Keith C. Clarke

A Self-Modifying Cellular Automaton Model of Historical Urbanization in the San Francisco Bay Area

In this paper we describe a cellular automaton (CA) simulation model developed to predict urban growth as part of a project for estimating the regional and broader impact of urbanization on the San Francisco Bay areas climate. The rules of the model are more complex than those of a typical CA and involve the use of multiple data sources, including topography, road networks, and existing settlement distributions, and their modification over time. In addition, the control parameters of the model are allowed to self-modify: that is, the CA adapts itself to the circumstances it generates, in particular, during periods of rapid growth or stagnation. In addition, the model was written to allow the accumulation of probabilistic estimates based on Monte Carlo methods. Calibration of the model has been accomplished by the use of historical maps to compare model predictions of urbanization, based solely upon the distribution in year 1900, with observed data for years 1940, 1954, 1962, 1974, and 1990. The complexity of this model has made calibration a particularly demanding step. Lessons learned about the methods, measures, and strategies developed to calibrate the model may be of use in other environmental modeling contexts. With the calibration complete, the model is being used to generate a set of future scenarios for the San Francisco Bay area along with their probabilities based on the Monte Carlo version of the model. Animated dynamic mapping of the simulations will be used to allow visualization of the impact of future urban growth.

The spatiotemporal form of urban growth: measurement, analysis and modeling

This study explores the combined application of remote sensing, spatial metrics and spatial modeling to the analysis and modeling of urban growth in Santa Barbara, California. The investigation is based on a 72-year time series data set compiled from interpreted historical aerial photography and from IKONOS satellite imagery. Spatial metrics were used both specifically to assess the impact of urban development in four administrative districts, and generally to analyze the spatial and temporal dynamics of urban growth. The metrics quantify the temporal and spatial properties of urban development, and show definitively the impacts of growth constraints imposed on expansion by topography and by local planning efforts. The SLEUTH urban growth and land use change model was calibrated using the multi-temporal data sets for the entire study region. The calibrated model allowed us to fill gaps in the discontinuous historical time series of urban spatial extent, since maps and images were available only for selected years between 1930 and 2001. The model also allowed a spatial forecast of urban growth to the year 2030. The spatial metrics provided a detailed description of the accuracy of the models historical simulations that applied also to forecasts of future development. The results illustrate the utility of modeling in explaining the amount and spatial pattern of urban growth. Even using modeling, however, the forecasting of urban development remains problematic and could benefit from further research on spatial metrics and their incorporation into the model calibration process. The combined approach using remote sensing, spatial metrics and urban modeling is powerful, and may prove a productive new direction for the improved understanding, representation and modeling of the spatiotemporal forms due to the process of urbanization.

The use of remote sensing and landscape metrics to describe structures and changes in urban land uses

Remote sensing technology has great potential for acquisition of detailed and accurate land-use information for management and planning of urban regions. However, the determination of land-use data with high geometric and thematic accuracy is generally limited by the availability of adequate remote sensing data, in terms of spatial and temporal resolution, and digital image analysis techniques. This study introduces a methodology using information on image spatial form—landscape metrics—to describe urban land-use structures and land-cover changes that result from urban growth. The analysis is based on spatial analysis of land-cover structures mapped from digitally classified aerial photographs of the urban region Santa Barbara, CA. Landscape metrics were calculated for segmented areas of homogeneous urban land use to allow a further characterization of the land use of these areas. The results show a useful separation and characterization of three urban land-use types: commercial development, high-density residential, and low-density residential. Several important structural land-cover features were identified for this study. These were: the dominant general land cover (built up or vegetation), the housing density, the mean structure and plot size, and the spatial aggregation of built-up areas. For two test areas in the Santa Barbara region, changes (urban growth) in the urban spatial land-use structure can be described and quantified with landscape metrics. In order to discriminate more accurately between the three land-cover types of interest, the landscape metrics were further refined into what are termed ‘landscape metric signatures’ for the land-use categories. The analysis shows the importance of the spatial measurements as second-order image information that can contribute to more detailed mapping of urban areas and towards a more accurate characterization of spatial urban growth pattern.

The role of spatial metrics in the analysis and modeling of urban land use change

The paper explores a framework combining remote sensing and spatial metrics aimed at improving the analysis and modeling of urban growth and land use change. While remote sensing data have been used in urban modeling and analysis for some time, the proposed combination of remote sensing and spatial metrics for that purpose is quite novel. Starting with a review of recent developments in each of these fields, we show how the systematic, combined use of these tools can contribute an important new level of information to urban modeling and urban analysis in general. We claim that the proposed approach leads to an improved understanding and representation of urban dynamics and helps to develop alternative conceptions of urban spatial structure and change. The theoretical argument is then illustrated with actual examples from the urban area of Santa Barbara, California. Some questions for future research are finally put forward to help strengthen the potential of the proposed framework, especially regarding the further exploration of urban dynamics at different geographic scales.

