Geographic information system‐based edge effect correction for Ripley'sK‐function under irregular boundaries

Abstract

AbstractRipley'sK‐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'sK‐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'sK‐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.