The detection of natural cities in the Netherlands—Nocturnal satellite imagery and Zipf’s law

How to detect the true extent of cities in highly urbanized countries? This paper addresses the delineation of natural urban and non-urban space and its change based on a wider understanding of spatial heterogeneity. The Netherlands is selected as a case study. “Natural” means the extent of urban space irrespective of administrative boundaries. The database, used for this study, is radiance-calibrated nocturnal satellite imagery from the Defence Meteorological Satellite Program (DMSP). Extraction of cities is done by K-means segmentation. Based on the variance of luminosity it is possible to detect natural urban space. After removal of outliers in the skewed pixel distributions and after correction of “blooming” (over-glow of light emission) Zipf’s law is then applied as a test for segmentation adequacy. The comparative analysis for the years 1996 and 2011 shows that the rank-size distribution of natural cities is well confirmed by Zipf’s law, in contrast to that of administrative cities.ZusammenfassungWie lässt sich die wahre Ausdehnung von Städten in hochgradig urbanisierten Staaten erkennen? Die Studie behandelt die Differenzierung von natürlichem städtischen und nicht-städtischen Raum und seinem Wandel in einem erweiterten Sinne von räumlicher Heterogenität. Die Niederlande werden als Fallstudie betrachtet. „Natürlich“ meint hierbei die Unabhängigkeit städtischer Ausdehnung von administrativ gezogenen Grenzen. Die verwendete Datenbasis sind radianzkalibrierte Nachtsatellitenbilder des Defence Meteorological Satellite Program (DMSP). Die Extrahierung der Städte erfolgt unter Anwendung der K-means-Segmentierung. Auf Basis der Varianz der Lichtemission lässt sich so der natürliche städtische Raum sichtbar machen. Nach Beseitigung von statistischen Ausreißern in den schiefen Pixel-Verteilungen und nach Korrektur der Verzerrungen durch Überstrahlungseffekte wird die gewonnene Segmentierung mit Hilfe des Zipf-Gesetzes auf Angemessenheit getestet. Die vergleichende Analyse für die Jahre 1996 und 2011 zeigt, dass die Rangverteilung der natürlichen Städte durch das Zipf-Gesetz bestätigt wird, ganz im Gegensatz zur Rangverteilung der Städte in ihren Verwaltungsgrenzen.

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