How to measure large-scale complex urban network structures using night-time light satellite databases. Application to European metropolitan regions

Abstract

This article uses new methods and evidence from satellite data on night lighting to assess the urban network structure of 100 European metropolitan regions. Its aim was to develop indicators to test the hypothesis that complex urban networks are more efficient economically and less dependent on energy consumption owing to better information organization. It uses NPP-VIIRS NTL satellite data on night lighting (NTL) and employs a topographical representation of NTL intensities to detect urban centers. Based on the distribution of NTL intensities in urban centers represented as a Lorenz curve, it develops two new indicators of monocentricity and polycentricity to evaluate large-scale urban network structures. The results show that polycentric urban networks create more innovation, which allows them to be more economically efficient and less dependent on energy consumption. Further research should study in greater detail the relationships between urban network structures and their social, economic, and ecological performances.

Keywords

large-scale metropolitan structures complex urban networks polycentricity monocentricity sustainable urban progress

Introduction

Ever since the emergence of industrial cities in the nineteenth century, urban areas around the world have continued to expand and become more complex (Batty, 2005; Lall et al., 2021), and have been referred to by Lang and Nelson, (2009) as “large-scale trans-metropolitan urban structures.” Today’s metropolitan regions and “polycentric urban regions” (PURs) have become a key concept in regional studies, both in analytical terms and as objects of regional development policies (Ben et al., 2022).

The development of metropolitan regions is both the cause and consequence of the densification and acceleration of numerous socioeconomic processes that engender ever-more complex urban networks (Marull et al., 2015). In economic terms, the metropolitan-region scale of organization is seemingly hastening global change (Grazi et al., 2008) and appropriating a huge and growing amount of the world’s population, production, and innovation, which leads to higher per capita income and greater creativity (Camagni, 2016; Camagni and Capello, 2011; OECD, 2015, UN, 2017; Ross, 2009).

Metropolitan regions are defined as “complex open systems” made up of “urban networks” (Wilson, 2009). The concepts of “system,” “network,” and “assemblage” (Dematteis, 1991; Camagni and Salone, 1993; De Landa, 2006) represent a transition that links cities at several scales: from the idea of the nodal city to that of the local labor market; then from this scale to the notion of the metropolitan area; and finally, to the trans-metropolitan scales such as the metropolitan region or even the megaregion (Florida et al., 2007; Trullén et al., 2013). If a metropolitan region is indeed an urban network, then we need to know more about its functional organizational structure. Increasing complexity causing a metropolitan region to change its structure and replace energy with information will also increase its relative levels of efficiency and stability (Marull et al., 2019).

So, it is vital to know how metropolitan regions are organized and how categories of nodes are distributed in the graph according to their relative positions. This will generate a set of network typologies, the most-used of which are the division into vertical (hierarchical), horizontal (non-hierarchical), and polycentric networks (Dematteis, 1991). The relative hierarchical position of nodes in a network plays a crucial role in how information is transmitted (Webber, 1972).

In order to assess the organizational structures of an urban network and to compare them with other such structures, the nodes of the graph can be divided into three classes according to their degree of centrality. The highest centrality values correspond to the category “centres” (higher hierarchical level; i.e., big cities); the second to “sub-centres” (intermediate hierarchical level; i.e., medium-sized cities); and the third to “other cities” (lower hierarchical level; i.e., towns). Next, we can determine three types of urban networks (Marull et al., 2015)—monocentric (a few nodes with high centrality levels); reticular (a considerable number of nodes with similar centrality levels); and polycentric (where there is a functional structure with different centrality levels)—that measure the complexity of the urban network (as organized information).

In analytical and policy terms the relevant question is whether or not the different types of urban structures (monocentric, reticular, and polycentric) can be related to different levels of economic, social, and ecological performance. Therefore, the identification of an organizational structure of urban networks via a robust methodology that can be applied to a wide range of metropolitan regions is a first necessary step and will fill a gap in researchers’ toolboxes when attempting to analyze metropolitan phenomena.

Procedures designed to delineate metropolitan regions mostly rely on morphological approaches (Ross, 2009) and population statistics (Ben et al., 2022). However, the availability of satellite-based data has facilitated the use of a new type of morphological approach that takes advantage of night-time satellite images. The night light intensity data obtained from satellite sensors can be used as a measure of energy consumption or economic activity in urban centres (Marull et al., 2013) and so determine their degree of centrality in a way that differs from previous attempts (Zhang et al., 2021). The limitations of these procedures are evident when compared with the more detailed flux-based methodologies used to define local labor markets and metropolitan regions (Trullén et al., 2013).

Nevertheless, there are several drawbacks to light-based methodologies and, for example, it is only possible to capture a limited range of light intensities, and economic activities such as agriculture that take place in the dark are overlooked (although agriculture is not a very important activity in urban areas in developed countries). This type of approach is attractive to researchers because focusing on fluxes is not always possible due to a lack of data, and because comparable data are more difficult to obtain when research embraces several countries or large-scale economic areas (Donaldson and Storeygard, 2016). The use of traditional morphological or more modern points-of-light approaches makes it possible to fill important gaps in the data and to provide a simple and straightforward method for identifying urban networks (Florida et al., 2007; Zhang et al., 2021; Li and Du, 2021).

The aim of this article was thus to use satellite data on night lighting to develop a new method for evaluating the urban network structure of 100 European metropolitan regions to help fill knowledge gaps on this subject. It tests the hypothesis that complex urban networks are more efficient economically and less dependent on energy consumption. The number of metropolitan regions selected coincides with the proposal made by Mazzucato (2021) for fighting climate change in Europe by 2030 using 100 Carbon Neutral Cities.

The article is structured as follows: after this introduction, next section adapts a previously published methodology to establish the categories of urban centres based on night lighting data and proposes two new indicators of urban network structure, which are analyzed in conjunction with a series of social, economic, and ecological variables. Then the results obtained for European metropolitan regions are presented and, finally, the last section draws a number of conclusions.

