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.

模拟城市过程的元胞自动机（CA）应用程序通常采用离散的土地利用类别来表征物理环境。然而，越来越需要模拟子单元水平上的定量变化的城市土地覆盖模型。拟议的定量状态元胞自动机模型（QCA）通过放宽CA定义的一部分并考虑反映物理意义的量度的实值定量元胞状态来解决此问题。QCA包含变更的两个组成部分：过渡潜力和变更量。潜在成分解决了单元中发生任何更改的可能性，而数量成分则估计了更改的幅度。QCA概念说明了布鲁塞尔和法兰德斯（比利时）一部分的密封表面密度（SSD）过渡。互信息（MI）方法用于定义邻域交互框架。QCA模型分别使用Landsat派生的1987–2001和2001–2013 SSD在30 m分辨率上的变化进行了校准和验证。结果表明，QCA成功地模拟了城市发展的空间格局，并且在固态硬盘变化的数量和空间分布方面明显优于随机模型。通过在建议的工作流程中明确整合社会经济信息，可以实现进一步的改进。并且在SSD变化的数量和空间分布方面明显优于随机模型。通过在建议的工作流程中明确整合社会经济信息，可以实现进一步的改进。并且在SSD变化的数量和空间分布方面明显优于随机模型。通过在建议的工作流程中明确整合社会经济信息，可以实现进一步的改进。