Following the population of European urban areas in the last half century (1961-2011): the TRADEVE database

régionales du ralentissement de la croissance démographique des villes au cours de cette période. D’après une Classification Ascendante Hiérarchique effectuée sur les trajectoires démographiques des villes entre 1961 et 2011, il apparaît que 22% des villes ont connu des trajectoires de décroissance relative, soit 870 sur les 3930 considérées. L’article s’accompagne de la mise en ligne en accès libre de la base TRADEVE et de la documentation qui en détaille la conception.


Introduction 1
The following of European cities' population has received an increased interest in the last decades due to various major issues. A first subject of interest deals with the general evolution of urban systems, the analysis of historical cyclic urban development and the way these cycles are spreading differently among hierarchical levels and regions. In that respect, one of the main questions tackled has long been related to the interpretation of the major turnaround of growth slowdown in the 1970s and to the questioning of the counter-urbanization concept (Cattan et al., 1999;Champion, 2001). More recent works participating in the theoretical field of complex systems have focused on the relation between urban system dynamics and the diffusion of innovations, by articulating the urban hierarchy structures on macro-geographical scales and the trajectories of the cities themselves on micro-geographical level (Favaro and Pumain, 2011;Cottineau, 2014;Pumain et al., 2015;Raimbault, 2018). Beyond this theoretical framework there have been for some years new investigations on the evolution of the rich heritage of small and medium-sized towns in Europe (Pumain, 1999), which comprises a worldwide concern for the shrinking cities issues (Martinez-Fernandez C. et al., 2016). The interest for this subject is related to major socio-demographic issues like the ageing process and slowing down of demographic growth (Bretagnolle et al., 2018;Rink et al., 2012). Along with this growing field of studies, the observation of more recent trends of a resurgence (regrowth after years of decline) has more recently made it necessary to consolidate comparative knowledge about the demographic future of cities (Rink et al., 2012, Wolff andWiechmann, 2017). 2 Beyond their diversity, these issues have reinforced a common interest for the establishment of a longitudinal urban database in Europe. However, such databases are especially difficult to process since they raise at least three problems at the same time: the harmonization of urban definitions from one country to another, the availability of population data for each date at the level of local administrative units (LAU) and the geometrical and statistical sources for constructing urban delineations at each date. The challenging difficulties related to the statistical following of urban objects through time (Mathian and Sanders, 2016) are here exacerbated by the international context of comparison. Different choices have been made by researchers in order to support these studies. Some of these works have emphasized the length of time series while focusing on large cities (Van den Berg, 1982;Turok et al., 2007). Others have included small and medium sized cities for a shorter period between 1990 and 2010 (Wolff and Wiechmann, 2017). The Europolis programme (Chatel, 2012) allows following cities over a longer period (1850-2010, with evolving perimeter since 1990); however, the data are not available in open access. 3 This paper aims at discussing the interest of a new data model used in order to process a longitudinal and harmonized database of European cities, the TRADEVE 1 one, which provides delineations and populations of European urban areas, defined by taking into account continuous built-up areas and minimal population threshold from 1961 to 2011. It is based on two original sources, a harmonized database that allows studying small and medium sized urban areas in 2000 (Urban Morphological Zones -UMZ) and the Historical Population Database of European LAUs (from Gloersen et al., 2013). More than 3,900 urban areas (exactly 3,946) comprising over 10,000 inhabitants are considered in 2011 for 29 countries. Beyond the single issue of the construction of a new database, this paper makes an important contribution to implementing an open access database (European Commission, 2016;Kosmopoulos and Pumain, 2018), which is the first one for the evolution of European cities over 50 years 2 . 4 First, we present the main conceptual models that are theoretically designed to integrate time into urban databases. Then we propose the data model used in order to provide evolving urban perimeters and which is based on the retropolation of UMZ 2000 back to 1961. Lastly, some insights into the resulting database are presented both at the macro level of countries and European regions (urbanization rate) and at the city level (population variation rates and clustering analysis of demographic trajectories).
