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12ème Colloque Européen de Géographie Théorique et Quantitative, St-Valéry-en-Caux, France, 7-11 septembre 2001

Time and space scales for measuring urban growth

Echelles de temps et d'espace dans la mesure de la croissance urbaine
Anne Bretagnolle, Fabien Paulus et Denise Pumain


A l’aube d’un XXIème siècle couronnant deux siècles d’expansion des villes, sans précédent à l’échelle de l’histoire, les questions concernant les tendances actuelles de la croissance urbaine sont lourdes de sens pour les années à venir. Deux processus sont examinés ici, celui de la concentration de la population dans les très grandes villes, qui entraîne le déclin relatif des villes petites et moyennes, et celui de la périurbanisation, caractérisée par le desserrement des centres des grandes villes au profit de leur couronnes périphériques. Partant de données récentes sur la population et les activités dans les aires urbaines françaises, nous montrons que le cadre spatial et temporel choisi pour donner la mesure de la croissance urbaine peut influencer considérablement les résultats, et donc l’interprétation finale des observations. Définir la ville à l’échelle de l’espace résidentiel bâti en continuité (agglomération) ou à l’échelle de l’espace des migrations alternantes des travailleurs (aire urbaine) modifie radicalement la valeur des indicateurs de concentration utilisés habituellement par les géographes. De même, l’analyse des trajectoires dans le temps long des différentes composantes spatiales de la ville (ville centre, banlieue, couronne périphérique) donne des résultats très différents selon les approches choisies.

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Notes de la rédaction

Paper presented at the 12th European Colloquium on Theoritical and Quantitative Geography, Saint-Valéry-en-Caux, 7-11 september 2001.

Texte intégral


1The last two centuries of urban growth and urban concentration were an unprecedented process in history. More than half of the world population nowadays live in towns and cities. In the most industrialised countries, where the spatial and social diffusion process of urbanisation seems to have come to an end, the question of the future evolution is in debate. Interpreting actual trends in urban growth in a correct way is a key for predicting further tendencies.

2The main issue is about continuity or reversal in urbanisation processes. Different interpretations have been given since the seventies, some of them describing a «counter-urbanisation» process (Berry, 1976), with a new dispersal of population and activities in the countries, others underline, in the contrary, the continuity of the concentration and hierarchisation in systems of cities (Pumain, 1982, Cattan and alii, 1994). This latter trend has been recognised everywhere in the nineties, and the term of metropolisation was coined to conceptualise a process of urban concentration as well as of local urban sprawl and emergence of more complex, polycentric metropolitan areas (Lacour, Puissant, 1999).

3The future trends in urbanisation are now predicted by most authors after the supposed impact of communication technologies and information society on social spatial interactions and practices. The capacity of distant communication through internet has exploded and seems to drastically weaken the agglomeration constraints. The apparent ubiquity of the connection facilities allows for direct relationship from anywhere and seems to abolish the distance constraints. As a consequence many authors predict the dilution of urbanisation in space and a weakening of the structuration of geographical space by urban hierarchy. New «horizontal» instead of «vertical» relations would support local and regional network organisations, following an «archipelago economy» (Dematteis, 1996, Veltz, 1996).

4We would like to develop here a different hypothesis. Even if new forms of urbanisation are emerging (especially more complex networks and secondary centres), continuous trends in urban attractivity and concentration can be observed if relevant methods for measuring urban growth in space are used. The aim of the paper is to throw light on the possible interpretation of the actual urbanisation processes in two ways : first, by recalling old debates which accompanied previous revolutions in communication technologies in XIXth century ; second, by exploring very carefully the urbanisation process in France, at two levels of analysis (inter-city and intra-city systems), during the second half of XXth century. A specific attention is given to the scales of time and space which are relevant for a correct appreciation of urban growth.

The recurrent debate about communication technologies and spatial differentiation

Expectations : velocity, mobility and spatial ubiquity

5The debates of today about the diffusion of new communication technologies are actually very similar to the discussions arose by other major innovations in the domain during historical times. The railway system, invented in the first half of XIXth century, appeared as a fantastic revolution replacing human and animal energy by mechanical energy. Meanwhile, many engineers and geographers of the time produced reflections and theories about its possible impact on space and society. A few among them predicted a total reversal in the evolution of settlement systems, which would reduce the differences between towns ans villages, and between cities and towns.

