This paper applies methods of multiple resolution map comparison to quantify characteristics for 13 applications of 9 different popular peer-reviewed land change models. Each modeling application simulates change of land categories in raster maps from an initial time to a subsequent time. For each modeling application, the statistical methods compare: (1) a reference map of the initial time, (2) ence map of the subsequent time, and (3) a prediction map of the subsequent time. The three possible two-map comparisons for each application characterize: (1) the dynamics of the landscape, (2) the behavior of the model, and (3) the accuracy of the prediction. The three-map comparison for each application specifies the amount of the prediction's accuracy that is attributable to land persistence versus land change. Results show that the amount of error is larger than the amount of correctly predicted change for 12 of the 13 applications at the resolution of the raw data. The applications are summarized and compared using two statistics: the null resolution and the figure of merit. According to the figure of merit, the more accurate applications are the 123Comparing the input, output, and validation maps for several models of land change 13 ones where the amount of observed net change in the reference maps is larger. This paper facilitates communication among land change modelers, because it illustrates the range of results for a variety of models using scientifically rigorous, generally applicable, and intellectually accessible statistical techniques. JEL Classification

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 spatiotemporal 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.

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.

The authors build on a recent development in urban geographic theory, providing evidence of an oscillatory behavior in spatiotemporal patterns of urban growth. With the aid of remotely sensed data, the spatial extent of urban areas in the Houston (USA) metropolitan region from 1974 to 2002 was analyzed by spatial metrics. Regularities in the spatial urban growth pattern were identified with temporal periods as short as thirty years by means of spatial metric values, including mean nearest-neighbor distance, mean patch area, total number of urban patches, and mean patch fractal dimension. Through changes in these values, a distinct oscillation between phases of diffusion and coalescence in urban growth was revealed. The results suggest that the hypothesized process of diffusion and coalescence may occur over shorter time periods than previously thought, and that the patterns are readily observable in real-world systems.

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