Material and methods

European metropolitan regions and night-time light satellite databases

This article analyses the urban network structure of the 100-most populated metropolitan regions in the European Union using NPP-VIIRS NTL satellite data on night lighting obtained from the U.S. National Oceanic Atmospheric Administration (https://ncc.nesdis.noaa.gov/VIIRS/) (see Figure 1).

Figure 1.

Distribution of the 100-most populated European metropolitan regions based on a night lighting image obtained from the NPP-VIIRS NTL satellite database, 2016 (light measured in nano W cm-2 sr-1).

The selected European metropolitan regions correspond to the NUTS-3 regions or groupings of NUTS-3 regions, which represent urban agglomerations of over 250 000 inhabitants identified using the Urban Audit’s Larger Urban Zones. These typologies have been developed by DG Regional and Urban Policy in co-operation with DG Agriculture and Rural Development, Eurostat, DG Joint Research Centre, and OECD (http://ec.europa.eu/regional_policy/sources/docgener/focus/2011_01_typologies.pdf). The social, economic, and ecological variables of these metropolitan regions, taken from the Eurostat database (https://ec.europa.eu/eurostat/web/metropolitan-regions/data/database), are as follows: service-sector employment: SSE (% of total employment); industrial-sector employment: ISE (% of total employment); productive diversity: PDV; gross domestic product per capita: GDP; number of registered patents per capita: NPT; unemployment rate: UER (% of unemployed people in the active working population); proportion of renewable energy consumption: REC (total energy consumption); primary energy consumption per capita: PEC (kilo-tonnes of oil equivalent); and greenhouse gas emissions per capita: GHG (thousands of tonnes of CO₂ equivalent). All variables (including satellite data on night lighting) refer to 2016 except the data for patents per capita, which were taken from 2014 to create a larger dataset.

Detecting urban centres using night-time light satellite databases

This research is based on a previous study by Chen et al. (2017) who used a novel method to detect urban centres based on NPP-VIIRS NTL satellite composite data and the Visible Infrared Imagine Radiometer Suite (VIIRS) sensor. Essentially, these authors represent the Night-Time Light (NTL) intensity data obtained from the NPP-VIIRS NTL satellite as a “topographical surface” and use light intensity contours to define the urban network structure. Consequently, NTL data for a metropolitan region can be understood as a continuous surface of human activity, in which an urban center can be interpreted as a “mount on the earth’s topography.” As in topographic maps, higher light intensity locations (NTL “mounts”) are differentiated by the greater proximity of concentric contour lines. The geographical distribution of NTL intensity highlights the spatial structure of human activity and is a good indicator of different phases of urban growth. Based on the analogy between urban structure and topography, an NTL contour map can be generated from the NPP-VIIRS NTL composite data and an NTL contour tree can be constructed by using a “localized contour tree method.”

The localized contour tree method approach has been successfully used with topographical data to identify the hierarchical structure of surface depressions (Wu et al., 2015). A contour tree is composed of “nodes” and “links.” A node indicates a contour line, while a link represents the topological relationship between any two adjacent nodes (Kweon and Kanade, 1994). Wu et al. (2015) state that surface topography can be represented by raster-based digital elevation models or by vector-based equal elevation contour lines. In a vector-based contour representation, a surface depression is indicated by a series of concentric closed contours in which the inner contours are at a lower elevation than the surrounding ones. The first key technical component included in the algorithm of this method is the identification of the “seed” contours and how they can be used to construct local contour trees and represented the topological relationships between adjacent closed contours based on graph theory.

Two criteria were taken into account—a minimum urban center size (5 km²) and the contour interval (1 nano-Wcm−2sr−1)—in the computational efficiency of the contour tree construction (Chen et al., 2017). By applying both criteria, this method builds the NTL contour line, in which “elemental centres” are identified as contour tree leaf nodes. The most significant steps in the methodology are follows: (1) Database elements: the polygon layer of metropolitan regions obtained from Eurostat (https://ec.europa.eu/eurostat/web/metropolitan-regions/data/database) and the VIIRS image obtained from Payne Institute and Colorado School of Mines (https://eogdata.mines.edu/download_dnb_composites.html); (2) Study area projection: the projection of the polygon layer of the metropolitan regions and the VIIRS raster layer were changed from WGS84 to ETRS_1989_LAEA in order to adjust to the study area; (3) Selection of urban areas: a filter was applied to smooth the VIIRS raster layer, limiting the light intensities (minimum pixel intensity = 19u) to be considered as urban environments; (4) Detection of elementary centres: using raster calculator tools the resulting layer of the previously applied filter and the layer resulting from the reclassification considering the light intensity were combined; and (5) Generating contour lines: the lines were generated with the NTL contour interval and finally converted to polygons. As a result, 943 elemental urban centres in the 100 selected metropolitan regions were identified. The unit of measure of VIIRS was nano W cm-2 sr-1, where W = watts, cm = centimeters, Sr = steroradian (the three-dimensional equivalent of radian). So, 19u means that the VIIRS reaches the value 19 in the indicated unit of measure. The selection of this threshold is regarded as the limit that best suits urban areas following the different tests carried out on this image from 2016 by overlapping it and comparing it with the 2018 version of the Corine Land Cover Map.

Mathematical night-time light remote sensing approach

We followed the approach presented by Chen et al. (2017) but adapted it to a massive and automatic application over a large set of European metropolitan regions. It is based on a topographical representation of NTL intensities as a contour-line surface, analogous to terrain characteristics. This approach allows us to delimit the urban centres of a metropolitan region and analyze their relationships and hierarchies, distinguishing between elemental and composite centres of different degrees on a topological tree graph, with nodes representing certain selected contour lines and links expressing the topological relationship between two adjacent nodes at different levels. Nevertheless, due to problems derived from the fact that we needed to apply the procedure to a large number of metropolitan regions (See Note S1 in the Supplementary Material), we derived a simplified algorithm to obtain the urban centres of any given metropolitan region.