6Such interpretations, which could be coined as «ubiquitous», suggest that new railway will progressively scatter in space, until it gives access to the most remote villages (the metaphor of a net is often used by an engineer like Constantin Pecqueur, around 1830, or the geographer Elisée Reclus in the second half of the century). Moreover, the growing speed of the railways and their expected progresses suggest that distance constraints could disappear (Brunhes, 1910). A new representation of the country is provided, showing space shrinking in a uniform way, as the speed of transportation is increasing. «France of railway», according to Michel Chevalier, Constantin Pecqueur, Elisée Reclus or Jean Bruhnes, appears as twenty to thirty times smaller than the «France of postal coaches», since the railway circulates five to six times faster than the horses. The same type of computation is made by Emile Cheysson, engineer and cartographer, who built in 1888 the first maps with an unipolar anamorphosis. At different dates, the relative situation of Paris and other towns is represented by distances whose ratios are function of average communication speed of each period.

7The two ideas, of a spatial dispersal of the new communication means, and of the abolition of distance constraints through the increasing speed of circulation, sound familiar to the observer of today’s issues which are debated about new technologies of information and communication (NTIC). Similarities in argumentation are surprising because the two communication means are technically different, one being for transportation and the other for communication, the railway network moving persons and goods whereas computer networks move information. However, similar social and spatial impacts are expected from these new communication means. Ubiquity and speed are supposed to change the relationship with space, and to modify the concentrations of population in places. At a local level, the imagination of an urban diffusion which would cover all the country by an «immense town»(Constantin Pecqueur) is already present. It is supported by the idea that the hierarchical differences between cities, towns and villages will be reduced because industries can locate in villages. The same idea will appear again during years 1930’s when electric energy diffused, with American authors like Henry Ford, Gifford Pinchot or Joseph Hart (quoted by Dupuy, 1991). At the scale of urban systems, the prediction is that the spatial convergence of towns will provide a «common life» and «a kind of ubiquity» (Reclus, 1877) which would induce a less hierarchised system (the expression of «polycentrism» is not yet given).

Observations : spatial concentration and increasing inequalities

8Such theories were not unanimously accepted by authors of last century. Several geographers, among them Halford Mackinder (1902) and Paul Vidal de la Blache (1911), vigorously contradict the ubiquitous hypothesis and suggest conversely a hierarchical diffusion of the railway. By irrigating first the large cities, the new transportation mean would contribute to increase the demographic and functional inequalities. Processes of «geographical selection» are described by Mackinder, whereas, as soon as the beginning of twentieth century, Vidal announces the emergence of «regional metropolises» becoming the main nodes of the country and supported by the revolution of the railway.

9Quantitative observations about the diffusion of railway systems and its impact on urban hierarchies confirmed these last hypotheses. According to Pumain (1982) and Bretagnolle, (1999), accessibility to railway is actually a function of city size: in 1861, when the network as conceived by A. Legrand in 1842 is almost achieved, 90% of towns with 10 000 inhabitants and more are accessible by railway whereas this is the case for less than a third of towns smaller than 5000 inhabitants. When the network is completed according to Freycinet recommendations of 1872, by 1900-1910, the time lag is recaptured and 95% of towns have their railway station. However, accessibility differentials remain as visible as before and can be measured with reference to the connectivity of the nodes: two thirds of towns under 5000 inhabitants are dead ends or simple stops on lines where the railway circulates at an average speed below 50 km/h, whereas 80% of towns with 10 000 inhabitants and more are in a position of railway crossing, half of them benefiting of lines where the speed is above 50 km/h (figure 1).

10Similar observations can be made for new transportation networks during XXth century, like airlines, highway and high speed trains networks (Bretagnolle, 1999). Even if some are still under construction, the same remarks can be made about most large cities being accessible in a first stage and keeping the better accessibility at the end of the diffusion process. Moreover, cumulative effects are perceptible from one period to the next : the most accessible towns by royal roads in 1836 are also the best accessible nodes in the railway network of 1900 (with the notable exception of industrial towns whose accessibility is improving during nineteenth century). The same remark can be made by comparing the railway network of 1900 and the airlines, highways and high speed trains networks in 1990 (the exception are this time a few touristic centres). The more recent networks are even more hierarchised, since the number of nodes where it is possible to enter the network is reducing when speed is increased (Plassard, 1995). Space becomes more discontinuous because of a larger gap in speed according to the transportation network in use, time convergence is not uniformly shrinking space. A tentative representation of accessibility of towns according to their position on several networks on a single map requires an «unfolding» of the surface of the map according to different accessibility levels (L’Hostis, 1997).

