RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
“Growth of metropolitan limits and its influence on the urban structure. A retrospective analysis (1991-2001) for the Barcelona Metropolitan Region”
†∗ Masip Tresserra, JAUME
ABSTRACT: In recent decades due to the overflowing of the administrative boundaries by urbanization, the literature has studied various approaches to delimit the urban and metropolitan areas. Simultaneously, these urban dynamics have also led t he m etropolitan systems to polycentric structures characterized by dispersion and co ncentrated decentralization of employment and population, breaking with the paradigm of the monocentric city. However, few studies have f ocused on s tudying dyn amically (over t ime) and j ointly the del imitation of t he m etropolitan boundaries and its influence on the urban structure of the metropolitan areas. In t his paper, the retrospective ur ban dynamics (1991-2001) and i ts influence on t he ur ban structure of t he Barcelona Metropolitan Region is analyzed. Firstly, by analyzing travel-to-work data, the functional metropolitan borders are del imited by the ye ars: 1991 , 1996 a nd 2001 . T hen, t his paper s tudies how t he gr owth o f t he metropolitan limits influence on the urban structure by using a functional approach to characterize the changes in terms of metropolitan structure for the analyzed period of time. In doing so, the urban structure is characterized by three key points: identification of ur ban subcentres by using a m obility approach ( residence-to-work flows), the complexity grade of the metropolitan system and the measurement of the polycentrism level. By having a d ynamic perspective (1991-2001), r esults suggest a process of ur ban e xtension of the metropolitan borders what it could entail: an increment of sub-centres due mainly to the changes of the residential and labour markets, a more polynucleated structure of the urban system and a bigger grade of its complexity.
Keywords: Metropolitan Areas, urban structure, new urban economy & polycentrism.
0. INTRODUCTION One of the fundamental characteristics that define and differentiate our society from other in the past is the new nature and scale of the urban processes and phenomena. Faced with the vision of a physically self- contained reality with well-defined limits, which represent the traditional city, the spatial and functional processes that have taken place in our advanced societies, have modified fundamentally the shape and the function of cities, leading t o r adically different territorial realities, blurring boundaries and overflowing w idely t hese administrative entities associated with them. Thus, t he m assive extension of the urbanization process, the physical separation between the place to residence and other basic activities such as working or shopping and the increased mobility of goods and people have entailed to a new regional realities that should define, identify and delimit properly. In 1932, the Census Bureau United States stated: “The city’s population defined administratively often offers a very inadequate i dea of t he popul ation cl ustered i n and a round t he ci ty. I f w e w ant t o have a vi sion o f t he clustering or the concentration of population in large urban areas it is necessary to establish metropolitan districts that show the extent of each population centers. (Bureau of the Census, 1932); (Berry et al,1970). This paragraph is a clear expression of both theoretical and policy concerns about how to properly define the urban reality beyond their administrative boundaries at the time that represent a starting point for a task that from since initially in the United States, and then in most advanced countries have taken into account by public and academic authorities. In this sense, the specialized literature has proposed various approaches in order to delimit the urban systems and the metropolitan areas from a clear consolidation of a long tradition of studies about this new shape of city and how t o de fine, i dentify and de limit it. Administrative aspects (municipalities), morphological methods (the
† PhD C andidate, M aster S cience i n U rban M anagement and V aluation, A rchitect. C entre of Land P olicy and Valuations, CA1, Polytechnic University of Catalonia, Av.Diagonal 649, 4th Floor, 08028. Barcelona, Spain. Email: [email protected]. ∗ The author would like to acknowledge his PhD Supervisor, Josep Roca Cladera (Director of the Center of Land Policy and Valuations, Polytechnic University of Catalonia) for his suggestions and critics to this work and Montserrat M oix (researcher af filiated t o t he C enter of La nd P olicy and V aluations, P olytechnic University of Catalonia) for her help in order to delimit protosystems, sub-systems and functional metropolitan areas.
1 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
urban continuous), aspects related to the existence of economies of agglomeration (population and employment densities, urban economic activities…), or functional interactions (commuting residence-to-work) have been used in order to definition the metropolitan fact. Consequently, these reflections have led to overcoming the old concept of city and i ts replacement by other that have tried to understand the new territorial phenomena. Metropolitan districts and statistic metropolitan areas (Bureau of the Budget, 1964); (Berry et al.,1970), urban clusters and agglomerations (Serra et al., 2002), daily urban systems (Coombes et al., 1978) (Coombes et al., 1979), local labor markets (Smart, 1974); (Carmichael, 1978); (Sforzi, 1987); (Casado & Taltavull, 2003); (Coombes & Casado, 2005); (Boix & Galleto,2006); (Moretti, 2010), ar eas of c ohesion (Castañer, 199 4), c ontinued s ystems of s ettlements (Governa & Dematteis, 19 99), functional urban regions (FUR) (GEMACA, 1996), functional urban areas (FUA) (ESPON, 2006), the new concept of city-region (Hall, 2001); (Scott, 2001); (Davoudi, 2008) have been, among other concepts, that have tried to replacing the “outdated” notion of city. At the same time, it has developed in recent years, a l arge literature that has come to reveal the increasing tendency of ur ban s tructures t o pol ycentrism. This concept, pol ycentric dev elopment, has ga ined w idespread currency in planning and territorial development, though it remains a r ather fuzzy concept as it seems to mean different things to different actors and different scales. The scale on which the concept is applied ranges from individual cities to city regions, to nation-states and finally to the European scale (CEC, 1999). At global scale, (Snyder & Kick, 1979); (Taylor, 1997); (Beaverstock & Taylor, 1999); (Taylor & Walker, 2001); (Derudder e t al ., 2 003a); (Derudder et a l., 20 03b); (Alderson & B eckfield, 200 4); (Taylor, 2005) . A t E uropean scale and national scale, (Bruinsma & Rietveld, 1993); (Hohenberg & Lees, 1995); (NORDREGIO, 2005); (Hall, 2002); (van der Laan, 1998); (Nystuen & Dacey, 1961). The European Spatial Development Perspective (EDSP) presents as a major objective the development of a balanced and polycentric urban system mainly located in the ‘pentagon’ (CEC, 1999); (CEC,2001). The objective of polycentric development is currently being taken further in the current debate about European cohesion policy where it is argued that the economic potential of all regions of the EU can only be utilized through the further development of a more polycentric European settlement structure at the time that a more polycentric development could reduce the regional disparities. In the third cohesion report the main emphasis is territorial cohesion, which is placed on an equal footing as economic and social cohesion in the (ungratified) Constitutional Treaty. So, also many European countries pursue a polycentric development, often addressing the dominance of their prime city to diminish regional disparities. Within ESPON (European Spatial Planning Observation Network) framework there have also been attempts recently to measure polycentricity on the scale of countries and the European Union. However, one of the major reasons w hy t he c oncept of pol ycentricity i s s till r ather v ague i s t hat i t is sometimes as sociated w ith both morphological aspects and functional relationships between cities. As this paper will be try to explain further on, it is possible to measure polycentricity within the intra-metropolitan scale with using an “integrated approach” that could take into account at the same time these two dimensions of the polycentric concept. At the metropolitan scale, the notion of polycentricity is associated with the concentrated-decentralization from CBD to sub-centres. (Berry, 1960); (Alperovich, 1983); (McDonald, 1997); (Guiliano & Small, 1991); (McDonald & Prather, 1 994); (Clark & Ku ijpers-Linde, 199 4); (Gordon & R ichardson, 199 6); (McMillen & McDonald, 1998); (Cervero & Wu, 1998); (Bogart & Ferry, 1999); (Shearmur & Coffey, 2002); (Small & Song, 1994); (Song, 1994); (Nielsen & Hougesen, 2005); (Readfearn, 2007); (García-López, 2007); (Roca et al., 2009). Summarizing, few studies have focused on studying dynamically (over time) and jointly the delimitation of the metropolitan boundaries and its influence on the urban structure of the metropolitan areas. Thus, the aim of this study is analyse the retrospective urban dynamics (1991-2001) and its influence on the urban structure of the Barcelona Metropolitan Region. So, the specific objectives of this paper are the following: (i) delimit the functional metropolitan borders by analysing travel-to-work- data and by the years 1991, 1996 and 2001; (ii) characterizing the changes in terms of metropolitan structure for the analysed period of time. In doing so, this paper proposes characterize t he ur ban s tructure by t hree k ey po ints: i dentification of ur ban sub-centres by using a m obility approach (residence-to-work flows), the measurement of the polycentrism level and the complexity grade of the metropolitan system. Finally, iii) this paper tries to propose a “new integrated approach” (taking into account the morphological and t he f unctional nat ure of t he p olycentrism c oncept simultaneously) in or der to qua ntify empirically the two last mentioned urban structure key points. The rest of the paper is organized as follows i) firstly, the theory on methods to delimit metropolitan limits are discussed at the time that candidates to sub-centres by using mobility approach are identified; ii) secondly, the measurement and the evolution of the polycentrism level is quantified by using three different approaches: the morphological, t he f unctional and t he “ integrated” m ethod proposed by t his paper ; i ii) t hirdly, t he l evel of metropolitan complexity – hierarchy and its evolution over time is defined; iv) and finally, in conclusion, the main findings are presented and the further research steps are explained in detail.
2 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
1. DEFINING THE FUNCTIONAL METROPOLITAN LIMITS AND IDENTIFYING THE URBAN SUB-CENTERS (1991-2001) The characterization of the metropolitan structures involved, at least two steps; first detect the metropolitan limits and then the elements that have a structuring role; the centre - CBD and the urban sub-centers.
1.1. DELIMITATION OF METROPOLITAN LIMITS The identification of metropolitan limits can be carried out using three basic approaches: the administrative, the “morphological” and the functional approach. The administrative approach identifies metropolitan areas on the basis o f s tatus of pr eviously def inite legal or ad ministrative uni ts. I t i s c onceptualised as an i nstrument f or purposes of governance and control. The identification departs from local or provincial boundaries and applies some c riteria t o di stinguish bet ween m etropolitan an d non -metropolitan limits ( population t hresholds, governmental decisions, historical reasons etc...). The “morphological” approach identifies metropolitan areas as those continuous urban settlements that reach certain thresholds of density, dimension or degree of urbanization. The metropolitan area is conceptualized as a physical object, without referring to any relation consideration. (NUREC, 1994) which returned to the criterion of 200 meters of the UN provides an ex ample of this criterion and ot her examples are delimiting the metropolitan areas by using continued geographical units that exceed certain thresholds of density that can be considered as urban (e.g. central services) and/or which together have a significant critical mass (Serra et al., 2002). The functional approach, for reasons that are obvious, is the most dominant, because it is possible to detect urban systems without taking into account the physical continuity of its urbanization, and therefore it is appropriate in f ront o f t he e merging p aradigm o f t he n etwork-cities an d diffuse-cities (Indovina, 199 0); (Castañer, 19 94); (Roca, 2004). In this sense, the analysis of the interaction that arouses between the two major urban markets, in short, between the labour and the residential, whose physical reflection has its maximum expression in the flows residence-to-work, has become a key element in order to determinate the spatial confines of this interaction. The mobility, therefore, is seen from this point of view, as a significant for the essence of the urban. In t he U nited S tates, t he f lows r esidence-to-work ha s be en us ed m any t imes i n or der t o det ect s tatistical metropolitan areas (OMB, 2000) as it happened in many other countries such as France, Italy, UK, or Canada (Julien, 2000); (Martinotti, 1991); (Murphy, 2003) or across in different EU countries (Cheshire & Gornostaeva, 2003); (Hall & Pain, 2006); (ESPON, 2006); (UrbanAudit, 2008). In Spain, apart from the morphological approaches1, (Castañer, 1994) delimited “cohesion areas” based on the functional criteria similar to those used in the Statistical Metropolitan Areas. The pioneer work of (Clusa & Bachiller, 19 95) appeared al ong w ith (Castañer, 199 4) which i mported f or f irst t ime t he B ritish l ocal l abour markets, which was continued by (Casado, 2001) in Valencia. Although, the philosophy of this definition differs diametrically2 from the objectives of delimiting the metropolitan limits, their common denominator is taking into account t he s patial interactions b efore m entioned. Using dat a f rom 2001 nat ional c ensus (Roca et a l.2005) delimited 7 S panish metropolitan areas based on t he methodology used by the Bureau of US Census for New England in 1991 (since the urban structure is quite similar), (Feria, 2008 and 2010) using own algorithms of adscription3 also have delimited metropolitan borders across the country.
1 It is worth mentioning the work of the “Dirección General de Urbanismo” of (Ministerio de Vivienda, 1965 and 1967); and the latest work: “Atlas del Ministerio de la Vivienda”. (Ministerio de Vivenda, 2000, 2005 and 2007) 2 The local labor markets (LLM) what is pursue is to define the areas where self-containment of resident working populations is enough high (but not the highest possible) to make reasonable decisions about this market like public interventions in terms of unemployment reduction. Metropolitan areas (MAs) are more complex systems, where self-containment is definitely higher to what is usually asked to LLM, at the time that a medium or big MA may contain more than one LLM inside it. 3 The basic principle consist in identify an urban centre with a population of at least 100,000 people (although the author also incorporates as centres those could articulate a metropolitan belt of 50,000 people and its population is between 50,000 to 100,000 people). After identifying centres the process attaches surrounding municipalities that send at least 100 workers to the centre and it is the biggest outgoing commuter flow. If the flow is inferior to 1,000 the municipalities must sent 20% of their resident working population to the centre; if the flows are higher than 1,000 the municipalities must send 15% of their resident working population. A surrounding municipality also may be i ntegrated to the centre when the centre sends to it the aforementioned flows and % of jobs in such a municipality. I t i s t o s ay per ipheral m unicipalities m ay be a ttached t o c entre i f a given % ( and a gi ven c ritical mass) of their resident working population go to the centre for working, or when a given % (and a given critical mass) of their localized employment is occupied by people living in the centre. In total the delimitation system uses 2 interactions from the first integration in order to delimit the metropolitan system. Finally the municipalities which do not have territorial interaction with the metropolitan area are eliminated.
3 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
The methodology used by (Roca et al., 2005) which had already been used by (Clusa & Roca, 1997), consist in: i) detect urban centres, as those municipalities with a population superior to 50,000 people; ii) integrated and detect those municipalities that send at least 15% of their resident working population (RWP) to the urban centre previously detected; iii) aggregate the centre with the dependent municipalities in one metropolitan belt; iv) repeat the process indicated in (ii) and (iv), 3 more times. In such a way, by means of 4 iterations, it is possible to detect both P rimary M etropolitan A reas ( with o nly one centre) and C onsolidated M etropolitan A reas i n w hich t he existence of more than one centre is possible. Following this procedure they have detected the borders of seven metro areas: Madrid, Barcelona, Valencia, Bilbao, Seville, Zaragoza and Málaga. (Boix & Veneri, 2009) have replicated this same methodology throughout the Spanish and the Italian territory with a little modification4 for adapting to polycentric realities and in order to find what they denominated as “dynamic metropolitan areas”. To our knowledge, these are approximations across5 the entire Spanish territory based on functional methods. The m ain pr oblem of t he (Roca et al ., 200 5) method i s t hat t he 15 % l imit ( without c onsidering a ny c ritical mass) tends to integrate in the metropolitan area very small municipalities located in the outskirts in which the 15% threshold can be easily reached (for that reason other authors like (Feria, 2008 Op. Cit.), have tried other thresholds and combined them with critical mass criteria). In order to solve these shortcoming (Marmolejo et al., 2010) have modified the method used by (Roca et al., 2005) by putting ad hoc thresholds for each metropolitan area analyzed in Roca’s study. The procedure used by these aut hors hav e consisted by m eans of a d ispersion p lot, detect f rom w hich t hreshold of resident w orking population -RWP- percentage (using a precision of 1%), the increment of the artificialised land, population and economic activity is marginal; in other words, from which point (threshold) the inclusion of more municipalities in the metropolitan area does not entail a significant increments in relation to what previously has been integrated. Nevertheless, (Marmolejo et al., 2010) methodology has two problems: i) in a polycentric framework there is the possibility t hat t he h interlands o f s ubcentres ( which may be l ocated at m etropolitan out skirts) m ay not be incorporated in the metropolitan system ii) since only out-to-in (i.e. periphery-to-centre) flows are accounted there is t he possibility t hat per ipheral municipalities v ery specialized in some economic ac tivity ( e.g. m anufacturing parks) m ay not be i ncorporated into the metropolitan area in t he c ase t hat t heir scarce r esident working population do not reach on the % threshold. Despite the above problems, in this paper has not been given to use a functional method of delimitation since as indicated by (Boix & Veneri, 2009 Op. Cit) “if the purpose of analysis (metropolitan delimitation) is the study of a pol ycentric ur ban s ystem o r i n gener al t he s patial structure; t he f unctional ap proach seems t o be t he m ost appropriate method”. For that reason, in this paper has sought a method that i) it is not based on relative and absolute mobility thresholds; ii) it would be capable of detecting the subtle formation of influence areas defined by peripheral sub-centers, and above all, iii) it considers bidirectionally the mobility as it happens in the reality of the complex and mature metropolitan systems (Castañer, 1994). Thus, the methodology used to delimit metropolitan areas in this paper has followed the proposal made by (Roca et al., 2009) and used by (Roca, Arellano & Moix, 2011a) for the purpose of compare the metropolitan Systems of Barcelona and Madrid. This method is also based in travel-to-work data, having as a particularity that reflexive ( transitive) i nteractions ar e conjointly c onsidered; i t i s t o s ay t he bi directional r elation bet ween municipalities. By doing so, it is possible to integrate in one municipality which result complementary including peripheral municipalities specialized in economic activities (i.e. employment agglomerations) in which work people residing in other municipalities. This transitive integration is possible due t o the interaction value. As defined by (Roca & M oix, 2005) , f ollowing (Coombes & O penshaw, 1982) , t he i nteraction v alue ( IV) b etween t wo municipalities can be expressed as follows:
2 2 fij f ji IVij = + (1) RWPLTL ji RWP LTLij
4 This m odification c onsist o f at taching a s subordinated s ub-centres t o t he centrals m unicipalities, those municipalities that not only are they accomplish the condition of having 50,000 people, but also send more than 15% of their resident working population (RWP) to the central municipality. In addition in those cases in which exists a reciprocal relation of 15% between two municipalities with more than 50,000 people, are merge into one. 5 At regional scale it is worth mentioning, the following works which are also based on functional approaches: (Trullén & Boix, 2000); (Boix & Galleto, 2006) in Catalonia and (Salvador et al., 1997) in Barcelona.
4 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Where IVij is the interaction value between the municipalities (i) and (j), where (fij) and (fji) are the existing flows, and w here RWP is t he r esident w orking po pulation and LTL are t he l ocalised w ork pl aces w ithin municipalities (i) and (j). The interaction value has a special interest over other indicators of urban interaction; given that it weights the flows by virtue of the totality of the “masses” of the municipalities in relation. In addition, this weighting is carried out in a ‘transitive’ way, considering not only the attraction in one direction (i.e. the ‘larger’ over the ‘smaller’), but also in the opposite direction.