Here we describe how to use this simplified algorithm, which is based on the NTL-intensity contour lines. As already stated, the minimum NTL-intensity unit to be considered is 19u, referred as the “localized contour tree method” (Chen et al., 2017). From the NTL-intensity contour lines, the seed centres are detected (peaks with a surface superior to a threshold of 5 km²) and categorized as level 1. The successive contour lines containing a single seed are assigned to the same level and constitute a branch. If a contour line contains two or more seeds and their branches, it is categorized as level 2. This process is iterated: successive contour lines are assigned to level 2 until a contour line contains a new seed or there are no more lines to be assigned. A “contour tree” is constructed with contour lines represented as nodes and topological dependences represented as linking lines. Finally, the branches are simplified by taking into account on each branch only one node per level, which is the widest contour line of this branch and level (representing a “mount”). The set of nodes at level 1 that remain after the selection are called “elemental urban centres,” while the centres at higher levels are termed “composite urban centres” (see Figure S2 in the Supplementary Material for a further explanation of this procedure).

Chen et al. (2017) regard different areas of a given region as connected components of NTL intensity and draw a regular contour tree for each connected area, which explains the hierarchical topological structure in these areas. To be able to apply this procedure massively to a large number of metropolitan regions, we simplified these authors’ algorithm by disregarding compound urban centres and preserving only the elementary urban centres, regardless of whether they come from one connected area or from many unconnected areas in the same metropolitan region (see Figure S3 in the Supplementary Material). Therefore, we ignored the dependencies of the simplified contour tree and the only hierarchy we considered was the one given by the elemental centers intensity, sorted from lowest to highest according to the ranking of the total intensities. This procedure can also be applied to averaged intensities, although the results discriminate metropolitan regions less well since the mean is in itself a smoothing filter. As the unit of analysis is the metropolitan region, we implicitly assume that urban centres in the same region are related.

Reticular, polycentric, and monocentric urban network patterns

For a given metropolitan region R, composed of N elemental centres whose NTL intensities in ascending order are defined by a numerical vector (X₁, …, X_N) and denoted by p_obs, the vector of proportions representing the metropolitan region will be

R : (X_{1}, \dots, X_{N}) \to p_{o b s} = (\frac{X_{1}}{T}, \dots, \frac{X_{N}}{T}), T = \sum_{i = 1}^{N} X_{i}

As an example, we can compare the p_obs distribution from several different metropolitan regions (see Figure S4 in the Supplementary Material). The idea is to take characteristic distributions, which we will call “patterns,” and compare them with the observed proportions in a given metropolitan region R. We define three characteristic patterns: “reticular,” “monocentric” and “polycentric” (Marull et al., 2015). The latter pattern corresponds to a set of N centres configured in such a way that there is a proportion $x$ of small centres (towns), a proportion $\frac{x}{2}$ of medium centres (intermediate cities) and a proportion $\frac{x}{3}$ of large centres (big cities). The small, medium, and large centres have the inverse proportion of the total intensity of the metropolitan region: $\frac{x}{3}$ of the intensity is distributed in the small centres, $\frac{x}{2}$ of the intensity in the medium centres, and a proportion $x$ in the large centres; the small, medium, and large percentages add up to 100 (see the details in Definition 1).

We call this pattern “harmonic-polycentric” because it corresponds to a harmonic progression, which is inverse in number and intensities. This is a particular case of Zipf’s distribution (it gives a rank k to a probability proportional to $k^{- s},$ in our case, s = 1) and formulates an inverse relation between ranks and frequencies (Zipf, 1949). This formulation has been used to fit population ranks into a system of cities (Gabaix, 1999; Vitanov et al., 2015). It is a power law distribution and models scale-free phenomena.

Definition 1

For any given metropolitan region, we can define three urban network patterns (monocentric, polycentric, and reticular, with the reticular being the inverse of the monocentric): R-monocentric:

(\overset{N - 1}{0, \dots, 0}, T) \to p_{m o n} = (\overset{N - 1}{0, \dots, 0}, 1)

R-polycentric: Take x such that $x + \frac{x}{2} + \frac{x}{3} = 1$

(\overset{x N}{\frac{T}{3 N}, \dots, \frac{T}{3 N}}, \overset{\frac{x}{2} N}{\frac{T}{N}, \dots, \frac{T}{N}, \frac{3 T}{N}} \overset{\frac{x}{3} N}{, \dots, \frac{3 T}{N}}) \to p_{p o l} = (\overset{x N}{\frac{1}{3 N}, \dots, \frac{1}{3 N}}, \overset{\frac{x}{2} N}{\frac{1}{N}, \dots, \frac{1}{N}, \frac{3}{N}} \overset{\frac{x}{3} N}{, \dots, \frac{3}{N}})

where the values of

x, \frac{x}{2}

and

\frac{x}{3}

are 0.54545, 0.27273 and 0.18182, respectively

R ‐ r e t i c u l a r : (\overset{N}{\frac{T}{N}, \dots, \frac{T}{N}}) \to p_{r e t} = (\overset{N}{\frac{1}{N}, \dots, \frac{1}{N}})

Note that the monocentric distribution does not really depend on N but corresponds to N = 1 center. As the number of centres N is usually small (from 1 to 37 in our database) and the proportions $x N, \frac{x}{2} N, \frac{x}{3} N$ must be rounded off to integer values, the results are necessarily approximate. This causes distortion, and the numeric values must be corrected when the number of centres is below the median or any other threshold.

The Lorenz curve and urban network structure indicators

The proposed indicators (monocentric $I_{m o n}$ , polycentric $I_{p o l}$ ) measure the closeness of a given observed distribution to a particular urban network pattern. Our approach is based on the Lorenz curve (Lorenz, 1905) and the Gini coefficient G (Gini, 1936), two widely used techniques for visualizing and measuring income inequality. G is twice the area between the Lorenz curve and the diagonal line in the unit square, while the Lorenz curve is a line representing the proportions of cumulative incomes relative to the proportion of cumulative population. If the curve matches the diagonal line, this indicates that income is perfectly equally distributed and G = 0. Conversely, if one person has all the income and everyone else has none, the income distribution is totally unequal. In this case, the Lorenz curve crosses the horizontal axis and the right vertical line of the unit square and G = 1. For a metropolitan region R, we adopted the Lorenz curve framework to represent the cumulative distribution of elemental center intensities relative to the proportion of the cumulative number of elemental centres in the region.