Modelling the evolution of the population of cities: theoretical approaches 5 Many scholars have already stated that measuring cities' demographic change in the medium-and long-term sounds "misleadingly simple" (Bernt, 2015, quoting Wolff, 2011. Seemingly, population data are easily available, reliable and comparable in regards to social or employment statistics. However, several difficulties still represent important challenges to such measures. 6 Firstly, longitudinal data of local populations are often difficult to access. Even if the data in itself is easily available at each census, the monitoring over time of local population trends is complicated because LAUs (Local Administrative Units) have undergone many geometrical changes through time. Secondly, from a territorial perspective, cities are complex geographical objects that can be analyzed through different definitions and perimeters , from administrative to morphological and functional ones. The international harmonization of such delineations remains often a huge task, even though much progress has been registered in recent years for Europe (see a recent state of art in Bretagnolle et al. 2015). Thirdly, from a temporal perspective, cities are evolving objects and the following of urban objects through time is thus a complex issue (Bretagnolle, 2009), especially when the study extends over a relatively long period of 50 years.

7
This latter question about time integration has been rarely addressed in the literature on demographic changes of European cities, although it has considerable influence on the measure of urbanization. From an empirical perspective, some studies at a national scale have shown that the results of urban demographic trends largely depend on whether the delineation of cities is stable or evolving through time (Berry and Okulicz-Kozaryn, 2012;Bretagnolle et al., 2015;Pumain et al., 2015). The choice of a stable or evolving perimeter is especially critical from the 1960s due to the importance of the urban sprawl process itself. In France for instance, at the level of functional urban areas ("aires urbaines"), Paulus (2004) has demonstrated that more than 10 million inhabitants lived in municipalities that are currently comprised in functional urban areas' delineations in 1999, without being identified as urban following the same definition of functional urban areas in 1968. This is also the case for the morphological urban areas (MUA) ("unités urbaines") as urban settlements also develop in spatial continuity with the urban core: if less pronounced, the spatial extension of built-up areas has also been very significant and about 3.2 million inhabitants have been gained through updating urban area perimeters.

8
In light of these considerations, a previous work has formalized the identification of four different conceptual models that can be used for following urban areas through time   (Figure 1). This distinction depends on the richness of the statistical and geometrical data available at each date and on the partially or fully automated process of the database creation.
• In case A, there is a time series for urban objects, but it results from a process that recreates delineations from scratch at each date, without any link with the previous period. Urban areas are indeed independent from one year to another since there is no relation between them through time and no genealogy established through a common ID code. The result amounts to the production of "snapshots", which are quite simple to process. This is the case for the UMZ database, which is defined by CORINE Land Cover classes at three dates: 1990, 2000 and 2006 (and next, 2012). There has been an update for the delineation assessment of these zones; however, the database in itself does not allow us to follow the evolution of each UMZ since its identity is not conserved from one date to another. Even though such an approach is sufficient to provide general measures of urbanization (evolution of urbanization rates at different periods), it is not relevant for the analysis of urban trajectories.
• Case B corresponds to the most common case in longitudinal studies about population changes and is the easiest solution to implement. In this time series, the delineation of cities is the same for all dates. It presupposes choosing a reference year, which is generally fixed as the most recent date. It is, for instance, the approach adopted by Wolff and Wiechmann (2017) in their study about Europe's shrinking cities between 1990 and 2010.
