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Towards Q-Analysis Integration in Discrete Global Grid Systems: Methodology, Implications and Data Complexity

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Towards Q-Analysis Integration in Discrete Global Grid Systems: Methodology, Implications and Data Complexity Towards Q-analysis Integration in Discrete Global Grid Systems: Methodology, Implications and Data Complexity by Veniamin Bondaruk A thesis presented to the University of Waterloo in fulfilment of the thesis requirement for the degree of Master of Science in Geography Waterloo, Ontario, Canada, 2020 © Veniamin Bondaruk 2020 Author’s Declaration I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract Spatial data is characterized by rich contextual information with multiple characteristics at each location. The interpretation of this multifaceted data is an integral part of current technological developments, data rich environments and data driven approaches for solving complex problems. While data availability, exploitation and complexity continue to grow, new technologies, tools and methods continue to evolve in order to meet these demands, including advancing analytical capabilities, as well as the explicit formalization of geographic knowledge. In spite of these developments Discrete Global Grid Systems (DGGS) were proposed as a new comprehensive approach for transforming scientific data of various sources, types and qualities into one integrated environment. The DGGS framework was developed as the global data model and standard for efficient storage, analysis and visualization of spatial information via a discrete hierarchy of equal area cells at various spatial resolutions. Each DGGS cell is the explicit representation of the Earth surface, which can store multiple data values and be conveniently recognized and identified within the hierarchy of the DGGS system. A detailed evaluation of some notable DGGS implementations in this research indicates great prospects and flexibility in performing essential data management operations, including spatial analysis and visualization. Yet they fall short in recognizing interactivity between system components and their visualization, nor providing advanced data friendly techniques. To address these limitations and promote further theoretical advancement of DGGS, this research suggests the use of Q-analysis theory as a way to utilize the potential of the hierarchical DGGS data model via the tools of simplicial complexes and algebraic topology. As a proof of concept and demonstration of Q-analysis feasibility, the method has been applied in a water quality and water health study, the interpretation of which has revealed much contextual information about the behaviour of the water network, the spread of pollution and chain affects. It is concluded that the use of Q-analysis indeed contributes to the further advancement and development of DGGS as a data rich framework for formalizing multilevel data systems and for the exploration of new data driven and data friendly approaches to close the gap between knowledge and data complexity. iii Acknowledgements First and foremost I would like to express gratitude and appreciation to my supervisor, Dr. Steven A. Roberts, for his professional guidance, expertise in the field and commitment to this research. Without a doubt this work would not have been be possible without him. Particular recognition goes also to Dr. Colin Robertson for his valuable suggestions, constructive feedback and input, which had a significant impact on the direction and quality of this research. I am also thankful to the examining reader, Dr. Rob Feick, for taking the time to review this work and validate its quality, as well as for sharing his expert knowledge and committing to this integral responsibility. Thank you to the Global Water Futures Programme and the Global Water Citizenship Project for funding this research. I wish to thank Dr. Brent Doberstein, Dr. Richard Kelly and the Department of Geography and Environmental Management at the University of Waterloo for providing administrative support, academic guidance and financial assistance. Certainly, their hard work and efforts were vital and meant a lot to me. I also want to thank all my colleagues and fellow researchers in The Spatial Lab at Wilfrid Laurier University. It was a pleasure working with them and I am glad our paths have crossed. Finally, I want to express special gratefulness to my family and church for taking on this journey with me, their endless love and encouragement without measure. I love them a lot. iv Dedication For the glory of Christ Jesus. v Table of Contents Author’s Declaration ..................................................................................................................................... ii Abstract ........................................................................................................................................................ iii Acknowledgements ...................................................................................................................................... iv Dedication ..................................................................................................................................................... v Table of Contents ......................................................................................................................................... vi List of Figures .............................................................................................................................................. ix List of Tables ............................................................................................................................................. xiii Chapter 1 Introduction .................................................................................................................................. 1 1.1 Research Scope ................................................................................................................................... 3 1.2 Thesis Outline ..................................................................................................................................... 3 Chapter 2 Literature Review ......................................................................................................................... 5 2.1 Introduction to DGGS ......................................................................................................................... 5 2.1.1 Base Polyhedron .......................................................................................................................... 6 2.1.2 Polyhedron Registration ............................................................................................................... 8 2.1.3 Hierarchical Tessellation ............................................................................................................ 11 2.2 OGC Abstract Specification.............................................................................................................. 15 2.3 DGGS Implementations .................................................................................................................... 18 2.4 DGGS Analytics and Q-analysis....................................................................................................... 20 2.5 Q-analysis Concepts .......................................................................................................................... 21 2.5.1 Hierarchical Cover Sets ............................................................................................................. 22 2.5.2 Relational Thinking.................................................................................................................... 23 2.5.3 Geometric Representation .......................................................................................................... 26 2.6 Hierarchical Backcloth and Traffic ................................................................................................... 28 2.7 Q-analysis Applications .................................................................................................................... 31 Chapter 3 Methodology .............................................................................................................................. 34 3.1 Exploring DGGS ............................................................................................................................... 34 3.1.1 Embedded DGGS ....................................................................................................................... 34 3.1.2 Scalability .................................................................................................................................. 36 3.1.3 OGC Compliance ....................................................................................................................... 37 3.2 Understanding Complexity ............................................................................................................... 37 3.2.1 Matrix Construction ................................................................................................................... 38 vi 3.2.2 Geometric Visualization ............................................................................................................ 40 3.3 Q-analysis and DGGS ....................................................................................................................... 42 3.3.1 Defining Hierarchical Backcloth ..............................................................................................
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