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Review of Regional Research

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12-04-2018 | Original Paper

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

Author: Rolf Bergs

Published in: Review of Regional Research | Issue 2/2018

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Abstract

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.

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While spatial heterogeneity usually represents the first-order moments of space, spatial dependence is conceived as its second-order property. However, there are arguments that the relationship is contrary, namely that spatial heterogeneity is of higher order. Jiang (2015, p. 6) argues that “… Spatial heterogeneity is a kind of hidden order, which appears disordered on the surface, but possesses a deep order beneath. This kind of hidden order can be characterized by a power law or a heavy-tailed distribution in general. …”. So if just viewing the visible heterogeneity at the surface only part of its complex underpinnings is regarded.

In comparing levels of urbanization among EU countries with data from the European Commission and Eurostat, the Netherlands and the UK can be depicted at the top of the ranking (Eurostat 2017).

Care is definitively needed to use the term in an interdisciplinary dialogue as it had been also used in philosophical debates, such as the issue of reintegrating the natural with the urban (e.g. Stefanovic and Scharper 2012).

https://www.ngdc.noaa.gov/eog/dmsp.html (accessed 23 February 2017).

Jiang et al. (2015) found exponents close to −1 in the range of any size, but notably those in the range above ten square kilometers, thus well-fitting Zipf’s law at the world, continental and national scales.

Analyses cover estimates for cities proper and city agglomerations. A problem with both approaches has been definition and international comparison.

This is also confirmed by Jiang et al. (2015) at world and European scale.

Further to that, the study of Jiang et al. (2015) finds substantially stronger evidence of Zipf’s law for industrialized countries vs. developing and emerging countries. Estimates by Brakman et al. (1999) and Soo (2005)—both for population based estimates—do not indicate a systematic difference between levels of economic development.

A plausible explanation for that is the influence of asymmetric industrial shocks in addition to symmetric policy and regional shocks (Gabaix 1999b), violating the assumption of scale invariance at least temporarily for the rank distribution of the bigger cities. By applying a maximum likelihood ratio test, Malevergne et al. (2011) show for the US cities, that the upper tail of the distribution is in fact Pareto and not lognormally distributed.

Cf: https://www.ngdc.noaa.gov/eog/dmsp/download_radcal.html. The radiance-calibrated composites are based on a limited set of observations where the gain of the detector was set much lower than its typical operational setting. The combination of those sparsely acquirable data at low gain settings with the operational data retrieved at high gain settings made it possible to produce a set of global nighttime lights products with no sensor saturation. However, the pixel values of the radiance-calibrated images are not digital numbers (DN). They are deemed unitless because of the lacking on-board calibration. The images thus show the true variation of luminosity but not the absolute radiance. The range in the images explored in this study is between 0 and 1,237 (https://ngdc.noaa.gov/eog/dmsp/radcal_readme.txt). Since 2012, the 14-bit onboard-calibrated VIIRS images (Visible Infrared Imaging Radiometer Suite) are available. Those images are much more precise, but a long-run analysis of urbanization and evolution of Zipf’s law is not yet possible.

Inter-calibration is based on the methodology of Hsu et al. (2015). This study addressed the issue of missing inter-calibration (and thus comparability of images) by relating all radiance-calibrated composites to the annual one for 2006 by linear regression. 2006 was selected as it provides a better cloud-free coverage over the world. Hence the matrix of pixel values in the images is multiplied by different annual coefficients and constants.

Principally, with both, K-means as well as Isodata clustering it could be also possible to detect the typical peri-urban range or further differentiation from rural to urban, because it is not restricted to just two clusters. Isodata segmentation can be a superior choice when looking for inherent spectral clusters (Pandiya et al. 2013).

In case of selecting K > 2, the threshold separating the upper segment from the remaining distribution is preferred. Any other threshold would be rather arbitrary since the final classification is a binary one: urban vs. non-urban.

