Negative Exponential Model Parameters and the Size of Large Urban Areas in the U.S., 1950-2010

Abstract

The density of urban development tends toward a negative exponential decline with distance from the center. The density gradient has been observed to be inversely related to the size of the urban area, while the central density is directly related. If the negative exponential density decline holds, the size of the urban area, the density gradient, and the central density are necessarily mathematically related. This relationship is derived, and a simplified approximation is compared with the sizes of large urban areas and the estimated density gradients and central densities. The results generally confirm the expectations, although the coefficient for the central density is larger than expected, possibly because of the use of gross rather than net residential density in estimating the parameters for the negative exponential model.