Geographic information system-based edge effect correction for Ripley's K-function under irregular boundaries

摘要

Ripley's K-function is a test to detect geographically distributed patterns occurring across spatial scales. Initially, it assumed infinitely continuous planar space, but in reality, any geographic distribution occurs in a bounded region. Hence, the edge problem must be solved in the application of Ripley's K-function. Traditionally, three basic edge correction methods were designed for regular study plots because of simplified geometric computation: the Ripley circumference, buffer zone, and toroidal methods. For an irregular-shaped study region, a geographic information system (GIS) is needed to support geometric calculation of complex shapes. The Ripley circumference method was originally implemented by Haase and has been modified into a Python program in a GIS environment via Monte Carlo simulation (hereafter, the Ripley-Haase and Ripley-GIS methods). The results show that in terms of the statistical powers of clustering detection for irregular boundaries, the Ripley-GIS method is the most stable, followed by the buffer zone, toroidal, and Ripley-Haase methods. After edge effects of irregular boundaries have been eliminated, Ripley's K-function is used to estimate the degree of spatial clustering of cities in a given territory, and in this paper, we demonstrate that by reference to the relationship between urban spatial structure and economic growth in China.