In accordance to Hsu et al. (2015) as described earlier.

The medcouple is a robust measure of distribution skewness of a distribution function F:\(MC(F)=\underset{x_{1}<m_{F}<x_{2}}{\text{med}}\cdot h(x_{1},x_{2})\), where m_F is the median of F and the kernel function h is \(h(x_i,x_j)=\frac{(x_j-m_F)-(m_F-x_i)}{x_j-x_i}\).

Dissimilarity measure: continuous; Distance: Euclidian; the random seed is unimportant in univariate clustering as results do not differ.

The Gabaix-Ibragimov approach aims to remove the bias of the simple OLS estimates when samples are small. This coefficient is obtained by reducing the rank by ½ and then using the standard OLS approach, i.e.: ln (R − 1/2) = c − α ln(S). The standard error of the Pareto exponent differs from the OLS standard error. It is asymptotically (2/n)^1/2α (cf. Gabaix and Ibragimov 2011, p. 30).

The lower tails of the logarithmic regressions are concavely bowed. For the 2011 data (K = 2) a Shapiro-Francia normality test on the 50 lower tail observations of the log-transformed observations could not reject the Null hypothesis (= normal distribution) at the 95% level, while for 21 upper tail observations (see above) p < 0.0001, thus strongly rejecting the Null hypothesis.

The purpose of the Pseudo-F statistic is not to define a minimum threshold but rather to find the optimum choice of K in terms of intra- and inter-cluster variance. Hence, a two-cluster segmentation of the images is not per se inappropriate. Only the proportion of the variances is lower than for K = 3 or K = 4.

In the extraction of segmented space, the natural city area of Leeuwarden has a size of 85 pixels and belongs thus to the truncated tail of patches <100 pixels for the 2011 analysis. According to the Centraal Bureau voor de Statistiek, in 2011 the number of inhabitants of Leeuwarden was 94,838. In 1996, the city area of Dordrecht has a size of 109 pixels, thus selected within the tail with patches >100 pixels. The number of inhabitants of that city was 118,810.

The coefficient and the constant were originally estimated in a restricted study on twenty lighted settlements in California (Elvidge et al. 2004). Small et al. (2005, p. 287–288) confirmed those prior results by comparing it with an estimate on lateral blooming of small and large urbanized islands worldwide. The idea behind this exercise was the fact that urbanized island coasts represent an unambiguous boundary between potential sources of urban light emission and unlighted water. The results of both were consistent and were deemed by the authors to provide a basis for correcting the blooming problem. It is to be stressed, that this statistical correction still does not necessarily represent the true extent of natural Dutch cities. Blooming effects cannot be removed from the maps.

The distribution of lit areas below that threshold is flatter than for the non-adjusted data. The reason for that is a strongly stretched lower tail converting sizes <1 pixel into negative logarithmic values.

The map, showing the extent of administrative cities, is based on an available shapefile from 2015. It is not exactly congruent with the 2011 boundaries, but the boundaries of all highlighted municipalities remained constant during that period. Between 2011 and 2015 there have been few minor municipal reforms so-called “Gemeentelijke Herindelingen” described in: Wikipedia (2017).

Cf. Jiang et al. (2015, p. 509), saying that “… for all cities of a country to constitute a whole, the country must usually be of a certain size. A country might not be a legitimate unit for Zipf’s law …”.

The functional division of urban and rural space must have an economic foundation because of the uneven spatial distribution of production factors and accessibility (thus the non-homogeneity of space) and the resulting incentive for people to move (cf. Starrett 1978, p. 36; Brakman et al. 2009, pp. 51 ff.).

