A Bayesian approach to complex land use change modelling

Historically, attempts to apply Constrained Cellular automata (and similar) models to real cities or regions have faced a number of challenges. The complex relationship between model parameters and the resulting dynamics makes the parameters of land use change models notoriously hard to estimate. The parameter space in many applications is large and unstructured.

Constrained Cellular automata models are stochastic, resulting in a large variation of optimal parameters for different data set or model runs; hence, understanding the parameter uncertainty is crucial. In particular, parameter estimation is often based on relatively short periods of data availability and small geographical areas. The signal to noise ratio of real changes versus apparent changes due to errors in the input data can be problematic.

A Bayesian approach

We proposed a framework to calibrate land use Constrained Cellular automata models automatically based on urban genesis with a novel application of Markov Chain Monte Carlo Approximate Bayesian Computation (MCMC-ABC). We brought together four components in this framework: a Constrained Cellular automata model that has a parameter space as small as possible while retaining the characteristic complexity and predictability of the model, a goodness-of-fit measure that captures the spatial structure of an urban area, the urban change data, and a likelihood-free parameter estimation method Markov Chain Monte Carlo Approximate Bayesian Computation.

Working with the proposed framework, we performed parameter calibrations of the proposed Constrained Cellular automata land use model for two UK cities – Oxford and Swindon, based on CORINE Land Cover (CLC) data. We were able to automatically calibrate parameters and understand their uncertainty. The calibrated parameters captured the spatial structures of Oxford and Swindon. Specifically, we demonstrated Constrained Cellular automata land use model calibration based on urban genesis could lead to better land use change predictions than short term location-to-location calibration.

Overall, our proposed framework and results develop an objective evidence-based approach to complex land use change modelling. The reduced parameter space and the probabilistic approach to parameter estimation created opportunities to investigate a wider range of possible model outcomes and be better informed about the uncertainty in future land use trajectories. By comparing parameter estimates for different regions, we identified different modes of land use change and have used these to explore alternative scenarios for future land use. Thus, decision makers can have a fuller insight in an inherently uncertain domain.