From the IV can be found not only the functional limits of a metropolitan area (Roca & Moix, 2005) but also it is possible to identify candidates to sub-centres (Roca et al., 2009) in a process that consists of: 1. The joining up of the metropolitan municipalities as a function of their maximum interaction value. Th is determines, as a ge neral rule, the joining together of the municipalities with the greatest number of LTL (and therefore, the candidates to be sub-centres) with those to which they are most linked. 2. The f ormation of t hese gr oupings i n protosystems. T he previous joining up process c ulminates when a closed system is ac hieved. Thus, for example, if A, B and C have a maximum relation with D, they will conform a protosystem only if D has its maximum relation with A or B or C. By contrast, if D has its maximum r elation w ith E , they w ill al l “ gravitate” t owards E, c ompleting t he pr otosystem if E has it s maximum relation with one of the municipalities aggregated to it (being D or another one). 3. The protosystems are only consolidated if they are physically continuous6. Otherwise the discontinuities are corrected, forcing the different municipalities to integrate in the protosystem with which they have the greatest interaction value. Thus, the protosystems represent the basic elements which the metropolitan- regional territory is structured and they are the original seeds of polycentrism: a metropolitan area with more internal protosystems tends to have a greater trend towards decentralization. 4. Likewise, t he consolidation r equires a minimum level of 50% self-containment7. I n t he ev ent t hat a protosystem does not reach this degree of autonomy, it is aggregated with the protosystem with which it has a maximum level of interaction, and this continues in an iterative form until the resultant protosystem guarantees t his c ondition of self-containment. I n t his ca se i t i s co nsolidated a s a n urban sub-system, where the municipality with most density and critic mass, is who structures its urban system, therefore the candidate to sub-centre.
If the urban sub-systems are jointed though an interactive process where each iteration represents the union of the two urban sub-systems w ith higher VI, it i s po ssible t o d elimit metropolitan ar eas, i n other w ords, t he second step i n m etropolitan del imitation has c onsisted i n aggr egate urban sub-systems ac cording t o the interaction value among them. In such process, in the first instance, the subsystems which are the most central and important or m ature fall into the gr avitational field of t he c entral s ubsystem (Barcelona- CBD); then, i n a second instance, the subsystem which fall into the gravitational field of the central subsystem are the most peripheral and/or the most emerging ones. These last sub-systems, when they fall into the central sub-system, tend to be incorporated other even more peripheral sub-systems and less linked to the center. In this paper, the process of iteration is from the data of forced mobility (residence-to-work) query for the years 1991, 19 96 and 2001 at C atalonia scale, an d t his i terative pr ocess is s topped i n a t hreshold of a n interaction value equivalent to 1/1.000 except in the case of 1991 where stops in the IV of 1.9/1.000. In establishing a stop- value of the formation process for the metropolitan area (MA) studied for each year (1991, 1996 and 2001) in this paper was analyzed in detail. After an interaction value of 1/1.000 (for the years 1996 and 2001) it is necessary to wait a significative number of iterations to aggregate more urban sub-systems to the metropolitan area. In the case of 1991, the formation process stops in the IV of 1.9/1.000 because it is necessary to wait 47 i terations to aggregate the next sub-system8. It is to say, such a thresholds, allows for integrate highly linked sub-systems. In the next (figure 1), is exposed the iteration process for the Barcelona (MA) for each year analyzed (1991, 1996 and 2001). In the X axis is presented the IV, and in the Y axis is presented the accumulation of population and the localised workers (LTL) meanwhile the formation process to delimit the (MA) is doing.
6 It n eeds t o be poi nted out that t he physical di scontinuities r esulting f rom t he process of aggr egating t he municipalities to the protosystems are minimal. The interaction algorithm shows its extreme potential, though not requiring in practice, the assumption of additional geographical requirements. 7 For self-containment is understand by the percentage of Resident working population (RWP) that work in the same municipality (or protosystem), in other words: RW / RWP (where RW are the resident workers of the municipality (or protosystem) and the RWP the resident working population). 8 In or der t o de termine t he c ut-off t hreshold i t has b een studied i n det ail t he process of f ormation o f t he Metropolitan Barcelona Area for each year, so that the value used in each year responds to the limit that the “waiting time” in terms of number of iterations in order to integrate marginally a urban sub-system which entails that t he M A l engthens c onsiderably; i n o ther w ords, i s t he abov e l imit w hich t he ur ban s ub-systems mo re interconnected are jointly together and with the central sub-system.
5 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
As one could observe, the last urban sub-systems to aggregate to the central sub-system for each year are Mataró, Piera and Pineda de Mar, respectively. In addition, the eruptions in the graph (with a f ew increments of IV, higher increments of accumulation of population and localised workers, e.g. the case of Sabadell) represent the most important urban sub-systems within the MA apart from the central sub-system of Barcelona.
Figure 1: Interaction Value and accumulation of Population and Localised workers
7.000.000
6.500.000 PINEDA DE MAR
6.000.000
PIERA
5.500.000 MATARÓ SABADELL
5.000.000
4.500.000 SABADELL SABADELL BARCELONA - CBD POPULATION + LOCALISED WORKERS (ACCUMULATED) 4.000.000
BARCELONA - CBD BARCELONA - CBD 3.500.000 0,000 0,002 0,004 0,006 0,008 0,010 0,012 0,014 0,016 0,018 0,020 INTERACTION VALUE 1991 1996 2001
The s ignificance of t he interaction v alue ( IV) methodology i s t hat can b e r ecognized simultaneously, the “seeds” of the territorial structure (the protosystems), the basic elements of this territorial structure (the urban sub- systems) and their articulation and delimitation in a more complex structures (metropolitan areas – MA). Thus, the methodology pr oposed by (Roca & M oix, 2005) and u sed i n (Roca et al ., 2 009) and (Roca et al ., 2011a), recognizes the f undamental elements of this t erritorial complex s tructure ( metropolitan ar ea): the residence market (place of origin of the flows in the matrix of commuting residence-to-work) and the labour market (place of destination of the flows in this mentioned matrix) within the metropolitan urban system.
The Barcelona Metropolitan System for the years 1991-1996-2001 The application of t he pr evious m ethodology depicts (figures 2-4), the changes an d t he ev olution of t he Barcelona Metropolitan system in terms of metropolitan boundaries for the years 1991, 1996 and 2001. For each metropolitan system, apart from identify how many urban sub-systems define each metropolitan limit, i t is a lso analysed at sub-system scale, the nº of municipalities and protosystems that there are within each urban sub- system, its population and localised workers (LTL) as well as its degree of self-containment and self-sufficiency9.
9 The degree of self-containment for a municipality, urban sub-system or protosystem is defined as: where 𝑅𝑅𝑅𝑅𝑖𝑖 RWi are t he r esident w orkers of t he municipality, s ub-system or pr otosystem ( i) a nd RWPi are t he r esident 𝑖𝑖 working population of this entity (i). In addition, the degree of self-sufficiency for a municipality, urban𝑅𝑅𝑅𝑅𝑅𝑅 sub-system or pr otosystem i s defined a s: where R Wi are t he r esident w orkers of t he m unicipality, s ub-system o r 𝑅𝑅𝑅𝑅𝑖𝑖 protosystem (i) and LT Li are the localised workers (RW -resident workers- and IF –incommuting flows-) of this 𝑖𝑖 entity (i). 𝐿𝐿𝐿𝐿𝐿𝐿
6 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Finally in the (figure 5) is depicted the three delimitation of the Barcelona Metropolitan System (1991, 1996 and 2001) at the time that it is represented the administrative limit of the Barcelona Metropolitan Region (RMB). In this figure, apart from to put on t op the four metropolitan delimitation, it is also defined for each delimitation its population, localised workers (LTL), nº of urban sub-systems, nº of protosystems and the nº of municipalities. The dy namic c omparison b etween t he t hree p eriods o f time shows t hat d uring t hese 10 y ears, the metropolitan limits had grown faster. As a result, the area (km2) of the metropolitan system had been duplicated: in 1991 the area of the metropolitan system was 1807,83 square kilometres and 3759,96 in 2001. That it means an i ncrement of t he m unicipalities w hich ar e c ontained within t he metropolitan s ystem: i n 199 1 t he B arcelona Metropolitan System had 100 municipalities and 184 in 2001 (an increment of 84%). In addition, that growth of the metropolitan limits implies a considerably increment of the population and the localised workers (LTL): in 1991 the population was 4.018.099 people and the localised workers were 1.467.321, while in 2001 the population was 4.530.254 and the localised workers (LTL) within the metropolitan system were 1.854.082.
The Barcelona Metropolitan System - 1991 Figure 2: Barcelona Metropolitan System - 1991
9.000.000
8.000.000
7.000.000
Barcelona Metropolitan Region 6.000.000 Mataró
5.000.000
4.000.000
POPULATION + LOCALISED WORKERS (ACCUMULATED) Barcelona - CBD 3.000.000 0 20 40 60 80 100 120 140 160 180 200 NUMBER OF ITERATIONS
LTL Self-containment Self-sufficiency Subsystem (name) nº municipalities nº protosystems Population (working places) (RWi/RWPi) (RWi/LTLi)
Arenys de Mar 6 2 28.206 7.956 74,98% 89,96% Barcelona 18 6 2.695.745 998.893 92,45% 91,33% Garriga (La) 2 1 12.809 5.108 64,98% 63,23% Gavà 6 2 121.280 29.844 55,52% 78,78% Granollers 6 2 87.120 34.917 76,68% 73,07%
Martorell 8 2 54.821 20.491 77,36% 72,02%
Mataró 11 3 169.053 55.277 80,30% 89,84%
Molins de Rei 8 2 68.240 21.265 54,73% 65,53%
Mollet del Vallès 4 1 51.186 16.624 52,32% 59,16%
Montornès del Vallès 4 1 20.423 9.638 61,54% 50,23%
Palau-solità i Plegamans 5 1 27.140 12.145 69,00% 60,32% Parets del Vallès 3 1 19.873 14.509 59,98% 32,62% Rubí 2 1 89.342 33.134 59,83% 62,05% Sabadell 11 2 386.256 139.838 75,47% 75,36% Sant Andreu de la Barca 2 1 19.458 13.366 66,72% 37,30% Terrassa 4 1 167.147 54.316 81,14% 85,78%
Source: Own Elaboration 7 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
The Barcelona Metropolitan System - 1996 Figure 3: Barcelona Metropolitan System - 1996
9.000.000
8.000.000
7.000.000 Barcelona Metropolitan Region 6.000.000 Piera 5.000.000
4.000.000 Barcelona - CBD
POPULATION + LOCALISED WORKERS (ACCUMULATED) 3.000.000 0 20 40 60 80 100 120 140 160 180
NUMBER OF ITERATIONS
LTL Self-containment Self-sufficiency Subsystem (name) nº municipalities nº protosystems Population (working places) (RWi/RWPi) (RWi/LTLi) Barcelona 32 9 2.740.659 949.830 90,52% 90,35% Cardedeu 6 2 23.439 6.981 54,28% 70,28% Garriga (La) 2 1 15.247 5.466 53,93% 57,92% Granollers 6 1 89.794 36.459 68,26% 64,07% Martorell 7 1 62.051 32.273 70,75% 48,95% Mataró 13 3 184.972 52.966 72,86% 88,79% Mollet del Vallès 7 2 77.999 33.208 54,51% 49,88% Montornès del Vallès 4 1 22.723 10.519 54,67% 45,68%
Palau-solità i Plegamans 5 1 31.887 14.766 60,09% 50,73%
Piera 6 1 18.218 4.868 54,76% 71,51%
Rubí 2 1 101.295 37.919 53,27% 54,09%
Sabadell 13 2 396.439 144.762 71,18% 69,91% Sant Andreu de la Barca 2 1 24.603 14.919 56,83% 37,46% Sant Celoni 8 1 22.219 7.704 75,45% 79,74% Sant Martí Sarroca 2 1 4.089 984 51,12% 73,98% Sant Sadurní d'Anoia 6 1 17.648 6.077 75,22% 80,14% Terrassa 7 2 177.800 58.054 75,91% 80,39% Vilafranca del Penedès 14 3 44.004 17.746 81,05% 76,86% Vilanova i la Geltrú 6 1 90.435 26.169 72,85% 89,73% Breda 2 1 4.672 1.322 67,49% 76,17% Arboç (L') 5 1 8.848 3.587 63,49% 54,73% Vendrell (El) 9 1 41.956 11.575 69,69% 86,49%
Source: Own Elaboration 8 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
The Barcelona Metropolitan System - 2001 Figure 4: Barcelona Metropolitan System - 2001
10.000.000
9.000.000
8.000.000 Barcelona Metropolitan Region 7.000.000 Pinedade Mar
6.000.000
5.000.000
4.000.000 POPULATION + LOCALISED WORKERS (ACCUMULATED) Barcelona - CBD 3.000.000 0 200 400 600 800 1000 1200 NUMBER OF ITERATIONS
LTL Self-containment Self-sufficiency Subsystem (name) nº municipalities nº protosystems Population (working places) (RWi/RWPi) (RWi/LTLi)
Arenys de Mar 4 1 30.810 9.204 59,27% 79,34%
Barcelona 18 4 2.450.517 1.030.553 88,10% 84,03%
Cardedeu 6 2 28.628 9.773 53,06% 67,40%
Garriga (La) 2 1 17.863 7.312 55,64% 56,70%
Granollers 10 3 123.086 59.999 69,09% 61,49%
Malgrat de Mar 4 1 31.985 12.014 68,15% 72,22%
Martorell 13 3 98.282 54.012 70,67% 55,68%
Mataró 13 3 202.973 70.589 70,95% 85,51% Mollet del Vallès 9 3 120.717 59.834 54,98% 49,34% Palau-solità i Plegamans 4 1 28.831 15.537 57,39% 48,78% Pineda de Mar 4 2 40.410 13.827 69,29% 77,88% Rubí 2 1 116.128 54.026 54,80% 54,17% Sabadell 11 2 383.721 154.924 70,17% 71,13% Sant Andreu de la Barca 9 4 94.287 40.445 51,23% 52,63% Sant Boi de Llobregat 8 2 236.664 68.522 51,00% 73,27% Sant Celoni 10 2 29.618 10.931 73,33% 79,72% Sant Sadurní d'Anoia 7 1 17.451 7.401 73,99% 73,06% Terrassa 6 1 192.483 72.953 74,04% 80,80% Vilafranca del Penedès 18 2 54.241 24.350 81,11% 75,56% Vilanova i la Geltrú 5 1 105.704 34.871 71,22% 89,29% Blanes 3 1 57.438 20.502 86,53% 88,98% Hostalric 4 1 4.897 2.680 65,86% 47,50% Arboç (L') 4 1 8.537 2.835 58,76% 66,46% Vendrell (El) 10 1 54.983 16.988 70,50% 86,56%
Source: Own Elaboration 9 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 5: The Barcelona Metropolitan System by the years 1991, 1996, 2001 and the administrative delimitation of the Barcelona Metropolitan Region (RMB)
Metropolitan Limit Area (km2) Population LTL (working places) nº subsystems nº protosystems nº municipalities 1991 1807,83 4.018.099 1.467.321 16 29 100 1996 3332,85 4.200.997 1.478.154 22 38 164 2001 3759,96 4.530.254 1.854.082 24 44 184 RMB 164
Source: Own Elaboration
1.2. IDENTIFYING THE URBAN SUB-CENTERS The v ast m ajority of m ethodologies have f ocused on t he identification o f s ub-centres by al ternatively studying: a) how dense in employment terms is a site (controlling or not the distance to CBD); or b) the influence of a site in organizing the commuting flows in a more complex urban system. Such criteria have clearly defined two families of sub-centre i dentification, the family based on the ana lysis of density and the family based on functional relations. Chronologically, the literature to identify urban sub-centres by using a method based on density analysis10 was m ainly def ined by h istorical and or administrative c riterions in t he 80 ’s (Greene, 1980); (Griffith 19 81a);; (Griffith 19 81b) and (Heikkila et al ., 19 89). T hen i n t he 90’ s (McDonald, 198 7); and (Giuliano & S mall, 199 1). Finally t he m ost significant a nd i nfluence l iterature was since at t he e nds of t he 90 ’s. (Bogart & F erry 19 99);; (Cervero & W u, 1998); (Craig & N g, 2001) ; (Gordon & R ichardson, 1996) ; (McDonald & McMillen, 1990) ;; (McDonald & P rather, 199 4); (McMillen, 200 1); (McMillen, 2003); (McMillen, 2004); (McMillen & Le ster 200 3);; (Readfearn, 2 007) and (García-Lopez, 200 7). A s a r esult, the pr evious appr oaches ha ve enabl ed t o m ake a significant progress in the analysis of the polycentric structure of the contemporary urban systems. However, most of the newly developed empirical literature suffers from a fundamental limitation: it defines the sub-centres exclusively under the condition of employment density, dismissing what it could be the essential element of polycentrism: the generation of urban structure. For that reason, in the literature appeared a s econd family to identify sub-centres based on t he functional relations, a s m entioned be fore: t aking i nto a ccount t he influence of a p lace i n or ganizing an d s tructuring t he commuting flows in a m ore complex urban system. That it means, understanding that sub-centres are not only abnormally dense zones in the metropolitan space, but also structural nodes that can strengthen the functional
10 The literature and the methods to identify urban sub-centres based on density analysis are explained in more detail in (Marmolejo, Masip & Aguirre, 2011)
10 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
relationship with their surrounding municipalities. In that sense, this approach is closer to the conception that centres in a network of cities function as nodes, without the necessity of being dense spots. The methods based on t he analysis of f unctional interactions w ere de signed t o del imit t erritorial systems (Nel·lo, 2001), i ncluding Travel To Work Areas in England, Statistical Metropolitan Areas in the USA and Functional Urban Areas, and some focused on detecting sub-centres that structure such territorial systems. References in this field include (Bourne, 1989), (Gordon & Richardson, 1996), and t he revised literature in section 1.1 where with the methodology proposed by (Roca et al., 2009); and (Roca et al., 2011a) at the time that the metropolitan system is delimited the urban sub-centres are identified. Thus, according to (Roca et al., 2009) and (Roca et al., 2011a) the sub-centres cannot only be understood as local pea ks in t he t opography of t he em ployment de nsity s urface. R ather, t hey m ust c onfigure nodes of t he metropolitan structure that imply significant tensions of urban mobility. The sub-centres should constitute real poles of i nfluence and t erritorial r eference t hat s urround t hem i n c ultural, s ocial and e conomic as pects. I n addition (Roca et al., 2009) states that in order to be truly considered as centres, they should generate authentic cities within their surroundings and, therefore, configure the metropolis as a city of cities.