• In case C, an evolving delineation is based on simple selection criteria applied to building blocks. The minimal distance between built-up areas is only assessed for one year (reference year), in general in the latest year. A retropolation method is then processed at each date by checking the urban nature of each building block (minimal threshold of population or density) and if they are spatially concentrated (contiguity of building blocks). For instance, a constant minimum density applied at different census periods enables following the urban sprawl of a city by aggregating the surrounding villages that exceed this threshold at each date. The perimeter can therefore be different at each date if the city has been expanding or retracting. That method has been chosen for the Geopolis database (Moriconi, 1994(Moriconi, ) until 1990. It is also the method chosen for the TRADEVE database. -Case D relies on an evolving delineation based on a reassessment (at each date, with a distinct reference year) of the continuous built-up criteria, in general a maximal 200 meters' distance between buildings or urban spots, based on aerial photographs or satellite images. This is the most rigorous method, but it remains costly and time consuming 3 . Only few countries use it to our knowledge (France, Sweden and Denmark). Consequently, it can be seen from the above that methodological and technical considerations explain to a large extent the choice of a database model rather than another. Evolving perimeters are not usually delivered by national statistical institutes. For instance, in France, INSEE (Institut National de la Statistique et des Etudes Economiques) provides the data about functional urban areas but only from 1990 to 2010. They have thus to be reconstructed by researchers. Furthermore, the longitudinal local data are not easy to obtain. It raises also the issue of the structure of the database itself, since evolving urban perimeters imply retracing a complex genealogy of objects (fusions, scissions, apparitions, disappearances) (Mathian and Sanders, 2016). 10 The preference for either of these models also depends on the temporal coverage under consideration. The need to choose evolving perimeters or definitions may actually be justified by a medium or a long-term period (for instance, 1960-2010), especially if the extension of cities has been considerable during this period, whereas fixed limits are often preferred for the 1990-2010 period. On long periods, the choice of a constant delineation excluding spatial growth would lead to overestimating the initial population and to underestimating demographic urban growth. For instance, Paulus (2004) has shown for France that updating the delineation of urban areas between 1968 and 1999 included about 1 more million urban inhabitants at each reference year, as compared to the results obtained with evolving delineation. As a result, the rhythm of urbanization is fairly different (1.4% for evolving limits, against 1.1% for constant ones), even though Following the population of European urban areas in the last half century (19... Cybergeo : European Journal of Geography , Espace, Société, Territoire global trends remain the same (a general slowdown of urban growth), apart from the latest period between 1990 and 1999 (a stabilization for evolving limits versus a slowdown trend for constant perimeter). Evolving perimeters appears thus preferable for longer periods, even though it supposes to tackle the sensitive issue of the fusions between cities. From theory to implementation: the TRADEVE database Geometrical and statistical sources 12 Considering the time period (50 years characterized by a strong urban spatial extension), the TRADEVE project relies on evolving perimeters (case C of Figure 1). This choice has been motivated by the recent availability of two original sources.
13 The first is a harmonized database of morphological urban areas in Europe. The UMZ database from the European Environment Agency offers a reference for the delineation of urban areas in 2000. Originally defined by the European Environment Agency from CORINE Land Cover images and continuous built-up areas criteria (Milego, 2007), UMZ were poorly used for urban studies until they were enriched in the ESPON Database by other indicators, such as a name for each agglomeration and a correspondence dictionary with LAU2 (smallest Local Administrative Units) that allows joining other statistical datasets. A population density grid from the Joint Research Centre (Gallego, 2010) was used for attributing populations to these urban areas (Bretagnolle et al., 2016a and Map 1). This 100-metre resolution grid was constructed by using information from CORINE Land Cover in order to disaggregate LAU2 populations at a finer scale of observation (a weighting coefficient is attached to each category of land use and gives the share of the urban population to be reallocated). We also validated the use of the UMZ database by comparing urban populations or surfaces with those from national urban databases in Sweden, Denmark and France (Guérois et al., 2012).

Map 1: Population and density of European Urban Morphological Zones in 2011
14 The choice of a morphological definition is supported by the fact that it allows us to take into account the evolution of small and medium sized cities, even if it underestimates the growth of population in urban peripheries of the largest cities. Compared to other morphological databases, the UMZ database allows us to embrace a large range of city sizes (over 10,000 inhabitants) in a comparable way. The MUAs defined by C. Vandermotten et al. (1999) are much less numerous, as their minimal threshold is 20,000 inhabitants: we find 1,988 MUAs instead of 3,982 Tradeve-UMZ in 2000. The new Larger Urban Zones, delineated in a harmonized way by DG Regio, Urban Audit and OECD, are much fewer, using a minimal threshold of 50,000 inhabitants (Djijstra and Poelman, 2012). Turok and Mykhnenko (2007) started from Cheshire's database (1995) and tried to enlarge the timespan, but only for cities larger than 200,000 inhabitants. Wolff and Wiechmann (2017) used population, density and morphological criteria, but different definitions, of cities in Europe ("unités urbaines" were used for France) and a constant delineation.

