Spatial and Temporal Topological Analysis of Landscape Structure using Graph Theory Alan Kwok

154 Pages·2015·5.74 MB·English

by  Alan Cheung

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Spatial and Temporal Topological
Analysis of Landscape Structure
using Graph Theory

Alan Kwok Lun Cheung

A thesis submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy in Geography, The University of Auckland, 2015.
Abstract
System behaviours of juxtaposed landscape elements can be revealed by analysing
compositional and configurational properties of a landscape. Traditional approaches to spatial
analysis mainly entail the use of spatial statistics and classical spatial data structures to analyse
the composition of a landscape. However, such analyses are unable to capture the essence of
landscape configuration because spatial relationships are treated as end products, rather than
means to an end. In this regard, landscape structure is not being appreciated appropriately in
an empirical way. Since the basis of any analytical method is invariably tied to the form of the
data, it is necessary to go beyond existing data structures and create new ways to ‘see’ the data.
In this thesis, spatial relationships in the form of spatial topology are exploited to provide
insights on the interactive properties of landscape elements through time and space.

The introduction chapter of this thesis presents an overview of the history and heritage of
GIScience that led to the current state of affairs in spatial analysis. It then outlines the rationale
for analysis of landscape configuration based on a new approach to assessment of spatial
topology. The next four chapters are written as publications. The first three papers document
the methodology, using case study examples from the published literature. The fourth paper
applies these new methods to a case study in Qinghai Province, western China. The papers are
followed by a summary discussion chapter.

The first paper (Chapter 2) outlines a new data structure based on graph theory. The Spatio-
Temporal Relational Graph (STRG) is created to record spatial phenomena through space and
time. STRG has the advantage of being an extension of mainstream spatial data structures that
can be easily applied to existing datasets. Graph edit distance and graph bridges were adapted
to STRG from mathematical graph analysis. Analysis of the effectiveness of these procedures
showed that relational changes between landscape elements play a big part in explaining
landscape structure and dynamics. The results also showed the relevance of graph-based
analytics to geographic theories. Based on these findings, graph edit distance was shown to
provide a useful tool in monitoring and explaining spatio-temporal dynamics of landscapes.

The second paper (Chapter 3) extends the toolset of graph analytics by introducing subgraph
identification and analysis. Subgraphs are aggregated landscape elements that are topologically
linked together. Analytical procedures in the form of regular equivalence are described and
applied on the premise that topological relations play a part in explaining how elements are
arranged on the landscape. The results show that similar subgraphs reoccur often, suggesting
the existence of patterns and structures. Furthermore, certain subgraphs display traits that can
be interpreted to represent ecological phenomena such as transition zones, succession level of
vegetation, relative abundance, and land degradation.

The third paper (Chapter 4) presents the use of statistical methods to assess the significance of
subgraphs. By using odds ratios and standard statistical tests, this study identifies prominent
subgraphs/patterns that define the structure of a landscape, reinforcing the findings from
Chapter 3. In particular, the significance of particular ecological phenomena are demonstrated
using combined interpretation of occurrence and statistical significance. This study also
introduced synthetic scenarios of random and procedurally generated urban landscapes. While
the random landscape did not produce significant patterns, the urban landscape provided
patterns which are readily interpreted using the graph methods.

The fourth paper (Chapter 5) is a case study which applies the suite of STRG and analytical
methods to landscapes of the Qinghai-Tibetan Plateau. By combining results from spatial
statistics and graph analytics through space and time, different landscape systems that
characterise and act on the landscape are delineated. In line with landscape ecology theories,
systems involving natural grassland system are found to be more dynamic than human tended
agricultural systems. The combined use of graph analytics and spatial statistics is shown to
create greater meaning than their individual use, enhancing prospects to meaningfully test
landscape ecology concepts and principles relating to fragmentation and patch dynamics. In
particular, spatial topology is used to provide evidence that perforation is the main degradation
mechanism in one of the study areas.

