Stable models for metastable systems? Lessons from sensitivity analysis of a Cellular Automata urban land use model

This research suggests that the degree of variability in a Cellular Automata (CA) urban land use model application may be linked to the application's suitability for modelling complex urban systems. Although highly stable models may be perceived as desirable, because they produce reliable, realistic-looking land use simulations, there is a risk that they may not be able to simulate true urban complexity. To test this hypothesis, variability was analysed through a sensitivity analysis in which a calibrated CA land use model application was modified repeatedly to produce a range of model variants with different characteristics. Since model scale is a key attribute known from literature to strongly influence model results, sensitivity analysis was conducted with reference to the scale-related elements (cell resolution, neighbourhood effect) in the model. Variation was found to be slight even between applications having widely differing cell resolutions and neighbourhood distance decay effects. It is contended that this is not an application-specific question, but a feature of these types of models more generally, where simple rules, strong constraints and a low degree of stochastic variation tend to produce highly stable simulation outcomes. To address the question of whether such stable model applications are really suitability for simulating urban complexity, the applications are discussed with relevance to three key indicators of complexity; 1) spontaneous emergence, 2) bifurcation; and 3) critical transitions. Finally, we ask whether the requirement of metastability necessary for calibration of such models violates the assumption of freedom from systemic constraints that would allow true complexity to be simulated. Some suggestions are made as to how these issues might be resolved in future, allowing a new generation of models to emerge.