11So the predictions of the authors who were in favour of a large diffusion of new transportation means and more ubiquitous locations linked to an increase of speed were not actualised. It seems that, on the contrary, inequalities between towns and cities have increased through the diffusion of railway. Another innovation related to communication, not transportation, like the telephone, diffused more widely in space, and ultimately connected even the remotest places. But the spatial effects of the diffusion of telephone over one century are hardly perceptible, either in terms of increasing spatial concentration or reducing it. Predictions had been made about its possible substitution to individual mobility, but on the contrary it seems to have promoted more movement. So one may wonder about the possible impact of NTIC, which have been diffusing very rapidly during the last thirty year, by questioning the recent evolution of settlement system, as compared with what happened in the past : is there any perceptible transformation in the concentration levels and is the trend oriented towards more dispersion ?

Figure 1 :Railway accessibility and city size (1900)

Measures of concentration in systems of towns and cities

Measuring urban settlement sizes

12Classical measures of concentration in an urban system are based on inequalities in towns and city sizes. Even if many alternative measures have been suggested (Pumain, 1982), most studies refer to the slope of the Pareto law adjusted to the population size distribution according to the so-called «rank size rule» by Zipf. It has been shown that other measures of concentration (for instance, Hoover or Gini indexes, or entropy measures) give about the same results and in any case the same trend over time (Bretagnolle, 1999).

13More important than the choice of any particular index are the options in use for defining and demarcating urban settlements. The concept of an urban unit has evolved over time : whereas in the middle ages period it was clearly defined, both physically and legally, by a clear cut boundary with the countryside, usually materialised by a wall, the towns have progressively overflowed the limits of municipalities as administrative units. The concept of urban agglomeration (called urban area in UK, unité urbaine in France, Verdichtungsraum in Germany) was recommended as soon as in the 60’s by UNO for harmonising the statistical definitions of urban settlements, which differ very much from one country to the next, and to avoid the bias of counting in administrative units only whose surface show considerable variation. About at the same time, the diffusion of commuting practices by means of cars and the extensive sprawling of the suburbia led first US statistical services then UK geographers (Hall, 1973) to define daily urban systems, or Standard Metropolitan Statistical Areas, which included in an urban entity the population living in rural areas around an urban centre and commuting to this centre for work. The French statistical system came to a similar definition only in the last decade by defining «aires urbaines», which aggregate around poles of at least 5000 jobs all communes sending more than 40% of their resident population in the centre or in already aggregated communes of its periphery (INSEE, 1996). The concept is then less extensive than the one of Standard Metropolitan Areas but can recognise the existence of smaller urban centres. About 360 aires urbaines were defined in France (Le Jeannic, 1996).

14Even if defined from the 1990 census only, and again in 1999, the concept has to be used earlier. Signs of «rurbanisation» (Bauer, Roux, 1976) or «peri- urbanisation» were described in the early 70’s, and as soon as in the sixties for Paris agglomeration. We have then reconstituted aires urbaines from the 1968 census on. In order to avoid a bias in the long term comparisons of city size distributions, the list has to be completed with smaller towns having less than 5000 jobs and which are not defined as centres of an aire urbaine. For those smaller units, the concept of urban agglomeration has to be accepted as still valid, even if a few rural commuters may actually create a field of polarisation around them, as a matter of fact with a weaker intensity and a smaller spatial range than in the larger ones.

A set of converging results : reinforcement of urban hierarchy

15Considering either urban agglomerations or aires urbaines provides a different answer to the question of the continuity in urban concentration. When the restrictive definition of urban agglomeration is used (urban units), the historical series shows a trend of increasing concentration since at least 1850, with a clear reversal from 1975 on (table 1 and figure 2). A conclusion could be that, thanks to changes in French society (including a broader interest for environment, quality of life, heliotropism) or to rightly chosen planning policies, the traditional trend to increasing spatial inequalities in a very centralised country had been victoriously dominated and that more attention and development capacities were given to remote parts of the territory.


Minimal population

Number of urban units

Slope of the fitted Pareto distribution*





























































Table 1 : Evolution of concentration index of city size distribution (urban units, 1809-1999)

* : The R-square of the fitted Pareto distribution is superior to 0.99, at each date.

Source : Bulletin des Lois, Dénombrement de la population et RGP-INSEE.

16The trouble is that if a measure of the size of urban settlements is chosen which better integrates the evolution of their capacity of attraction, the result is quite different (table 2 and figure 3). Instead of a reversal, the graph shows a clear trend to an increasing concentration of urban population. This is confirmed by a comparison of the mean growth rates of urban units and aires urbaines during the last third of the century : whereas large urban agglomerations seemed to grow less rapidly than the smallest, when observed in the more relevant spatial limits given by the aires urbaines definition, the trend is more in favour of the large urban centres (figure 4). The growth rates of urban units according to their geographical situation give a similar result : the ones which are included in a daily urban system have a much stronger growth than the ones which are situated out of a daily urban system (table 3).


