A pixel-based method to calculate the urban compactness and its preliminary application

Abstract

A pixel-based method was provided to calculate the urban compactness. Remote sensing technology was used to extract urban-used land information and the urban pixels in the classification image were directly used to calculate the urban compactness, which will be more proper. The method was basing on the assumption that the urban with a circle form is the most compact. 40 virtual circular cities with different radius were constructed to seek a formula to quantify the urban compactness. For each virtual city, 2 data can be acquired which are the circle area and the average distance (AD) of till the pixels to the circle center. Regression analysis shows that there is a good relationship between the urban area and the AD. The 40 data pairs of circle areas (y) and average distances (x) were used for regression analysis and it can be found that a curve function of y = 6.9351x(2.0039) can simulate the points perfectly (r=1). Obviously, this curve is educed by countless virtual circular cities with different radius and the same compactness. Actually, for each real city in the classification image, a specific area anti an average distance can be calculated directly. With the two specific data, there is one exclusive point and also there is one and only one curve with function of y = 6.9351 x(D) passing the point. Studies showed that the value of D can be used to quantify the urban compactness. The method was applied to Dongguan city in the Pearl River delta, China and the compactness of Dongguan in the year of 1990 and 2003 were separately 1.76 and 1.87. The results accorded with the fact and showed the effect of the method.