In this paper, in order to detect sub-centres by using mobility approach begins also with the same notion of polycentrism that in (Roca et al., 2009) and (Roca et al., 2011a) in which nodes represent not only a significant employment concentrations but also must configure nodes of metropolitan structure. It is assumed, therefore that centres and sub-centres configure the metropolitan area as a city of cities (Roca et al., 2009) defined by urban sub-systems characterized by more or less monocentrism, polycentrism and dispersion. However, in this paper, although it is agreed with the same notion of polycentrism, it differs from the work of (Roca et al.2009) and (Roca et al., 201 1a) in t erms of i dentify urban sub-centres by introducing t he f ollowing modification: In Roca’s work, it defined an urban sub-centre as those municipalities leading each sub-system by using its methodology to delimit metropolitan areas (section 1.1) by using the following explained expression (1):
f 2 f 2 ij ji IVij = + )1( RWPLTL ji RWP LTLij
In that sense, on the one hand, the sub-centres that Roca finds are self-contained because the urban sub- systems are only consolidated if they have a minimum level of 50% of self-containment. So, it guarantees that the sub-centres can highly retain their resident working population. On the other, it is also guaranteed that the sub- centre c ould structure th eir urban s ystem bec ause t he m unicipality w ho l eads eac h ur ban s ub-system i s t he municipality with most density and critic mass within each sub-system11. However, it is not guaranteed if these sub-centres can be an important nodes within the metropolitan system in t erms of incommuting f lows ( IF), i n other words, i f t hey c an significantly attract fl ows fr om the w hole o f the metropolitan area and become an attractive node to work. This point is accordance with (McMillen 2003) state: “a sub-centre should be municipalities that (i) represent structural elements within metropolitan systems and at the same time (ii) are attractive to live and work in”. Due t o t he pr evious r eason, t he aut hor of t his pap er with Marmolejo and A guirre in (Marmolejo, Masip & Aguirre, 2011), tr y to identify s ub-centres by using i n a ddition a c utoff c ondition: it w ould be a sub-centre t he urban sub-system which its LTL (localised workers: RW –resident workers- + IF –incommuting flows-) are above of the 1% of the LTL of the metropolitan system. So, the expressions used in (Marmolejo, Masip & Aguirre, 2011) in order to identify sub-centres are the explained expression (1) and the next expression (2):
2 2 f ij f ji IV = + )1( LTL ≥ %1 LTL )2( ij RWP LTL RWP LTL ∑ BMR ji ij
However, this second condition, using a LTL threshold, has the following problems. Firstly, the problems that entail the previous stage: defining a mass critic level by local knowledge is very subjective task and the results are very dependent on the threshold employed; and secondly, another important drawback is that it is likely that what is an appropriate cutoff for a metropolitan area and a year (e.g. in 2001) it is not a for a another one (e.g. in 1991), which makes it hard to compare results for the same metropolitan area over time (the case of study of this paper).
11 If this paper had followed step by step the Roca’s methodology in order to identify urban sub-centres, it would have found the next ones: in 1991, it would have been 16 candidates to urban sub-centres (see figure 2) because the methodology to delimit the Barcelona Metropolitan System for the year 1991, defines a 16 urban sub-systems within the metropolitan area; in 1996 i t would have been 22 candidates to urban sub-centres (see figure 3); and finally in 2001 it would have been 24 candidates to urban sub-centres (see figure 4).
11 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
For these reasons, in this paper, the author proposes the following second condition instead of the previous explained one: it would be a sub-centre the urban sub-system which will be an attracting – dominant node within the whole of the metropolitan system, what it means, attracting more flows than the average IF –incommuting flows- of the metropolitan area. That condition can be formulated as follows (3):
2 2 f ij f ji IVij = + )1( RWP LTL ji RWP LTLij
( ) = and the condition will be satisfy if > 1 (3) 𝐼𝐼𝐼𝐼𝑢𝑢 −𝑠𝑠𝑠𝑠𝑠𝑠 𝑖𝑖 𝐼𝐼𝐼𝐼 𝑢𝑢−𝑠𝑠𝑠𝑠𝑠𝑠 𝑚𝑚𝑚𝑚 𝐷𝐷𝐷𝐷𝑢𝑢−𝑠𝑠𝑠𝑠𝑠𝑠 𝐷𝐷𝐷𝐷 𝑛𝑛 Where I FU-SUB are the i ncommuting f lows that the ur ban s ub-system (i) c an a ttract; IFMS are t he t otal incommuting flows within the metropolitan system (the sum of all the IFU-SUB (I)); n are the total number of urban sub-systems a nd are t he a verage at tractive of I F –incommuting flows- of t his metropolitan s ystem. Observe that in comparison𝐼𝐼𝐼𝐼𝑚𝑚𝑚𝑚 with the previous condition (2); this new condition (3) does not have the problems of using a subjective threshold.𝑛𝑛 It is objective (local knowledge it is not necessary in order to identify the urban sub- systems which their DIu-sub is above of the average attractive) and it is appropriate in order to make a comparative analysis as t his p aper t ries: the v alue o f t he av erage at tractive i s c hanging a ccording t o the each d ifferent metropolitan limits (1991, 1996 and 2001) which has been defined previously.
As in this paper, it is trying to identify sub-centres by using a functional approach; it is worth mentioning that one could identify sub-centres by using protosystems instead of urban sub-systems as a spatial unit to analysis and t hen u sing the explained c ondition ( 3). A s w e ex plained before, t he pr otosystems r epresents t he b asic elements which the metropolitan-regional territory is structured and they are the original “seeds” of polycentrism: a metropolitan area with more internal protosystems tends to have a greater trend towards decentralization. So, in this paper, it is also proposed that the protosystems which are defined as the previous explained expression (1), if they accomplish at the same time the condition (3), they can be considered as a candidate to subcentre.
So, the application of the previous proposed methodology, allow us to identify the candidates to sub-centres by using a mobility approach at urban sub-system territorial scale (figure 6-8) and at protosystem territorial scale (figure 9 -11) within the Barcelona Metropolitan System for the years 1991, 1996 and 2001. The results are presented in the following maps.
Sub-centres at Urban sub-system territorial scale Figure 6: Candidates to sub-centres. Barcelona Metropolitan System - 1991
Sabadell
Terrassa
Rubí
Barcelona - CBD
3 candidates to sub-centres + CBD (Barcelona). The sub-centres are: Sabadell, Terrassa and Rubí
12 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 7: Candidates to sub-centres. Barcelona Metropolitan System - 1996 Sabadell
Terrassa
Martorell
Granollers
Mollet del Vallès Rubí
Barcelona - CBD
6 candidates to sub-centres + CBD (Barcelona).
The sub-centres are: Sabadell, Terrassa, Rubí, Mollet del Vallès, Granollers and Martorell
Figure 8: Candidates to sub-centres. Barcelona Metropolitan System - 2001
Sabadell
Terrassa
Martorell Granollers
Mollet del Vallès
Rubí
Barcelona - CBD
8 candidates to sub-centres + CBD (Barcelona). Sant Andreu Sant Boi de The sub-centres are: Sabadell, Terrassa, Rubí, de la Barca Llobregat Mollet del Vallès, Granollers, Martorell, Sant Andreu de la Barca and Sant Boi de Llobregat Sub-centres at Protosystem territorial scale Figure 9: Candidates to sub-centres. Barcelona Metropolitan System - 1991
Sabadell
Terrassa
Rubí Barcelona - CBD
Cornellà 4 candidates to sub-centres + CBD (Barcelona). The sub-centres are: Sabadell, Terrassa, Rubí and Cornellà del Llobregat 13 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 10: Candidates to sub-centres. Barcelona Metropolitan System - 1996
Sabadell
Terrassa
Martorell
Granollers
Cerdanyola del Vallès
Rubí
Barcelona - CBD
8 candidates to sub-centres + CBD (Barcelona). Sant Feliu Cornellà de The sub-centres are: Sabadell, Terrassa, Rubí, de Llobregat Llobregat Granollers, Cerdanyola del Vallès, Martorell, Sant Feliu de Llobregat and Cornellà del Llobregat
Figure 11: Candidates to sub-centres. Barcelona Metropolitan System - 2001
Parets del Sabadell Vallès
Terrassa
Martorell
Granollers Sant Andreu de la Barca Santa Perpètua de Mogoda
Cerdanyola del Vallès
Rubí
Barcelona - CBD
12 candidates to sub-centres + CBD (Barcelona). Cornellà de The sub-centres are: Sabadell, Terrassa, Rubí, Llobregat Granollers, Cerdanyola del Vallès, Martorell, Sant Feliu de Llobregat, Cornellà, Parets del Vallès, Sant Sant Feliu de Sant Boi del Andreu de la Barca, Sant Boi de Llobregat and Llobregat Llobregat Sant Perpètua de Mogoda.
2. MEASURING POLYCENTRISM AT REGIONAL SCALE: A MORPHOLOGICAL, FUNCTIONAL AND A PROPOSED “INTEGRATED” APPROACH (1991-2001) In this section, the measurement and the evolution (1991-2001) of the polycentrism level at regional scale it is achieved. The specialized l iterature claims that the concept of polycentrism and its m easurement ar e still considered as a vague and fuzzy concept (Meijers, 2008). For that reason, it is worth providing some underlying notions of polycentricity, by describing how it can refer to different scales and, at the time, how it can be described from different perspectives. As it is mentioned previously, in the introduction, the notion of polycentricity can be referred to in at least three spatial scales: the global, the European, and the metropolitan scale (from individual
14 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
cities to city regions, to nation-states and to the European scale). In addition, the analytical perspectives that the literature used in order to measure polycentricity are: the morphological and the functional dimensions. In that sense, ESPON 1.1.1 (NORDREGIO, 2005) explained that polycentricity is an ambiguous, multi-escalar and i ll-defined n ormative c oncept. The ESPON’s s tudy s tresses t hat t wo s tructural e lements ar e particular relevance to polycentricity: on the one hand, the morphological elements that they laying out the size and the territorial distribution of urban areas in a given territory, and on the other hand, the relational-functional elements, based on net works of f lows and c o-operation bet ween urban ar eas on d ifferent s cales. Compared t o t his mentioned ESPON’s s tudy, the ESPON 1.4.3 (IGEAT, 2 007), does not dep art f rom an explicit f unction o f polycentricity, other than emphasing that according to them, polycentricity is a purely morphological issue. That implies that in ESPON 1.1.1, is included the aspects of relationships or flows between spatial units (FUAs), next to morphological indicators such as size and spacing of that spatial units (FUAs); and in the case of ESPON 1.4.3 is focused solely on the size distribution of the analyzed spatial units (FUAs in that study). This debate is continued by (Meijers 2008 Op. Cit) ESPON 1.1.1 starts from rank-size distribution of FUAs, the more flat this distribution is, and thus the regression line that best fits this distribution; the more polycentric is the urban r egion. B asically, pol ycentricity r efers t o t he plurality of centers i n a gi ven area and is thus by nature a morphological issue. In a synthesis of the defining conditions of a polycentric urban region (Parr, 2004) points so, among ot hers t he s eparation of c ities an d t he s ize di stribution of c ities12. I t appear s t hat m orphological characteristics such as the size and s pacing of cities are determining factors in establishing if or not any given area is polycentric or the opposite, monocentric. Summarizing, following ESDP terminology, a country or a region, can be considered more polycentric when: 1. There is less hierarchy in the size of cities (FUAs), in other words, when the cities are more equally sized and no city dominates the others. 2. The cities are more evenly distributed across a country’s or regional territory.
In order to measure the morphological polycentrism, (Meijers,2008) and (Meijers & Sandberg, 2008) used the following analytical expression of the rank-size distribution:
Pop (Lg 10) = C + RankPop(Lg 10)5T (4)
This two mentioned studiesβ are focusing on the main cities and regarding to the sample (Meijers,2008 Op. Cit) explains that it can be: 1) a fixed number of cities, or 2) a fixed threshold, and or 3) a size above which the sample accounts for some given proportion of a country or regional population (for example taking into account the cities which are above of the standard deviation). Therefore, according to (Meijers, 2008 Op. Cit) when measuring polycentricity on the basis of the rank-size distribution, the sample size could be best based on a fixed number of FUAs. The question then is what this number should be. (Meijers, 2008 O p. Cit) this is an open discussion, but should in any case be limited. However, calculations show that results for a sample size of n=10, correlate strongly with sample size n=5 or n=20. In addition, apart from the studies of (Meijers, 2008) and (Meijers & Sandberg, 2008); in (Hall & Pain, 2006) is also used the rank-size distribution in order to measure morphological polycentricity. (Hall & Pain, 2006 Op. Cit): “population size can be used to generate a first and admittedly crude measure of relative polycentricity by using the rank-size index. This has been a staple measuring tool of urban geography since the 1960s (Hagget, 1965); (Chorley & H agget, 1 967) and i s s till r egularly us ed-normally at a nat ional s cale, but equally appl icable a t a regional scale. When FURs within a nat ion or region are arrayed by size on doubl e-log graph paper, the “log- normal” distribution takes the form of a straight line at 45 –degree angle from the vertical; divergences towards a
12The ot hers according to (Parr, 2004) are: the po lycentric urban r egions as a cluster of s imilar s ettlements, separated by open spaces with interactions between them above the average, and having a specialized economic structure. In this line, (Champion, 2001), suggest that there are three basically features that define the polycentric urban region depending on the degree of restriction: 1) a variety of settlements within the region (less restrictive), 2) as above, but w ith s ome i nteraction bet ween t he s ettlements, 3) as abov e, but e ach c entre has a s pecialized function w ithin t he r egion ( the m ost r estrictive); t hen (Spierkermann a nd Wegerner, 2 004) develop a f ormal definition of polycentrism based on the rank-size of the settlements of the urban systems. Suggest that polycentrism can b e m easured f rom t hree ba sic requirements: 1) in a p olycentric ur ban s ystem, there i s a distribution of large and small cities, 2) in this polycentric urban system, the rank-size distribution is log-linear and 3) the polycentric urban system is not dominated by one large city. Finally in (Kloosterman and Musterd, 2001) state that the urban polycentric configurations should have the next summarized features: 1) a number of different historical cities, 2) a lack of city-dominant leader, 3) a small number of cities of similar size with each other and a large number of small towns, 4) proximate location between the cities which are constituent of the system (within the maximum commuting distance, and 5) constituent cities are spatially and politically different from one to other.
15 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
more a more concave pattern (a tendency to ‘primacy’) indicate a hi erarchical system by one or maybe two or three leading cities as (Hall & Hay, 1980) showed for different European countries: France and t he UK have a strongly primate distribution dominated by a capital city, while the Netherlands and the former West Germany had a di fferent d istribution do minated by a number of top c ities o f r oughly equ al r ank". Therefore, the r ank-size estimations are widely used in the literature about spatial distribution of economic activity. In particular, they have been used to estimate the Zipf’s Law13, the well-known empirical evidence which holds that the slope of the expression (4) given by the estimated ( 5T ) indicates the level of hierarchy, and thus the level of the polycentricity within the region or metropolitan system: as it is mentioned before, the more flat this distribution is, and thus the regression line that best fits this distribution,β the more polycentric is the urban region. In fact, the rank-size distribution synthesizes the hierarchies in terms of population and hence, economic activity across space. However, even if this analysis provides a synthetic outline of the degree of polycentricity in the urban regions, it does not capture the many other aspects of this urban phenomenon, since it focuses on the size-distribution of centres. Firstly, it does not consider the spacing of centres and the limits on centre separation: so, for instance a more flat distribution over time could mean a t ransition towards a pol ycentric structure, but it could also imply a dynamic of s prawl and coalescence bet ween cities; and s econdly by us ing t he r ank-size di stribution i t i s not possible to capture the specialization and the interaction among centres. Therefore, it is reasonable that rank-size distributions ar e no t en ough i n or der t o d efine an d measure the polycentrism l evel within t he m etropolitan systems. This is why in this paper, another measure has been analyzed: the functional polycentrism and then, from these two previous vectors this paper tries to propose an “integrated” approach (measuring polycentrism by taking into account at the same time the morphological and the functional perspectives).
In order to measure the degree of functional polycentric development, literature suggests various interaction indicators based o n f low dat a t hat u sually r egard commuting14. T he s tarting po int of t hese i nteraction methodologies consist in conceptualizing the spatial aggregate under analyses –here at intra-metropolitan scale- as a s ystem c omposed of node s or t erritorial un its (municipalities, i n t his s tudy: u rban s ub-systems a nd protosystems) an d r elations a mong t hese nod es (Boix, 20 02). P olycentric regions should be c haracterized by highly interconnected urban nodes, following the idea that the more the interconnected the centres, the more the polycentric the system. However, a more important aspect is that connections should be balanced among nodes, without a full centralization of flows towards a s ingle node. This latter condition refers to the fact that polycentric regions ar e c haracterized by m ore t han one c entrality, s o t hat t here s hould ex ist s everal node s t hat ar e i n a similar hierarchic position. One indicator based on commuting flows is the Entropy Index, using the Shannon form15 as follows:
= =1( · [ ( )]) (5) 𝑛𝑛 𝐿𝐿𝐿𝐿𝐿𝐿 𝑖𝑖 𝑖𝑖 𝑖𝑖 ( [ ( )]) 𝐸𝐸Where𝐼𝐼 EILTL −is the∑ LTL Entropy𝐿𝐿𝐿𝐿𝐿𝐿 Index𝐿𝐿𝐿𝐿 for 𝐿𝐿𝐿𝐿𝐿𝐿the whole of the metropolitan system, · is the LTL Entropy Information for each analyzed spatial unit (municipality, protosystem or urban sub-system) and finally 𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 𝐿𝐿𝐿𝐿 𝐿𝐿𝐿𝐿𝐿𝐿𝑖𝑖 LTLi is the probability (proportion) to find LTL in the analyzed spatial unit (i) (municipality, protosystem or urban sub-system) w ithin t he m etropolitan s ystem. The E ntropy Shannon Index i ndicator r anges from 0 t o ∞ and it measures h ow t he t otal i nteraction is di stributed a mong n odes. Values close to 0 means that almost trips are toward a s ingle node, hence the region should be strongly monocentric. Conversely, high values indicate strong entropy of f lows, h ence a strong i nteraction among no des, w hich is compatible w hich a po lycentric urban structure. However, this very general indicator may not strictly describe the degree of polycentricity, but the
13 In order to know more about the Zipf’s Law, it is worth mentioning the work of (Roca & Arellano, 2011c). 14 A clear examples are: on the one hand, the studies in the literature that used the flow data in order to measure the travel-to-work intensity between cities, where “a situation with intense commuter flows in both directions would be a sign of integration and of polycentrism” (NORDEGIO, 2005 Op. Cit); but also on the other hand other types of flows can be studied, for instance, (Camagni & Salone, 1993) propose to utilize the total amount of communications and information flows going out of and into each centre. 15 There are other studies in the specialized literature where is used another form of the Entropy Index. These are the c ases of (Limtanakool, 2007, 200 9) which are u sed the n ormalized ( or evenness) E ntropy Index. The ( )· ( ) Limtanakool’s Entropy Index expression is the following one: = In addition, it is worth =1 ( ) . 𝑍𝑍𝑍𝑍 𝐿𝐿𝐿𝐿 𝑍𝑍𝑍𝑍 mentioning that (Limtanakool, 2007, 2009) by analyzing the flow data, provides𝐿𝐿 a useful set of indicators in order 𝑖𝑖 𝑖𝑖 to characterize the structure of the urban systems within the insights𝐸𝐸𝐸𝐸 of− the∑ network𝐿𝐿𝐿𝐿 theory𝐿𝐿 and by referring at the same t ime the ent ire system ( region), t he nodes ( cities) or t he l inks be tween nod es ( flows). C oncretely t he Limtanakool’s proposed indexes referring both to the entire system and the single centres and the link –in order to describe the “S-dimensions” that his studies define: structure, strength and symmetry of spatial systems.