Findings from the thesis are summarised and related back to the international literature in the
discussion chapter. The combined use of graph-based tools and spatial statistics is considered
to provide useful empirical evidence on the interacting components of landscape systems and
their dynamics. Graph-based landscape analytics are shown to hold great promise as a tool that
can help to unlock patterns hidden within data sets, making these patterns self-evident. It is
contended that concepts such as graphs that originated from external fields of research are
converging with GIScience to provide a new suite of analytical tools to assess spatial topology
from the perspective of data structures themselves. Possible future directions for STRG and its
associated analytics are outlined.
Acknowledgement

This research has been an interesting and enlightening journey which completed only with the help of
many others. First I would like to express my gratitude to my supervisors Gary Brierley and David
O’Sullivan, both devoted a lot of time, energy and patience to align me with feasible research directions
through lengthy meetings and e-mails. Thank you again Gary for providing the opportunity (and finding
a scholarship!) for me to do this research in the immense landscapes of the Qinghai-Tibetan Plateau.
Thank you again David for all the discussions on technologies whether related or not to my research!

I am grateful to have travelled with Simon Aiken, Brendon Blue and Tami Nicoll in my grand
adventures in Qinghai. The journey would have been dull without you around. Thank you to colleagues
in the PhD office in the University of Auckland, especially Cheng Liu and Hironori Matsumoto, for we
spent countless nights together debugging and writing. Thank you also to Ning Li for having in depth
discussion in statistics and others.

My gratitude goes to our overseas colleagues in the Qinghai University, Tsinghua University and
Chinese Academy of Science for organizing the logistics of our field work. In particular I would like to
thank Professor Xilai Li of Qinghai University for being our host in China, and also to Master Song and
Master Chen for driving us more than 15,000km through the rugged landscapes of the Qinghai-Tibetan
Plateau.

Thank you to my colleagues in the Department of Cartography, Technical University of Munich for
hosting me as a visitor while I was in Germany, where half of this thesis was written. Thank you to
Patrick Laube of Züricher Hochschule für Angewandte Wissenschaften for hosting me in Zurich and
for the discussion about my research.

This work was in part supported by Program for Changjiang Scholars and Innovative Research Team
in University, MOE, Grant No. IRT13074; International Science & Technology Cooperation Program，
Qinghai Science and Technology Department, Grant No. 2013-H-801 and National Natural Sciences
Foundation of China, 41161084.

Table of Contents
Table of Contents ……………………………………………………………………………………... 1
Table of Figures and Tables …………………………………………………………………………... 3
Chapter 1 Introduction - How landscape analysis is restricted by data
structures and spatial statistics ...................................................................... 6
1.1 Landscape patterns in geography and landscape ecology ....................................................... 7
1.2 Patches – the building blocks of a conceptual and analytical landscape ................................ 8
1.3 Landscape Composition and Configuration ............................................................................ 9
1.4 Characteristics, analytical capability and limitation of mainstream data structures ............. 10
1.4.1 Data models began with graphics models ....................................................................... 10
1.4.2 Object-Field data models ................................................................................................ 11
1.4.3 Heritage from Cartography ............................................................................................. 13
1.4.4 Problems that emerged as a result of conventional cartographic heritage ...................... 14
1.5 Delineating patterns from traditional data lattices with spatial statistics .............................. 16
1.6 Problems with spatial statistics ............................................................................................. 18
1.7 Topologically enabled data structure and analytical techniques ........................................... 20
1.7.1 Spatial Topology ............................................................................................................. 20
1.7.2 Topology into current data structures .............................................................................. 21
1.8 Questions addressed in this thesis ......................................................................................... 23
1.9 Structure of this thesis ........................................................................................................... 23
Chapter 2 Graph-assisted Landscape Monitoring ........................................ 25
2.1 Introduction ........................................................................................................................... 25
2.2 Graph theory ......................................................................................................................... 27
2.3 Basics of Landscape Graph Structure ................................................................................... 28
2.4 Implementation ..................................................................................................................... 30
2.4.1 Objective 1: Establishment of Neighbourhood Graphs ................................................... 32
2.4.2 Objective 2: Entity Tracking ........................................................................................... 32
2.4.3 Objective 3: Unified Data Structure ................................................................................ 34
2.4.4 Objective 4: Harvesting information from data structure ............................................... 34
2.5 Conclusion ............................................................................................................................ 47
2.6 Appendices ............................................................................................................................ 49
2.6.1 Appendix A. New Hampshire Landcover Transitional Matrix 1986 – 1993 .................. 49
2.6.2 Appendix B. New Hampshire Ranked GED Results ...................................................... 50
2.6.3 Appendix C. .................................................................................................................... 52
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