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	Urban Density Gradient Model	Accessibility Analysis
分野	Human Geography	Human Geography
系統	Regression model	Process / pipeline
提唱年	1951	1959
提唱者	Colin Clark; Edwin Mills & Richard Muth (theory); Bruce Newling (quadratic form)	Walter G. Hansen
種類	Family of functional models of urban population density as a function of distance from the centre	Spatial index of the ease of reaching opportunities from a location
原典	Clark, C. (1951). Urban population densities. Journal of the Royal Statistical Society. Series A (General), 114(4), 490–496.	Hansen, W. G. (1959). How accessibility shapes land use. Journal of the American Institute of Planners, 25(2), 73–76.
別名	Urban Density Function, Population Density Gradient, Density-Distance Function, Monocentric Density Model	Hansen Accessibility, Gravity Accessibility Measure, Potential Accessibility, Spatial Accessibility Index
関連	4	4
概要	The urban density gradient model is the broad family of functional relationships that describe how population density varies with distance from a city's centre. Its canonical member is Colin Clark's 1951 negative-exponential form, but the family also includes Bruce Newling's quadratic-exponential function that permits a density crater at the core, simpler linear and Smeed forms, and the economic micro-foundation supplied by the Muth-Mills monocentric city model. Together these give planners and economists a compact, comparable language for urban spatial structure.	Accessibility analysis measures how easily opportunities — jobs, shops, clinics, parks — can be reached from a given location, combining the attractiveness (size) of destinations with the cost of travelling to them. The gravity-based formulation introduced by Walter Hansen in 1959 sums the opportunities at all destinations, each discounted by a distance-decay function of travel cost, producing a single accessibility score per origin that has become a foundational concept in transport geography and urban planning.