Minimal population

Number of daily urban systems and urban units

Slope of the fitted Pareto distribution*





















Table 2 : Evolution of concentration index of city size distribution (daily urban systems, 1968-1999)

* : The R-square of the fitted Pareto distribution is superior to 0.99, at each date.

Source : RGP-INSEE.

Geographical situation in 1999

Number of units

Mean growth

Standard deviation

Growth decline (%)

Core or suburb





Outer ring





Out of a daily urban system





Whole set of units





Table 3 : Growth rates of urban units according to their geographical situation (1975-1999)

Table 3 : Growth rates of urban units according to their geographical situation (1975-1999)

17We are forced to conclude that the last period of diffusion of communication technologies and of society of information does not interrupt the secular powerful trend towards a more concentrated urban system where contrasts in size among cities have been continuously increasing. This evolution is compatible with observations of urban systems dynamics in the past (Pred, 1977) showing a process of hierarchical diffusion of innovations which accumulate the effects of initial advantages in the largest urban centres and a process of short circuit which tends to eliminate the smallest centres from the competition, because the increase in speed and facilities of communication is extending the spatial range and the attractivity of the largest.

Measures of urban sprawl and spatial reorganisation

18Urban sprawl is a very general and complex process, which should be observed at various levels and in many aspects for a full understanding (Guérois, Pumain, 2001). In this first step we will limit our analysis to a simple description of the process, at the aggregated level of urban entities and without differentiating social or economic groups inside the population who are concerned.

Measuring urban sprawl

19During the last fifty years, the urbanisation process combined two types of dynamics : a cyclical aspect in time, growth rates being at their highest level during the sixties and seventies and then decreasing, and a bifurcation in the spatial expression of urban growth with a first stage of increasing urban population densities being followed by a stage of diminishing density gradients and considerable spatial extension of urbanised areas.

20Measurement of these trends are depending upon the way of delimiting urban units. Using the definition of the daily urban systems (aires urbaines) instead of the urban agglomeration, we have collected data about the evolution of their three spatial components : the central commune, the «classical» suburbs and the new urban developments in rural communes at the periphery.

21Measuring urban sprawl is also depending upon the theoretical conception of geographical space. Two methods are suggested here. In the first one, we maintain a classical representation of topographical space, with constant physical properties. We keep fixed limits (as they are in 1999) for what will be called the centre, the classical suburbs and the peri-urban ring and watch how population numbers and densities evolve in each of this type of space. In the second method, we consider that the definition of the urban space must be readjusted at each date, because geographical space is an interaction space, so we have to define for each period a different spatial framework. When computing at each date new limits for centre, suburb and outer ring, the spatial components of the aires urbaines are variable in topographic space but can be taken as a proxy for a delimitation which would remain constant in time space. Two arguments are in favour of this interpretation : first, surveys have demonstrated that, during the period, the commuting distances had increased by a factor two, whereas the commuting time remained the same ; second, the average speed of vehicles is different according to the type of urban space: it has remained almost constant (around 15 km/h) in urban centres, it is about 30 km/h in continuously built –up suburbs and above 50 km/h in outer rings (Orfeuil, 1999).

A wave-like diffusion of growth in topographical space

22Figure 5 shows the cyclical aspect of the evolution of urban areas growth rates when measured in this frame, under constant spatial delimitation over time. As observed and formalised by several authors (Korcelli, 1972, Klaassen et alii, 1983, Cattan et al., 1994), the spatial distribution of growth is also cyclical, including the relative loss of weight of population of the centres (from 49 to 37 % of total population) followed by a recent stage of recovering, the early and large gain by classical suburbs (from 32 to 42% of total population, surpassing the centres from 1982 on), recently slowing down, and the recent (after 1975) but limited gain of outskirts (from 19 to 21 %). After a remarkable coherence in curves showing the maximum gain for outskirts at the same time (1975-1982) as the deepest loss for the centre, the three curves are converging around slightly positive growth rates. Reflecting the stabilisation of demographic growth, it may also signify a trend toward a stabilisation of population redistribution inside urban areas.

23Besides such average trends, there is a large variety in individual trajectories of the cities. A principal component analysis made on the shares of each component of urban space in total urban population at each census date between 1954 and 1999 produce one trajectory for each city. Trajectories are then classified in three main types of urban sprawling processes (figure 6).