Method and parameters
16 Despite the importance of such original sources, the definition of evolving perimeters for urban areas from 1960 to 2010 is far from evident. Indeed, National Statistical Institutes seldom provide evolving perimeters' databases. The most complete approach would assume to apply the same rules to the data at each date, with, for instance, a 200-metre criteria for delineating the built-up areas extension for urban areas. However, the availability of such data on a European scale is not guaranteed for each reference year.
17 An alternative approach comprises reconstructing past delineations in an indirect way, on the basis of present-day criteria (case C of Figure 1). This approach implies to set up rules in order to identify the administrative units that are part of an urban area at each date. On the basis of the most recent perimeter (UMZ 2000 delineation), it assumes it is possible to build urban areas' delineations at each date by selecting only the LAUs that are considered as urban and that are contiguous. In this regard, the most discussed step relies on the identification of what is an urban LAU at each date. Two criteria can be chosen in order to select urban building blocks at each date between 1961 and 2001: minimal density and minimal population 5 . 18 We compared both methods and three different thresholds for each one, and finally chose the minimal population method and the 2,000-inhabitant threshold. The reconstruction of urban areas based on the most restrictive thresholds of population or density (10,000 inh. or 650 inh/km²) leads to a strong fragmentation in the year 2000 as compared to the reference situation (UMZ 2000 perimeter). Consequently, choosing the 2,000 inhabitants or the 150 inh/km 2 seemed to be more appropriate (Table 1). Among those criteria, the density threshold introduced too much heterogeneity as it tends to reduce spatial coverage for countries characterized by large administrative units such as in Central and Eastern Europe, and conversely tends to improve spatial coverage for countries with small units.    Figure 3 shows the data model that has been constructed to organize the different links between spatial entities (in red), statistical sources (in white) and functions (in green) and the way they are evolving through time.
Following the population of European urban areas in the last half century (19... Cybergeo : European Journal of Geography , Espace, Société, Territoire Implementation and validation 21 The method has been implemented to construct 3,982 urban areas evolving from 1961 to 2011. In terms of urban spatial extension, the results are very different from one country to another, depending on the average size of the LAUs (see the differences between Paris and Madrid, Map 2) and inequality of LAU2 size between large and small cities in Central and Eastern Europe (see Budapest and Prague compared to other cities). Indeed, in this part of Europe, the urban sprawl that began at the end of the 19 th century throughout the construction of suburban railways was followed by successive annexations of surrounding LAU2 by the central municipality. Consequently, the size of the eponymous LAU2 (for instance, Prague or Budapest) was progressively enlarged, absorbing the new suburbs. However, the TRADEVE database allows to follow the rise of some new urban areas, as illustrated, for instance, in the north and east of Czech Republic. In order to validate the results, we compared the TRADEVE urban areas and the French urban areas defined by INSEE and named "unités urbaines" larger than 10,000 inhabitants in 1999 (the same minimal threshold as for TRADEVE). Only two TRADEVE urban areas are not corresponding to a "unité urbaine" (Belleville, in the north of Lyon and Givet near the Belgium border). Conversely, 78 "unités urbaines" do not correspond to a TRADEVE urban area but are rather small (71 have a population lower than 15,000 inh. and 7 are between 15,000 and 25,000 inh.). This comparison shows that the TRADEVE urban areas are less fragmented than the "unités urbaines" (and consequently their total number is lower), which is easily understandable considering the method used by INSEE for constructing urban areas in France 7 .
23 With the originality of the TRADEVE method being related to the evolving delineation of urban areas through time, it is worth assessing the consequences of this specific approach on the evolution of urban populations and delineations. An important concern lies in the measure of urban population from 1961 to 2001 and in the changes implied by the choice of an evolving perimeter rather than a constant one. When considered at a macro level (total urban population in Europe), differences seem to be very small ( Table 2). Among the 3,217 cities present in the database at each date (without considering cases of appearance, fusion…), 15% of them show changing limits. This could be interpreted as a very limited result, but one has to consider the fact that the large majority of cities are small ones (urban areas from 10,000 to 50,000 inhabitants represent 70% to 90% of the total number of cities in each European country, (Bretagnolle et al., 2018)) and these small cities are generally composed of only one LAU.  24 This ratio steadily increases with city size so that it reaches 37% of the cities of over 200,000 inhabitants ( Figure 4). It also depends on the countries compared, as illustrated by the opposition between the cases of strong stability (in Poland, Hungary, Germany, but also the Netherlands or Sweden) and the cases where changes are much more frequent (in France, United Kingdom, Denmark…). This "changing rate" ranges from 0% (Poland) to 67% (Denmark). Some extreme values sometimes concern large cities, like the "new cities" of Milton Keynes (area multiplied by 4 during the half century) and Reading (multiplied by 3). 25 Some inherent limitations due to sources' availability or data geometries should therefore be taken into consideration. First, regarding the 2011 population results, it has not been possible to use more recent urban perimeters than those from UMZ 2000. The perimeters built from CORINE Land Cover 2012 are not available yet and there is still no update of the population density grid which was used to build the dictionary of correspondence with LAUs. As a consequence, the 2011 LAU populations have been attributed to the 2000 perimeter for now and we hope that it will be possible to update them later.
Following the population of European urban areas in the last half century (19... Cybergeo : European Journal of Geography , Espace, Société, Territoire 26 Furthermore, the model does not consider cases of spatial retraction: in the data model, when a building block is considered as urban at a particular date, it is conserved later on even if its population decreases under 2,000 inhabitants, for internal coherence reasons (see step 3 of Figure 2). 27 Lastly, the heterogeneity of LAU sizes partly impacts the measure of the spatial expansion or stability of urban areas in three different ways. First, one can assume that the measure of spatial expansion in time will be quite sensitive to the heterogeneity of LAU sizes between countries at the same date: small morphological variations are more easily registered/detected when the mesh is tight (like in France) than when it is quite loose (like in Nordic countries). For similar reasons, it is harder to register some spatial variations when territorial divisions have been adjusted to urban expansion: in Central and Eastern Europe, for instance, territorial divisions for cities are usually modified and adapted in order to better fit the spatial expansion of the built-up area. Lastly, the differing stability of LAUs that covers from one reference year to another might also influence the measure of urban growth or decline. That being said, this original method constitutes real progress as compared to former longitudinal studies.
Five decades of urban change in Europe in the light of the TRADEVE database: a multilevel insight 28 The harmonized database TRADEVE is a useful tool to carry out a comparative approach at the European level. Using the same morphological definition of urban areas allows us to perform some reliable multilevel insights. In this section, the first investigations of the TRADEVE database are presented on the basis of different core indicators about urbanization, first at the macro level of countries (urbanization rates) then at the level of the cities (average population variation). This last sub-section will focus primarily on population decreasing issues through a clustering analysis of demographic trajectories.
