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Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. ProQuest Information and teaming 300 North Zeeb Road, Ann Artx)r, Ml 48106-1346 USA 800-521-0600 UMI NEW METHODS FOR SPATIAL STATISTICS IN GEOGRAPHIC INFORMATION SYSTEMS DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Department of Civil and Environmental Engineering and Geodetic Science of The Ohio State University By Yaron A. Felus, B.S., M.S. ***** The Ohio State University 2001 Dissertation Committee: Approved by: Prof. Alan Saalfeld, Adviser Prof. Burkhard Schaffrin, Co-Adviser Prof. Noel Cressie Adviser Graduate program in Geodetic Prof. Beàta Csathô Science and Surveying UMI Number: 3031199 UMI* UMI Microform 3031199 Copyright 2002 by Bell & Howell Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and teaming Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 ABSTRACT This thesis is concerned with the development of new methods to implement advanced spatial statistics procedures within Geographic Information Systems. Two approaches are investigated; the first uses Delaunay triangulation data structure to select an appropriate subset of the data and perform Ordinary Kriging interpolation. The second studies an advanced spatial statistics procedure, the optimal biased kriging, which is more efficient in terms of the Mean Squared Prediction Error. Spatial statistical prediction, also called Kriging, has been proved to be an accurate and reliable interpolation method. However, geostatistical interpolation is a computationally very consuming process since it involves the inversion of a n*n matrix where n is the number of sampled points. The common way to overcome this problem is to include only "nearby" points in the Kriging process. Nevertheless, the choice of the Kriging points, we will call it support, has a significant effect on the accuracy of our prediction. Consequently, we will investigate the use of a well-established computational -geometry algorithm - the Delaunay triangulation - as a data structure to select our interpolation support. During this investigation we will develop an efficient algorithm and build up understanding about the statistical effect of a limited neighboriiood on the interpolation. Moreover, we will test and evaluate the proposed innovative method using newly acquired aeromagnetic data collected at the West Antarctic mountains. Optimal Biased Kriging is an efficient geostatistical method that gives up ii unbiasedness to gain improvement in the mean squared prediction error. We will apply this theory on a set of laser- scanning topographic data. In the implementation we will use a relatively new spatial coherency measure, the homeogram, also known as the non­ centered covariance function. Moreover, we use a pre-interpolation spatial sorting to obtain a band-limited sparse coherency matrix. The sparseness of the coherency matrix is used to enhance the interpolation algorithm. Ill ACKNOWLEDGMENT I wise to express my deepest appreciation to my advisors: Professor Alan Saalfeld for introducing me the topics of geocomputation and for his extraordinary patience and support throughout the course of my studies. Professor Burkhard Schaffrin for his invaluable input, ideas, and fioiitful discussions that solidified much of the material in this dissertation; his scholarly and constructive remarks really helped in shaping this work. I am also deeply indebted to my committee members; Professor Noel Cressie for his tips and thoughtful comments that directed me during these research studies. I owe much gratitude to the discussions I had with Professor Beata Csatho whose views are always enlightening and provided a strong impetus for this research. My deepest thanks to Professor Terry Wilson who supported me through out the research and gave me a lifetime experience with the research expedition in Antarctica. I thank the friends, students, colleagues at the Geomatics Laboratory for Ice Dynamics (GLID) and at the Byrd polar research center for providing environment inductive to learning and high- quality research. I am also grateful to many people at the Ohio-State University: Professor Toni Schenk for the constructive conversations and suggestions. Professor Ron Li for his support and guidance. Professor Ralph Von-Frese for the stimulating discussion and advice, and Irene Tesfai for being available always and offering a warm advice. Finally, I will be ever grateful for the love of my parents, my children, and especially my spouse. Without you all being there, this dissertation would never have been completed. iv VITA June 26, 1968 ............... Bom in Helen, Israel 1986-1990 .................... B.S. in Electrical and Computer Engineering at the Ben-Gurion University of the Negev, Beer-Sheva, Israel 1994-1995 .................... M.S. at the Geoinfermatics Department of the International Institute for Aerospace Survey and Earth Sciences (ITC), Enschede, The Netherlands 1996-1998 .................... Diploma studies for Licensed Surveyor Certificate In the Department of Geodetic Science and Civil Engineering, Technion, Haifa, Israel 1996-1998 .................... Research and Development manager at Halperin-Felus Surveying and Photogrammetry LTD, Israel 1998-2001 .................... Graduate Research Associate at the Byrd Polar Research Center of the Ohio State University, Columbus, Ohio 2000-2001.................... Graduate Teaching Assistant at the Department of Civil and Environmental Engineering and Geodetic Science of the Ohio State University, Columbus, Ohio FIELDS OF STUDY Major Field: Geodetic Science and Surveying TABLE OF CONTENTS ABSTRACT...................................................................................................................... ii ACKNOWLEDGMENT..................................................................................................iv VITA................................................................................................................................. iv TABLE OF CONTENTS....................................................................................................v LIST OF FIGURES......................................................................................................... vii LIST OF TABLES............................................................................................................. x LIST OF ACRONYMS AND NOTATION......................................................................xi 1. INTRODUCTION.____________________________________________________ I 1.1 Spatial statistics and GIS .......................................................................................... 1 1.2. Research problems ...................................................................................................4 1.3 Description of our case studies.................................................................................7 1.3.1 TAMARA - Aeromagnetic data .........................................................................7 1.3.2 Ocean city- Laser scanning data ......................................................................11 1.4 Organization of the report .......................................................................................13 2. GEOSTATISTICAL INTERPOLATION METHODS_______________________ 15 2.1 Review of interpolation methods ............................................................................15 2.1.1 Classification of methods .................................................................................15 2.1.2 Inverse distance weighting ...............................................................................17 2.1.3 Trend surface analysis......................................................................................18 2.1.4 Minimum curvature interpolation.................................................................... 19 2.1.5 Area stealing interpolation .............................................................................. 21 2.1.6 The geostatistical paradigm (Kriging) .............................................................23 2.2 Estimation of spatial coherency fimctions ..............................................................25