Spatial and Temporal Topological Analysis of Landscape Structure using Graph Theory

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.