As an example, Figure S5 in the Supplementary Material shows the Lorenz curve for the Barcelona and Madrid metropolitan regions (solid black line), along with the monocentric (red dots), polycentric (green dots) and reticular (blue dots) patterns. In our case, the monocentric distribution corresponds to the perfectly unequal case (i.e., one center having all the NTL intensity) and the indicator of monocentricity will simply be the Gini index G of the Lorenz curve. The larger the G, the more monocentric the metropolitan region is. The reticular distribution corresponds to the perfectly equal case in which the reticular indicator is 1 – G. Finally, polycentric distributions lie in intermediate positions on the monocentric-reticular distributions and we use the area between the observed and the polycentric Lorenz curves. Formal definitions of these indicators are given below.

Definition 2

For any given metropolitan region R, the distribution of the NTL intensities observed in its elementary centres is p_obs, while p_pat is the distribution pattern of its centres. To calculate the area of the difference between the observed Lorenz curve and the pattern Lorenz curve, and to make it relative to the maximum possible area reached in one of the extreme patterns (the monocentric or the reticular Lorenz curves), the indicator can be defined as follows

I_{p a t} (p_{o b s}) : = 1 - \frac{A (L (p_{o b s}) - L (p_{p a t}))}{\max {A (L (p_{m o n}) - L (p_{p a t})), A (L (p_{r e t}) - L (p_{p a t}))}}

The distribution of the pattern can be monocentric, reticular, polycentric, or take on any other distribution of interest for researchers. The following properties can be checked (see Remark 1 at the end of this section):

1. ${0 \leq I}_{p a t} \leq 1$

2. $I_{p a t} = 1 \Leftrightarrow A (L (p_{o b s}) - L (p_{p a t})) = 0 .$

The two Lorenz curves coincide and the observed relative frequencies are the relative frequencies of the pattern.

3. $I_{p a t} = 0 \Leftrightarrow A (L (p_{o b s}) - L (p_{p a t})) = \max {A (L (p_{m o n}) - L (p_{p a t})), A (L (p_{r e t}) - L (p_{p a t}))}$

In general, the zero value is reached in only one of the two extreme distributions, monocentric or polycentric. It is only zero for both if they are equidistant from the pattern Lorenz curve.

4. When the pattern is reticular, the indicator for this specific pattern is:

$I_{r e t} (p_{o b s}) : = 1 - \frac{A (L (p_{o b s}) - L (p_{r e t}))}{A (L (p_{r e t}) - L (p_{m o n}))} = 1 - G (p_{o b s})$

where G(p) denotes the Gini coefficient of any distribution p.

5. For the monocentric pattern, which is the opposite of the reticular pattern in the Lorenz curve setting, the indicator is:

$I_{m o n} (p_{o b s}) : = \frac{A (L (p_{o b s}) - L (p_{r e t}))}{A (L (p_{r e t}) - L (p_{m o n}))} = G (p_{o b s})$

6. The polycentric pattern indicator is

$I_{p o l} (p_{o b s}) : = 1 - Q : = 1 - \frac{A (L (p_{o b s}) - L (p_{p o l}))}{\max {A (L (p_{m o n}) - L (p_{p o l})), A (L (p_{r e t}) - L (p_{p o l}))}}$

The polycentric indicator needs some refinement, which we give below. A correction of $I_{p o l}$ is necessary when the number of centres is not too large due to the distortion commented on in the discussion of polycentric patterns after Definition 1. We used a corrected version $I_{p o l}^{N}$ depending on N (the number of centres), which penalizes lower values, specifically when N is lower than the median number of centres:

Definition 3

The corrected polycentric indicator is defined as

I_{p o l}^{N} (p_{o b s}) : = 1 - Q^{\log (N, m d)}, if N \leq m d

where

Q = Q (p_{o b s})

is the quotient of the Lorenz areas in the definition of

I_{p o l}

and

\log (N, m d)

is the logarithmic base of the sample median,

m d,

of the number of elemental centres in the whole set of European metropolitan regions.

Note that $0 \leq Q \leq 1$ and $\log (N, m d) < 1$ when N is below the median, which implies that in this case $Q^{\log (N, m d)} \geq Q$ and thus $I_{p o l}^{N} \leq I_{p o l}$ . Figure S5 illustrates the value of $I_{m o n}$ for the Barcelona and Madrid metropolitan regions as it corresponds to the relative proportion of the shaded area in relation to the area of the under-diagonal triangle. It is not far from 1 in Madrid (monocentric) and nearly 0.5 in Barcelona. The reticular indicator is the opposite of the monocentric indicator, ${I_{r e t =} 1 - I}_{m o n}$ and is represented by the unshaded area under the black curve relative to the under-diagonal triangle. In order to visualize the areas that appear in the calculation of $I_{p o l}$ , see Figure S6 in the Supplementary Material for the case of Barcelona, as a good example of a polycentric metropolitan region. The numerator is the grey area in the left-hand graph, while the denominator is the largest of the light-blue and coral-colored areas in the right-hand graph.

Remark 1

The right inequality $I_{p a t} \leq 1$ in property 1 and the statements in properties 2 to 6 are immediate. For the left inequality ${0 \leq I}_{p a t}$ , we do not yet have any formal proof for the general case. When applied to our data, the inequality is always true. In addition, a large set of possible pairs of observed and pattern distributions have been simulated and the inequality still holds. However, we have not been able to formally prove that any pair of Lorenz curves satisfy the inequality given that the two curves are increasing and have an increasing derivative (increasing increments in the discrete case). The problem depends on considering intersecting Lorenz curves, which is a highly complex problem that should be addressed for the more general case (Aaberge, 2009).

