A vector-based geographical cellular automata model to mitigate scale sensitivity and to allow objects' geometric transformation

Raster-based cellular automata (CA) models have been increasingly used over the last decades to simulate a wide range of spatial phenomena, but recent studies have illustrated that they are scale sensitive, that is their results vary with the cell size and neighbourhood configuration. Two solutions have been proposed to mitigate this problem: a sensitivity analysis to determine the most appropriate cell size and neighbourhood configuration that capture the dynamics of the study area, and the implementation of an object or vector-based cellular automata model independent of the cell size and the neighbourhood configuration. Several researchers have begun to implement vector-based CA models that define space based on the GIS (Geographic Information Systems) vector model, but these models have several limitations. First, the polygons and the neighbouring relationships are mainly based on Voronoi boundaries which are automatically defined in the model. The polygons do not necessarily correspond to meaningful entities and spatial relationships; characteristics such as attractivity, connectivity or accessibility are not taken into account. Second, their sensitivity to the neighbourhood configuration has not been tested; the number and distribution of the neighbours determine the change of state of an object, therefore their selection could affect the simulation outcomes. Finally, these models do not allow the change of shape of the objects, which represent an essential component of their spatial evolution through time. 
In this research, a new vector-based cellular automata (VecGCA) model is proposed to overcome the cell size and neighbourhood configuration sensitivity of the classical raster-based CA models and the limitations of the previous implementations of vector-based CA models. In the VecGCA model, space is represented as a collection of geographic objects where each object corresponds to a real-world entity of irregular shape and size (e.g. a forest, a city, a lake). Each geographic object has its own geometric representation (polygon) which evolves through time according to a transition function that depends on the influence of its neighbours. This evolution is expressed by the change of shape and size of the objects and it is performed using a geometric transformation procedure. This procedure reduces the area of an object in the region nearest to the neighbour that exerts an influence on it and increases the area of that neighbour. 
Two neighbourhood definitions were tested: a buffer of influence and a dynamic neighbourhood. In the first case, the neighbourhood is considered as the region of influence on each geographic object, where the neighbours are all geographic objects located within the region of influence; the transition function determines the area of an object that must change state for the state of its neighbours. In the dynamic neighbourhood, the neighbourhood is the whole geographic space and the neighbours are defined based on the properties of each geographic object; two objects are neighbours if they are separated by 0, 1 or more objects whose states favour the state transition between them. The transition function defines the distance, from the closest point to the neighbour to a point in its interior, where the influence of that neighbour is equal to a threshold value, which represents the resistance of an object to change state. 
The model was used to simulate land-use/land-cover changes in two regions of different landscape complexity, in southern Quebec and southern Alberta, Canada. The results obtained show that VecGCA represents well the dynamics in the study areas through an adequate evolution of the geometry of the geographic objects which are independent of the cell size. The geometric transformation procedure introduced in VecGCA executes the change of shape of a geographic object by changing its state in a portion of its surface, allowing a more realistic representation of the evolution of the landscape. Additional results reveal that when using the first neighbourhood definition, VecGCA is sensitive to the neighbourhood size and that this sensitivity varies with the landscape configuration. When applying a dynamic neighbourhood, the land-use patterns generated by the model are very similar to the reference maps in each study area. With the implementation of a dynamic neighbourhood, VecGCA becomes independent of spatial scale, including both cell size and neighbourhood configuration.

Topic: Land Use and Ecosystem Services
Subfield: Global and Planetary Change
Field: Environmental Science
Domain: Physical Sciences