عنوان مقاله [English]
نویسندگان [English]چکیده [English]
There have been different types of analytical functions for the recognition of geographic phenomenon distribution patterns which have been introduced in GIS so far, which among them K Function known as Ripley’s K function is the evolved one. Based on this function the distribution of a geographic phenomenon in the region compared to random distribution is assessed and the level of clustering (concentration) is measured through different distances. So In this research the level of clustering of urban development has been measured at different distances and time periods.
Urban growth is a process combining spontaneous and self-organizing growth (Wu,2000). The self-organizing reflects a process that results from the previous development in the immediate neighborhood (Wu, 2002). The resulting pattern of this process is most agglomerated or clustered. The existence of an environmental or socio-economic factor in a region can contribute to clustering of development and as a result another process called spontaneous growth is outlined. This process occurs under of impacts of such factors that are beyond of neighborhood areas. The clustering level of development is less in areas which are more affected by spontaneous development, in other words in this process the level of clustering is less in shorter distances.
The main issue in the evaluation of clustering level is acquiring an index whereby the clustering or dispersion levels of developed area in different distances and in overall are somehow measured, that in this research it’s been implemented by using K Function in GIS.
The counting of points which are placed in each distance zone, is the basis of calculating the Ripley’s K Function. The Transformed K Function is often referred to as L(d) in many references. This function is used for better recognition of point distribution pattern against random distribution and to ease drawing of graphs and is defined as the below equation: (Mitchell, 2005)
In which L(d) is the transformed K Function value at distance d, I(dij)=1 if the distance of point i to j is less than d and otherwise I(dij)=0. A is the area of region and N is the number of observed points in the region.
One of the disadvantages in calculating K Function is the existing points near the border of study area and emergence of edge effects. The most reliable way to eliminate the edge effects is simulating random distribution of points and comparing the outcomes with real observed points. If the calculated value of L(d) results from observed points is bigger than L(d) values from random points, then it can be said that observed points are clustered.
Given the remarkable development of urban areas on the suburbs of south eastern Tehran, the extents of towns: Islamshahr, Robatkarim and Nasim Shahr were chosen separately in this research and the level of clustering of urban developments was measured at time periods: 1992 to 1996 and 1996 to 2002.
The developed urban areas were extracted from Spot satellite images, then the raster development layer of urban areas were extracted in the form of points in which each point represents one developed 20m*20m pixel, Eventually used as K Function input.
For the true judgment and comparison about clustering level of development in different time periods there must be a relative index defined for the comparison of real distribution of points with random distribution.
If LS(d) is assumed as K Function’s maximum value in the definite distance of d amongst implemented random simulations (Monte Carlo simulation) – in this research, random simulations executed 9 times (to reach the significant level of 90%) – and assuming LO(d) as the value of K Function for observed (real) distribution of points at distance d, then ?L(d) which is indicative of clustering measurement of development in the specified d distance is defined as follows:
The above equation is calculated separately for each distance (d) in each study area. The bigger index demonstrates more clustering of developed points and closeness to zero demonstrates the resemblance of developed points to random distribution. Eventually can be defined according to the following equation as an index for total clustering measurement of development in the entire extent of each study area:
In which n is the number of considered distances for implementation of K Function, the bigger indicates more clustering of development in the study area.
In this research ArcGIS 9.2 software was used for implementation of Ripley’s K Function. This software has also the capability of executing the simulation of random points.
The K Function was implemented for developed points in the years of 1996 and 2002 for every three town extents. Random distribution was also simulated for every region and ultimately the indexes: LO(d), LS(d) and were separately calculated for each of them.
The resulting outcomes from calculation of - as an index for overall measurement of clustering in the study area for developed areas- showed that the clustering of development has significantly decreased in both Nasim shahr and Robat karim from 1996 to 2002 therefore we can conclude that the development process in the determined area in these two regions are heading towards more dispersion but in the Islamshahr the clustering of development was higher than previous period.
Generally, we can say that Ripley’s K Function provides a proper estimate of the clustering of urban development at different periods and distances that can be a beacon for researchers in recognition of different patterns of the development process.