Alexander C (1965) The city is not a tree. Arch Forum 122(1):58–62

Amaral S, Monteiro AVM, Camara G, Quintanilha JA (2006) DMSP/OLS night-time light imagery for urban population estimates in the Brazilian Amazon. Int J Remote Sens 27(5):855–870CrossRef

Bagan H, Yamagata Y (2015) Analysis of urban growth and estimating population density using satellite images of nighttime lights and land-use and population data. Gisci Remote Sens 52(6):765–780CrossRef

Bergs R (2012) Cross-border Cooperation, Regional Disparities and Integration of Markets in the EU. J Borderl Stud 27(3):345–363CrossRef

Brakman S, Garretsen H, van Marrewijk C, van den Berg M (1999) The return of Zipf: understanding the rank-size distribution. J Reg Sci 39(1):183–213CrossRef

Brakman S, Garretsen H, van Marrewijk C (2009) The new introduction to geographical economics. Cambridge University Press, CambridgeCrossRef

Budde R, Neumann U (2016) Gravitation and dispersion—a disaggregate view on urban agglomeration and sprawl in Germany. Paper, Scorus Conference, Lisbon

Duranton G (2007) Urban evolutions: the fast, the slow, and the still. Am Econ Rev 97(1):197–221CrossRef

Eeckhout J (2004) Gibrat’s law for (all) cities. Am Econ Rev 94(5):1429–1451CrossRef

Egger PH, Lumeau G, Püschel N (2017) Natural city growth in the people’s republic of China. Asian Dev Rev 34(2):51–85CrossRef

Elvidge CD, Safran J, Nelson IL, Tuttle BT, Hobson VR, Baugh KE, Dietz JB, Erwin EH (2004) Area and position accuracy of DMSP nighttime lights data. In: Lunetta RS, Lyon JG (eds) Remote sensing and GIS accuracy assessment. CRC Press, Boca Raton, pp 281–291CrossRef

Eurostat (2017) Urban-rural typology. http://ec.europa.eu/eurostat/statistics-explained/index.php/Urban-rural_typology#Database. Accessed 30 May 2017

Fujita M, Krugman P, Venables AJ (1999) The spatial economy: cities regions and international trade. MIT Press, Cambridge (Mass.)

Gabaix X (1999a) Zipf’s law and the growth of cities. Am Econ Rev 89(2):129–132CrossRef

Gabaix X (1999b) Zipf law for cities: an explanation. Q J Econ 114(3):739–767CrossRef

Gabaix X (2016) Power laws in economics: an introduction. J Econ Perspect 30(1):185–206CrossRef

Gabaix X, Ibragimov R (2011) Rank-1/2: A simple way to improve the OLS estimation of tail exponents. J Bus Econ Stat 29(1):24–39CrossRef

Gan L, Li D, Song S (2006) Is the Zipf law spurious in explaining city-size distributions? Econ Lett 92(2):256–262CrossRef

Gehlke CE, Biehl K (1934) Certain effects of grouping upon the size of the correlation coefficient in census tract material. J Am Stat Assoc 29(185A):169–170CrossRef

Ghosh T, Powell RL, Elvidge CD, Baugh KE, Sutton PC, Anderson S (2010) Shedding light on the global distribution of economic activity. Open Geogr J 3:147–160CrossRef

de Groot H, Marlet G, Teulings C, Vermeulen W (2015) Cities and the urban land premium. Edward Elgar, CheltenhamCrossRef

Haartsen T, Huigen PPP, Groote P (2003) Rural Areas in the Netherlands. Tijdschr Econ Soc Geogr 94(1):129–136CrossRef

van der Hejde P (2012) New urban centres in the Netherlands. Tijdschr Econ Soc Geogr 103(3):362–373CrossRef

Henderson V, Storeygard A, Weil DN (2011) A bright idea for measuring economic growth. Am Econ Rev 101(3):194–199CrossRef

Hsu FC, Baugh KE, Ghosh T, Zhizhin M, Elvidge CD (2015) DMSP-OLS radiance calibrated nighttime lights time series with intercalibration. Remote Sens (Basel) 7(2):1855–1876CrossRef

Jiang B (2015) Geospatial analysis requires a different way of thinking: the problem of spatial heterogeneity. GeoJournal 80(1):1–13CrossRef

Jiang B, Miao Y (2014) The evolution of natural cities from the perspective of location-based social media. Prof Geogr 67(2):295–306CrossRef

Jiang B, Yin J, Liu Q (2015) Zipf’s law for all the natural cities around the world. Int J Geogr Inf Sci 29(3):498–522CrossRef

Krugman P (1996) The self organizing economy. Blackwell, Cambridge (Mass.)

