Urban Percolations

The UPon project aims for a deeper understanding of the percolation properties of cities and the urban fabric. The goal is to find out how the spatial organization of cities and settlements determines the percolation threshold and based on which factors the critical value can be ‘predicted’. Moreover, the project work aims at understanding why and how the exponent of the city size distribution depends on the aggregational scale. Therefore, mostly empirical data analysis will be conducted, whereas city size will be defined as the area of urban clusters. Usually, the city size refers to the population of the considered city. However, the measurement of population size is subject to a few problems. Such figures are normally based on administrative boundaries and due to historic development cities of two or more different units might have grown together or when an administrative unit is large from the beginning, it might involve already more than one city or settlement. Moreover, the administrative units of different countries are not consistently defined. The usage of urban land cover data represents a more objective alternative which avoids these issues. Urban land cover information is derived from remote sensing and is by definition more objective. A drawback is, however, that the size is then given as area instead of the conventional population number. As population and area are correlated via a power-law, this problem only represents a minor complication. Moreover, percolation is a spatial phenomenon, so that for consistency reasons it makes sense, to consider the spatial size of cities. In order to better explore the practical applicability of urban percolation, also the poles of inaccessibility will be investigated. The idea is to identify them and to understand how big those areas are, being defined by maximum distance to any settlement. To the best understanding of the applicant, the question of poles of inaccessibility is completely new to percolation theory. In landscape ecology it is of high relevance since such locations can have high ecological importance. Identifying clusters of urban land cover, basically consists of assigning labels to those raster cells which are urban. If they carry the same label, then they belong to the same cluster, if the label is different, then the they belong to different clusters. CCA assigns any two cells to the same cluster if their distance is smaller than or equal to a predefined threshold. So far, the Euclidean distance is used as distance measure (or the orthodromic distance, which for small values can be approximated by the Euclidean distance). One of the innovations of UPon will be to also explore travel time. On the one hand, there is no good reason not to use travel time as metric. On the other hand, it is interesting to understand city definition under the perspective of travel time. First results indicate that (at night) the travel time as a function of the distance into the city center follows a power-law with exponent smaller than 1. This can be understood, as large distances are usually traveled faster (e.g. on highways). The consequence is, however, that then the triangle inequality is violated for travel time and the consequences for the percolation properties are non-trivial. Fundamental to percolation of cities and urban land cover is CCA. However, as a set of clustering alternatives is available, within UPon the various methods will be compared. Ideally, a parameter-free clustering algorithm will be developed which itself will be based on the idea of percolation but then does not permit any more to study percolation. Nonetheless, such a new method will be valuable for many applications.

In order to better understand the percolation phenomenon of cities and the urban fabric in general, the following problems will be addressed: • What determines the percolation threshold of the urban fabric and how is the critical threshold related to other structural or socio-economic properties? • Why and how is the Zipf exponent influenced by the system’s proximity to criticality? • How is the spatial organization of cities correlated and how does it relate to the percolation properties?

Percolation of urban land is closely linked with the fragmentation of non-urban lands. This means that if urban land percolates, by definition natural land does not and is fragmented. Then, possible green corridors are interrupted. Fragmented landscapes add to the biodiversity loss - one of the planetary boundaries. Moreover, when land is considered as a global common, then the understanding gained via urban percolation adds to the understanding of the depletion of this resource.


Oct 01, 2021 until Sep 30, 2024

Funding Agency

DFG - Deutsche Forschungsgemeinschaft

Funding Call



Diego Rybski