At the level of countries, urbanization rates 29 The European urbanization level (54% of the total population is living in cities in 2011) seems to be low, compared to the World Urbanization Prospect (WUP) 2014 (74% for UE28). This is because the WUP is a collection of national urban definitions that are not harmonized and most of the time not even representative of the definitions adopted by national statistical boards. Moreover, it is based on a minimum population size/density of urban areas much smaller than in the TRADEVE database 8 . Figure 5 displays the evolution of urbanization levels computed for 24 countries 9 . The curve representing the average (Europe) is characterized by a slight increase since 1991 (only 0.8%), which may be explained by the definition of cities adopted in the database: as we do not take into account functional urban areas, we do not include the rural areas located in the fringes of the largest cities and settled by commuters, a phenomenon that increased with the diffusion of automobiles and highways in the recent decades. Nevertheless, using a harmonized definition of urban areas reveals the intensity of the contrasts between highly urbanized countries (84% in the Netherlands, 81% in Belgium in 2011) and the less urbanized ones (47% in Slovakia, 48% in Lithuania in 2011). If we distinguish countries according to geographical criteria (North-Western Europe, Atlantic and Mediterranean periphery and Central and Eastern Europe), results clearly show that in North-Western Following the population of European urban areas in the last half century (19... Cybergeo : European Journal of Geography , Espace, Société, Territoire countries, urbanization has been more or less steady (with a slight increase in Sweden and Finland), whereas it has been increased mainly in the 1960s and 1970s in the Atlantic and Mediterranean periphery, and also in the 1980s in Central Europe. In these latter countries, stagnation occurs from 1991/2001, except for Bulgaria and Croatia (both show a total population decline). 2) tends to underestimate population growth. Beyond this general trend towards slowing growth until 2011, differences are clearly displayed according to city size ( Figure 6). The pace of growth decreases steadily according to city size, except for large cities (between 100,000 and 200,000 inhabitants), which grew more rapidly than small and medium-sized ones between 1961 and 1971. Progressively, there is a clear convergence towards lower rates, regardless of the size of the cities. The strong convergence observed during the last period is due to recovery of population growth for the largest cities (from medium-sized to very large cities) whereas population growth is still decelerating in small and over all very small cities. 1. Very small: 10,000 to 25,000 inh., 2. Small: 25,000 to 50,000 inh., 3. Medium-sized: 50,000 to 100,000 inh., Large: 100,000 to 200,000 inh., Very large: over 200,000 inh.
NB: The cities characterized by exceptional rates (less than -15% and over 15% per year) have been removed from the corpus at each period. They concern mainly polders cities in Netherlands, new cities in United Kingdom or cities with large housing estates in Madrid suburbs. They are 30 between 1961 and 1971, 16 between 1971 and 1981, 8 between 1981 and 1991, 3 between 1991  33 Since 1991 (Map 4-d), Europe has passed through an equilibration of urban growth rates and the regional tendencies have taken an opposite direction comparing to the previous period. Indeed, Central and Eastern European urban areas have experienced slightly Following the population of European urban areas in the last half century (19... Cybergeo : European Journal of Geography , Espace, Société, Territoire negative growth rates due to the spread of suburbanization, to the sharp decline in the birth rate related to the post-socialist transition and, for the smallest cities, to the collapse of small-town industrial plants that had been established in the centrally planned economy era (Pirisi and Trocsanyi, 2014;Zdanowska, 2016). The growth rates in Western Europe have switched to slightly above zero (between 0% and 1%, and between 1% and 2.5% in the case of London). Moreover, urban areas with the highest average urban growth rates have become exceptions (suburbs of Madrid, Barcelona, Paris, Athens, and Klaipeda in Lithuania). The beginning of the 21 st century (Map 4-e) is marked by a certain recovery of urban growth in a few regions of Europe presenting average annual growth rates just above zero. This is the case of the whole United Kingdom, Central and Southern France, Belgium, the Netherlands, Denmark, Spain, Italy and Poland. Nevertheless, many urban areas in Germany, Hungary, Romania, Lithuania and Latvia have been still losing population as their annual growth rates were between -0.5% and -17.5%. An interesting point is that German central-eastern urban areas have never reached positive annual growth rates throughout the whole period 1961-2011, which confirms the results from Figure 6.
Map 4. Variations of population growth and decrease across Europe  At the level of cities, a cluster analysis of population trajectories 34 These first outcomes can be completed by a hierarchical cluster analysis performed on demographic trajectories of 3,962 TRADEVE 11 urban areas. In order to conduct these data explorations, we applied the Ward method (which tends to minimize intra-class variance and to maximize inter-class variance) using Chi-2 distance on a matrix which resulted from a correspondence analysis on the temporal population table. This methodology is Following the population of European urban areas in the last half century (19... Cybergeo : European Journal of Geography , Espace, Société, Territoire convenient since it highlights the urban trajectory similarities and it understates stock effects 12 . 35 According to the intra-class and inter-class distances, a classification in four classes is the most adapted despite the number of cities analyzed. A first map (Map 5) displays those classes according to urban patterns, that means only considering the spatial distribution of cities, independently of populations. More than 60% of European urban areas belong to the clusters 1 (in orange) and 2 (in yellow), characterized by a certain growth of population during the whole period with a slight slowdown since 1991. They correspond in the majority to medium-sized and large cities settled in North-Western Europe (slight growth, in yellow) or Southern and Eastern peripheral countries (in orange).
Map 5. Four main demographic trajectories of European urban areas , mapped according to the spatial distribution of cities 36 The cluster 4 (in red) is the smaller one (only 330 urban areas) and it shows a strong population growth profile. It is a very specific profile, concerning an important share of small and medium sized urban areas; for instance, those which are settled at the fringe of large cities and which benefit from urban sprawl (see around Madrid, London, Paris, Stockholm, etc.) or which are located on the sunny coastal areas (Spain, France, Italy, etc.). These small and medium sized cities are more apparent in Map 6, representing urban populations instead of urban patterns.
Following the population of European urban areas in the last half century (19...
Cybergeo : European Journal of Geography , Espace, Société, Territoire Map 6: Four main demographic trajectories of European urban areas , mapped according to urban populations in 2011 37 Finally, the cluster 3 (in blue) aggregates stagnation and decay profiles and includes some large urban areas in Germany, central Great Britain and Northern Italy, also a large number of small cities in these latter countries, but also in France, Portugal, Scandinavia, Baltic countries, Hungary, Austria, Romania, etc. It concerns 870 urban areas, representing 22% of all the European cities, two thirds of which are located in only three countries (Germany, Italy and France) ( Table 3). These results sound very similar to those obtained by Wolff and Wiechmann (2017), who conclude after an in-depth study of growth rates that 20% of urban areas were decreasing in Europe during the period 1990-2010.

Conclusion 38
The TRADEVE database presented in this paper is part of a larger research field focused on the investigation of urban systems over several decades and on the necessary spatiotemporal harmonization of urban objects. The originality of this work lies in four main contributions: the data extend over a long period (from 1961 to 2011), they allow specific studies on small and medium sized cities , Gourdon et al., 2019, they take into account the spatial expansion of cities and bring new discussions about the interest of a retropolation method, and finally they aim at the operational objective to be an open database, fully documented with metadata. Even though functional delineations would be important to consider in order to take into account suburban transformations, this is still impossible at this macro-regional scale and for that period of time. In turn, it is essential to recall the importance and interest of urban areas databases that allow to work on small entities: if the majority of European inhabitants live in urban areas (58%, according to the TRADEVE-UMZ database in 2001), nearly half live in small size ones populated by less than 50,000 inhabitants.
39 First thematic insights of the TRADEVE database allow following the hierarchical and regional expressions of urban growth slowing down during this period. In North-Western countries, urbanization has been more or less steady between 1961 and 2011, whereas it has been increased mainly in the 1960s and 1970s in the Atlantic and Mediterranean periphery, and between the 1960s and the 1980s in Central Europe. In these latter countries, stagnation generally occurs from 1991/2001. The average annual variation rate shows a progressive fall of growth between 1971 and 2011. Beyond this general trend, the pace of growth decreases steadily according to city size, apart from large cities (between 100,000 and 200,000 inhabitants), which grew more rapidly than small and medium-sized ones between 1961 and 1971. Progressively, there is a clear convergence towards lower rates, regardless of the size of the cities. Finally, a cluster analysis performed on the demographic trajectories of cities shows that 60% of European urban areas are characterized by a certain growth of population during the whole period, with a slight slowdown since 1991. They correspond in the majority to medium-sized and large cities settled in North-Western Europe or Southern and Eastern peripheral countries. Around 18% of European urban areas are characterized by a strong population growth profile and correspond in majority to small and medium sized urban areas settled at the fringe of large cities and which benefit from urban sprawl or located on the sunny coastal areas. Lastly, 22% of European areas are decreasing, i.e. 870 out of the 3,930 considered in the  (114). It remains to be analyzed whether these cities belong to metropolitan areas or not.