16 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
dispersion of activities over the territory, which would even describe features of urban sprawl. For that reason, this paper after m easuring t he p olycentrism l evel by t aking i nto ac count onl y t he LT L E ntropy I ndex i t i s al so measured the functional polycentricity level by taking into account simultaneously the % LTL or % LTL Entropy Information in sub-centres (identified in section 1) and the LTL Entropy Index of the metropolitan system. As this paper will be try to present further on, with measuring the polycentrism level with this last functional approach, it is possible to conclude that during the analyzed period of time (1991-2001) the urban dynamics of urban sprawl within the Barcelona Metropolitan system has been d ecreased, meanwhile the polycentricity level has been increased (% LTL Entropy Information in sub-centres are higher than the % LTL Entropy Information in the rest of the metropolitan system) (figure 61-62). Another indicator to measure the degree of functional polycentricity is the Dominance Index defined by the expression (3), used in section 1 as a second condition in order to identify urban sub-centres (depending on the considered spatial scale: urban sub-systems or protosystems):
( ) = (3) 𝐼𝐼𝐼𝐼𝑢𝑢 −𝑠𝑠𝑠𝑠𝑠𝑠 𝑖𝑖 𝑢𝑢−𝑠𝑠𝑠𝑠𝑠𝑠 𝐼𝐼𝐼𝐼𝑚𝑚𝑚𝑚 𝐷𝐷𝐷𝐷 𝑛𝑛 As this indicator is defined at node level (urban sub-systems or protosystems) and it takes into account the ratio of in-commuting flows to a urban sub-system or protosystem respect to the total commuting of a metropolitan system, the intuition is clear: the DIu-sub or DIu-PROTO (depending on the analyzed spatial scale) aims to measure to what extent a urban sub-system or protosystem attracts flows from the other centres, respect to the average degree of “attractiveness of the metropolitan system. In other words, it measures whether a node dominates the network of not. Hypothetically the maximum value of the Dominance index (for example, taking into account the urban sub-system scale for the year 1991 the maximum value will be 16 because n=16) would indicate that every interaction in the network is associated to the node with that maximum value, while a z ero value would indicate that the node is not involved at all in the network. The maximum degree of polycentrism, hypothetically, would happen if this Dominance Index is equal to 1 for every node: it would mean that every urban sub-system or protosystem (or the spatial unit that has been considered) attracts the same intensity of flows. In addition, it is interesting to know how this indicator is distributed. A high standard deviation of this index indicates that higher values are associated with one or few nodes attracting flows from the other, while a more even distribution of the index would characterize polycentric metropolitan systems, since the in-commuting flows to each node are similar to each other. So, the indicator can be useful to rank the nodes and to see of the metropolitan system presents strong or less hierarchies: the latter should happen in the polycentric metropolitan systems. In this paper, is analyzed the evolution of the Dominance Index over time (1991 to 2001) at urban sub-system and protosystem scale within the metropolitan system as well as the measurement and the evolution of the % Dominance Index in CBD, in sub-centres and in the rest of the metropolitan system (figure 61-62). By analyzing the functional polycentricity level by taking into account the % Dominance Index in sub-centres and LTL Entropy Index within the metropolitan system the results are the same as previous (taking into account the % LT L i n s ubcentres or % LT L E ntropy I nformation i n s ub-centres and t he LT L E ntropy I ndex of t he metropolitan system): the metropolitan system of Barcelona has become a more polycentric structure.
So, in this section, the measurement of the polycentrism level at regional scale and its evolution over time (1991-2001) is achieved. In doing so, firstly, the morphological dimension of polycentrism is estimated at municipality, pr otosystem and ur ban s ub-system sca le from 1991 t o 2001 by us ing t he r ank-size di stribution (expression 4) and taking into account as an observation sample n= the total of nodes and n=10 Secondly, t he f unctional d imension of polycentricity i s al so m easured, but t his t ime at sub-system and protosystem scale by 1) analyzing the LTL Entropy Index; then 2) by taking into account the % LTL in sub-centres and the LTL Entropy Index; and finally, 3) by the % Dominance Index in sub-centres and the LTL Entropy Index. In that point, the paper tries to analyze the relationships between morphological and f unctional indicators by carrying out a correlation analysis (taking into account the sub-systems, the protosystems and the municipalities as a spatial unit from 1991 to 2001). So, the used functional indicators in this paper are: % LTL, the Dominance Index ( DI) and t he LT L E ntropy Index ( EI). I n ad dition, the us ed morphological indicators ar e: % P opulation, Population (Lg10), Rank Population (Lg10), and the Population Entropy Index (EI). Then, the “integrated” approach that this paper proposes is estimated at urban sub-system and protosystem territorial scale by taking into account at the same time the next morphological and functional indicators: % population in sub-centres and the LTL Entropy Index (EI) of the metropolitan system. Finally, these urban structure dynamics from 1991 to 2001 at urban sub-system and pr otosystem scale are summarized in two synthetic tables (figure 61-62).
17 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
2.1. MEASURING THE MORHOPHOLOGICAL POLYCENTRISM LEVEL (1991-2001) In t his s ection, t he pol ycentricity l evel and i ts ev olution over t ime a ccording t o t he m orphological no tion o f polycentrism is achieved. In doing so, the urban sub-system, the protosystem and the municipality territorial scale are analyzed. The results suggest an increment of the polycentricity within the Barcelona metropolitan system from 199 1 t o 200 1, s o the di stributions (rank-size) of t he anal yzed node s ( sub-systems, p rotosystems a nd municipalities) have become more flat, and thus the regression lines that best fit these distributions.
Urban sub-system territorial scale (n= total of nodes) Morphological Polycentrism, Subsystems 1991 (n=16) Morphological Polycentrism, Subsystems 1996 (n=22)
15 15 Barcelona - CBD R2=0,966 Barcelona - CBD R2=0,941
14 14
13 13 Sabadell Sabadell Terrassa 12 Granollers 12 Mollet del Vallès Terrassa Rubí Rubí 11 Martorell
11 Population (LG10)Population Population (LG10)Population 10
10 9
POP (LG 10)= 14,41 - 1,69RANK (LG10) POP (LG 10)= 14,54 - 1,74RANK (LG10) 9 8 0 0,5 1 1,5 2 2,5 3 0 0,5 1 1,5 2 2,5 3 3,5 Rank Population (LG10) Rank Population (LG10) Figure 12: Rank-size distribution, Sub-systems 1991. Slope Figure 13: Rank-size distribution, Sub-systems 1996. Slope regression line: -1,69. (n=16, R2=0,966), (labelled the sub- regression line: -1,74. (n=22, R2=0,946), (labelled the sub- systems that are identified in section 1 as a sub-centres) systems that are identified in section 1 as a sub-centres)
Morphological Polycentrism, Subsystems 2001 (n=24) Morphological Polycentrism, Subsystems 1991-1996-2001 15 16 Barcelona - CBD R2=0,901 15 14 Barcelona - CBD (1)
14 Sant Boi de 13 Llobregat (3) Sabadell 13 Terrassa Mataró (4) Mollet del Sabadell(2) Sant Boi de Terrassa(5) 12 Vallès Granollers(6) Llobregat Rubí 12 Martorell Mataró (3) Mollet del Granollers Vallès (7) Sant Andreu de la Barca Terrassa(4) 11 11 Rubí (8) Rubí (6)
(LG10)Population Granollers (7)
Population (LG10)Population 10 10 Martorell (9) 9 y = -1,692x + 14,41 y = -1,743x + 14,54 y = -1,501x + 14,50 9 R² = 0,965 R² = 0,941 R² = 0,901 8 POP (LG 10)= 14,50 - 1,50RANK (LG10) n=all Subsystems 1991 1996 2001 8 7 0 0,5 1 1,5 2 2,5 3 3,5 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3 3,25 3,5 Rank Population (LG10) Rank Population (LG10) Figure 14: Rank-size distribution, Sub-systems 2001. Slope Figure 15: Rank-size distribution, Sub-systems 1991 to regression line: -1,50. (n=16, R2=0,901), (labelled the sub- 2001. The slope of the regression line, become more flat, systems that are identified in section 1 as a sub-centres) from -1,69 in 1991 to -1,50 in 2001, so more polycentric.
Analyzing the evolution over time (1991 to 2001) of the rank-size distribution at urban subsystem territorial scale, the results are clear: the Barcelona Metropolitan system has become a more polycentric urban region because the slope of the regression line is more flat in 2001 (-1,50) than in 1991 (-1,69). However two points are worth mentioning, the first that in 1996 the metropolitan system was more monocentric (in 1996 the slope of the regression l ine w as -1,74) s o, t he urban dy namics f rom 1991 t o 20 01 h as defined by a pr ocess f irst towards monocentrism and then to polycentrism. Then, the second point, is that in 2001 the Barcelona Metropolitan system although is more polycentric than in 1991, is still monocentric in comparison with other European regional or national systems; for instance in (Meijers, 2008); (Meijers & Sandberg, 2008); defined the Germany urban system as a very polycentric (-0,571), Sweden as average (-1,118) and Greece as very monocentric (-1,894).
18 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Protosystem territorial scale (n= total of nodes)
Morphological Polycentrism, Protosystems 1991 (n=29) Morphological Polycentrism, Protosystems 1996 (n=38)
16 16 2 2 R =0,861 Barcelona - CBD R =0,778 15 Barcelona - CBD 14 14 Sabadell 13 12 Rubí Terrassa Granollers Cornellà Sant Feliu del Cornellà Llobregat Sabadell Cerdanyola 12 del Vallès Terrassa Martorell 10 11 Rubí
10 8 Population (LG10)Population (LG10)Population
9 6 8 POP (LG 10)= 14,54 - 1,64RANK (LG10) POP (LG 10)= 14,84 - 1,70 RANK (LG10)
7 4 0 0,5 1 1,5 2 2,5 3 3,5 0 0,5 1 1,5 2 2,5 3 3,5 4 Rank Population (LG10) Rank Population (LG10) Figure 16: Rank-size distribution, Protosystems 1991. Slope Figure 17: Rank-size distribution, Protosystems 1996. Slope 2 2 regression line: -1,64. (n=29, R =0,861), (labelled the sub- regression line: -1,70. (n=38, R =0,778), (labelled the sub- systems that are identified in section 1 as a sub-centres) systems that are identified in section 1 as a sub-centres)
Morphological Polycentrism, Protosystems 2001 (n=44) Morphological Polycentrism, Protosystems 1991-1996-2001 16 16 2 R =0,850 15 Barcelona - CBD (1) 15 Barcelona - CBD Sant Boi de 14 14 Llobregat (3) Terrassa 13 13 Sabadell (4) Mataró Terrassa Cerdanyola (2) (6) Rubí(7) Sabadell 12 Cerdanyola 12 Sant Boi del Vallés Terrassa (8) Vilanova i la Granollers del Llobregat Cornellà (3) Mataró Geltrú (9) Rubí Martorell 11 11 (6) Rubí (7) Granollers Sant Feliu de Santa Perpètua 10 Cerdanyola (10) Llobregat 10 Parets del (8) Granollers 9 (9)
Vallès (LG10)Population
Population (LG10)Population Sant Andreu Mollet del 9 de la Barca Vallès 8 (12) 8 7 y = -1,643x + 14,53 y = -1,699x + 14,83 y = -1,468x + 14,55 R² = 0,861 R² = 0,783 R² = 0,853 7 6 POP (LG 10)= 14,55 - 1,46RANK (LG10) n=all Protosystems 1991 1996 2001 6 5 0 0,5 1 1,5 2 2,5 3 3,5 4 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3 3,25 3,5 3,75 4 Rank Population (LG10) Rank Population (LG10) Figure 18: Rank-size distribution, Protosystems 2001. Slope Figure 19: Rank-size distribution, Protosystems 1991 to 2 regre ssion line: -1,46. (n=44, R =0,850), (labelled the sub- 2001. The slope of the regression line, become more flat, systems that are identified in section 1 as a sub-centres) from -1,64 in 1991 to -1,46 in 2001, so more polycentric.
Analyzing the evolution over time (1991 to 2001) of the rank-size distribution but in this time at protosystem territorial scale, the results that this paper achieved, suggest the same “clone” conclusions as if the spatial unit was t he ur ban sub-systems: t he B arcelona M etropolitan system f rom 19 91 t o 20 01 h as b een increased its polycentricity level. However, when the analyzed spatial units are the protosystems (“seeds of polycentrism”), two points are significantly remarkable: on the one hand, the descending process of the slope of the regression line has also been shifted, so in 1991 it was -1,64; for ascending until -1,70 in 1996, and finally descending to -1,46 in 2001, and on the other hand, the Rsquare of the regression are lower (0,861 in 1991; 0,778 in 1996; and 0,850 in 2001) in comparison with the Rsquare when the spatial units were the urban sub-system (0,966 in 1991; 0,941 in 1996; and 0,901 in 2001), although the urban sub-systems regressions have less observations for each year. Finally, it is worth mentioning that when the spatial unit of analysis is the sub-systems either the protosystems from 1991 to 2001 the number of identified urban sub-centres has been increased. Concretely, in the case of sub- systems from 3 to 8; and in the case of protosystems from 4 to 12; so it’s likely that behind of such urban dynamic is the explanation for why the slopes of these regressions lines have become more and more flat.
19 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Municipality territorial scale (n= total of nodes)
Morphological Polycentrism, Municipalities 1991 (n=100) Morphological Polycentrism, Municipalities 1996 (n=164)
16 16
R2=0,877 R2=0,872
14 Barcelona 14 Barcelona CBD CBD Sabadell Badalona Terrassa Terrassa Mataró 12 L'Hospitalet Cerdanyola del Vallès 12 L'Hospitalet Badalona Sabadell Rubí Granollers Mataró Sant Cugat del Vallès Sant Cugat del Vallès Granollers Rubí 10 10 Cerdanyola del Vallès Martorell Martorell
8 8 Population (LG10)Population Population (LG10)Population
6 6
POP (LG 10)= 14,95 - 1,62RANK (LG10) POP (LG 10)= 15,30 - 1,65RANK (LG10)
4 4 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 Rank Population (LG10) Rank Population (LG10) Figure 20: Rank-size distribution, Municipalities 1991. Slope Figure 21: Rank-size distribution, Municipalities 1996. Slope regression line: -1,62. (n=100, R2=0,877) regression line: -1,65. (n=164, R2=0,872)
Morphological Polycentrism, Municipalities 2001 (n=184) Morphological Polycentrism, Municipalities 1991-1996-2001 16 15 R2=0,873
14 14 Barcelona Barcelona CBD CBD 13 Sabadell Badalona Terrassa Terrassa 12 L'Hospitalet 12 L'Hospitalet Sabadell Sant Cugat del Vallès Badalona Rubí Mataró Granollers Rubí 11 Santa Sant Cugat del Vallès 10 Coloma Granollers Cerdanyola 10 Mataró del Vallès Cerdanyola del Martorell Vallès 9
8 (LG10)Population
Population (LG10)Population 8
6 7 y = -1,626x + 14,95 y = -1,651x + 15,30 y = -1,549x + 15,18 R² = 0,876 R² = 0,872 R² = 0,873 POP (LG 10)= 15,18 - 1,54RANK (LG10) 6 n=all Municipalities 1991 1996 2001 4 5 0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5 5,5 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 2,75 3 3,25 3,5 3,75 4 4,25 4,5 4,75 5 5,25 Rank Population (LG10) Rank Population (LG10) Figure 21: Rank-size distribution, Municipalities 2001. Slope Figure 22: Rank-size distribution, Municipalities 1991 to 2 regression line: -1,54. (n=184, R =0,873) 2001. The slope of the regression line, become more flat, from -1,62 in 1991 to -1,54 in 2001, so more polycentric.
In that case, the spatial unit of analysis across the Barcelona Metropolitan system has been the municipalities. The results taking into account a dy namic perspective, from 1991 t o 2001, lead to the same conclusions as the two previous territorial scales, but with the following slight differences. Firstly, although t he urban dynamic of de scending process of the s lope of t he r egression l ines f ollows t he same pa ttern: (-1,62) in 19 91 t o (1,54) in 2001, i n t his territorial scale, t his pr ocess i s l ess ac celerated i n comparison with the others. Secondly, by analyzing the municipalities which has the higher Population (Lg10) and at the same time its Dominance Index (DI) is above of 1 (the labelled municipalities) one could realize that these municipalities h as not ex perimented any s ignificant change i n t erms of R ank P opulation ( Lg10); w hat i t c ould mean t hat t his process t owards a m ore p olycentric s tructure, has o ccurred w hen it is takes into a ccount t he municipalities as a spatial unit of analysis and the medium and small cities: in the previous figure 22 it is showed how the medium and small cities (from a v alue of 3 to 4,5 of Rank Population – Lg10) are the cities which their value of P opulation ( Lg10) h as m ore bee n i ncreased: f or i nstance G ranollers or Cerdanyola del V allès as a n examples of medium cities.
20 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Urban sub-system, protosystem and municipality territorial scale (n= 10) In this section, the observations sample in order to define the rank-size distribution for each year (1991 to 2001) a nd f or ea ch an alyzed t erritorial scale ( sub-system, pr otosystem and municipality) is a f ixed num ber of cities, concretely n=10 as it proposed by (Meijers, 2008) and (Meijers & Sandberg, 2008). The results suggest the same conclusions as when it has been taken into account as a observations sample n= the total of nodes but with the next t wo s ignificant d ifferences: f irstly, when i t i s analyzed t he s ub-system e ither the pr otosystem a nd t he municipality scale, it is depicted a more polycentric region (the slopes of the regression lines are more flat; around -1,1 -1,2); and secondly, the process towards a higher level of polycentricity is gradually (not shifted as previous): there is no occurs that from 1991 to 1996 the slope of the regression line has ascended (higher monocentricity) and from 1996 to 2001 the slope has decreased (more flat, higher polycentricity).
Morphological Polycentrism, Subsystems 1991-1996-2001
15 Barcelona - CBD y = -1,570x + 14,28 14,5 R² = 0,941
y = -1,580x + 14,31 14 R² = 0,941
13,5 y = -1,252x + 14,14 R² = 0,902
13 Sabadell Mataró 12,5 Sant Boi de Terrassa Llobregat
(LG10)Population 12 Granollers Mataró Terrassa Rubí Martorell 11,5 Rubí
11 Granollers n=10 Subsystems Mollet del Vallès 10,5
0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5 SU1991 SU1996 SU2001 Rank Population (LG10)
Figure 22: Rank-size distribution, Sub-systems 1991 to 2001 (n=10). The slope of the regression line, become more flat, from -1,57 in 1991 to -1,25 in 2001, so more polycentric.
Morphological Polycentrism, Protosystems 1991-1996-2001
15
y = -1,313x + 13,98 Barcelona - CBD 14,5 R² = 0,875
y = -1,208x + 13,90 14 R² = 0,856
13,5 y = -1,181x + 13,94 R² = 0,869 13 Sant Boi de Llobregat
12,5 Sabadell Terrassa
Terrassa Cornellà
Population (LG10)Population 12 Mataró Vilanova i la Cornellà Rubí Geltrú Gavà Granollers 11,5 Mataró Rubí
11 Cerdanyola n=10 Protosystems Granollers 10,5 0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5
Proto1991 Proto1996 Proto2001 Rank Population (LG10) Figure 23: Rank-size distribution, Protosystems 1991 to 2001 (n=10). The slope of the regression line, become more flat, from -1,313 in 1991 to -1,181 in 2001, so more polycentric. 21 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Morphological Polycentrism, Municipalities 1991 - 1996-2001
15
y = -1,226x + 13,87
14,5 R² = 0,931
Barcelona - CBD y = -1,194x + 13,80 14 R² = 0,927
13,5 y = -1,181x + 13,78 R² = 0,915 13
L'Hospitalet 12,5 Terrassa Badalona (LG10)Population 12 Santa Coloma Sabadell Sant Boi de 11,5 Llobregat Mataró
Cornellà 11 El Prat de n=10 Municipalities Llobregat 10,5
0 0,25 0,5 0,75 1 1,25 1,5 1,75 2 2,25 2,5
Mun1991 Mun1996 Mun2001 Rank Population (LG10) Figure 24: Rank-size distribution, Municipalities 1991 to 2001 (n=10). The slope of the regression line, become more flat, from -1,313 in 1991 to -1,181 in 2001, so more polycentric.