Urban network factorial analysis

Confirmatory factor analysis (CFA, Jöreskog, 1969) is used to check whether or not a number of observed measures (the variables of interest, X) can be expressed as a linear combination of a smaller number of unobservable latent constructs (the factors or common factors, F), thereby allowing residual or unexplained terms (the specific factors, U) in the model equation

X = Q F + U

where Q is the loadings matrix. A non-zero loading

q_{i j}

expresses the positive or negative direct effect of the factor

F_{j}

on the variable

X_{i}

CFA is a particular type of structural equation model (Westland, 2015) in which common factors are not assumed to be linked directly to each other, although some correlation between them is allowed. Based on a priori theoretical hypotheses, the number of underlying factors and some constraints on the loadings can be tested.

Our conceptual hypothesis is that the sustainable progress of metropolitan regions involves not only socioeconomic (SSE, ISE, PDV, GDP, NPT, EBU) and socioecological (REC, PEC, GEH) variables but also the structure of the urban network ( $I_{m o n}$ ; $I_{p o l}$ ) indicators. In previous related research (Marull et al., 2019), a three-factor model was adjusted using only socioeconomic and socioecological indicators. In the present work, a four-factor model is fitted to a broader set of variables, which includes the new indicators ( $I_{m o n}$ ; $I_{p o l}^{N}$ ).

The assumptions made regarding the factors (common factors F are constrained to have unit variance but may be correlated to each other; specific factors U are pairwise uncorrelated and uncorrelated with the common factors) imply the decomposition of the correlation matrix of X to be

R = Q Σ_{F} Q^{t} + Ψ

The object $Σ_{F}$ is the within-common factors correlation matrix and $Ψ$ is the diagonal matrix of the variances of the specific factors. Various methods such as the maximum likelihood method and minimum least squares can be implemented using statistical software, and enable us to estimate the parameters of the model ( $Q$ , $Σ_{F}$ and $Ψ$ ) and compute the estimated correlation matrix $\hat{R}$ implied by the model. The validation of the fit obviously depends on the theoretical support, although additional evidence is provided by testing alternative models and analyzing the differences between the observed and estimated correlation matrices. We used the R lavaan package (Rosseel, 2012) to estimate the coefficients and obtain the reproduced correlation matrix.

Results and discussion

The indicators $I_{p o l},$ $I_{p o l}^{N}$ , and $I_{m o n}$ were evaluated using the total NTL intensities of the elemental centres in 100 European metropolitan regions. The relationship between the monocentricity and the polycentricity indicators in these regions is shown in Figure S7 in the Supplementary Material. The numerical results for the European metropolitan regions evaluated in this study are given in Table S1 in the Supplementary Material. The corrected and uncorrected polycentricity indicators are identical when the number of centres is high but differ when the number of centres is lower ( $I_{p o l}^{N}$ depends on the number of centres N and penalizes small N values).

Figure 2 shows representative images of each of the three identified categories: monocentric, reticular and polycentric urban areas. These images correspond to the regions of London, as an example of a monocentric urban area, Gothenburg, as an example of a reticular urban area, and the Ruhrgebiet, as an example of a polycentric urban area. The selection of these urban areas was based on the following criteria: Monocentric urban area: region with high $I_{m o n}$ and low $I_{p o l}^{N}$ ( $I_{p o l}^{N}$ = 0.23, $I_{m o n}$ = 0.92); Reticular urban area: region with identical or nearly identical $I_{m o n}$ and $I_{p o l}^{N}$ ( $I_{p o l}^{N}$ = 0.72, $I_{m o n}$ = 0.74); Polycentric urban area: region with a higher $I_{p o l}^{N}$ and a lower $I_{m o n}$ ( $I_{p o l}^{N}$ = 0.90, $I_{m o n}$ = 0.58).

Figure 2.

Examples of different types of urban regions: London, monocentric urban area; Gothenburg, reticular urban area; the Ruhrgebiet, polycentric urban area.

Figure 3 shows the values of the monocentricity $I_{m o n}$ and polycentricity $I_{p o l}$ indicators for all the analyzed European metropolitan regions. These two indicators reflect the great structural variety present in the urban networks of the main European metropolitan regions and determine a series of different typologies. Thus, there are metropolitan regions that show a predominantly polycentric structure, possibly related to economies that are more intensive in terms of innovation and energy efficiency (e.g., Ruhrgebiet, Stockholm, and Barcelona). Other metropolitan regions seem to have more monocentric-type structures, possibly as a result of more centralized economic policies (e.g., London, Paris, and Madrid). In addition, it is interesting to see how intermediate or incipient metropolitan regions develop one or other strategy (e.g., Bergamo, Grenoble, and Cadiz all have a polycentric structure, while Dresden, Toulouse, and Brno are more monocentric).

Figure 3.

Monocentricity $I_{m o n}$ and polycentricity $I_{p o l}^{N}$ indicators applied to the 100 most populated European metropolitan regions.

Remarkably, the proposed indicators show that both types of structures (monocentric and polycentric) are found simultaneously in certain countries (Figure 3) and also in countries characterized by very different levels of income and productivity, thereby reflecting the complexity of relationships between urban form, economic performance, knowledge creation, and energy consumption.

We fitted a four-factor model to the correlation matrix to test the relationships between social, economic, ecological, and urban network structure variables in the 100 European metropolitan regions (Table 1). The correlation matrix between the original nine variables and the new monocentricity

I_{m o n}

and polycentricity

I_{p o l}^{N}

indicators indicates a moderate correlation between the different variables used in the analysis (see Table S2 in the Supplementary Material). The negative correlation (−0.57) between the two structural variables (

I_{p o l}^{N}

and

I_{m o n}

) seems coherent, while the negative correlation (−0.27) between

I_{m o n}

and NPT, and the negative correlation (−0.25) between

I_{p o l}^{N}

and GHG are especially interesting. The more polycentric metropolitan regions (

I_{p o l}^{N}

) tend to emit less greenhouse gas (GHG) and when the metropolitan regions are more monocentric (

I_{m o n}

) they tend to generate knowledge less intensively, as evaluated by the number of patents (NPT).

