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USM Toolset - The USM Toolset was developed to facilitate the calculation of Weighted Urban Proliferation (WUP) and all components of urban sprawl for landscapes that include built-up areas (e.g., dispersion (DIS), land uptake per person (LUP).

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Weighted Urban Proliferation (WUP) has three components: PBA, DIS and LUP (or UD). The proportion of built-up areas (PBA) is the proportion of the size of built-up areas to the size of the landscape (reporting unit): PBA = Area of built-up area / Area of reporting unit. Degree of urban dispersion (DIS) measures the dispersion of built-up areas based on the distances between any two points within the built-up areas (Jaeger et al. 2010b). DIS is expressed in urban permeation units per square meter of built-up area (UPU/m2). The more dispersed the built-up areas, the larger the value of DIS. Therefore, more compact built-up areas have lower values of DIS than more dispersed built-up areas. Land Uptake per person (LUP) is the area of land that is used per inhabitant or job within the built-up areas and expressed in square meters per inhabitant or job (m2/(inh. or job)) (LUP = Area of built-up areas/Number of inhabitants and jobs). High LUP values indicate that more space is used per inhabitant or workplacecompared to areas where LUP values are lower. LUP is in fact the reciprocal of UD: LUP = 1/UD.