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Nearly, half the world's population of six-and-a-half billion now live in cities, a substantial increase from the ten percent in 1900 that marks rapid and continuing urbanization at a global scale. Concomitantly, there has been growth in the spatial extent and diversity of cities with the erstwhile centralized city expanding into surrounding regions and transforming our most basic concepts of cities. This growth has been fostered by waning communication costs and increased global interdependence that have greatly strengthened the connectivity of local and global processes in both top-down (e.g., global manufacturing firms seek out low labor cost regions of the world) and bottom-up (e.g., natural locations attract households and spur economic growth) directions. The implication is that 21st century urban systems are even more likely to exhibit the characteristics of complex, nonlinear systems than their predecessors. This raises important policy questions about the management of these systems. Increased interactions can reduce the robustness of urban and natural systems by making them more susceptible to external shocks. Interactions can also lead to increased diversity of people or economic activity within a region, which can enhance robustness. Understanding urban spatial systems as complex, nonlinear and adaptive systems is, therefore, critical for fostering the sustainability of these systems and of the natural systems on which they depend.

Current urban and regional economic models—highly stylized, typically spatially abstract models that rely on equilibrium solutions to describe higher-scale patterns —are often analytically tractable, but inadequate for the purpose of understanding multiscale pattern dynamics that are not well approximated by equilibrium models. A few models of urban systems as complex, nonlinear systems have been put forward over the years and evidence on the macro patterns of cities demonstrate scaling phenomena that are common to complex systems. However, due to a lack of spatially and temporally detailed data at a micro scale, these models have failed to elucidate the dynamics of actual urban systems and how they evolve over time from microscale dynamics. Yet this hypothesis, that microscale interactions shape higher-scale urban form, has become a central working hypothesis of mainstream urban spatial theory, from economics (knowledge spillovers among firms lead to subcenter formation) to geography (cities are shaped by face-to-face communications) to sociology (racial preferences lead to neighborhood segregation) and public policy (sprawl results from local jurisdictional competition).

Spatially referenced data defined for small areas (e.g., a parcel or patch) are increasingly available due to GIS technologies that are now commonly used to manage these data. Recently, PI Irwin and coauthor Bockstael (PNAS, Dec 2007) have used extensive land-use data for Maryland from 1973 and 2000 to study urban sprawl and shown that substantial increases in mean fragmentation have occurred across urban and surrounding rural regions. Their results provide evidence of new urban dynamical patterns, but the lack of temporal data precludes any investigation of the underlying processes driving these changes. This lack of temporally rich spatial microdata is not unusual. In fact, we know of no study that has used such data to empirically investigate microscale interactions and emergent dynamics at multiple higher scales. In the absence of detailed data, theoretical models have limited value and methodological progress has slowed, so that even with the right data in hand, the methods for multiscale analysis of emergent patterns in complex human systems are unknown.

We propose to address these shortcomings by collecting spatially referenced, temporally rich micro data on urban patterns and applying multiscale analysis tools and agent-based models to elucidate complex dynamics. Our primary research goal is to better understand the emergence of urban dynamical patterns at multiple scales (e.g., neighborhood, suburb, metro area) from the microscale heterogeneity and dynamics of agents (households, firms, local governments) with the long-term goal of examining policies that enhance the sustainability and robustness of urban and natural systems. The success of this data-driven approach clearly depends on the data themselves. We will construct a spatially referenced, annual time series of residential, commercial and industrial development at the land parcel scale from 1900-present for several large U.S. regions, supplemented with time series data on economic, demographic, amenity and policy variables. These data will provide a unique opportunity to adapt a variety of multiscale techniques and apply them in new ways to analyzing urban spatial dynamics from the bottom up.

Scientific Contribution of Proposed Research

The proposed interdisciplinary research will provide new empirical evidence on emergent urban patterns and dynamics at multiple scales; break new ground in linking higher-scale emergent dynamics with process-based models of agent behavior; and facilitate the development of new multiscale analysis tools that provide a systematic approach to summarizing higher-scale dynamical patterns from lower level heterogeneity.

Empirical evidence on emergent patterns and dynamics at multiple scales

Empirical analysis of urban patterns has typically been conducted with relatively aggregate data, e.g., population or employment counts at the census enumeration scale of tracts or jurisdictions, and with data limited to urban areas. Estimates of aggregate population and employment density surfaces are a common approach. Such studies have demonstrated the existence of multiple urban subcenters and declining population and employment gradients with distance from these centers, a result that is consistent with the basic urban economic model.

Spatially detailed data—i.e., data that represents the process at the scale at which it occurs—is only limitedly available but where it is, suggests a more complex set of processes. Our recent examination of urban land use dynamics in the state of Maryland (PNAS, Dec 2007) reveals substantial spatial heterogeneity in the evolution of urban patterns and only limited support for the dynamic predictions of the urban economic model.

The proposed work will build on this spatially-detailed empirical analysis by collecting spatially referenced, temporally rich data at the micro scale on urban development and other key variables for several large U.S. regions. Empirical evidence of complex dynamics is given by the systematic emergence of statistically significant patterns at higher scales from lower-scale heterogeneity and dynamics. This approach will allow us to empirically examine the proposition that the complexity of urban spatial dynamics has increased over time and to identify some of its potential causes, e.g., by disentangling lower-scale interaction effects from top-down policy effects.

Linking emergent patterns with agent decisions and interactions

It is often the case that urban pattern analyses are performed independently of process-based modeling. Our research will link physical characterizations of emergent patterns with functional agent-based models of interactions that can be simulated in a two-dimensional environment to generate predicted patterns of agent location and land use. This approach will allow us to iterate between empirical analysis of multiscale dynamics and simulated dynamical patterns generated by household and firm decision-making and interactions. By varying the microscale features, e.g., agent heterogeneity and scale lengths of the externalities generated by agents, we will systematically explore how changes in lower-level processes manifest themselves in higher-scale patterns and dynamics.

Agent-based models are being increasingly applied to studies in which interactions and agent or environment heterogeneity are important, but nonetheless the modeling methodology is still in its infancy. For example, agent-based models that are consistent with economic models of land and labor markets have not been fully developed and thus our work will make an important contribution to agent-based modeling in economics and land change science.

New tools for analyzing emergence in complex systems

The main appeal of agent-based models, that more realistic decision rules can be considered, is also a substantial limitation since more complicated decision rules yield more complicated microscale patterns from which it is difficult to discern higher-scale patterns. The task of multiscale analysis is even more difficult with actual data that reflect substantial heterogeneity and spurious variation. The key challenge in either case is to identify the right collective variables that describe the system at different scales and their time evolution. We will do this by generalizing coarse-graining methods, for example, wavelet and cluster analysis that have used in physics to study simple homogeneous systems, and applying them to empirical and simulated data to deduce statistically significant conclusions on emergent dynamical patterns. The generalization of these tools to heterogeneous systems such as ours is beneficial for other studies of complex systems in which spatial heterogeneity and interaction are primary sources of complexity.

Societal Significance

The research will bring together extensive empirical data with sophisticated theoretical techniques across multiple disciplines to address a significant social problem, the evolution of urban form and function. In so doing, it offers a new and important approach to the study of urban systems that will encourage even greater collection of detailed and variegated data that in turn can be studied using methods for complex systems analysis of the kind that will be developed in this project. Through continuous iteration between data analysis and model building, this approach will yield new models of the complex dynamics of urban systems that go beyond theory and pedagogy to providing the necessary realism for guiding policies and the sustainability of urban and natural systems.