Cities & Satellite Imagery: Models for Regional Change

Cities are constantly evolving, complex systems; and modeling them, both theoretically and empirically, is a complicated task. In this paper, we develop a methodology to spatially model urban areas based on a grid system of data largely derived from satellite images. The work emphasizes spatial relationships between various geographic, land-use, and demographic variables characterizing fine zones across and around regions. It derives and combines land use cover data for the Austin, Texas, region from a panel of satellite images, cartographic maps and U.S. Census of Population data. A variety of spatial attributes, including land use mix, are computed, and several land use and demographic models are run INTRODUCTION Urban systems are intricate, multifaceted and constantly evolving. Their evolution is dictated by a large number of influences, including public policy, individual preferences and actions, the physical landscape, technology and history. All of these factors (and more) interact in myriad ways. Discerning how and why urban systems evolve is, from the start, an extremely difficult task. There is great benefit to uncovering the dynamics underlying urban systems. Understanding the ways in which geographic, economic, demographic, political and other factors interact is of interest to transportation engineers and land use planners, economists as well as historians, policymakers and the public. Models that reliably track these interactions illuminate how policy impacts land use and travel patterns, welfare and development, congestion and air quality, and more. The desire to understand the evolution of urban systems certainly is nothing new. Christaller (1954) introduced “central place theory” in the 1930s, hypothesizing that urban “centers” of varying size, economic power and function, would arrange themselves according to regular, geometric patterns. Allen (1997) and Sonis (2001) have applied this concept to models of both real and theoretical cities, with some success. However, in applying such a restrictive model to the real world, embedded structural features – rather than reality – can dominate and skew the application. In order to “grow” urban systems, Weidlich (2000) applied purely theoretical concepts from synergetics, systems, and random utility theory. Though his cities appear realistic, they are purely theoretical, and the practical application of the work is not obvious. This problem is fundamentally the same as that with central places theory: the connection between theory and reality is tenuous. Care must be taken when attempting to apply theories, calibrated on the basis of empirical data, to actual urban systems. Parker, et. al. (2003) discussed the wide range of many land-use/cover change (LUCC) models recently developed. They pointed out that, due to the complexity of the systems encompassing land-use/cover, no one existing model is of more use than others; thus, a wide range of models, from the theoretical to the empirical, are being investigated. In this paper, a closer connection between the real world and the model, as opposed to largely theoretical work, is sought. This parallels some recent models, developed for use by planning organizations for regional forecasting and policymaking. The regional models most similar to the work undertaken here are UrbanSim, What If?, and CUF2. UrbanSim (Waddell 2002) micro-simulates the effects of location, land use, and policy decisions by households, workers, developers and policymakers on the land use patterns and rents across a region. Land use and development is modeled at the level of single parcels. Others are related to a relatively fine grid. Klosterman’s (1999) “What if?” model of land use assigns land uses to a set of homogeneous zones in a bottom-up fashion, derived from socioeconomic, geographic, transportation and zoning information. Landis and Zhang’s (1998) California Urban Futures 2 (CUF2) model employs multinomial models of land-use change per hectare (or other unit of observation) to predict future land use patterns. These models share qualities with the models pursued here. This work’s distinction lies in its acquisition and interpretation of data. This paper introduces a framework to analyze urban growth, relying largely on landcover data derived from satellite images. The following sections detail the data sets developed, along with model specifications and results for an Austin, Texas, application. DATA DESCRIPTION Satellite data offer excellent opportunities and considerable challenges. A serious and recurring problem for modeling urban systems has been the lack of panels of spatially detailed data. Remote sensing, imaging technology, and geographical information systems are making accurate land cover maps far more accessible to the researcher, and to the public. In particular, global satellite imaging, initiated in the early 1970s, provides highly detailed images regularly. And image analysis software can classify these by various general categories. GIS software combines data maps of various types, dramatically facilitating spatial analysis. The United States launched LandSat 1 in 1972. Passing over Austin every 18 days, this early satellite provides images with 79 m x 79 m pixel resolution. LandSat 4 was launched in 1982, and resulted in 185 km x 185 km images with 30 m x 30m resolution with a repeat orbit cycle of 16 days. 1999’s LandSat 7 has essentially identical orbit and image characteristics to LandSat 4, with the exception of a more extensive imaging system. This system works by scanning multiple passes (each representing one pixel) over an area and recording the reflectance of six distinct spectral bands (Richards and Jia 2000). Some image distortion results from the satellite’s motion during scanning, the fact that the scanner is effectively a point rather than a strip, and the overlap of individual scans. Pre-processing of the image corrects much of this, for viewing on a flat surface. When comparing pixels from the same image or across images, cloud cover, time of day and sun location (vis-à-vis the satellite) also can introduce errors. The methods of rectifying a LandSat image are distortions themselves. And they do not guarantee image accuracy, for a given projection, when imported into a GIS or other image processing software. Thus, a large amount of post-processing may be necessary by the consumer in order to further correct image distortion. In the data set used here, the LandSat 7 image had to be matched with Digital Ortho Quarter Quadrangles (DOQQ’s), which are rectified aerial photographs maintained by the U.S. Geological Survey. The land-cover data used here was derived from a 48.5 km x 55.8 km, 30m x 30m resolution LandSat 7 image taken at 4:30 pm on September 4, 2000. It is of Austin, Texas, and the surrounding region (Trelogan 2002). Using a process called supervised classification (see, e.g., Richards and Jia 1999), planning professor Dr. Barbara Parmenter and students created a land-cover map from the original LandSat data. Using USGS topographic maps and DOQQ’s as guides, they created a set of training data by classifying sections of the LandSat image. These were used to generate a set of decision rules by which the entire LandSat image was then classified. Spatial filtering also was performed, in order to remove residual noise from the processed map (Trelogan 2002). Each 30m x 30m pixel’s resulting land-cover data is classified into 9 categories: water, barren, forest/woodland, shrubland, herbaceous natural/semi-natural, herbaceous planted/cultivated, fallow, developed residential, and developed industrial/commercial/transportation. From these, secondary land-cover maps were developed, by combining different categories into single land-cover specifications. Figure 1 shows a secondary land-cover map using three classifications: developed residential, developed industrial/commercial/transportation and undeveloped. Figure 1. Secondary land-cover map of the Austin, Texas region distinguishing developed (both residential and industrial/commercial) from undeveloped land. Using these data, one additional spatial statistic is calculated here. It is land mix, characterizing diversity in land cover. (Kockelman 1997) Mix is an index of adjacent pixels’ dissimilarity; it measures the level of homogeneity between a central pixel’s use type (X0) and those of its neighbors (Xi). Here, the eight immediately surrounding pixels are considered (as in Figure 2). Mathematically, the index can be defined as follows: