On the heterogeneity of urban expansion proﬁles in Europe Paul Kilgarriff1 Rémi Lemoy2 and Geoffrey Caruso13

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On the heterogeneity of urban expansion proﬁles in

Europe

Paul Kilgarriff1, Rémi Lemoy2, and Geoffrey Caruso1,3

1Luxembourg Institute of Socio-Economic Research (LISER), Luxembourg

2University of Rouen, IDEES Laboratory UMR 6266 CNRS, France

3University of Luxembourg

Version: October 25, 2022

Abstract

The difference of a city’s artiﬁcial land use (ALU) radial proﬁle to the average ALU pro-

ﬁle is examined for 585 European cities. Using Urban Atlas 2012 data, a radial (or mono-

centric) approach is used to calculate a city’s land use proﬁle in relation to distance to the

city centre. A scaling law is used which controls for city size and population. As a conse-

quence, cities of varying degrees of size can be contrasted in a comparable way. Utilising

the mean ALU proﬁle for the entire sample of 585 cities, the difference to the mean proﬁle

is calculated for each city. Using these differences allows us to examine heterogeneity of

the ALU across European cities but also examine these differences within cities. We utilise

city groupings by city size and country to attempt to understand these differences. Com-

bining Urban Atlas and Corine Land Cover data, the impact of water on the ALU proﬁles

is examined. A city classiﬁcation is also introduced which considers the difference to the

average curve. Ordering methods are used to visualise cities within these classiﬁcations.

Results highlight the level of heterogeneity between cities. Removing water, we can see

that the cities with the highest levels of water have a higher level of ALU on average. Spain

and France are found to have contrasting levels of ALU, Spanish cities having below aver-

age ALU and France above average. Using seriation techniques enables us to group and

order cities into a typology which can be used to benchmark cities.

1 Introduction

There is a romantic notion that a single entity of a European city exists, one which has a mono-

centric structure alongside high density and compactness. Such a narrative could be consid-

ered naive as it assumes European cities are homogeneous. Although, structures exist in Eu-

ropean cities which set them apart from US cities (Schneider and Woodcock; 2008; Patacchini

et al.; 2009). Within Europe, many cities possess a common urban form, with a similar gradi-

ent of built-up land in relation to distance to the centre, irrespective of their size (Lemoy and

Caruso; 2018). However, high levels of heterogeneity between cities remain. The challenge

is how this heterogeneity can be measured. Two types of heterogeneity exist in relation to

cities, inter (between cities) and intra (within cities between areas). Given the overall mono-

centric nature of European cities (Oueslati et al.; 2015), urbanisation forms a radial structure,

and there is a decrease of density as one moves away from the centre, as theorised by urban

economics (Alonso; 1964; Mills; 1972; Muth; 1969; Fujita; 1989). The aim of this paper is to de-

scribe this decreasing density with distance for European cities, and how this differs from the

overall average urban density gradient. The work of Lemoy and Caruso (2018) is updated for

2012 to examine how 585 European cities are different from the ’average’ European city. This

examination of heterogeneity is important as it has consequences in relation to sustainability

and efﬁcient allocation of resources.

Examining differences between a city’s artiﬁcial land use gradient and the average gradient,

will identify distances where a city is more or less urbanised. It matters whether a city is more

arXiv:2210.13322v1 [physics.soc-ph] 24 Oct 2022

urbanised near the core or periphery, particularly in relation to aspects such as sustainabil-

ity and accessibility. The accessibility aspect of a city is important, and mainly related to the

distance to the city centre and how compact a city is at various distances. The level of com-

pactness will have positive and negative inﬂuences on the sustainability of cities (Lin and

Yang; 2006; Neuman; 2005; Burton et al.; 1996). Densiﬁcation of urban areas is associated

with overcrowding and air pollution, while reversing patterns of decentralisation towards a

compact city may not be feasible in all situations (Breheny; 1995). Despite this, there are ob-

vious advantages and disadvantages of higher urban density related to mobility, resources,

social equity, economic output and energy consumption (see Boyko and Cooper (2011) for a

comprehensive review). The more compact a city is, the greater the level of economy of scale

efﬁciencies, especially for public transport provision. A trade-off exists between capacity, fre-

quency and location. Modes such as train or light rail have a higher capacity compared to

buses, however costs are also higher therefore limiting the number of stations and stops. The

cost effectiveness of different modes of shared transport is therefore dependant on the com-

pactness of a city. A compact city also encourages walking and cycling for shorter distances. A

city may be expanding in ways which make it difﬁcult for policy makers to provide adequate

services on limited budgets. In that way, heterogeneity of cities will impact on the sustain-

ability levels if there are inefﬁcient resource allocation and losses as a result of being over- or

under-urbanised.

This is not the ﬁrst time that urban forms and heterogeneity have been examined in a Eu-

ropean context. Interestingly some earlier studies were also monocentric or radial, focusing

on the internal structure of cities (Berry et al.; 1963; Clark; 1951; Fooks; 1946). Radial analysis

can provide rich data on the level of urbanisation within a city. Recent studies however ig-

nored the distance effect and focused on landscape metrics, with a few exceptions (Jiao; 2015;

Guérois and Pumain; 2008). The rise in the popularity of using landscape metrics was largely

driven by the focus on urban sprawl and the organisation of land (EAA; 2006; EEA and FOEN;

2016), fragmentation indices were viewed as the best method of examining both the level of

urbanisation but also how fragmented parcels of land were. Measures used in ecology such

as the Shannon index (Shannon; 1948) and Simpson index (Simpson; 1949) offer a means of

measuring fragmentation quantitatively. Landscape metrics place a greater emphasis on the

local context as opposed to the overall land use proﬁle. Whereas in ecology the local envi-

ronment is important for biological diversity, richness and regularity (Tucker et al.; 2017), in

a human context, movement in a city and accessibility to the centre is crucial (Rode et al.;

2017). Although landscape metrics are useful, the lack of distance to the centre makes them

less informative. It is not only the ’what’ but also the ’where’ which is important in relation

to urbanisation and compactness of cities. Accounting for both the level of compactness and

where this compactness occurs, is required to access the overall sustainability of cities. Land-

scape metrics will vary both within and between areas in a city and its surrounding areas. The

use of landscape metrics to measure urban sprawl and compactness should act as a comple-

ment to the distance/radial based approach (Irwin and Bockstael; 2007).

Previous studies have examined the level and (temporal) change in built-up area, urban land

or residential area. Others have examined urban areas using landscape metrics or using an

urban density, population change, urban expansion, urban sprawl and soil sealing approach.

Patacchini et al. (2009) used data from the Urban Audit (Eurostat) to examine the characteris-

tics of urban sprawl using measures of land area, population density and the ratio of working

age population to land area for 263 European cities over the period 1991-2001. Others have

used landscape metrics to examine the impact of local culture (Netto et al.; 2020) on urban

form. Kasanko et al. (2006) used a sample of 15 cities to examine urban expansion and het-

erogeneity between the 1950s to 1990s using the MOLAND model (JRC) (Engelen et al.; 2004).

They found the surroundings and typography of a city and the historical onset of urbani-

sation are some of the determinants of city heterogeneity. EAA (2006) also using data from

the MOLAND model (JRC), examined sprawl at the UMZ level but introduced an additional

distance measure in the form of three buffer zones outside of the UMZ (0-5km, 5-10 km, 10-

20km). Schwarz (2010) used data from CORINE and the Urban Audit to measure urban form

using several landscape and socio-economic metrics for 231 European cities. Utilising clus-

ter analysis, statistically signiﬁcant differences were found with respect to urban form among

cities.

Siedentop and Fina (2012) measured urbanisation within 20km grid cells using CORINE data

to compare urban land use change over time both within and between 26 European coun-

tries. Heterogeneity within and between countries was found. Turok and Mykhnenko (2007)

showed the majority of European cities experienced growth in population (1960-2005), with

regional differences experienced. Angel et al. (2011) used MODIS 500m land cover data along

with UN and Brinkhoff (2010) population data to examine urban land cover and population

for 3,646 world cities using a morphological deﬁnition of cities. Wolff et al. (2018) delineated

cities using a combination of Urban Morphological Zone (UMZ) and density thresholds to

examine the relationship between residential area change and population change in 5,692

European urban areas. Oueslati et al. (2015) examined the determinants of urban sprawl for

282 European cities at the LUZ level, for the years 1990, 2000 and 2006. Two indices of ur-

ban sprawl where used, one measure reﬂecting the scale of the change (growth of artiﬁcial

area) and the other fragmentation (scatter index). Although the ﬁndings are useful partic-

ularly related to the causes of urban expansion, using an aggregate measure is likely to be

sensitive to the scale of the study area. Taubenböck et al. (2009) found urban structure to

be scale dependent in an analysis of Indian cities. Six concentric rings of 10km increments

were used to show heterogeneity in built-up density. They concluded that overall, the urban

structure is scale dependent. These ﬁndings are consistent with previous work which showed

that landscape metrics are scale dependent and the use of metric scaleograms is necessary to

adequately quantify spatial heterogeneity (Wu et al.; 2002). These issues of scale and extent

relate to the issue of modiﬁable areal unit problem (MAUP) (Openshaw; 1984).

Several studies examined urbanisation utilising landscape metrics taking account of differ-

ences between the core, suburbs and periphery. Schwarz (2010); Kasanko et al. (2006) recom-

mend delineating cities using buffers around the central business district (CBD) or examine

the gradient. Improving on only reporting landscape metrics for the entire urban area, Seto

and Fragkias (2005) used three buffer zones to examine landscape metrics, however the same

distance buffers are used for cities of different populations. The focus of the study was the

change of landscape metrics across time and cities and not whether they are scale depen-

dent. Arribas-Bel et al. (2011) made the distinction between the core and non-core across

209 European urban regions and cores using CORINE, Urban Morphological Zones (UMZ)

and Urban Audit data for period 1999-2002. Multiple indexes were measured; connectivity

(average commute time), decentralisation (population of people living in the non-core as a

share of those living in the core), density using only urban area, scattering (ratio of patches to

population), availability of open space and land use mix using Simpson’s index of diversity. A

self-organising map (SOM) algorithm was used to group cities in supra-national regions and

observe regional patterns and overall urban sprawl.

Studies have attempted to account for these scale issues by using a radial approach. Schneider

and Woodcock (2008) used 1km rings to examine urban expansion, urban density, fragmen-

tation and population density. The cut-off of the urban core was the point at which urban

land density fell below 50% . Areas outside of this core were divided into three 8 km rings

representing the fringe, periphery and hinterland. The core distances for cities ranged from

3-27km. Only US and Chinese cities were found to exhibit regional differences/similarities.

Urban density was found to increase the most in the core followed by the fringe, for all groups

of cities. Guérois and Pumain (2008) measured built up land using CORINE data and 1km

concentric rings. They found a steep decline in built-up area before a leveling off: two gra-

dients were used, one for the central area (steep), and one for the periphery (shallow curve),

with a ﬁrst break at the historic centre of the city. The authors conclude that the geographical

space is ’still shaped by the attractive power of the city centres’ (Guérois and Pumain; 2008).

Jiao (2015) overcame scaling issues by using a monocentric analysis combined with a model

ﬁtting for Chinese cities. The majority of cities reduced compactness and became more dis-

persed over the period 1990-2010, with more dispersion occurring in the latter decade. Urban

land use was found to decrease from the city centre according to the inverse s-shape rule. See

table ?? in the appendix for a selection of relevant studies.

What is clear from the review of studies is that many studies have focused on landscape met-

rics or the change in urban land cover over time. For temporal studies, ﬁnding consistent data

is a challenge, which impacts the level of data disaggregation and detail. Whereas others have

examined the intra-urban structure and radial proﬁles, the present work is the ﬁrst to examine

such a large sample of cities, at a small scale (141m rings as opposed to 1km).

In this study the heterogeneity of European cities is examined. Heterogeneity in the sense of

the difference between a city’s observed artiﬁcial land use (ALU) proﬁle and the average ALU

proﬁle for 585 European cities. This measure of heterogeneity will indicate whether a city is

over or under artiﬁcialised compared to the average. Points on a curve which fall above or

below the average may be considered to be over or under expanded. Levels of over expansion

in the suburbs and periphery are consistent with patterns of urban sprawl.

Attempting to identify patterns in very large datasets is a difﬁcult process. Methods such as

clustering have typically been used to group observations together. Clustering algorithms

are data driven, removing typology type grouping from the process. This paper introduces a

conceptual framework to group cities together based upon their heterogeneity. Utilising the

level of urbanisation as measured by the percentage of artiﬁcial surface within concentric cir-

cles, the difference to the average across 585 European cities is examined. This will enable

cities to be classiﬁed as being more compact in the core, more sprawled in the periphery, or

perhaps both. Using a scaling methodology developed by Lemoy and Caruso (2018) enables

us to compare cities of various sizes in a consistent manner. Urban scaling helps to identify

deviations by using scale independent urban indicators (SAMIs) to measure cities (Betten-

court and Lobo; 2016). Combining scaling with an ordering technique, has the ability to use

both nomothetic and idiographic approaches to geographic information (Goodchild; 2001).

Nomothetic in the sense that we are generalising cities irrespective of size, so that they can be

classiﬁed, and idiographic in that speciﬁc characteristics of generalised groups or individual

cities can then be analysed.

2 Concepts

The homothetic scaling of artiﬁcial land use can be expressed with mathematical relations.

Lemoy and Caruso (2018) found that the radial artiﬁcial land use proﬁles s(r) of different cities

are quite similar if the distance r to the city center is rescaled to a distance r0given by

r0=r×kwith k=rNLondon

N, (1)

where Nis the population of the city being analysed and NLondon the population of London,

the largest city in the dataset, which is arbitrarily chosen as a reference. kis the rescaling

factor: k=1 for London.

We note s(r0) the ALU share at rescaled distance r0and s(r0) the average (over all cities) ALU

share at distance r0. We study heterogeneity using the difference h(r0)=s(r0)−s(r0) between

s(r0) and s(r0), for each city, at each rescaled distance r0. This difference to the average (or het-

erogeneity) h(r0) is used in a two-tier classiﬁcation, in an attempt to group similar cities. The

ﬁrst tier classiﬁcation examines the sign and the magnitude of the heterogeneity h(r0). Cities

are classiﬁed based on whether the difference to the average h(r0) is always positive (that is,

positive for all values of the distance r0to the CBD), always negative or a mix between the two.

Figure 1 shows schematically how these differences to the average proﬁle (represented by a

red dotted line) may appear. For the mixed category, the heterogenity proﬁle h(r0) will cross

the zero horizontal axis at least once.

Figure 1: First tier of the two-tier proﬁle classiﬁcation

The second tier classiﬁcation examines the form of the difference to the average proﬁle for

each city. Figure 2 conceptualises the trends expected in difference to the average proﬁles.

As the second tier classiﬁcation focuses on the shape or form of the proﬁle, the proﬁle can

be categorised as downward or upward sloping however all values can be positive or negative

in relation to the average. Second tier classiﬁcation describes whether the periphery, sub-

urbs or core of a city is more or less urbanised in relation to each other. In that sense second

tier classiﬁcation examines more within city compared to the ﬁrst tier. Colouring is added

to the visualisation of the two-tier classiﬁcation with red used to represent values above the

average and blue to represent values below the average. Within each grouping the possibility

exists of having differences in the magnitude to which a city corresponds to that classiﬁca-

tion, in which case an ordering method offers a useful method to order cities, improving our

understand of the nature of ALU, urban expansion and urban sprawl and its determinants.

Using a two-tier classiﬁcation introduces a hierarchy of measures as a city can be both all

positive/negative and also one of the six second tier classiﬁcations.

Figure 2: Second tier of the two-tier proﬁle classiﬁcation

3 Methods & Data

The scaling methodology developed by Lemoy and Caruso (2018) and used in this analysis,

requires a city’s population. For this purpose the functional urban area (FUA) boundary, as

deﬁned in the urban atlas database is used to delineate urban areas. Population data from the

Eurostat GEOSTAT 1km grid is down-scaled to residential land use areas from the urban at-

las. A city’s population is then calculated as the total down-scaled population located within

a city’s FUA. To overcome issues related to areas which fall outside the FUA boundary but

within a concentric ring, CORINE data is combined with Urban Atlas data. With the CORINE-

Urban Atlas dataset, any concentric rings drawn around the CBD will have complete land use

information. This will also prove useful for deﬁning coastal and non-coastal cities. 3 details

the procedure and steps involved in calculating the ALU proﬁles for each city. In the follow-

ing sections the data used (Urban Atlas, CORINE and GEOSTAT) is discussed followed by the

processing and the radial analysis. This is followed by a discussion on how the scaling law is

applied. The ﬁnal subsections describe the characterisation and grouping of city proﬁles.

Figure 3 outlines the procedure used to calculate the ALU city proﬁles.

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OntheheterogeneityofurbanexpansionprolesinEuropePaulKilgarriff1,RémiLemoy2,andGeoffreyCaruso1,31LuxembourgInstituteofSocio-EconomicResearch(LISER),Luxembourg2UniversityofRouen,IDEESLaboratoryUMR6266CNRS,France3UniversityofLuxembourgVersion:October25,2022AbstractThedifferenceofacity'sarticiallandus...

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On the heterogeneity of urban expansion proﬁles in Europe Paul Kilgarriff1 Rémi Lemoy2 and Geoffrey Caruso13

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