A Metric of Compactness of Urban Change Illustrated to 22 European Countries

Most metrics of urban spatial structure are snapshots, summarizing spatial structure at one particular moment in time. They are therefore not ideal for the analysis of urban change patterns. This paper presents a new spatio-temporal analytical method for raster maps that explicitly registers

changes

in patterns. The main contribution is a transition matrix which cross-tabulates the distance to the nearest urbanized location at the beginning and end of the analyzed period. The transition matrix by itself offers a powerful description of urban change patterns from which further metrics can be derived. In particular, a metric that is an indicator of the compactness of urban change is derived. The new metric is applied first to a synthetic dataset demonstrating consistency with existing classifications of urban change patterns. Next, the metric is applied country by country on the European CORINE land cover dataset. The results indicate a striking contrast in change patterns between Western and Eastern European counties. The method can be further elaborated in many different ways and can therefore be the first in a family of spatio-temporal descriptive statistics.