Calibration of the SLEUTH urban growth model for Lisbon and Porto, Portugal

The SLEUTH model (slope, landuse, exclusion, urban extent, transportation and hillshade), formerly called the Clarke Cellular Automaton Urban Growth Model, was developed for and tested on various cities in North America, including Washington, DC, and San Francisco. In contrast, this research calibrated the SLEUTH model for two European cities, the Portuguese metropolitan areas of Lisbon and Porto. The SLEUTH model is a cellular automaton model, developed with predefined growth rules applied spatially to gridded maps of the cities in a set of nested loops, and was designed to be both scaleable and universally applicable. Urban expansion is modeled in a modified two-dimensional regular grid. Maps of topographic slope, land use, exclusions, urban extents, road transportation, and a graphic hillshade layer form the model input. This paper examines differences in the model’s behavior when the obviously different environment of a European city is captured in the data and modeled. Calibration results are included and interpreted in the context of the two cities, and an evaluation of the model’s portability and universality of application is made. Questions such as scalability, sequential multistage optimization by automated exploration of model parameter space, the problem of equifinality, and parameter sensitivity to local conditions are explored. The metropolitan areas present very different spatial and developmental characteristics. The Lisbon Metropolitan Area (the capital of Portugal) has a mix of north Atlantic and south Mediterranean influences. Property is organized in large patches of extensive farmland comprised of olive and corkorchards. The urban pattern of Lisbon and its environs is characterized by rapid urban sprawl, focused in the urban centers of Lisbon, Oeiras, Cascais

Spatial Metrics and Image Texture for Mapping Urban Land Use

The arrival of new-generation, high-spatial-resolution satellite imagery (e.g., Ikonos) has opened up new opportunities for detailed mapping and analysis of urban land use. Drawing on the traditional approach used in aerial photointerpretation, this study investigates an “object-oriented” method to classify a large urban area into detailed land-use categories. Spatial metrics and texture measures are used to describe the spatial characteristics of land-cover objects within each land-use region as derived from interpreted aerial photographs. In assessing how land-use categories vary in their spatial configuration, spatial metrics were found to provide the most important information for differentiating urban land uses. A detailed land-use map with nine categories was derived for the Santa Barbara South Coast Region area. Results from our work suggest that the region-based method exploiting spatial metrics and texture measurements is a potential new avenue to extract detailed urban land-use information from highresolution satellite imagery.

Computation of the fractal dimension of topographic surfaces using the triangular prism surface area method

Abstract A new method is proposed to calculate the fractional (fractal) dimension of topographic surfaces. The method uses a three-dimensional geometric equivalent of the “walking dividers” method in two dimensions. that is it takes elevation values at the corners of squares, interpolates a center value, divides the square into four triangles, and then computes the surface areas of the tops of the prisms which result from raising the triangles to their given elevations. By repeating this calculation for different size squares, the relationship between the total area of the topographic surface and the spacing of the squares is established, and used to estimate the fractal dimension. A computer program in the C programming language is presented to read digital terrain matrices and compute the fractal dimension of the surface using the method. Some test data sets are provided along with their computed fractal dimensions. Finally, the advantages and disadvantages of the method are discussed.

Spatio‐temporal dynamics in California's Central Valley: Empirical links to urban theory

This paper explores an addition to theory in urban geography pertaining to spatio‐temporal dynamics. Remotely sensed data on the historical extent of urban areas were used in a spatial metrics analysis of geographical form of towns and cities in the Central Valley of California (USA). Regularities in the spatio‐temporal pattern of urban growth were detected and characterized over a hundred year period. To test hypotheses about variation over geographical scale, multiple spatial extents were used in examining a set of spatial metric values including an index of contagion, the mean nearest neighbor distance, urban patch density and edge density. Through changes in these values a general temporal oscillation between phases of diffusion and coalescence in urban growth was revealed. Analysis of historical datasets revealed preliminary evidence supporting an addition to the theory of urban growth dynamics, one alluded to in some previous research, but not well developed. The empirical results and findings provide a lead for future research into the dynamics of urban growth and further development of existing urban theory.

The Use of Scenarios in Land-Use Planning

Land-development scenarios as a means of representing the future have been in the planners toolkit for several decades. In this paper we provide a systematic view of four basic issues that concern scenarists and scenario users—the concepts, functions, credentials, and efficacy of land-development scenarios. Drawing upon the wealthy and expanding pool of knowledge and experience as reported in the literature, we put forward the notion that a land-development scenario set is both a bridge that connects the process of modeling with that of planning and a cognitive apparatus that stretches peoples thinking and broadens their views in planning. The dual function entitles a scenario set to be a favored member of a family of innate instruments that humans operate in making decisions. Under this overarching framework, we propose three credentials that are by no means exhaustive yet are claimed to be essential for a scenario set to perform best the dual function. These are plausible unexpectedness, informational vividness, and cognitively ergonomic design. After exploring the efficacy issue of a scenario set with respect to its impacts on communities at large, we suggest that basic research efforts be underway that aim at the development of unified theories of land-development scenarios, or even scenarios in general, under a possible name of scenariology—the study of scenarios.

Toward Optimal Calibration of the SLEUTH Land Use Change Model

SLEUTH is a computational simulation model that uses adaptive cellular automata to simulate the way cities grow and change their surrounding land uses. It has long been known that models are of most value when calibrated, and that using backcasting (testing against known prior data) is an effective calibration method. SLEUTH’s calibration uses the brute force method: every possible combination and permutation of its control parameters is tried, and the outcomes tested for their success at replicating prior data. Of the SLEUTH calibration approaches tried so far, there have been several suggested rules to follow during the brute force procedure to deal with problems of tractability, most of which leave out many of the possible parameter combinations. In this research, we instead attempt to create the complete set of possible outcomes with the goal of examining them to select the optimum from among the millions of possibilities. The self-organizing map (SOM) was used as a data reduction method to pursue the isolation of the best parameter sets, and to indicate which of the existing 13 calibration metrics used in SLEUTH are necessary to arrive at the optimum. As a result, a new metric is proposed that will be of value in future SLEUTH applications. The new measure combines seven of the current measures, eight if land use is modeled, and is recommended as a way to make SLEUTH applications more directly comparable, and to give superior modeling and forecasting results.