Krugman P (1997) Development, geography and economic theory. MIT Press, Cambridge (Mass.)

Liu Q (2014) A Case Study on the Extraction of the Natural Cities from Nightlight Image of the United States of America. Master thesis, University of Gävle

Malevergne Y, Pisarenko V, Sornette D (2011) Testing the Pareto against the lognormal distributions with the uniformly most powerful unbiased test applied to the distribution of cities. Phys Rev E 83(3):36111CrossRef

Mellander C, Stolarick K, Matheson Z, Lobo J (2013) Night-time light data: a good proxy measure for economic activity? Martin Prosperity Institute, Toronto

OECD (1994) Creating indicators for shaping territorial policy. OECD, Paris

OECD (2013) Definition of Functional Urban Areas (FUA) for the OECD metropolitan database. OECD, Paris

Pandiya M, Baxi A, Potdar MB, Kalubarme MH, Agarwal B (2013) Comparison of various classification techniques for satellite data. Int J Sci Eng Res 4(1):1–6

Reggiani A, Nijkamp P (2015) Did Zipf anticipate Socio-economic Spatial Networks? Environ Plann B 42(3):468–489CrossRef

Rosen KT, Resnick M (1980) The size and distribution of cities: an examination of Pareto law and primacy. J Urban Econ 8(2):165–186CrossRef

Small C, Pozzi F, Elvidge CD (2005) Spatial analysis of global urban extent from DMSP-OLS night lights. Remote Sens Environ 96(3–4):277–291CrossRef

Soo KT (2005) Zipf’s law for cities: a cross country investigation. Reg Sci Urban Econ 35(3):239–263CrossRef

Starrett D (1978) Market allocations of location choice in a model with free mobility. J Econ Theory 17(1):21–37CrossRef

Stefanovic IL, Scharper SB (eds) (2012) The natural city: re-envisioning the built environment. University of Toronto Press, Toronto

Suedekum J, Giesen K (2011) Zipf’s law for cities in the regions and the country. J Econ Geogr 11(4):667–686CrossRef

Sutton P (1998) Modelling population density with night-time satellite imagery and GIS. Comput Environ Urban Syst 21(3–4):227–244

Vandervieren E, Huber M (2004) An adjusted box-plot for skewed distributions. In: Antoch J (ed) Compstat 2004 Symposium. Physica, Springer, Heidelberg, pp 1933–1940

Wikipedia (2017) Gemeentelijke Herindelingen. https://nl.wikipedia.org/wiki/Gemeentelijke_herindelingen_in_Nederland. Accessed 18 Dec 2017

Wu S (2015) Zipf’s Law for Natural Cities Extracted from Location-Based Social Media Data. Master thesis, University of Gävle

Yang W, Hou K, Liu B, Yu F, Lin L (2017) Two-stage clustering technique based on the neighboring union histogram for Hyperspectral remote sensing images. IEEE Access 5:5640–5647

Zipf GK (1949) Human behaviour and the principles of least effort. Addison Wesley, New York

Title: The detection of natural cities in the Netherlands—Nocturnal satellite imagery and Zipf’s law
Author: Rolf Bergs
Publication date: 12-04-2018
Publisher: Springer Berlin Heidelberg
Published in: Review of Regional Research / Issue 2/2018
Print ISSN: 0173-7600
Electronic ISSN: 1613-9836
DOI: https://doi.org/10.1007/s10037-018-0122-6

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