Mapping the morphology of sprawl and blight: A note on entropy

The urban expansion from the city center to the suburb and beyond is indicated by Shannon entropy, a robust and versatile measure of sprawl. However, the metropolitan regionwide entropy masks the morphology of land cover and land use consequential to urban expansion within the city-region. To surmount the limitation, we focus on the block-group, which is a US census defined socio-spatial unit that identifies the metropolitan region\u27s development pattern structurally, forming tracts that comprise neighborhoods. The concentration and dispersion of land use and land cover by block-group reveals a North American metropolitan region\u27s commonly known but rarely measured spatial structure of its urban and suburban sprawl. We use parcel data from county assessor of property (GIS) and land cover pixel data from the National Land Cover Data (NLCD) to compute block-group land-use and land-cover entropy. The change in block group entropy over a decade indicates whether the city- region\u27s land use and land cover transition to a concentrated or dispersed pattern. Furthermore, we test a hypothesis that blight correlates with sprawl. Blight and sprawl are among the key factors that plague the metropolitan region. We determine the correlations with household income as well as (block group) distance from the city center. It turns out, blight is among the universally held distance-decay phenomena. The share of the block group\u27s blighted properties decays (nonlinearly) with distance from the city center. Highlights for public administration, management and planning: •The metropolitan region\u27s outward growth is highlighted by mapping the changing morphology of the block group within the city-region. •The block group entropy is computed with land use (parcel) and land cover (pixel) data. •The block group entropy change indicates the pattern of the land use and land cover transition with concentration or dispersion. •We test the hypothesis that blight correlates with sprawl with statistical models. •The block group\u27s blighted properties decrease (nonlinearly) with distance from the city center