Complexity and performance of urban expansion models

Urban expansion and spatial patterns of urban land have a large effect on many socioeconomic and environmental processes. A wide variety of modelling approaches has been introduced to predict and simulate future urban development. These models are often based on the interpretation of various determining factors that are used to create a probability map. The main objective of this paper is to evaluate the performance of different modelling approaches for simulating spatial patterns of urban expansion in Flanders and Brussels in the period 1988–2000. Hereto, a set of urban expansion models with increasing complexity was developed based on: (i) logistic regression equations taking various numbers of determining variables into account, (ii) CA transition rules and (iii) hybrid procedures, combining both approaches. The outcome of each model was validated in order to assess the predictive value of the three modelling approaches and of the different determining variables that were used in the logistic regression models. The results show that a hybrid model structure, integrating (static) determining factors (distance to the main roads, distance to the largest cities, employment potential, slope and zoning status of the land) and (dynamic) neighbourhood interactions produces the most accurate probability map. The study, however, points out that it is not useful to make a statement on the validity of a model based on only one goodness-of-fit measure. When the model results are validated at multiple resolutions, the logistic regression model, which incorporates only two explanatory variables, outperforms both the CA-based model and the hybrid model.