Table 4 : Types of urban sprawl according to the evolution of weights of components (1954-1999, topographical space)

24The first group is composed of cities which were pioneer in the process of urban sprawl (63 cities). Their centre start to decline in 1954 for the first sub-group, in 1968 for the second, with a big loss in population (from 40 to 20% in the first sub-group, 55 to 40% in the second). Most of large cities belong to this group (the average population is over 200 000 inhabitants), showing a clear hierarchical diffusion of the process.

25The second group (184 cities) represent trajectories where the loss in population arrived later (after 1975) and was less intense (from 50-57% to 48-50%). They are smaller towns (40 to 100 000 inhabitants) and scattered in the whole country.

26The third group (107 cities) is made of towns which «resisted» to urban sprawl, either because outer suburbs were already important (more than half of total population) in 1954 (example of old industrial conurbation), or because outer rings have only a small share of population (less than 10%).

27In topographical space, the process of urban sprawl shows interurban and temporal variations which appear cyclical according to the spatial urban components, urban hierarchy and specialisation of urban functions. Moreover, the gain in urbanised space appears as a dramatic increase, between 1968 and 1999 (figure 7). However, when the same phenomena are observed in a time-space, the conclusions are different.

Urban expansion in time-space : a continuous process?

28As speed of communication is increasing over time, space which would remain equivalent for spatial interaction is expanding, relative to fixed topographic space. One may infer that in time space, if population growth corresponds to a given time of accessibility, the limits of urban areas would remain constant and urban growth would appear in each component as a continuous process. Whereas in topographical space, urban growth appears as a wave-like spatial process from centre to the periphery, in time space, there is a constant limit between the urbanised area and the surrounding countryside (figure 8).

29The empirical data concerning variable limits of daily urban systems are coherent with these theoretical attempts. Figure 9 shows that the «spatial» pattern is quite different from what (seems to) happen in topographical space. As time space is the reference, the spatial expansion of each component is logically a part of its demographic growth. The centres encounter a continuous loss of their share of urban population (56 to 37%). The classical suburbs remain remarkably stable (40%) whereas the outer rings clearly appear as the dynamic part of urbanised areas, with a growing weight (from 4 to 21%). As a whole, the aires urbaines have a continuous demographic growth whereas the countryside keep loosing population all over the period.

Table 5 : Evolution of population and surface in daily urban systems (1968-1999 ; time-space)


30New technologies always have given rise to speculations about their possible effects in changing society dramatically. As it was already suggested in the case of railways or telephone, new communication technologies are supposed to transform spatial processes by counteracting the traditional centre-periphery asymmetrical developmental trends, by transforming hierarchical differentiation into more reciprocal network relationships and by allowing a new spatial diffusion of housing far away from metropolitan concentrations.

31Experience from the past is a first reason for asking more carefulness in geographical predictions. The previous revolutions in communication technologies of XIXth century did not allow for any expected settlement dispersal; on the contrary, they contributed to reinforce spatial concentration.

32Our observations on urban growth in France in the second half of XXth century at two levels of analysis are another ground for questioning a possible reversal in spatial trends. These observations have been made according to a concept of geographical space which is no longer a topographical surface but a space of social interactions. For measuring inter-urban differences in growth, we have chosen to observe towns and cities no longer as physical agglomerations of built-up areas but as daily urban systems, including rural areas which are in close connection with urban centres. For measuring urban growth trends around metropolitan areas, we have considered time- space instead of distances in kilometres. At both levels, urban growth must then be reinterpreted as a continuous process of attraction by urban centres and of concentration in larger metropolitan areas.

33Of course, the spatial evolution since the fifties is only the first stage of the impact of new communication technologies and information society on geographical space and further effects could be different. However, a reversal would be surprising, since the actual trends are in continuity with those which were observed in the past. When measured in the real geographical human space, which means space where social interactions can occur, urban attraction appears as an almost invariant process over the last two centuries.

34This observation is not a plea for further spatial concentration of urban space. Establishing a fact does not imply that the result is socially acceptable. But a correct evaluation of the meaning of actual trends in urbanisation is a first necessary step for thinking about policies which could aim at their regulation.

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Anne Bretagnolle, Fabien Paulus et Denise Pumain, « Time and space scales for measuring urban growth  », Cybergeo: European Journal of Geography [En ligne], Dossiers, document 219, mis en ligne le 25 juillet 2002, consulté le 27 février 2024. URL : ; DOI :

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Anne Bretagnolle

UMR Géographie-cités, CNRS et Université Paris 1, 13 rue du Four, 75006 Paris, France

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Fabien Paulus

UMR Géographie-cités, CNRS et Université Paris 1, 13 rue du Four, 75006 Paris, France

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Denise Pumain

UMR Géographie-cités, CNRS et Université Paris 1, 13 rue du Four, 75006 Paris, France

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