....................................................................................................187
viii Contents
8. Basic Approach of HASM to Dynamic Simulation .............................191
8.1 Introduction .......................................................................................191
8.2 Basic Formulation..............................................................................193
8.2.1 Solving Procedure of HASM ..............................................193
8.2.2 Factorization of the HASM Coefficient Matrix ................195
8.2.3 Formulation of HASM-F by Dynamically Adding
Information ...........................................................................196
8.2.4 Formulation of HASM-F by Dynamically
Removing Information ........................................................197
8.3 Numerical Test ...................................................................................198
8.4 Conclusions and Discussion ............................................................202
References .....................................................................................................203
Section II Surface Modeling of Environment
Components of Earth Surface
9. Surface Modeling of DEM ........................................................................207
9.1 Introduction .......................................................................................207
9.2 SRTM Void Filling .............................................................................208
9.2.1 HASM ....................................................................................211
9.2.2 Materials and Verification Procedures .............................212
9.2.3 Comparative Analyses of Void-Filling Results ................215
9.3 Surface Modeling of DEM Based on
Height-Sampling Points ...................................................................218
9.4 Surface Modeling of DEM Based on Topological Maps ..............219
9.5 Discussion and Conclusions ............................................................222
9.5.1 SRTM Void Filling ................................................................222
9.5.2 DEMs Based on Height-Sampling Points
and on Topological Maps ....................................................225
References .....................................................................................................225
10. Surface Modeling of Population Distribution .....................................231
10.1 Introduction .......................................................................................231
10.2 SMPD Method ...................................................................................234
10.3 SMPD-Based Population Simulation on a National
Level of China....................................................................................236
10.3.1 Background of Major Data Layers .....................................236
10.3.1.1 Elevation ................................................................236
10.3.1.2 Water Systems .......................................................236
10.3.1.3 Land Use and Net Primary Productivity .........239
10.3.1.4 Spatial Distribution of Cities
and Urbanization .................................................240
10.3.1.5 Spatial Distribution of Transport
Infrastructure in China .......................................241
Contents ix
10.3.2 Population Growth ..............................................................243
10.3.2.1 Change Trend of Population ...............................243
10.3.2.2 Population Projection ..........................................244
10.3.3 SMPD Operation ..................................................................249
10.3.4 Change Trends in Population Distribution ......................259
10.3.5 Scenarios of Population Distribution ................................262
10.3.6 Brief Summary .....................................................................264
10.4 SMPD in Beijing ................................................................................266
10.4.1 Specification of SMPD .........................................................266
10.4.2 Descriptions Related to Data Sets......................................268
10.4.2.1 Baseline Situation of Beijing in 2000 ..................268
10.4.2.2 Beijing Master Plan ..............................................270
10.4.2.3 Land-Use Plan .......................................................273
10.4.2.4 Beijing Transportation Infrastructure
Plan .........................................................................274
10.4.3 Simulation of Change Trends and Scenarios ...................274
10.4.3.1 Validation of the Specified SMPD ......................274
10.4.3.2 Changing Trends ..................................................275
10.4.3.3 Scenarios ................................................................281
10.4.4 Brief Summary .....................................................................285
10.5 Conclusions and Discussion ............................................................286
References .....................................................................................................287
11. Surface Modeling of Human Carrying Capacity .................................293
11.1 Introduction .......................................................................................293
11.1.1 Definitions of Carrying Capacity ......................................293
11.1.2 Estimates of Human Carrying Capacity
on a Global Level..................................................................294
11.2 Method................................................................................................296
11.2.1 Ecological Thresholds .........................................................296
11.2.1.1 Entropy, Entropy Production, and Excess
Entropy Production ..............................................297
11.2.1.2 Logistic Equation of Population
Growth ...................................................................299
11.2.1.3 Theoretically Reasoning the Range of
Sustainable Growth Population .........................299
11.2.1.4 Brief Summary ......................................................301
11.2.2 Models for Food Provision Capacity of Terrestrial
Ecosystems ............................................................................301
11.3 Data Sets .............................................................................................303
11.3.1 Data Sets for Ecosystem Classification of Terrestrial
Ecosystems ............................................................................303
11.3.2 Data Sets for the Calculation of Food
Provision Capacity ...............................................................304
11.4 Food Provision Capacity of Terrestrial Ecosystems .....................304