Table 1.

Factorial analysis of the 100-most populated European metropolitan regions based on social, economic, ecological, and urban network variables. The loading matrix, factor correlation matrix, and specific variances are shown.

Loading matrix					Factor correlation matrix
Variables	Factor 1	Factor 2	Factor 3	Factor 4	Factors	Factor 1	Factor 2	Factor 3	Factor 4
SSE	1.00	0.00	0.00	0.00	Factor 1	1.00	−0.12	−0.23	0.05
ISE	−0.88	0.00	0.00	0.00	Factor 2	−0.12	1.00	0.32	0.06
PDV	−0.83	0.00	0.00	0.00	Factor 3	−0.23	0.32	1.00	−0.07
GDP	0.44	0.94	0.00	0.00	Factor 4	0.05	0.06	−0.07	1.00
NPT	0.00	0.67	0.00	0.40	—	—	—	—	—
UER	0.00	−0.46	−0.39	0.00	—	—	—	—	—
REC	0.00	0.40	−0.50	0.00	—	—	—	—	—
PEC	0.00	0.00	0.74	0.00	—	—	—	—	—
GHG	0.00	0.00	0.95	0.00	—	—	—	—	—
$I_{p o l}^{N}$	0.00	0.00	0.00	0.64	—	—	—	—	—
$I_{m o n}$	0.00	0.00	0.00	−0.73	—	—	—	—	—

Specific variances
SSE	ISE	PDV	GDP	NPT	UER	REC	PEC	GHG	$I_{p o l}^{N}$	$I_{m o n}$
−0.01	0.22	0.32	0.03	0.36	0.52	0.72	0.45	0.10	0.59	0.46

Variables: service-sector employment (SSE); industrial-sector employment (ISE); productive diversity (PDV); gross domestic product (GDP); number of registered patents (NPT); unemployment rate (UER); renewable energy consumption (REC); primary energy consumption (PEC); greenhouse gas emissions (GHG); indicator of monocentricity ( $I_{m o n}$ ); and indicator of polycentricity ( $I_{p o l}^{N}$ ).

The loadings matrix reveals the constraints of the CFA model: each variable is directly influenced by one—or at most two—factors. However, all variables are influenced in some way by the other factors in the model via correlations within F, as can be seen in the factor correlation matrix. The specific variances of the observed variables indicate the amount of variability not explained by the model. The existence of a moderate degree of specific variance is not disabling because the analysis of the factors aims to explain the correlations rather than the variances. A negative estimate of the SSE specific variance is not significant and of no further importance. The mean absolute difference between the observed correlations R and the estimated correlations $\hat{R}$ is 0.07. The adjustment of the R matrix given by the model is acceptable, although there are a few poor estimates with a maximum absolute difference of 0.22 in the correlation between PDV and UER.

The analysis describes the behavior of Factor 1 (“economic activity”), Factor 2 (“knowledge economy”), Factor 3 (“energy consumption”) and Factor 4 (“urban network structure”) at European metropolitan region level (Table 1). Factor 1 is positively determined by service-sector employment (SSE) and gross domestic product (GDP) but negatively determined by industrial-sector employment (ISE) and productive diversity (PDV). The fragmentation of value chains in light of the development of transport and information technologies has blurred the distinction between industrial and service activities and led to changes in urban systems (Boix and Trullen 2007; Zhang et al., 2020). Factor 2 is positively determined by GDP and the number of patents (NPT) but negatively determined by the unemployment rate (UER). Factor 3 is positively determined by greenhouse gas emissions (GHG) and primary energy consumption (PEC) but negatively determined by the percentage of renewable energy consumption (REC) and UER. Finally, Factor 4 is positively determined by the polycentric urban networks ( $I_{p o l}^{N}$ ) and NPT but negatively determined by the monocentric urban networks ( $I_{m o n}$ ).

In terms of measuring large-scale complex urban network structures using night-time light satellite databases, it is especially notable (Factor 4) how urban complexity (polycentric urban networks) is positively related to innovation (measured by the number of patents), while monocentric urban networks are negatively related to innovation (Table 1). The “urban structure” (Factor 4) is negatively related to “energy consumption” (Factor 3) as it is more efficient in terms of the consumption of resources and reduces the entropy of the system (fewer emissions of greenhouse gases). Furthermore, Factor 4 is positively related to “economic activity” (Factor 1), above all in terms of service-sector activity, and to “knowledge economy” (Factor 2) and increasing employment. These results seem to confirm our starting hypothesis that more complex urban networks facilitate an increase in internal organized information (knowledge), which in turn allows them to be more economically efficient and less dependent on energy consumption.

Conclusions

This article presents a new method based on NPP-VIIRS NTL satellite data on night lighting for evaluating the structure of 100 European metropolitan regions. This approach, based on a topographical representation of Night-Time Light (NTL) intensities, allows us to delimit the elemental urban centres of a metropolitan region and analyze their interrelationships and hierarchies. After identifying these elemental urban centres, this method describes three types of urban networks: monocentric (a few nodes with greater centrality), reticular (a number of nodes with similar levels of centrality) and polycentric (with a functional structure with different levels of centrality) networks that measure the complexity of the urban network as organized information.

To evaluate large-scale urban network structures, we developed two indicators (monocentricity-reticularity, and polycentricity) whose application reveals the great structural variety in European metropolitan regions and defines different typologies. On the one hand, there are metropolitan regions characterized by polycentric urban network structures, possibly linked to economies based on network agglomeration economies (e.g., Frankfurt, Stockholm, and Barcelona), while, on the other hand, there are metropolitan regions whose monocentric structures are likely to be more related to centralizing economic policies (e.g., London, Paris, and Madrid).

