Four-dimensional agent-based approaches for modeling spatial dynamic phenomena using complex systems and GIScience theories

Spatial phenomena are often perceived as complex systems (CS) that cannot be fully represented through equation or statistical modeling as they are spatial, dynamic, and nonlinear. This requires alternate methods such as geographic automata systems (GAS) including cellular automata (CA) and agent-based modeling (ABM), based on geographic information science (GIScience), geographic information systems (GIS), and CS theories, to achieve a bottom-up representation of spatial processes that generate spatial patterns. However, most GAS use two-dimensional space over time to represent the dynamics of change of spatial systems, while in reality these systems exist in three-dimensional (3D) space that is perpetually changing over time, thus are four-dimensional (4D). Developments have advanced data representation into 3D space using several GIS data formats, LIDAR data and voxel automata, the 4D equivalent of CA. However, the ABM frameworks have not experienced the same progress, and therefore, the main objective of this dissertation includes the development and implementation of a novel 4D ABM theoretical framework applied on two case studies. The first case study implements the 4D ABM approach to represent the propagation of forest-fire smoke in British Columbia, Canada. The second case study implements the 4D ABM approach to represent the predator-prey dynamics of the Southern Resident Killer Whale and Chinook Salmon in the Salish Sea, Canada and USA, and identifies locations for marine environment preservation. One challenge of 4D ABM approaches is the model testing methods, specifically the availability of comparison techniques for 3D map and simulation outcomes. Therefore, in addition, this dissertation proposes new 3D and 4D map comparison techniques based on several 3D and 4D Kappa measures, using probability and fuzzy logic to calculate the similarity between two 3D maps. Obtained results indicate that the 4D ABM theoretical framework can effectively be implemented to represent 4D spatial dynamic phenomena for multiple proposed scenarios. The results of this dissertation have potential for use in decision-making, spatial planning and policy testing for conservation purposes and environmental protection. This thesis contributes to the advancements of the field of GIScience and modeling with multidimensional geographic automata systems.