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	Clark Density 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	Walter G. Hansen
種類	Empirical regression model of urban population density decline with distance	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	Clark's Law, Negative-Exponential Density Model, Exponential Population Density Gradient, Clark Density Gradient	Hansen Accessibility, Gravity Accessibility Measure, Potential Accessibility, Spatial Accessibility Index
関連	4	4
概要	The Clark density model is the classic empirical description of how urban population density falls with distance from the city centre, formulated by the economist Colin Clark in 1951. It states that density declines exponentially outward from a central peak, so that plotting the logarithm of density against distance yields a straight line whose slope is the density gradient. This negative-exponential 'law' became the standard model of urban spatial structure and the empirical foundation for later monocentric-city theory.	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.