The hypothesis of this article is that increasingly complex urban network structures are able to generate the information needed to reduce entropy and limit resource consumption, and therefore increase their efficiency and stability (Marull et al., 2019). This hypothesis provides a simple explanation for changes of scale in urban networks that lead to more complex structures such as metropolitan regions. Our results suggest that polycentric urban networks create more innovation (number of patents), which allows them to be more economically efficient and less dependent on energy consumption. These results could have important implications for pro-active policies designed to promote large-scale sustainable urban progress, and have a significant impact on regional planning and land-use policy at a global scale.

Supplemental Material

Supplemental Material - How to measure large-scale complex urban network structures using night-time light satellite databases. Application to European metropolitan regions

Supplemental Material for How to measure large-scale complex urban network structures using night-time light satellite databases. Application to European metropolitan regions by Joan Marull, Mercè Farré, Marta Andreu Espuña, Adrià Prior, Vittorio Galletto and Joan Trullén in Environment and Planning B: Urban Analytics and City Science

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iDs

Joan Marull

Mercè Farré

Marta Andreu Espuna

Vittorio Galletto

Joan Trullén

Supplemental Material

Supplemental Material for this article is available online.

Joan Marull. PhD in Ecology at the University of Barcelona (UB). Head of the Department of Ecology and Territory of the Barcelona Institute of Regional and Metropolitan Studies (IERMB) at the Autonomous University of Barcelona (UAB) and Director of the Metropolitan Laboratory of Ecology and Territory (LET). His main field of activity is land management and urban planning from a systemic approach. Currently, his research focuses on the study of social metabolism, ecological economics, landscape ecology, and territorial efficiency, as well as the application of satellite technology, in the analysis of land-use change, agroecological transition, and climate change. His transdisciplinary proposal integrates the study of socioecological processes to address research and policy issues at multiple time and space scales.

Mercè Farré is Senior Lecturer at the Department of Mathematics at the Autonomous University of Barcelona (UAB), in the area of Statistics and Operations Research. Graduated and doctorated at the Universsity of Barcelona, the first research stage was developed in the field of Stochastic Processes, especially Stochastic Analysis. His interests soon drifted towards the applications of mathematics to the modeling of phenomena arising from the productive processes, sciences and society, that is, to the field of the transfer of mathematics to industry, technology and the social and civic interest. He is a member of the research group on Mathematical Applications and Models (GRAMM, https://grupsderecerca.uab.cat/gramm/) and is responsible for various project-agreements of the Mathematical Consulting Service (MCS, http: //www.mcs- uab.com/perfil.html), the commercial front of the research group.

Marta Andreu Espuna holds a Degree in Geography from the University of Barcelona (2012), Master in Geographic Information Technologies (2014) and Official Master in Geoinformation (2018) at the Autonomous University of Barcelona (UAB). She has focused her professional orientation in the application of Geographic Information Systems (GIS) in health and urban planning through the elaboration, exploitation, and analysis of Spatial Databases. She has worked as a consultant in health planning consultancy participating in international projects using GIS. Since July 2016 she is working at the Cartography Service in the Barcelona Institute of Regional and Metropolitan Studies (IERMB) in the Autonomous University of Barcelona (UAB).

Adrià Prior is graduated in Mathematics from the Autonomous University of Barcelona (UAB). Under the supervision of the senior authors, he participated both in the data analysis and the mathematical discussion on the indicators and models developed in the conjoint work. In 2021, he published a mathematical article: "Factor analysis: Existence of solution to factor models". Reports@SCM 6 (2021), 1–9; DOI:10.2436/20.2002.02.23. 1. The electronic journal Reports@SCM is specially addressed to researchers at the initial period of their academic careers.

Vittorio Galletto is the director of the department of regional and urbans economics of the Barcelona Institute of Regional and Metropolitan Studies (Institut d’Estudis Regionals i Metropolitans de Barcelona-IERMB). He holds a PhD in Applied Economics from the Autonomous University of Barcelona (UAB). Before joining the IERMB, he worked at the Department of Applied Economics at the UAB as an associate professor and researcher. He has also worked in the private sector in consulting firms conducting local development projects for local governments and other institutions. Currently, his research at the IERMB is focused on inclusive urban growth, and the relationship between local productivity and competitiveness.

Joan Trullén is Senior Lecturer at the Department of Applied Economics at the Autonomous University of Barcelona (UAB). His main research fields are urban economics and policy, local economic development, metropolitan strategy, industrial districts and inclusive urban growth. Among his main publications on Barcelona Metropolitan Strategy are the studies on Barcelona-City of Knowledge, 22@Barcelona, The Delta Plan, and the current inclusive urban growth strategy. He has been Secretary General of Industry of the Government of Spain (2004-2008), director of the Barcelona Institute of Regional and Metropolitan Studies (IERMB) (2009-2015), director of the Department of Applied Economics at the UAB and director of the Universitat Internacional Menéndez Pelayo of Barcelona – Centre Ernest Lluch.

References

Aaberge

(2009) Ranking intersecting Lorenz curves. Social Choice and Welfare 33: 235–259. DOI: 10.1007/s00355-008-0354-4

Batty

(2005) Cities and Complexity: Understanding Cities with Cellular Automata. Agent-Based Models, and Fractals. Cambridge, MA, USA: MIT Press.

Ben

Derudder

Meijers

Evert

Harrison

John

et al. (2022) Polycentric urban regions: conceptualization, identification and implications. Regional Studies 56: 1–6. doi: 10.1080/00343404.2021.1982134.

Boix

Trullén

(2007) Knowledge, networks of cities and growth in regional urban Systems. Papers in Regional Science 86(4): 551–574. DOI: 10.1111/j.1435-5957.2007.00139.x

Camagni

Salone

(1993) Network urban structures in northern Italy: elements for a theoretical framework. Urban Studies 30(6): 1053–1064. DOI: 10.1080/00420989320080941

Camagni

Capello

(2011) Spatial Scenarios in a Global Perspective. Europe and the Latin Arc Countries. Camagni

Capello

(eds). Cheltemham, UK: Edward Elgar.

