Calibration of cellular automata urban growth models from urban genesis onwards - a novel application of Markov chain Monte Carlo approximate Bayesian computation

Abstract

Cellular Automata (CA) models are widely used to study spatial dynamics of urban growth and evolving patterns of land use. One complication across CA approaches is the relatively short period of data available for calibration, providing sparse information on patterns of change and presenting problematic signal-to-noise ratios. To overcome the problem of short-term calibration, this study investigates a novel approach in which the model is calibrated based on the urban morphological patterns that emerge from a simulation starting from urban genesis, i.e., a land cover map completely void of urban land. The application of the model uses the calibrated parameters to simulate urban growth forward in time from a known urban configuration.This approach to calibration is embedded in a new framework for the calibration and validation of a Constrained Cellular Automata (CCA) model of urban growth. The investigated model uses just four parameters to reflect processes of spatial agglomeration and preservation of scarce non-urban land at multiple spatial scales and makes no use of ancillary layers such as zoning, accessibility, and physical suitability. As there are no anchor points that guide urban growth to specific locations, the parameter estimation uses a goodness-of-fit (GOF) measure that compares the built density distribution inspired by the literature on fractal urban form. The model calibration is a novel application of Markov Chain Monte Carlo Approximate Bayesian Computation (MCMC-ABC). This method provides an empirical distribution of parameter values that reflects model uncertainty. The validation uses multiple samples from the estimated parameters to quantify the propagation of model uncertainty to the validation measures.The framework is applied to two UK towns (Oxford and Swindon). The results, including cross-application of parameters, show that the models effectively capture the different urban growth patterns of both towns. For Oxford, the CCA correctly produces the pattern of scattered growth in the periphery, and for Swindon, the pattern of compact, concentric growth. The ability to identify different modes of growth has both a theoretical and practical significance. Existing land use patterns can be an important indicator of future trajectories. Planners can be provided with insight in alternative future trajectories, available decision space, and the cumulative effect of parcel-by-parcel planning decisions.