2.2. MEASURING THE FUNCTIONAL POLYCENTRISM LEVEL (1991-2001) In this section, the polycentrism level and its evolution over time, from 1991 to 2001 is estimated by taking into account another dimension of the polycentricity notion: the relational – functional perspective. In doing so, in this section the urban sub-system and the protosystem territorial scale are analyzed meanwhile the municipality scale is not studied because as in this section in order to define the functional polycentricity level it is takes into account among other approaches, the % LTL and the % Dominance Index (DI) in urban sub-centres in order to solve the problems that results of using LTL Entropy as a polycentricity indicator (it can merge a dy namic of polycentrism and a process of urban sprawl, see section 2.0) and then because it can determinate at the same time if the polycentrism is reinforced or not and if the urban sprawl is decreased or increased (if the % LTL or Dominance Index in sub-centres, over time, is more increased in comparison with the % LTL or Dominance Index in the rest of the metropolitan systems, that it means a urban process of polycentricity, on the contrary, a dynamic of urban sprawl). As a r esult, it i s ne ed t o i dentify t he sub-centres f irst, an d i n t his pa per i t i s only us ed a f unctional approach in order to identify the sub-centres and delimit the metropolitan system for each year at the same time (section 1), so it is not possible to know the urban sub-centres at the municipality scale. The results, as it is try to explain further on, suggest an urban process towards a more polycentric structure either at the urban sub-system and protosystem territorial scale from 1991 to 2001 (figures 25–30).
Urban sub-system territorial scale In order to measure the polycentricity level, in this paper is analyzed the following functional approaches: 1) by analyzing the evolution of the LTL Entropy Index over time (from 1991 to 2001); 2) by taking into account the % LTL in sub-centres and the LTL Entropy Index within the metropolitan system; and finally 3) by studying the evolution of the % Dominance Index in sub-centres and the LTL Entropy Index. In the next (figure 25), the polycentricity level is measured by defining the LTL Entropy Index (as the analytical expression 5) and its evolution ov er t ime. A ccording to t hat, t he r esults ar e c lear: the B arcelona M etropolitan system towards to a more polycentric structure: in 1991 the LTL Entropy Index was 1,336 and i t has gradually ascended to 1,899 in 2001. However, as it mentioned before, by using only the Entropy Index, it is not possible to know if this process it also mean a process of urban sprawl. For that reason in the (figure 26) it is measured the polycentricity level by using not only the LTL Entropy Index, but also defining the % LTL in sub-centres (axis Y). So in the (figure 26) in the axis X is represented the Entropy Index and i n the axis Y the % LTL in sub-centres.
22 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
The size of the sphere by defining the share of employment in the CBD (Barcelona) it can be seen as an indicator of macrocephalia. As a result, in this second approach, it is possible to observe at the same time the dynamics of monocentricity, polycentricity and sprawl: from 1991 to 2001 the CBD-Barcelona has decreased its employment share from 68,08% to a 55,58% at the same time that the share in the identified urban sub-centres in section 1 has increased their employment share from 15,49% in 1991 to 30,46% in 2001 and where the dynamics of urban sprawl has decreased for the same period of time: in 1991 the share employment in the rest of the metropolitan system was 16,43% and in 2001 was 13,96%.
Figure 25: Measurement of the polycentrism level by using LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 2006
24 Subsystems
2001
YEAR
- 22 Subsystems
1996
PERIOD OF TIME 1991
16 Subsystems
1986 1,00 1,20 1,40 1,60 1,80 2,00 2,20 LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Urban Structure (Barcelona Metropolitan System) 1991 1996 2001
Number of subsystems 16 22 24 Barcelona (subsystem - CBD) 1 1 1 Number of subsystems beyond CBD 15 21 23 LTL Entropy Index (Metropolitan System) 1,36603 1,54287 1,89996
Source: Own Elaboration
Figure 26: Measurement of the polycentrism level by using % LTL in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 40%
55,58% LTL-CBD
30% 1996
1991 2001 20%
64,26% LTL-CBD LTL IN% SUBCENTRES 10% 68,08% LTL-CBD
0% 1,20 1,30 1,40 1,50 1,60 1,70 1,80 1,90 2,00
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
23 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Finally, in order to measure the functional polycentricity in this paper tries to do it by analyzing the evolution of the % D ominance I ndex i n s ub-centres and the LT L E ntropy I ndex (figure 27) . T his l ast pr oposed f unctional approach is quite more intelligent than the previous one: it is considered the capacity of urban nodes to attract flows (IF, in-commuting flows) above the average attractiveness of the metropolitan system, so it guarantees that these nodes are significantly within the metropolitan system in terms of being a place to work. This capacity is defined by the Dominance Index (section 1, expression 3). So, in the (figure 27) the axis X is represented the LTL Entropy I ndex, t he % D ominance Index ( DI) i n s ub-centres in t he axis Y and f inally t he s ize o f t he s phere is defined by t he % D ominance I ndex ( DI) i n t he C BD ( Barcelona ur ban s ub-system). A s a r esult, i n t his t hird functional approach, it is observed as the previous second approach the same urban retrospective urban dynamic: from 1991 to 2001, the Barcelona Metropolitan System has increased its polycentricity level. From 1991 to 2001 the CBD-Barcelona has decreased its Dominance Index (capacity of attract flows from other metropolitan nodes) from 40,67% to a 39,51% at the same time that the Dominance Index (DI) in identified urban sub-centres in section 1 has increased from 25,70% in 1991 to 47,62% in 2001 and in which the dynamics of urban sprawl has decreased for the same period of time: in 1991 the Dominance Index (DI) for the rest of the metropolitan system was 33,63% and in 2001 was 12,88%.
Figure 27: Measurement of the polycentrism level by using % Dominance Index (DI) in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 60%
2001
50% 1996
40% 39,51% 1991 35,58% DI-CBD DI-CBD 30%
20% 40,67% DI-CBD 10%
% DOMINANCE % INDEX (DI) IN SUBCENTRES 0% 1,20 1,30 1,40 1,50 1,60 1,70 1,80 1,90 2,00
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Protosystem territorial scale In the protosystem territorial scale, is analyzed the functional polycentricity by using the same three previous approaches: 1) by analyzing the evolution of the LTL Entropy Index over time (from 1991 to 2001); 2) by taking into account the % LTL in sub-centres and the LTL Entropy Index within the metropolitan system; and finally 3) by studying the evolution of the % Dominance Index in sub-centres and the LTL Entropy Index. The results are the following ones: in the (figure 28) is observed an increment of the LTL Entropy Index over time, in 1991 there was a value of 1,747 that has gradually ascended to 2,304 in 2001. This urban dynamic it also entails the creation of 15 protosystems: in 1991, within the metropolitan system there were 29 protosystems, and in 2001 the metropolitan system is defined by 44. In th e (figure 29) depicts t he f ollowing m etropolitan r etrospective dy namic: from 1991 to 2001 the CBD- Barcelona has decreased its employment share from 61,61% to a 50,30% at the same time that the share in the identified urban sub-centres in section 1 has increased their employment share from 17,12% in 1991 to 31,84% in 2001 and in which the dynamics of urban sprawl has decreased for the same period of time: in 1991 the share employment in the rest of the metropolitan system was 21,26% and in 2001 was 17,86%. In t he (figure 3 0) the m etropolitan s tructure i s d efined by the t hird f unctional a pproach, and t his appr oach depicts the metropolitan structure in terms of monocentricity, polycentricity and urban sprawl in the following way: from 1991 to 2001 the CBD-Barcelona has decreased its Dominance Index (capacity of attract flows from other metropolitan nodes) from 40,72% to a 35,83% at the same time that the Dominance Index (DI) in identified urban
24 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
sub-centres in section 1 ha s increased from 24,42% in 1991 to 46,53% in 2001 and in which the dynamics of urban sprawl has decreased for the same period of time: in 1991 the Dominance Index (DI) for the rest of the metropolitan system was 34,87% and in 2001 was 17,64%. Finally, as a last remark, it is worth mentioning that either by analyzing protosystems and sub-systems, by using functional approaches the results point out the same retrospective urban dynamics from 1991 to 2001: it has been a clear process to a more polycentric region.
Figure 28: Measurement of the polycentrism level by using LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 2006
44 Protosystems
2001
YEAR
- 38 Protosystems
1996
PERIOD OF TIME 1991
29 Protosystems
1986 1,50 1,60 1,70 1,80 1,90 2,00 2,10 2,20 2,30 2,40 2,50 LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Urban Structure (Barcelona Metropolitan System) 1991 1996 2001
Number of protosystems 29 38 44 Barcelona (protosystem - CBD) 1 1 1 Number of protosystems beyond CBD 28 37 43 LTL Entropy Index (Metropolitan System) 1,74738 2,09325 2,30492 Source: Own Elaboration
Figure 29: Measurement of the polycentrism level by using % LTL in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 40%
2001
1996 30%
1991 50,30% LTL-CBD 20% 54,09% LTL-CBD
LTL IN% SUBCENTRES 10% 61,61%
LTL-CBD
0% 1,50 1,60 1,70 1,80 1,90 2,00 2,10 2,20 2,30 2,40 2,50
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
25 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 30: Measurement of the polycentrism level by using % Dominance Index (DI) in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 60% 2001
50% 37,78% DI-CBD 40% 35,83% 1991 DI-CBD 30% 1996
20%
40,72% DI-CBD 10%
% DOMINANCE % INDEX (DI) IN SUBCENTRES 0% 1,50 1,60 1,70 1,80 1,90 2,00 2,10 2,20 2,30 2,40 2,50 LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
2.3. CORRELATIONS BETWEEN MORPHOLOGICAL AND FUNCTIONAL POLYCENTRISM (1991-2001) In order to see the relationships among indicators of polycentrism that we computed, a correlation analysis was c arried out from 19 91 t o 20 01 at t he following t erritorial s cales: urban s ub-system, protosystem and municipality. R correlation coefficients among the selected indicators are shown in the (figures 31-57). With reference to the morphological dimension the selected indicators are: % P opulation, Population (Lg10), Rank Population (Lg10), and finally the Population Entropy Index (EI). According to the functional dimension the analyzed indicators are the following ones: % LT L (localized workers); the Dominance Index (DI) and f inally the LTL E ntropy I ndex. B y ana lyzing a ll c orrelation m atrixes and with t aking i nto ac count t he m entioned t erritorial scales, the results suggest the next conclusion: the selected morphological indicators and the functional ones are strongly correlated. That it means, on the one hand, that both selected morphological and functional indicators are valid in order to explain the polycentricity phenomena and on the other that it confirms that the polycentrism notion are bi-dimensional (morphological and functional), so neither only by taking into account the morphological indicators nor the functional ones the notion of polycentricity is full explained. In that sense, in this section, apart from analyzing the correlation matrixes, it is also analyzed by plotting the regressions between morphological and functional polycentricity and find the spatial units (urban sub-systems, protosystems and municipalities) that are significantly in terms of both morphological and functional polycentricity or with on e of t hese di mensions. In doing so, i t i s de fined by ana lyzing the sample of t hese v ariables a nd by obtaining the mean value, so the spatial units that are above of it, would be significant.
Urban sub-system territorial scale In 1991, with r eference t o t he m orphological di mension, % P opulation a nd t he P opulation ( Lg10) or R ank Population ( Lg10) ar e consistently c orrelated: since the higher t he % P opulation i n the m ain c ity ( CBD) f or example, the lower the polycentricity level, so, the higher the Population (Lg10) or the lower the Rank Population. (Lg10) in this main city –which are a measures of monocentricity- the lower the level of polycentricity (if we had considered the s ub-centres, i nstead of the main c ity-CBD, i t w ould have been the contrary, hi gher t he % Population in sub-centres the higher the polycentricity level). Then r eferring t o t he f unctional di mension, i t i s ob served t he s ame pr evious r elations, f or ex ample I F- Dominance Index (DI) is highly correlated with LTL Entropy (EI): so the higher the IF-Dominance Index (DI) in sub-centres, t he h igher the polycentrism l evel, s o t he higher t he LT L E ntropy ( EI) i n s ub-centres ( Entropy Information) –which are a measure of polycentrism- the higher of polycentricity level. In the case of taking in to account as example the main city of Barcelona (CBD) the previous explanation would be conversely. Regarding t he r elationships bet ween f unctional and m orphological m easures, (figure 31) shows that fo r example Population Entropy Index or Population (Lg10) is correlated with both functional indicators, while Rank
26 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Population (Lg10) we negatively correlated with these functional selected indicators. So, a higher level of morphological polycentrism is associated with a higher the level of functional polycentrism when it is analyzing the sub-centres and conversely when it is considered the main city. In ad dition, w hen t he morphological po lycentricity i s m easured by P opulation ( Lg10) and t he f unctional dimension by LTL Entropy (EI), results from the two approaches are consistent (r2=0,951). The same relationship holds for taking into account the Population Entropy (EI) as morphological polycentricity and IF-Dominance Index (DI), but a lower extent (r2=0,825). These results suggest, as it was expected that even if polycentricity is tackled from the two different perspectives, results are consistent.
Figure 31: Correlation coefficients (Pearson) among indicators of polycentrism in 1991
Morphological Polycentrism Indicators Functional Polycentrism Indicators % Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI) % Population 1 0,795 -0,742 0,762 1,000 0,967 0,778 Population (LG 10) 0,795 1 -0,983 0,973 0,786 0,823 0,951 Rank Population (LG10) -0,742 -0,983 1 -0,986 -0,732 -0,779 -0,963 Population Entropy (EI) 0,762 0,973 -0,986 1 0,753 0,825 0,989 % LTL (localised workers) 1,000 0,786 -0,732 0,753 1 0,968 0,772 IF - Dominance Index (DI) 0,967 0,823 -0,779 0,825 0,968 1 0,858 LTL Entropy (EI) 0,778 0,951 -0,963 0,989 0,772 0,858 1 Source: Own Elaboration
A deeper look at the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 1991 at urban sub-system scale (figures 32-33); by identifying four gr oups ( the threshold a pplied t o discriminate t he h igh or l ow v alue of pol ycentricity i s g iven by t he m ean values of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by: 1) High degree of both morphological and functional polycentrism: 6 urban sub-systems (Population -Lg10- vs. LTL Entropy) and 4 sub-systems (Population Entropy Index vs. IF Dominance Index). 2) H igh m orphological and low f unctional po lycentricity: 1 ur ban sub-system ( Population -Lg10- vs. LT L Entropy) and 3 sub-systems (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 0 urban sub-subsystems in both cases. That it means probably that polycentricity notion could not understand without its morphological dimension. 4) Low degree of both morphological and functional polycentricity: 9 urban sub-systems in both cases.
Morphological vs. Functional Polycentrism - Subsystems, 91 Morphological vs. Functional Polycentrism - Subsystems, 91
15 7 R2=0,680 High Morph. - High Funct. R2=0,904 High Morph. - High Funct. Barcelona - CBD Barcelona - CBD 6 14
5 13 Sabadell 4 Terrassa Functional Polycentrism (axis Y) 12
Morphological Polycentrism (axis Y) Rubí 3
11 Low Morph. - High Funct. Sabadell 2 Rubí 10 Terrassa IF DOM (DI)= - 0,53+ 17,79 POP (EI) 1 POP (LG 10)= 9,57 + 18,72 LTL (EI) High Morph. - Low Funct.
Population (LG 10)Population 9 0
IF Dominance Index (DI) 0 0,05 0,1 0,15 0,2 0,25 0,3 0 0,05 0,1 0,15 0,2 0,25 0,3 Morphological Polycentrism (axis X) Functional Polycentrism (axis X) LTL Entropy Index (Shannon) POP Entropy Index (Shannon)
Figure 32: Population (Lg10) vs. LTL Entropy Index. Figure 33: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
27 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
In 1996, with reference to the morphological dimension and then referring to the functional dimension in terms of correlations, nothing it changed. The only point that it is worth mentioning is although, the correlation matrix does not change in terms that both functional and morphological selected indicators are still correlated, what is true is that this relation is lower certain extent (the R2 has decreased) in some cases and higher extent in others. So, for example, regarding the relationships between functional and morphological measures, (figure 34) shows that when the morphological polycentricity is measured by Population (Lg10) and the functional dimension by LTL Entropy (EI), results from the two approaches are consistent but less than in 1991 (r2=0,945 and r2=0,951 in 1 991). T he same r elationship holds f or t aking i nto account t he P opulation E ntropy (EI) as m orphological polycentricity and IF-Dominance Index (DI), but a lower extent and more consistent than in 1991 (r2= 0,879 and r2=0,825 in 1991). These results suggest, as it was expected that even if polycentricity is tackled from the two different perspectives, results are still consistent due to the changes are not significant.
Figure 34: Correlation coefficients (Pearson) among indicators of polycentrism in 1996
Morphological Polycentrism Indicators Functional Polycentrism Indicators % Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI) % Population 1 0,714 -0,704 0,774 1,000 0,930 0,781 Population (LG 10) 0,714 1 -0,970 0,945 0,715 0,813 0,945 Rank Population (LG10) -0,704 -0,970 1 -0,978 -0,703 -0,810 -0,967 Population Entropy (EI) 0,774 0,945 -0,978 1 0,774 0,879 0,992 % LTL (localised workers) 1,000 0,715 -0,703 0,774 1 0,936 0,784 IF - Dominance Index (DI) 0,930 0,813 -0,810 0,879 0,936 1 0,910 LTL Entropy (EI) 0,781 0,945 -0,967 0,992 0,784 0,910 1 Source: Own Elaboration
Analyzing the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 1996 at urban sub-system scale (figures 35-36); by identifying four groups (the threshold ap plied t o di scriminate t he hi gh or l ow v alue of pol ycentricity i s g iven b y t he m ean v alues of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by: 1) High degree of both morphological and functional polycentrism: 8 urban sub-systems (Population -Lg10- vs. LTL Entropy) and 6 sub-systems (Population Entropy Index vs. IF Dominance Index). 2) H igh m orphological and low f unctional po lycentricity: 4 ur ban sub-system ( Population -Lg10- vs. LT L Entropy) and 2 sub-systems (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 0 urban sub-subsystems (Population -Lg10- vs. LTL Entropy) and 1 urban sub-system in (figure 36). 4) Low degree of both morphological and functional polycentricity: 10 urban sub-system (Population -Lg10- vs. LTL Entropy) and 14 sub-systems (Population Entropy Index vs. IF Dominance Index).
Morphological vs. Functional Polycentrism - Subsystems, 96 Morphological vs. Functional Polycentrism - Subsystems, 96 16 9 2 High Morph. - High Funct. 2 R =0,893 R =0,773 High Morph. - High Funct. 15 Barcelona - CBD 8 Barcelona - CBD 7 14
6 13 Sabadell Terrassa 5 12 Functional Polycentrism (axis Y) Mollet del Vallès Rubí Morphological Polycentrism (axis Y) 4 Granollers 11 Sabadell Martorell 3
10 Low Morph. - High Funct. 2 Mollet del Vallès Rubí Terrassa Martorell 9 IF DOM (DI)= - 0,48+ 21,78 POP (EI) 1 POP (LG 10)= 9,31 + 19,83 LTL (EI) Granollers High Morph. - Low Funct.
Population (LG 10)Population 8 0
0 0,05 0,1 0,15 0,2 0,25 0,3 IF Dominance Index (DI) 0 0,05 0,1 0,15 0,2 0,25 0,3 Functional Polycentrism (axis X) LTL Entropy Index (Shannon) Morphological Polycentrism (axis X) POP Entropy Index (Shannon) Figure 35: Population (Lg10) vs. LTL Entropy Index. Figure 36: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
28 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
The previous analyzed dynamics in terms of correlations between functional and morphological indicators has become stronger in 2001. So, the correlations between selected indicators in 2001 are lower extent (the R2 has more decreased) in most cases. For example, regarding the relationships between functional and morphological measures, (figure 37) shows that when the morphological polycentricity is measured by Population (Lg10) and the functional dimension by LTL Entropy (EI), results from the two approaches are consistent but less than in 1996 (r2=0,936, r2=0,945 in 1996 and r2=0,951 i n 1 991). T he s ame r elationship ho lds f or t aking i nto a ccount t he P opulation E ntropy ( EI) a s morphological polycentricity and IF-Dominance Index (DI), but a quite lower than in 1996 (r2= 0,873, r2= 0,879 in 1996 and r2=0,825 in 1991). These results suggest, as it was expected that even if polycentricity is tackled from the two different perspectives, results are still in 2001 consistent due to the changes are not significant.
Figure 37: Correlation coefficients (Pearson) among indicators of polycentrism in 2001
Morphological Polycentrism Indicators Functional Polycentrism Indicators % Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI) % Population 1 0,705 -0,718 0,839 0,999 0,973 0,838 Population (LG 10) 0,705 1 -0,949 0,942 0,696 0,757 0,936 Rank Population (LG10) -0,718 -0,949 1 -0,977 -0,705 -0,766 -0,960 Population Entropy (EI) 0,839 0,942 -0,977 1 0,829 0,873 0,989 % LTL (localised workers) 0,999 0,696 -0,705 0,829 1 0,977 0,834 IF - Dominance Index (DI) 0,973 0,757 -0,766 0,873 0,977 1 0,896 LTL Entropy (EI) 0,838 0,936 -0,960 0,989 0,834 0,896 1 Source: Own Elaboration
Studying the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 2001 at urban sub-system scale (figures 38-39); by identifying four groups (the threshold ap plied t o di scriminate t he hi gh or l ow v alue of pol ycentricity i s g iven b y t he m ean v alues of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by: 1) High degree of both morphological and functional polycentrism: 10 urban sub-systems (Population -Lg10- vs. LTL Entropy) and 9 sub-systems (Population Entropy Index vs. IF Dominance Index). 2) H igh m orphological and low f unctional po lycentricity: 1 urban s ub-system ( Population -Lg10- vs. LT L Entropy) and 2 sub-systems (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 0 urban sub-subsystems in both cases. That it means probably that polycentricity notion could not understand without its morphological dimension. 4) Low degree of both morphological and functional polycentricity: 13 urban sub-systems in both cases.
Morphological vs. Functional Polycentrism - Subsystems, 01 Morphological vs. Functional Polycentrism - Subsystems, 01
16 10 2 R =0,877 High Morph. - High Funct. R2=0,762 High Morph. - High Funct. 9 Barcelona - CBD 15
Barcelona - CBD 8 14 7
13 Terrassa 6 Sant Boi de Llobregat Sabadell
12 Rubí Granollers Functional Polycentrism (axis Y) 5 Mollet del Vallès Morphological Polycentrism (axis Y) Martorell 4 11
Low Morph. - High Funct. 3 10 Mollet del Sabadell 2 Vallès Rubí Terrassa 9 Martorell Sant Boi de IF DOM (DI)= - 0,84+ 22,84 POP (EI) 1 Granollers Llobregat POP (LG 10)= 9,73 + 17,08 LTL (EI) High Morph. - Low Funct.
Population (LG 10)Population 8 0
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 IF Dominance Index (DI) 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 Functional Polycentrism (axis X) LTL Entropy Index (Shannon) Morphological Polycentrism (axis X) POP Entropy Index (Shannon) Figure 38: Population (Lg10) vs. LTL Entropy Index. Figure 39: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
29 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Protosystem territorial scale In 1991, w ith r eference t o t he m orphological di mension, % P opulation a nd t he P opulation ( Lg10) or R ank Population (Lg10) are consistently correlated but less in comparison when the spatial unit was the sub-systems: since the higher the % Population in the main city (CBD) for example, the lower the polycentricity level, so, the higher the Population (Lg10) or the lower the Rank Population. (Lg10) in this main city–which are a measures of monocentricity- the lower the level of polycentricity (if we had considered the sub-centres, instead of the main city- CBD, it would have been the contrary, higher the % Population in sub-centres the higher the polycentricity level). Then r eferring t o t he f unctional di mension, i t i s ob served t he s ame pr evious r elations, f or ex ample I F- Dominance Index (DI) is highly correlated with LTL Entropy (EI): so the higher the IF-Dominance Index (DI) in sub-centres, t he h igher the polycentrism l evel, s o t he higher t he LT L E ntropy ( EI) i n s ub-centres ( Entropy Information) –which are a measure of polycentrism- the higher of polycentricity level. In the case of taking into account as example the main city of Barcelona (CBD) the previous explanation would be conversely. Regarding t he r elationships bet ween f unctional and m orphological m easures, (figure 40 ) shows that fo r example Population Entropy Index or Population (Lg10) is correlated with both functional indicators, while Rank Population (Lg10) we negatively correlated with these functional selected indicators. So, a higher level of morphological polycentrism is associated with a higher the level of functional polycentrism when it is analyzing the sub-centres and conversely when it is considered the main city. In ad dition, w hen the m orphological polycentricity i s measured by P opulation ( Lg10) and t he f unctional dimension by LTL Entropy (EI), results from the two approaches are consistent (r2=0,889, and r2=0,951 when the sub-systems were analyzed). The same relationship holds for taking into account the Population Entropy (EI) as morphological polycentricity and I F-Dominance Index (DI), but a l ower extent (r2=0,865). These results suggest, as it was expected that even if polycentricity is tackled from the two different perspectives, results are consistent.
Figure 40: Correlation coefficients (Pearson) among indicators of polycentrism in 1991
Morphological Polycentrism Indicators Functional Polycentrism Indicators
% Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI) % Population 1 0,632 -0,671 0,821 1,000 0,982 0,816 Population (LG 10) 0,632 1 -0,928 0,905 0,621 0,691 0,889 Rank Population (LG10) -0,671 -0,928 1 -0,969 -0,659 -0,727 -0,952 Population Entropy (EI) 0,821 0,905 -0,969 1 0,812 0,865 0,989 % LTL (localised workers) 1,000 0,621 -0,659 0,812 1 0,982 0,812 IF - Dominance Index (DI) 0,982 0,691 -0,727 0,865 0,982 1 0,871 LTL Entropy (EI) 0,816 0,889 -0,952 0,989 0,812 0,871 1 Source: Own Elaboration
Morphological vs. Functional Polycentrism - Protosystems, 91 Morphological vs. Functional Polycentrism - Protosystems, 91
17 12 2 2 R =0,790 High Morph. - High Funct. R =0,749 High Morph. - High Funct. Barcelona - CBD 16
10 15
14 Barcelona - CBD 8
13
Cornellà Sabadell 12 Functional Polycentrism (axis Y) 6 Terrassa Morphological Polycentrism (axis Y) 11 Rubí 4 10 Low Morph. - High Funct. Sabadell
9 2 IF DOM (DI)= - 0,82+ 28,72 POP (EI) 8 POP (LG 10)= 9,22 + 21,08 LTL (EI) High Morph. - Low Funct. 0
Population (LG 10)Population 7
IF Dominance Index (DI) 0 0,05 0,1 0,15 0,2 0,25 0,3 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35
Functional Polycentrism (axis X) LTL Entropy Index (Shannon) Morphological Polycentrism (axis X) POP Entropy Index (Shannon)
Figure 41: Population (Lg10) vs. LTL Entropy Index. Figure 42: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
30 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
A deeper look at the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 1991 at protosystem scale (figures 41-42); by identifying four groups (the threshold applied to discriminate the high or low value of polycentricity is given by the mean values of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by: 1) High degree of both morphological and functional polycentrism: 9 protosystems (Population -Lg10- vs. LTL Entropy) and 4 protosystems (Population Entropy Index vs. IF Dominance Index). 2) High morphological and low functional polycentricity: 4 protosystems (Population -Lg10- vs. LTL Entropy) and 5 protosystems (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 0 protosystems in both cases. That it means probably that polycentricity notion could not understand without its morphological dimension. 4) Low degree of both morphological and functional polycentricity: 16 protosystems (Population -Lg10- vs. LTL Entropy) and 20 protosystems (Population Entropy Index vs. IF Dominance Index).
In 1996, with reference to the morphological dimension and then referring to the functional dimension in terms of correlations, nothing changes. The only point that it is worth mentioning is although the correlation matrix does not change in terms that both functional and morphological selected indicators are still correlated, what is true is that this relation is lower certain extent (the R2 has decreased) in some cases and higher extent in others. So, for example, regarding the relationships between functional and morphological measures, (figure 43) shows that when the morphological polycentricity is measured by Population (Lg10) and the functional dimension by LTL Entropy (EI), results from the two approaches are consistent but less than in 1991 (r2=0,831 and r2=0,889 in 1 991). T he same r elationship holds f or t aking i nto account t he P opulation E ntropy (EI) as m orphological polycentricity and IF-Dominance Index (DI), but a lower extent and more consistent than in 1991 (r2= 0,875 and r2=0,865 in 1991). These results suggest, as it was expected that even if polycentricity is tackled from the two different perspectives, results are still consistent due to the changes are not significant.
Figure 43: Correlation coefficients (Pearson) among indicators of polycentrism in 1996
Morphological Polycentrism Indicators Functional Polycentrism Indicators
% Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI) % Population 1 0,550 -0,655 0,842 0,999 0,979 0,838 Population (LG 10) 0,550 1 -0,885 0,840 0,542 0,610 0,831 Rank Population (LG10) -0,655 -0,885 1 -0,956 -0,645 -0,710 -0,940 Population Entropy (EI) 0,842 0,840 -0,956 1 0,835 0,875 0,989 % LTL (localised workers) 0,999 0,542 -0,645 0,835 1 0,981 0,837 IF - Dominance Index (DI) 0,979 0,610 -0,710 0,875 0,981 1 0,888 LTL Entropy (EI) 0,838 0,831 -0,940 0,989 0,837 0,888 1 Source: Own Elaboration
Morphological vs. Functional Polycentrism - Protosystems, 96 Morphological vs. Functional Polycentrism - Protosystems, 96
18 16 R2=0,690 High Morph. - High Funct. R2=0,766 High Morph. - High Funct. 14 Barcelona - CBD 16
12 14 Barcelona - CBD
Cornellà 10 Granollers Rubí 12 Sabadell Terrassa 8
Cerdanyola del Functional Polycentrism (axis Y) Martorell Vallès Morphological Polycentrism (axis Y) 10 Low Morph. - High Funct. 6
8 4 Sabadell Cerdanyola del Vallès 6 2 Martorell Rubí Granollers Terrassa IF DOM (DI)= - 0,82+ 32,32 POP (EI) POP (LG 10)= 9,01 + 22,12 LTL (EI) High Morph. - Low Funct.
Population (LG 10)Population 4 0
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 IF Dominance Index (DI) 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 Functional Polycentrism (axis X) LTL Entropy Index (Shannon) Morphological Polycentrism (axis X) POP Entropy Index (Shannon) Figure 44: Population (Lg10) vs. LTL Entropy Index. Figure 45: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
31 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Analyzing the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 1996 at protosystem scale (figures 44-45); by identifying four groups (the threshold applied to discriminate the high or low value of polycentricity is given by the mean values of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by: 1) High degree of both morphological and functional polycentrism: 14 protosystems (Population -Lg10- vs. LTL Entropy) and 9 protosystems (Population Entropy Index vs. IF Dominance Index). 2) High morphological and low functional polycentricity: 0 protosystems (Population -Lg10- vs. LTL Entropy) and 4 protosystems (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 0 protosystems in both cases. That it means probably that polycentricity notion could not understand without its morphological dimension. 4) Low degree of both morphological and functional polycentricity: 24 protosystems (Population -Lg10- vs. LTL Entropy) and 23 protosystems (Population Entropy Index vs. IF Dominance Index).
The previous analyzed dynamics in terms of correlations between functional and morphological indicators has become less strong in 2001. So, the correlations between selected indicators in 2001 are higher extent (the R2 has more increased) in most cases. For example, regarding the relationships between functional and morphological measures, (figure 46) shows that when the morphological polycentricity is measured by Population (Lg10) and the functional dimension by LTL Entropy (EI), results from the two approaches are more consistent than in 1996 (r2=0,863, r2=0,831 in 1996 and r2=0,889 in 1 991). The s ame r elationship ho lds f or t aking i nto a ccount t he P opulation E ntropy ( EI) a s morphological polycentricity and IF-Dominance Index (DI), but a quite higher than in 1996 (r2= 0,876, r2= 0,875 in 1996 and r2=0,865 in 1991). These results suggest, as it was expected that even if polycentricity is tackled from the two different perspectives, results are still in 2001 consistent due to the changes are not significant.
Figure 46: Correlation coefficients (Pearson) among indicators of polycentrism in 2001
Morphological Polycentrism Indicators Functional Polycentrism Indicators % Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI) % Population 1 0,594 -0,650 0,861 0,999 0,979 0,859 Population (LG 10) 0,594 1 -0,924 0,867 0,582 0,640 0,863 Rank Population (LG10) -0,650 -0,924 1 -0,945 -0,633 -0,688 -0,928 Population Entropy (EI) 0,861 0,867 -0,945 1 0,849 0,876 0,988 % LTL (localised workers) 0,999 0,582 -0,633 0,849 1 0,983 0,854 IF - Dominance Index (DI) 0,979 0,640 -0,688 0,876 0,983 1 0,894 LTL Entropy (EI) 0,859 0,863 -0,928 0,988 0,854 0,894 1
Source: Own Elaboration
Morphological vs. Functional Polycentrism - Protosystems, 01 Morphological vs. Functional Polycentrism - Protosystems, 01
18 18 R2=0,744 High Morph. - High Funct. R2=0,768 High Morph. - High Funct. 16
16 Barcelona - CBD 14
14 Barcelona - CBD 12
Sant Boi de Rubí 10 Cornellà Sabadell 12 LLobregat Terrassa Functional Polycentrism (axis Y) Granollers 8 Morphological Polycentrism (axis Y) Martorell 10 Cerdanyola del Low Morph. - High Funct. 6 Vallès 4 Martorell Cornellà 8 Cerdanyola Sabadell 2 Granollers Rubí Terrassa IF DOM (DI)= - 0,85+ 34,28 POP (EI)
POP (LG 10)= 9,31 + 20,12 LTL (EI) High Morph. - Low Funct. 6 0 Population (LG 10)Population
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 IF Dominance Index (DI) 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4
Functional Polycentrism (axis X) LTL Entropy Index (Shannon) Morphological Polycentrism (axis X) POP Entropy Index (Shannon)
Figure 47: Population (Lg10) vs. LTL Entropy Index. Figure 48: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
32 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Studying the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 1996 at protosystem scale (figures 47-49); by identifying four groups (the threshold applied to discriminate the high or low value of polycentricity is given by the mean values of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by: 1) High degree of both morphological and functional polycentrism: 13 protosystems (Population -Lg10- vs. LTL Entropy) and 10 protosystems (Population Entropy Index vs. IF Dominance Index). 2) High morphological and low functional polycentricity: 4 protosystems (Population -Lg10- vs. LTL Entropy) and 3 protosystems (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 0 protosystems in both cases. That it means probably that polycentricity notion could not understand without its morphological dimension. 4) Low degree of both morphological and functional polycentricity: 27 protosystems (Population -Lg10- vs. LTL Entropy) and 31 protosystems (Population Entropy Index vs. IF Dominance Index).
Municipality territorial scale In 1991, w ith r eference t o t he m orphological di mension, % P opulation a nd t he Population ( Lg10) or R ank Population (Lg10) are consistently correlated but less in comparison when the spatial unit was the protosystems and the urban sub-systems: since the higher the % Population in the main city (CBD) for example, the lower the polycentricity level, so, the higher the Population (Lg10) or the lower the Rank Population. (Lg10) in this main city–which are a measures of monocentricity- the lower the level of polycentricity (if we had considered the sub- centres, instead of the main city-CBD, it would have been the contrary, higher the % Population in sub-centres the higher the polycentricity level). Then r eferring t o t he f unctional di mension, i t i s ob served t he s ame pr evious r elations, f or ex ample I F- Dominance Index (DI) is highly correlated with LTL Entropy (EI): so the higher the IF-Dominance Index (DI) in sub-centres, t he h igher the polycentrism l evel, s o t he higher t he LT L E ntropy ( EI) i n s ub-centres ( Entropy Information) –which are a measure of polycentrism- the higher of polycentricity level. In the case of taking into account as example the main city of Barcelona (CBD) the previous explanation would be conversely. Regarding t he r elationships bet ween f unctional and m orphological m easures, (figure 49 ) shows that fo r example Population Entropy Index or Population (Lg10) is correlated with both functional indicators, while Rank Population (Lg10) we negatively correlated with these functional selected indicators. So, a higher level of morphological polycentrism is associated with a higher the level of functional polycentrism when it is analyzing the sub-centres and conversely when it is considered the main city. In ad dition, w hen t he morphological p olycentricity i s m easured by P opulation ( Lg10) and t he f unctional dimension by LTL Entropy (EI), results from the two approaches are consistent (r2=0,753, r2=0,889 in protosystems and r2=0,951 when the sub-systems were analyzed). The same relationship holds for taking into account t he P opulation Entropy ( EI) as m orphological pol ycentricity and I F-Dominance I ndex ( DI), but a l ower extent (r2=0,865). These results suggest, as it was expected that even if polycentricity is tackled from the two different perspectives, results are consistent.
Figure 49: Correlation coefficients (Pearson) among indicators of polycentrism in 2001
Morphological Polycentrism Indicators Functional Polycentrism Indicators % Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI) % Population 1 0,501 -0,599 0,868 0,992 0,991 0,895 Population (LG 10) 0,501 1 -0,936 0,774 0,439 0,468 0,753 Rank Population (LG10) -0,599 -0,936 1 -0,896 -0,522 -0,550 -0,860 Population Entropy (EI) 0,868 0,774 -0,896 1 0,808 0,820 0,980 % LTL (localised workers) 0,992 0,439 -0,522 0,808 1 0,995 0,853 IF - Dominance Index (DI) 0,991 0,468 -0,550 0,820 0,995 1 0,865 LTL Entropy (EI) 0,895 0,753 -0,860 0,980 0,853 0,865 1 Source: Own Elaboration
A deeper look at the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 1991 at municipality scale (figures 50-51); by identifying four groups (the threshold applied to discriminate the high or low value of polycentricity is given by the mean values of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by:
33 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
1) H igh de gree o f bot h morphological an d f unctional polycentrism: 30 municipalities (Population -Lg10- vs. LTL Entropy) and 19 municipalities (Population Entropy Index vs. IF Dominance Index). 2) High morphological and low functional polycentricity: 17 municipalities (Population -Lg10- vs. LTL Entropy) and 7 municipalities (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 0 municipalities (Population -Lg10- vs. LTL Entropy) and 4 municipalities (Population E ntropy I ndex v s. I F Dominance I ndex). That i t m eans pr obably t hat polycentricity notion could not understand without its morphological dimension. 4) Low degree of both morphological and functional polycentricity: 53 municipalities (Population -Lg10- vs. LTL Entropy) and 70 municipalities (Population Entropy Index vs. IF Dominance Index).
Morphological vs. Functional Polycentrism - Municipalities, 91 Morphological vs. Functional Polycentrism - Municipalities, 91
20 45
R2=0,567 High Morph. - High Funct. 42,5 R2=0,672 High Morph. - High Funct. 40 18 Barcelona - CBD 37,5
35 16 32,5 30 14 Hospitalet de Barcelona - CBD 27,5 Llobregat 25 Granollers Terrassa 12 22,5 Sabadell Functional Polycentrism (axis Y) 20
Morphological Polycentrism (axis Y) Badalona 17,5 10 15 Low Morph. - High Funct. 12,5 8 10 7,5 L'Hospitalet de Llobregat 6 5 Sabadell Badalona IF DOM (DI)= - 0,93+ 68,52 POP (EI) POP (LG 10)= 8,31 + 28,56 LTL (EI) 2,5 Terrassa Granollers 4 0 Population (LG 10)Population
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 IF Dominance Index (DI) 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 Functional Polycentrism (axis X) LTL Entropy Index (Shannon) Morphological Polycentrism (axis X) POP Entropy Index (Shannon)
Figure 50: Population (Lg10) vs. LTL Entropy Index. Figure 51: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
In 1996, with reference to the morphological dimension and then referring to the functional dimension in terms of correlations, nothing changes. The only point that it is worth mentioning is although, the correlation matrix does not change in terms that both functional and morphological selected indicators are still correlated, what is true is that this relation is lower certain extent (the R2 has decreased) in some cases and higher extent in others. So, for example, regarding the relationships between functional and morphological measures, (figure 52 ) shows that when the morphological polycentricity is measured by Population (Lg10) and the functional dimension by LTL Entropy (EI), results from the two approaches are consistent but less than in 1991 (r2=0,702 and r2=0,753 in 1 991). T he same r elationship holds f or t aking i nto account t he P opulation E ntropy (EI) as m orphological polycentricity and IF-Dominance Index (DI), but a lower extent, and more consistent than in 1991 (r2= 0,843 and r2=0,820 in 1991). These results suggest, as it was expected that even if polycentricity is tackled from the two different perspectives, results are still consistent due to the changes are not significant.
Figure 52: Correlation coefficients (Pearson) among indicators of polycentrism in 1996
Morphological Polycentrism Indicators Functional Polycentrism Indicators % Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI) % Population 1 0,447 -0,561 0,880 0,992 0,989 0,899 Population (LG 10) 0,447 1 -0,934 0,718 0,395 0,434 0,702 Rank Population (LG10) -0,561 -0,934 1 -0,859 -0,492 -0,532 -0,825 Population Entropy (EI) 0,880 0,718 -0,859 1 0,825 0,843 0,977 % LTL (localised workers) 0,992 0,395 -0,492 0,825 1 0,994 0,865 IF - Dominance Index (DI) 0,989 0,434 -0,532 0,843 0,994 1 0,886 LTL Entropy (EI) 0,899 0,702 -0,825 0,977 0,865 0,886 1 Source: Own Elaboration
34 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Analyzing the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 1996 at municipality scale (figures 53-54); by identifying four groups (the threshold applied to discriminate the high or low value of polycentricity is given by the mean values of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by: 1) H igh de gree o f bot h morphological an d f unctional polycentrism: 42 municipalities (Population -Lg10- vs. LTL Entropy) and 29 municipalities (Population Entropy Index vs. IF Dominance Index). 2) High morphological and low functional polycentricity: 37 municipalities (Population -Lg10- vs. LTL Entropy) and 12 municipalities (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 2 municipalities (Population -Lg10- vs. LTL Entropy) and 8 municipalities (Population Entropy Index vs. IF Dominance Index). 4) Low degree of both morphological and functional polycentricity: 83 municipalities (Population -Lg10- vs. LTL Entropy) and 115 municipalities (Population Entropy Index vs. IF Dominance Index).
Morphological vs. Functional Polycentrism - Municipalities, 96 Morphological vs. Functional Polycentrism - Municipalities, 96 22 60 2 2 R =0,493 High Morph. - High Funct. 55 R =0,710 High Morph. - High Funct. 20 Barcelona - CBD 50 18 45 16 40 Hospitalet de 14 35 Llobregat Barcelona - CBD Terrassa 12 Sabadell Functional Polycentrism (axis Y) 30 Badalona
Morphological Polycentrism (axis Y) 25 10 20 8 Low Morph. - High Funct. 15 6 10 L'Hospitalet de Llobregat Sabadell 4 POP (LG 10)= 7,89 + 32,84 LTL (EI) 5 Terrassa Badalona IF DOM (DI)= - 0,90+ 97,12 POP (EI)
2 0
Population (LG 10)Population 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 IF Dominance Index (DI) Functional Polycentrism (axis X) LTL Entropy Index (Shannon) Morphological Polycentrism (axis X) POP Entropy Index (Shannon) Figure 53: Population (Lg10) vs. LTL Entropy Index. Figure 54: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
The previous analyzed dynamics in terms of correlations between functional and morphological indicators has become less strong in 2001. So, the correlations between selected indicators in 2001 are lower extent (the R2 has more decreased) in most cases. For example, regarding the relationships between functional and morphological measures, (figure 55) shows that when the morphological polycentricity is measured by Population (Lg10) and the functional dimension by LTL Entropy (EI), results from the two approaches are less consistent than in 1996 (r2=0,697, r2=0,702 in 1996 and r2=0,753 in 1 991). The s ame r elationship ho lds f or t aking i nto a ccount t he P opulation E ntropy ( EI) a s morphological polycentricity and IF-Dominance Index (DI), but the correlation here are more consistent, a q uite higher t han i n 19 96 ( r2= 0, 855, r 2= 0, 843 in 1 996 and r 2=0,820 in 19 91). T hese r esults suggest, a s i t w as expected t hat ev en i f po lycentricity i s t ackled f rom t he t wo di fferent per spectives, r esults ar e s till i n 200 1 consistent due to the changes are not significant.
Figure 55: Correlation coefficients (Pearson) among indicators of polycentrism in 2001 Morphological Polycentrism Indicators Functional Polycentrism Indicators
% Pop. Pop (LG 10) Rank Pop. (LG10) Pop. Entropy (EI) % LTL Dominance (DI) LTL Entropy (EI)
% Population 1 0,446 -0,553 0,889 0,993 0,987 0,905
Population (LG 10) 0,446 1 -0,935 0,716 0,395 0,437 0,697
Rank Population (LG10) -0,553 -0,935 1 -0,850 -0,486 -0,530 -0,815
Population Entropy (EI) 0,889 0,716 -0,850 1 0,838 0,855 0,978
% LTL (localised workers) 0,993 0,395 -0,486 0,838 1 0,993 0,875
IF - Dominance Index (DI) 0,987 0,437 -0,530 0,855 0,993 1 0,898
LTL Entropy (EI) 0,905 0,697 -0,815 0,978 0,875 0,898 1
Source: Own Elaboration
35 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Studying the relationship between functional and morphological polycentric allows us to propose taxonomy of the Barcelona Metropolitan Region for 2001 at municipality scale (figures 56-57); by identifying four groups (the threshold applied to discriminate the high or low value of polycentricity is given by the mean values of Population (Lg10), Population Entropy, LTL Entropy and Dominance Index), characterized by: 1) H igh de gree o f bot h morphological an d f unctional polycentrism: 49 municipalities (Population -Lg10- vs. LTL Entropy) and 31 municipalities (Population Entropy Index vs. IF Dominance Index). 2) High morphological and low functional polycentricity: 44 municipalities (Population -Lg10- vs. LTL Entropy) and 15 municipalities in (Population Entropy Index vs. IF Dominance Index). 3) Low morphological and high functional polycentrism: 1 municipality (Population -Lg10- vs. LTL Entropy) and 7 municipalities (Population Entropy Index vs. IF Dominance Index). 4) Low degree of both morphological and functional polycentricity: 90 municipalities (Population -Lg10- vs. LTL Entropy) and 131 municipalities (Population Entropy Index vs. IF Dominance Index).
Morphological vs. Functional Polycentrism - Municipalities, 01 Morphological vs. Functional Polycentrism - Municipalities, 01
21 60 R2=0,485 High Morph. - High Funct. R2=0,730 High Morph. - High Funct. 55 Barcelona - CBD 19 50
17 45
40 15 35 Hospitalet de Barcelona - CBD Llobregat
13 Functional Polycentrism (axis Y) 30 Terrassa
Morphological Polycentrism (axis Y) Sabadell 25 Badalona 11 20 9 15 Low Morph. - High Funct. 10 L'Hospitalet de Llobregat 7 Sabadell POP (LG 10)= 8,05 + 32,46 LTL (EI) 5 Terrassa Badalona IF DOM (DI)= - 0,93+ 103,35 POP (EI)
Population (LG 10)Population 5 0 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 IF Dominance Index (DI) 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 Functional Polycentrism (axis X) LTL Entropy Index (Shannon) Morphological Polycentrism (axis X) POP Entropy Index (Shannon) Figure 56: Population (Lg10) vs. LTL Entropy Index. Figure 54: IF Dominance Index vs. POP Entropy Index Morphological vs. Functional Polycentricity Functional vs. Morphological Polycentricity
Summarising after analysed the correlations between morphological and functional polycentrism it is clear that even i f p olycentricity i s t ackled f rom t he t wo di fferent per spectives t hese t wo per spectives ar e c onsistent correlated and t hey bot h h ighly ex plain t he c oncept of polycentricity. H owever, i t i s w orth m entioning t hat depending on the analysed spatial scale (urban sub-system, protosystem and municipalities), and depending on the year (1991, 1996 and 2001), there are changes in terms of the correlation coefficients, but these changes are slight and they do not represent a conversely correlations over time. Referring of the dynamic analysis (1991-2001) for what spatial units (urban sub-systems, protosystems, and municipalities) are significantly in terms of both morphological and functional polycentricity or with one of these two dimensions (e.g.figure 50-1, 53-4, 56-7) the results lead to the next metropolitan trend: there is an overall urban dynamics of the spatial units (e.g. municipalities) towards a H-H values and L-L values of functional and morphological pol ycentricity d ue mainly to t he ef fects of the m etropolitan l imits gr owth. I n detail, the ur ban process of decentralization t hat it entails t he i ntegration of new l abour a nd r esidential markets w ithin t he metropolitan system because of the growth of its boundaries; implies that these ‘new’ integrated spatial units (urban s ub-systems, p rotosystems, and mu nicipalities) are the most responsible for these urban dynamics towards an increment of the morphological and functional polycentricity. For example, in terms of m unicipalities a nd by an alysing the po lycentricity phen omena by us ing t he I F Dominance Index (DI) as a functional dimension and the Population Entropy Index (EI) as a morphological the H- H values has increased in 1991 from 19 to 31 in 2001, and the L-L values from 70 to 131. That it means that the “new” i ntegrated m unicipalities f rom 19 91 t o 2001 ( from 1 00 municipalities t o 184) within t he B arcelona Metropolitan system are mostly significant both in functional and morphological polycentric because during the same period of time the L-H and the H-L values have not highly changed: in 1991 there were 7 municipalities and 15 in 2001 in terms of L-H and in the case of H-L there were 4 in 1991 and 7 in 2001.
36 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
2.4. AN “INTEGRATED” APPROACH TO MEASURE THE POLYCENTRISM LEVEL (1991-2001) Until now, it has analyzed the functional and the morphological of polycentrism notion separately. However, this paper, tries to unify these two dimensions of polycentricity to a unique one. In doing so, this paper proposes to m easure t he pol ycentricity level at intrametropolitan s cale by us ing: 1) as an i ndicator of t he morphological dimension the % Population in indentified sub-centres and 2) as an indicator of the functional perspective the LTL Entropy I ndex of t he metropolitan s ystem. S o, r epresenting t hese t wo v ariables i n graphs (figures 58 -59) it is possible to measure simultaneously if not only a metropolitan system towards to monocentricity, polycentrism or urban sprawl because it is also represented the share of population in CBD (sphere size) but also, know to which certain extent these urban dynamics is happening (figures 60-61).
Urban sub-system territorial scale
Figure 58: Measurement of the polycentrism level by using % Population in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 40%
2001
30%
1996
54,09% 1991 POP-CBD 20%
65,24% POP-CBD 10%
67,07% POPULATION % SUBCENTRES IN POP-CBD 0% 1,20 1,30 1,40 1,50 1,60 1,70 1,80 1,90 2,00 LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Protosystem territorial scale
Figure 59: Measurement of the polycentrism level by using % Population in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 40%
2001
30% 58,89% 1996 POP-CBD 48,18% POP-CBD 20% 1991 52,55%
POP-CBD
10%
% POPULATION % SUBCENTRES IN
0% 1,50 1,60 1,70 1,80 1,90 2,00 2,10 2,20 2,30 2,40 2,50
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
37 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
So, in this section it is measured the polycentricity level according to the previous approach16 and the results at urban sub-system (figure 58) and protosystem (figure 59) scale suggest a clear urban trend to polycentricity. In the case of urban sub-system scale, in 1991 the share of population in the CBD-Barcelona was 67,09% and in 20 01 i t de creased until 5 4,09%. T hat it m eans t hat t he C BD has l ost part of i ts m onocentricity b ecause simultaneously t he ur ban sub-centres hav e i ncreased t heir share o f po pulation an d t he E ntropy LT L of t he metropolitan system has also increased (from 1,366 in 1991 to 1,899 in 2001). This lost of share population in the centre - CBD, has led a urban dynamics of concentrated decentralization (towards a more polynucleated urban structure) be cause at t he t ime t hat t he popu lation ha s dec entralized t he s patial uni ts w hich ab sorb t his decentralization are the identified urban sub-centres and no the rest of the metropolitan system (in this case it would have mean a urban dynamic towards urban sprawl, so towards a more dispersed metropolitan system): in 1991 the share of population in sub-centres was 16,00% and in 2001, it has increased to 30,14% meanwhile the share of population in the rest of metropolitan system has decreased from 16,91% in 1991 to 15,77% in 2001. Referring to the protosystem scale, the same explained urban dynamics has occurred, but with a qui te more extent: less share of population in the centre-CBD and more share of population in urban sub-centres in 2001, but as it mentioned the differences are slight and it is not change the urban trend to polycentricity from 1991 to 2001.
2.5. SYNTHESISING THE URBAN STRUCTURE DYNAMICS (1991-2001) In this section, it is synthesized the urban structure dynamics at urban sub-system and protosystem scale in order to give a quick view about the main changes that has occurred in terms of metropolitan structure during the analyzed period of time: from 1991 to 2001. In doi ng s o, i n (figures 6 0-61)17 are r epresented t he s elected i ndicators in or der t o measure pol ycentricity (morphological a nd f unctional di mensions) a s w ell as its statistics de scription: mean, median a nd s tandard deviation. In addition, these indicators are analyzed for the next urban spatial levels: Barcelona-CBD, sub-centres and ‘rest of the metropolitan system’ in order to analyze the urban dynamics in more detail. Referring to the urban sub-system scale (figure 60): the LTL Entropy Index (EI) of the metropolitan system has increased: in 1991 it was 1,366 and i n 2001 it was 2001 as well as this urban dynamics has also occurred in terms of Population Entropy Index (EI): 1,381 in 1991 and 1,941 in 2001. The Population Entropy Index (EI) is defined as follows18:
= =1( · [ ( )]) (6) 𝑛𝑛 𝐸𝐸These𝐼𝐼𝑃𝑃𝑃𝑃 𝑃𝑃two dynamics,− ∑𝑖𝑖 the𝑃𝑃 increment𝑃𝑃𝑃𝑃𝑖𝑖 of𝐿𝐿 𝐿𝐿LTL𝑃𝑃 and𝑃𝑃𝑃𝑃 Population𝑖𝑖 Entropy Index from 1991 to 2001 combined with the i ncrement of share P opulation, LT L ( localized w orkers) and IF D ominance I ndex i n i dentified urban s ub- centres as well as the reduction of these shares in CBD (Barcelona, in the case of this study) and i n the rest of the metropolitan system (spatial units that are neither CBD nor sub-centres) leads (as it is previous explained) to a m ore polycentric structure of t he B arcelona M etropolitan S ystem. Another i ndicator i n t erms of metropolitan urban s tructure t hat is an alyzed i s t he R W (resident w orkers) E ntropy I ndex19: its dy namics ov er t ime i s ascending, so in 1991 it was 1,19 and 1,75 in 2001. That it might mean that the urban sub-systems are become more self-containment: they have the capacity to retain proportionally more workers (see figures 2-4).
16 Note that instead of using the % P opulation in sub-centres it is possible to use the % Entropy Population in these urban sub-centres. That it brings to the same conclusions, a clear urban trend to a more polycentric region. In the next (figures 60–61) it is possible to see easily and separately at urban sub-system and protosystem scale the urban trends from 1991 to 2001: the set of selected indicators in Barcelona-CBD are referred to monocentricity, the set ones in sub-centres to polycentricity and finally the set of selected indicators in ‘rest the metropolitan system’ (the spatial units that are neither the CBD nor the sub-centres) are closely related to the urban sprawl. 17 It is worth mentioning that all the selected Entropy Index is defined by Shannon form. There are studies that use the Evenness form of Entropy, such as the studies carried out by (Limtanakool et al., 2007, 2009). However, in this paper the results of using this latter Entropy form are not presented, because 1) after doing a comparative analysis between the results that are given by using Entropy Shannon form and Entropy Evenness form there is no difference in terms of changing the urban dynamics and 2) the Entropy Evenness tends to equalize (normalize) due to the denominator of the expression form has Ln (n), where (n) are the number of elements. 18 In (Roca, Moix & Arellano, 2011b) consider that the Population Entropy Index (EI) is an indicator of metropolitan complexity, how ever i n t his paper t he P opulation E ntropy I ndex ( EI) i s us ed a s an indicator of m easuring polycentricity if it is takes into account the Population Entropy that are in the CBD (in this case Barcelona), in identified sub-centres and the rest of spatial units that it defines the metropolitan system (see figure 60-61). 19 The RW Entropy Index (EI) is used in (Masip, 2011) as a one indicator in order to classify sub-centres into “emerging” and “consolidated”.