Camagni

(2016) Towards creativity-oriented innovation policies based on a hermeneutic approach to the knowledge-space nexus. In: Cusinato

Philippopoulos-Mihalopoulos

(eds) “Knowledge creating Milieus in Europe. Firms, Cities, Territories”: Springer, pp. 341–359.

Chen

Song

, et al. (2017) A new approach for detecting urban centers and their spatial structure with nighttime light remote sensing. IEEE Transactions on Geoscience and Remote Sensing 55: 6305–6319. DOI: 10.1109/TGRS.2017.2725917

De Landa

(2006) A New Philosophy of Society: Assemblage Theory and Social Complexity. London, UK: Bloomsbury.

10.

Dematteis

(1991) Sistemi local nucleari e sistemi a rete. un contributo geográfico all’interpretazione delle dinamiche urbane. In: Bertuglia

C.S.

La Bella

(eds) Sistemi Urbani. Milano: Franco Angeli.

11.

Donaldson

Storeygard

(2016) the view from above: applications of satellite data in economics. Journal of Economic Perspectives 30(4): 171–198. DOI: 10.1257/jep.30.4.171

12.

Florida

Gulden

Mellander

(2007) The Rise of the Mega Region. Toronto: JL Rotman School of Management, University of Toronto, The Martin Prosperity Institute.

13.

Gabaix

(1999) Zipf's law for cities: an explanation. The Quarterly Journal of Economics 114(3): 739–767. DOI: 10.1162/003355399556133

14.

Gini

(1936) On the Measure of Concentration with Special Reference to Income and Statistics. Colorado College Publication, General Series, 208, pp. 73–79.

15.

Grazi

van den Bergh

van Ommeren

(2008) An empirical analysis of urban form, transport, and global warming. The Energy Journal 29(4): 97–122. https://www-jstor-org-443.web.bisu.edu.cn/stable/41323183

16.

Jöreskog

(1969) A general approach to confirmatory maximum likelihood factor analysis. Psychometrika 34: 183–202. DOI: 10.1007/BF02289343

17.

Kweon

Kanade

(1994) Extracting topographic terrain features from elevation maps. GVGIP Image Understanding 59: 171–182. DOI: 10.1006/ciun.1994.1011

18.

Lall

Lebrand

Soppelsa

(2021) The evolution of city form. evidence from satellite data. Policy Research Working Paper. Washington, D.C., U.S.: World Bank Group, 9618.

19.

Lang

Nelson

(2009) Defining megapolitan regions. In: Ross

C.B.

Contant

(eds) Megaregions in America. Washington, DC: Island Press.

20.

(2021) Polycentric urban structure and innovation: evidence from a panel of Chinese cities. Regional Studies 56: 113–127. DOI: 10.1080/00343404.2021.1886274

21.

Lorenz

(1905) Methods of measuring the concentration of wealth. Publ. of the American Statistical Association 9(70): 209–219. DOI: 10.2307/2276207

22.

Marull

Galletto

Domene

, et al. (2013) Emerging megaregions: a new spatial scale to explore urban sustainability. Land Use Policy 34: 353–366. DOI: 10.1016/j.landusepol.2013.04.008

23.

Marull

Font

Boix

(2015) Modelling urban networks at mega-regional scale: are increasingly complex urban systems sustainable? Land Use Policy 43: 15–27. DOI: 10.1016/j.landusepol.2014.10.014

24.

Marull

Farré

Boix

, et al. (2019) Modelling urban networks sustainable progress. Land Use Policy 85: 73–91. DOI: 10.1016/j.landusepol.2019.03.038

25.

Mazzucato

(2021) Mission Economy. A Moonshot Guide to Changing Capitalism. London, UK: Penguin Books Allen Lane.

26.

OECD (2015) The Metropolitan Century: Understanding Urbanization and its Consequences. Paris, France: OECD Publishing.

27.

Ross

(2009) Megaregions: Planning for Global Competitiveness. Washington, DC, USA: Island Press.

28.

Rosseel

(2012) Lavaan: an R package for structural equation modeling. Journal of Statistical Software 48(2): 1–36. DOI: 10.18637/jss.v048.i02

29.

Trullén

Boix

Galletto

(2013) An insight on the unit of analysis in urban research. In: Kresl

P.K.

Sobrino

(eds), Handbook of Research Methods and Applications in Urban Economics. Cheltenham, UK: Edward Elgar, pp. 235–269.

30.

UN (2017) World Population Prospects: The 2017 Revision, Key Findings and Advance Tables. Department of Economic and Social Affairs, Population Division ESA/P/WP/248.

31.

Vitanov

Ausloos

Bian

(2015) Test of two hypotheses explaining the size of populations in a system of cities. Journal Applied Statistics 42(12): 2686–2693. DOI: 10.1080/02664763.2015.1047744

32.

Webber

(1972) Impact of Uncertainty on Location. Cambridge: M.I.T. Press.

33.

Westland

(2015) Structural Equation Modeling: From Paths to Networks. New York, NY, USA: Springer.

34.

Wilson

(2009) The thermodynamics of the city. evolution and complexity science in urban modelling. In: Reggiani

Nijkamp

(eds) Spatial Networks and Complexity. Berlin, Germany: Springer.

35.

Liu

Wang

, et al. (2015) A localized contour tree method for deriving geometric and topological properties of complex surface depressions based on high-resolution topographical data. International Journal of Geographical Information Science 29: 2041–2060. DOI: 10.1080/13658816.2015.1038719

36.

Zhang

Wang

Supriyadi

, et al. (2020) Evolution and optimization of Urban network spatial structure: a case study of financial enterprise network in Yangtze River Delta, China. International Journal of Geo-Information 9: 611.

37.

Zhang

Derudder

Liu

, et al. (2021) Defining ‘centres’ in analyses of polycentric urban regions: the case of the Yangtze River Delta. Regional Studies 56: 87–98. DOI: 10.1080/00343404.2021.1912725

38.

Zipf

(1949) Human Behavior and the Principle of Least Effort. Cambridge, MA, USA: Addison-Wesley Press, Inc.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB

0.79 MB