The measurement of residential segregation patterns and trends has been limited by a reliance on segregation measures that do not appropriately take into account the spatial patterning of population distributions. In this paper we define a general approach to measuring spatial segregation among multiple population groups. This general approach allows researchers to specify any theoretically based definition of spatial proximity desired in computing segregation measures. Based on this general approach, we develop a general spatial exposure/isolation index (P P*), and a set of general multigroup spatial evenness/ clustering indices: a spatial information theory index (H H), a spatial relative diversity index (R R), and a spatial dissimilarity index (D D). We review these and previously proposed spatial segregation indices against a set of eight desirable properties of spatial segregation indices. We conclude that the spatial exposure/isolation indexP P*-which can be interpreted as a

The concept of an isovist has had a long history in both architecture and geography, as well as mathematics. Tandy (1967) appears to have been the originator of the term isovist'. He presents isovists as a method of``taking away from the [architectural or landscape] site a permanent record of what would otherwise be dependent on either memory or upon an unwieldy number of annotated photographs'' (page 9). The same idea has a similarly long history in the guise of the`viewshed' in the field of landscape architecture and planning (Amidon and Elsner, 1968; Lynch, 1976) and in terms of intervisibility' in computer topographic models (Gallagher, 1972). The appeal of the concept is that isovists are an intuitively attractive way of thinking about a spatial environment, because they provide a description of the spacè from inside', from the point of view of individuals, as they perceive it, interact with it, and move through it. As such, isovists have particular relevance to architectural analysis. Benedikt (1979) introduced a set of analytic measurements of isovist properties to be applied to achieve quantitative descriptions of spatial environments. Benedikt starts by considering the volume visible from a location and then simplifies this representation by taking a horizontal slice through the`isovist polyhedron'. The resulting`isovists' are always single polygons without holes, as shown in figure 1 (see over). Consequently, Benedikt considers geometric properties of isovists, such as area and perimeter. Thus he begins to quantify space, or what our perception of space might be, and the potential for its use. Benedikt notes that, in order to quantify a whole configuration, more than a single isovist is required and he suggests that the way in which we experience a space, and how we use it, is related to the interplay of isovists. This leads

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The census tract-based residential segregation literature rests on problematic assumptions about geographic scale and proximity. We pursue a new tract-free approach that combines explicitly spatial concepts and methods to examine racial segregation across egocentric local environments of varying size. Using 2000 census data for the 100 largest U.S. metropolitan areas, we compute a spatially modified version of the information theory index H to describe patterns of black-white, Hispanic-white, Asian-white, and multi-group segregation at different scales. The metropolitan structural characteristics that best distinguish micro-segregation from macro-segregation for each group combination are identified, and their effects are decomposed into portions due to racial variation occurring over short and long distances. A comparison of our results to those from tract-based analyses confirms the value of the new approach.

vulnerability assessment, vulnerability indicators, vulnerability index, indicator weighting, Pareto ranking, social vulnerability, extreme weather events,