40 Two main methodological prospects are raised by this work. A first issue relates to the follow-up of the TRADEVE database in the short and medium term. For the 1961-2011 period, the increased concern about small towns justifies the interest for including urban areas between 5,000 and 10,000 inhabitants. Even though manual validation and expertise are still partly necessary, this upgrade should be greatly eased by the implementation of the process automation for naming UMZ and for constructing longitudinal urban objects. Similarly, there is still work to be done in shifting the year of reference for UMZ delineation, from the 2000 to the 2006 version, in order to better adjust the 2011 results to the actual extension of urban areas. Another matter of concern tackles the updating of the TRADEVE database in future periods and raises distinct challenges, where uncertainty prevails as far as the following up of the UMZ database seems gradually replaced by the European settlement data implemented as part of the Copernicus system (https:// land.copernicus.eu/pan-european/GHSL/european-settlement-map/view). Beyond these considerations related to the TRADEVE database upgrade and update, a second major issue lies in the potential explorations of the existing database. We provided here some first insights into classical views of urban population variations from 1961 to 2011; however, other promising focus on decay and stagnation trends requires more in-depth analysis in order to test alternative methods such as, for instance, temporal sequence analysis (Gourdon et al. 2019 (Bretagnolle et al., 2016b).

5.
Both have already been used: the MUAs (Vandermotten et al., 1999) are based on a 650 inh/ km² density threshold whereas the Geopolis database (Moriconi, 1994) is based on a 200m distance and a minimal population threshold (10,000 inh. for the building blocks).
6. R and Postgis were used in order to implement these methods (see Cybergeo data paper).
7. This method is described in : « Composition communale des unités urbaines, Population et délimitation 1999, Nomenclatures et codes », INSEE, mars 1999. This is a method adapted to the fine scale of French LAU2. Morphological patches are first defined using the continuous built-up areas' definitions (from photo-interpretation and field), with a maximum distance between buildings of 200 metres ("zones bâties"). Then only LAU2 with more than 50% of their population laying in these "zones bâties" are retained in the urban area. Consequently, some of these building blocks may be very small, with a total population much lower than 2,000 inhabitants.

8.
For instance, according to WUP data sources (https://esa.un.org/unpd/wup/DataSources/), these urban areas are represented by LAU2 larger than 5,000 inhabitants in Belgium (which gives an urbanization level of 98% instead of 81% in TRADEVE), larger than 200 inhabitants in Denmark (urbanization level of 88% instead of 56% in TRADEVE) and denser than 150 inh/km 2 in Germany (urbanization level of 75% instead of 65% in TRADEVE). The large differences between a harmonized approach and the heterogeneous definitions chosen by the United Nations leads us to question the assertion according to which the world population has been urban in the majority since 2003, an assertion which has been, however, cited by many researchers and political actors.

9.
Luxembourg, Slovenia, Cyprus, Malta and Lichtenstein were removed, due to the weak surface of the country (less than 600 km 2 ).

The Annual Average Growth Rate (AAGR) is calculated as follows:
where P is the population of the urban area and n is the number of years in the study period (t-1, t).

11.
In order to avoid blanks in the database, 20 small UMZ that had merged into larger agglomerations during the period 1961-2011 have been removed from the hierarchical cluster analysis.
12. This step was processed by using the Trajpop application, which was built by Robin Cura (UMR Géographie-cités). For methodological details and access to R code: Cura R., (2013) Pumain et al. (2015).
Following the population of European urban areas in the last half century (19...

ABSTRACTS
In this paper we present the methodological issues and choices related to the construction of the TRADEVE database, which allows following the population of European urban areas since 1961.
Whereas most of the recent academic works related to this issue focus either on time depth (for larger cities) or on the large coverage of urban hierarchy (for a shorter period), one of the main interests of the TRADEVE database is to extend over a relatively long period (from 1961 to 2011) and to cover small and medium sized cities at the same time. But, above all, it distinguishes by taking into account the spatial expansion of urban areas during a period characterized by a pronounced sprawling process. First insights are provided that allow studying the hierarchical