Towards a comprehensive framework for modeling urban spatial dynamics

The increasing availability of spatial micro data offers new potential for understanding the micro foundations of urban spatial dynamics. However, because urban systems are complex, induction alone is insufficient. Nonlinearities and path dependence imply that qualitatively new dynamics can emerge due to stochastic shocks or threshold effects. Given the policy needs for managing urban growth and decline and the growing desire for sustainable urban forms, models must be able not only to explain empirical regularities, but also characterize system-level dynamics and assess the plausible range of outcomes under alternative scenarios. Towards this end, we discuss a comprehensive modeling approach that is comprised of bottom-up and top-down models in which both inductive and deductive approaches are used to describe and explain urban spatial dynamics. We propose that this comprehensive modeling approach consists of three iterative tasks: (1) identify empirical regularities in the spatial pattern dynamics of key meso and macro variables; (2) explain these regularities with process-based micro models that link individual behavior to the emergence of meso and macro dynamics; and (3) determine the systems dynamical equations that characterize the relationships between micro processes and meso and macro pattern dynamics. Along the way, we also clarify types of complexity (input and output) and discuss dimensions of complexity (spatial, temporal, and behavioral). While no one to date has achieved this kind of comprehensive modeling, meaningful progress has been made in characterizing and explaining urban spatial dynamics. We highlight examples of this work from the recent literature and conclude with a discussion of key challenges.