Modelling transitions in sealed surface cover fraction with Quantitative State Cellular Automata

Cellular Automata (CA) applications simulating urban processes generally employ discrete land-use classes to characterise the physical environment. Yet there is an increasing demand for urban land cover models simulating quantitative change at the sub-cell level. The proposed Quantitative State Cellular Automata model (QCA) addresses this issue by relaxing part of the CA definition and considering real-valued quantitative cell states reflecting a physically meaningful measure. QCA entails two components of change: transition potential and quantity of change. The potential component addresses the likelihood of any change occurring in a cell, whereas the quantity component estimates the magnitude of change. The QCA concept is illustrated for Sealed Surface Density (SSD) transitions in Brussels and part of Flanders (Belgium). A Mutual Information (MI) approach is used to define the neighbourhood interaction framework. The QCA model is respectively calibrated and validated using Landsat-derived 1987–2001 and 2001–2013 SSD change on 30 m resolution. The results show that QCA successfully emulates spatial patterns of urban development, and significantly outperforms a random model in terms of quantitative and spatial distribution of SSD change. Further improvements can be achieved by explicitly integrating socio-economic information in the proposed workflow.