38 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 60: Urban structure dynamics at urban sub-system scale 1991-1996-2001
Urban Structure (Barcelona Metropolitan System) 1991 1996 2001
LTL Entropy Index (Metropolitan System) 1,36603 1,54287 1,89996 Mean 0,08538 0,07013 0,07916 Median 0,06050 0,04620 0,05336 Std.Desv. 0,06900 0,07036 0,07199 Population Entropy Index (Metropolitan System) 1,38104 1,50376 1,94132 Mean 0,08632 0,06835 0,08089 Median 0,06390 0,04153 0,05446 Std.Desv. 0,07292 0,07009 0,07352 RW Entropy Index (Metropolitan System) 1,19063 1,33033 1,75126
Mean 0,07441 0,06047 0,07297
Median 0,05113 0,03533 0,05560
Std.Desv. 0,06637 0,06404 0,06794 IF Entropy Index (Metropolitan System) 2,11134 2,24184 2,26948 Mean 0,13196 0,10190 0,09456 Median 0,11287 0,07524 0,05560 Std.Desv. 0,08621 0,09466 0,06794 OF Entropy Index (Metropolitan System) 2,18767 2,30848 2,52427 Mean 0,13673 0,10493 0,10518 Median 0,12697 0,06834 0,06100 Std.Desv. 0,09356 0,09062 0,08725 IF Entropy Index - OF Entropy Index (difference) -0,07634 -0,06664 -0,25480
Dominance Index 16 22 24
Mean 1 1 1 Median 0,53016 0,41943 0,27899 Std.Desv. 1,57345 1,73702 1,92499 BARCELONA (Subsystem - CBD of the Metropolitan System) Dominance Index 6,50697 7,82679 9,48149 % Dominance Index 40,67% 35,58% 39,51% LTL Entropy Information 0,26178 0,28419 0,32644 % LTL Entropy Information 19,16% 18,42% 17,18% LTL in CBD 998.893 949.830 1.030.553 % LTL in CBD 68,08% 64,26% 55,58% Population in CBD 2.695.745 2.740.659 2.450.517 % Population in CBD 67,09% 65,24% 54,09%
Population Entropy Information 0,26778 0,27865 0,33239 % Population Entropy Information 19,39% 18,53% 17,12% SUBCENTRES (within the Metropolitan System) Number of Subcentres 3 6 8 Dominance Index 4,11216 10,12920 11,42782 % Dominance Index 25,70% 46,04% 47,62% LTL Entropy Information 0,43165 0,70875 0,96790 % LTL Entropy Information 31,60% 45,94% 50,94% LTL in subcentres 227.288 342.675 564.715 % LTL in subcentres 15,49% 23,18% 30,46% Population in subcentres 642.745 905.378 1.365.368 % Population in subcentres 16,00% 21,55% 30,14% Population Entropy Information 0,44204 0,66489 0,94968
% Population Entropy Information 32,01% 44,22% 48,92% REST OF THE METROPOLITAN SYSTEM
Dominance Index 5,38087 4,04401 3,09069 % Dominance Index 33,63% 18,38% 12,88% LTL Entropy Information 0,67260 0,54993 0,60562 % LTL Entropy Information 49,24% 35,64% 31,88% LTL beyond nuclei 241.140 185.649 258.814 % LTL beyond nuclei 16,43% 12,56% 13,96% Population beyond nuclei 679.609 554.960 714.369 % Population beyond nuclei 16,91% 13,21% 15,77% Population Entropy Information 0,67122 0,56022 0,65925 % Population Entropy Information 48,60% 37,25% 33,96%
Source: Own Elaboration
39 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
In addi tion, ano ther s ignificant i ndicator in or der t o analyze t he whole of t he metropolitan s ystem i s t he I F Dominance Index; concretely the value of its standard deviation. The IF Dominance Index (DI) as is explained in section 1.2 is an indicator of the ratio of in-commuting flows to an urban sub-system or protosystem respect the total commuting of a gi ven metropolitan system. So, the maximum degree of polycentrism, hypothetically, would happen if this Dominance Index is equal to 1 for every node: it would mean that every urban sub-system or protosystem (or the spatial unit that has been considered) attracts the same intensity of flows. That it affects to the statistics distribution in terms of standard deviation, because a high standard deviation of this index indicates that higher values are associated with one or few nodes attracting flows from the other, while a more even distribution of the index would characterize polycentric metropolitan systems, since the in-commuting flows to each node are similar to each other. So, the indicator can be useful to rank the nodes and to see of the metropolitan system presents strong or less hierarchies: the latter should happen in the polycentric metropolitan systems. However, this should be an alyzed with more attention: it is possible that high values of standard deviation means an i ncrement of the polycentric structure of this metropolitan system if these high values of this indicator are concentrated in nodes that are urban sub-centres. This is the case of our study: in (figure 60) it is observed a clear increment of this index; in 1991 the standard deviation was 1,573 and 1,924 in 2001. Although, this increment of the standard deviation the structure of the metropolitan system has not become more monocentric: f rom 1991 t o 2 001 the I F D ominance I ndex ( DI) i n C BD ( Barcelona) has de creased (from 40,67% to 39,51%) as well as in the ‘rest of the metropolitan system’ (from 33,63% to 12,88%), meanwhile the identified urban sub-centres have become more dominant: in 1991 the sub-centres concentrated the 25,70% and 47,62% i n 2001. T herefore, t his s trengthen pr ocess of s ub-centres f rom 199 1 t o 2001 , i t m ight ex plain t he increment of t he s tandard d eviation v alue, s o what i t is likely t o h appen i s a ur ban dy namics towards a m ore hierarchical (not equipotential) polycentric structure instead of towards monocentricity when the increment of the standard dev iation of I F D ominance I ndex ent ails a n i ncrement of t he sub-centres D ominance I ndex and a reduction of the dominance in CBD and in the rest of the metropolitan system. Then in (figure 60) it is analyzed two more interesting indicators: the IF (in-commuting flows) Entropy Index and the OF (out-commuting flows) Entropy Index. The IF Entropy Index (EI) and the OF Entropy Index (EI) are defined as follows:
= =1( · [ ( )]) (7) 𝑛𝑛 𝐸𝐸𝐼𝐼𝐼𝐼𝐼𝐼−𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 − ∑𝑖𝑖 𝐼𝐼𝐼𝐼𝑖𝑖 𝐿𝐿𝐿𝐿 𝐼𝐼𝐼𝐼𝑖𝑖 = =1( · [ ( )]) (8) 𝑛𝑛 𝑂𝑂𝑂𝑂𝑂𝑂−𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 𝑖𝑖 𝑖𝑖 𝑖𝑖 𝐸𝐸According𝐼𝐼 to (Limtanakool− et∑ al., 2007,𝑂𝑂𝑂𝑂 2009)𝐿𝐿 the𝐿𝐿 Entropy𝑂𝑂𝑂𝑂 Index can be anal yzed at node level. However, in this paper from the Limtanakool’s idea has considered the IF and OF Entropy Index, as a spatial tool in order to find and m easure the relation (also the evolution) between the two main markets within a given metropolitan system: t he r esidential and t he l abour m arket. A s the I F Entropy I ndex c onsiders t he capacity o f a nod e ( IF Entropy I nformation) i n or der to at tract f lows, a hi gher v alue of I F E ntropy I nformation w ithin t he m etropolitan system it means that this node is an important pole in terms of economic activity and on the contrary, as the OF Entropy Index considers the workers that are leaving their residence in order to work in another place, a h igher value of OF Entropy Index it entails that this node would be significant in terms of residence pool. So, the comparison (difference) between these two Entropy Indexes, would allow measuring the separation that it exists between the residential and labour markets. Simultaneously, high values of the Entropy Index related to th e IF Entropy Index would m ean a pol ycentric s tructure i n t erms of j ob m arkets, w hile hi gh v alues of O F Entropy Index may mean a polycentric in residential structure. It is predicable that the OF Entropy Index is higher in c omparison w ith t he I F E ntropy I ndex, bec ause t he r esidential m arket t end t o be m ore di spersed t han t he labour market (more concentrated). Therefore, the higher is the difference between these two indexes the higher is the separation between residential and labour spaces. In our case of study, the IF Entropy Index (EI) either the OF Entropy Index (EI) has increased from 1991 to 2001. In 1991, the IF Entropy Index was 2,111 and the OF Entropy Index was 2,187, meanwhile in 2001 the IF Entropy Index has increased until 2,269 and t he OF Entropy Index to 2,524. So, it is clear that the separation between t he r esidential an d t he l abour m arkets h as al so i ncreased: i n 1991 the di fference was (-0,0763) and (-0,2548) in 2001 but this increment is mostly happened from 1996 to 2001 because the difference between IF and OF Entropy Index in 1996 was (-0,0664). Finally, according the protosystem territorial scale (figure 61), it is worth mentioning that the urban trends from 1991 to 2001 are identical as the explained urban dynamics at urban sub-system scale.
40 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 61: Urban structure dynamics at protosystem scale 1991-1996-2001
Urban Structure (Barcelona Metropolitan System) 1991 1996 2001
LTL Entropy Index (Metropolitan System) 1,74738 2,09325 2,30492
Mean 0,06025 0,05555 0,05238 Median 0,04565 0,03658 0,03294 Std.Desv. 0,06330 0,06268 0,05998 Population Entropy Index (Metropolitan System) 1,84389 2,15074 2,37602 Mean 0,06358 0,05660 0,05400 Median 0,04228 0,03737 0,03418 Std.Desv. 0,06564 0,06352 0,06118 RW Entropy Index (Metropolitan System) 1,52269 1,85729 2,08266 Mean 0,05251 0,04888 0,04733 Median 0,03214 0,02775 0,02791
Std.Desv. 0,05927 0,05897 0,05754 IF Entropy Index (Metropolitan System) 2,37169 2,54290 2,70710 Mean 0,05251 0,06692 0,06153 Median 0,07328 0,04013 0,03211 Std.Desv. 0,07769 0,07330 0,06778 OF Entropy Index (Metropolitan System) 2,66618 2,85859 3,03309 Mean 0,09194 0,07523 0,06893 Median 0,07199 0,05453 0,04639 Std.Desv. 0,07857 0,07150 0,06611 IF Entropy Index - OF Entropy Index (difference) -0,29449 -0,31569 -0,32599 Dominance Index 29 38 44
Mean 1 1 1
Median 0,53129 0,32114 0,27918 Std.Desv. 2,17884 2,34601 2,39387 BARCELONA (Protosystem - CBD of the Metropolitan System) Dominance Index 11,80805 14,35462 15,76714 % Dominance Index 40,72% 37,78% 35,83% LTL Entropy Information 0,29839 0,33239 0,34564 % LTL Entropy Information 17,08% 15,88% 15,00% LTL in CBD 904.055 799.543 932.639 % LTL in CBD 61,61% 54,09% 50,30% Population in CBD 2.366.458 2.207.464 2.182.836 % Population in CBD 58,89% 52,55% 48,18% Population Entropy Information 0,31180 0,33812 0,35181 % Population Entropy Information 16,91% 15,72% 14,81%
SUBCENTRES (within the Metropolitan System)
Number of Subcentres 4 8 12
Dominance Index 7,08061 14,56294 20,47210 % Dominance Index 24,42% 38,32% 46,53% LTL Entropy Information 0,52003 0,86822 1,11532 % LTL Entropy Information 29,76% 41,48% 48,39% LTL in subcentres 251.276 387.009 590.261 % LTL in subcentres 17,12% 26,18% 31,84% Population in subcentres 717.565 1.054.471 1.410.316 % Population in subcentres 17,86% 25,10% 31,13% Population Entropy Information 0,53913 0,83715 1,07080 % Population Entropy Information 29,24% 38,92% 45,07%
REST OF THE METROPOLITAN SYSTEM
Dominance Index 10,11134 9,08244 7,76076
% Dominance Index 34,87% 23,90% 17,64% LTL Entropy Information 0,92895 0,89264 0,84397 % LTL Entropy Information 53,16% 42,64% 36,62% LTL beyond nuclei 311.990 291.602 331.182 % LTL beyond nuclei 21,26% 19,73% 17,86% Population beyond nuclei 934.076 939.062 937.102 % Population beyond nuclei 23,25% 22,35% 20,69% Population Entropy Information 0,99297 0,97546 0,95341 % Population Entropy Information 53,85% 45,35% 40,13% Source: Own Elaboration
41 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
3. MEASURING THE HIERARCHY AND THE COMPLEXITY GRADE OF THE URBAN STRUCTURE (1991-2001) Functional approach also allows studying the hierarchy and the complexity in the structuration process of metropolitan areas. It is to say, the way in how urban sub-systems (the hinterlands structured by potential urban sub-centres) gravitates towards the central urban sub-system (the sub-system in which CBD is contained, in our case the CBD-sub-system is Barcelona). So, a polycentric urban region would organize in several ways. A simple way would consist of all subcentres interact directly to the centre – CBD (Barcelona sub-system). A more complex way would be the way that it creates a hierarchical ‘tree’, where some sub-systems c ould interact with ot her before interact and gravitate to the centre. In this second case, as much as ramified is the structure, the higher would be its complexity. In addition, as much later is this integration of these peripheral urban-subsystems or their ramifications to the central sub-system in terms of iterations (explained in section 1.1) the higher is their relative “functional independence” to the metropolitan centre (CBD) as a result, it is ascending automatically the complexity grade of the urban structure. In the following (figures 62-64) the hierarchy between urban sub-systems are defined for the analysed years: 1991, 1996 and 2001 following the functional tree suggested by (Roca et al., 2005) and where the identified urban sub-centres (in section 1.2) are marked in blue letters (those sub-systems which their IF Dominance Index –DI- is above of 1, it is consider as a candidate to sub-centres). So, the potential urban sub-centres marked in blue are those which function as hierarchic sub-centres and as nodes (they articulate travel-to-work flows). The rest of the urban sub-systems are those which basically work in a network schema. In 1991 (figure 62), the hierarchical sub-centres are: Sabadell (iteration 15), Rubí (iteration 29) and Terrassa (the m ost a utonomous a nd resilience o ne to i ntegrate t o t he c entre; i n c omparison with the t wo pr evious hierarchical sub-centres, it is integrated to the centre in the iteration 68). Note that the hierarchical sub-systems are the most dependent to the centre, meanwhile the most functional independent sub-subsystems to the centre are the sub-systems which their location are more peripheral: before joining to the central sub-system these sub- systems has integrated to others ones, so in terms of iterations their integration is subsequent. These are the cases of Martorell (iteration 48) or Mataró (iteration 76). Then in 1996 (figure 63), this previous urban dynamic has increased: in that time the hierarchical sub-centres are: Sabadell (iteration 12), Rubí (iteration 13), Mollet del Vallès (iteration 15), Martorell (iteration 20), Granollers (iteration 2 5) an d T errassa ( iteration 44) . On t he c ontrary, the most resilience s ub-systems a re V ilafranca del Penedès ( iteration 91) , S ant C eloni ( iteration 99) an d P iera ( iteration 107) . N ote t hat, at the t ime t hat t he hierarchical sub-systems is increased from 3 i n 1991 t o 6 in 2001 it i s m ore likely to find a ramified ur ban structure, so as it is try to explain further on, it also means a more complexity grade of this urban structure. And finally, in 2001 (figure 64), th e hierarchical s ub-systems ( potential sub-centres) are: Sant B oi de l Llobregat (iteration 9), Mollet del Vallès (iteration 18), Sant Andreu de l a Barca (iteration 47), Martorell (iteration 52), Rubí (iteration 82), Sabadell (iteration 83), Granollers (iteration 84) and Terrassa (iteration 140).
Figure 62: Hierarchy and complexity of the urban structure. Barcelona Metropolitan System 1991
In blue the urban sub-systems which their IF Dominance Index (DI) > 1. So, the candidates to sub-centres Source: Own elaboration
42 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 63: Hierarchy and complexity of the urban structure. Barcelona Metropolitan System 1996
In blue the urban sub-systems which their IF Dominance Index (DI) > 1. So, the candidates to sub-centres Source: Own elaboration
Figure 64: Hierarchy and complexity of the urban structure. Barcelona Metropolitan System 2001
In blue the urban sub-systems which their IF Dominance Index (DI) > 1. So, the candidates to sub-centres Source: Own elaboration
Referring to define the complexity grade of the urban structure for each metropolitan system: in 1991, 1996 and 2001 it i s c alculates a s i t i s pr oposed by t he aut hor of t his paper i n (Marmolejo, Masip & A guirre, 2 011): estimating the average needed steps in order to the municipalities interact directly or indirectly to the centre. As a result, if the metropolitan system would have only a one urban sub-system, the average was equivalent to 1 due
43 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
to with 1 st ep the municipalities would interact with t he centre-CBD. The hi gher is this average, t he higher t he complexity (“treelike”) grade of the metropolitan system is. Under this perspective, one could find that it exists a significant correlation between complexity and polycentricity. In other words, the higher the numbers of identified sub-centres are, the higher the probability to find an urban structure with ramified form is, in which some of them appear as a centralities between the centre-CBD and the more peripheral urban sub-systems. Therefore, in 1991, the average number of steps that a municipality takes to i nteract w ith the central sub- system (CBD-Barcelona) was 2,06; in 1996, 2,15 steps and 2,24 steps in 2001.
Figure 65: Evolution of Complexity level in the Barcelona Metropolitan System (1991-2001)
Evolution of Complexity Level (1991-2001) 2,3
2,24 2,25
2,2 2,15 2,15
2,1 2,06 2,05 COMPLEXITY INDEX (CI) INDEX COMPLEXITY
2
1,95 1991 6991 1002 PERIOD OF TIME - YEAR
4. CONCLUSIONS In the first part of the paper the delimitation of metropolitan areas is discussed and the urban sub-centres are detected using the same method to delimit them. After revising different methods to delimitation, it has been used that pr oposed by (Roca, M armolejo & M oix, 2009) and (Roca, Arellano & M oix, 2011b). S uch a m ethodology, using residence-to-work data, allows for integrate into small urban sub-system those municipalities that according to commuting flows are highly interlinked. Such residence-to-work integrated areas are called by “urban sub- systems” from defining before t he pr otosystems (‘seeds of the pol ycentrism’). The peculiarity of t his method in relation to other based on functional relations (e.g. GEMACA, US Census Bureau, etc.) are: 1) that not thresholds of interaction or critical mass ar e a p riori established; 2) r eflexive i nteractions are considered i nto and not only one-way commuting flows (using t he “ interaction va lue”). So, this used delimitation m ethod allows 1) t he delimitation of the metropolitan systems, 2) detecting sub-systems in complex metropolitan areas in which there is not one e conomic centre, and f irms do l ocate bot h in t he C BD, su bcentres and i n t he sp rawled hinterland articulated by them and, 3) the typology with the sub-system are organized to gravitate to the centre (CBD). After hav ing de limited urban sub-systems departing f rom m unicipalities in 1991 , 1996 an d 2001 , t he Barcelona metropolitan areas for these years are assembled by means of the st epwise-join of sub-systems using the “interaction value” among them. As a r esult of such a methodology t he B arcelona M etropolitan system i n 1991 appear 100 municipalities, 29 protosystems and 16 urban sub-systems; the Barcelona Metropolitan system in 1996 has 164 municipalities, 38 pr otosystems and 22 urban sub-systems and finally in 2001 t he metropolitan system increased t heir spatial units to 184 municipalities, 44 pr otosystems and 24 sub-systems. Therefore, the metropolitan limits growth implies from 1991 to 2001 a highly increment in terms of area ( km2), population and LTL (localised workers). So, for example in 1991 the area in square kilometers of the metropolitan system was 1807,83 and in 2001 it has been duplicated: 3759,96 square kilometers. Referring to the population (from 4.018.099 to 4.530.254) and to the localised workers (from 1.467.321 to 1.854.082). Then, in this first part of this paper, it is also identified the urban sub-centres for each analyzed year. In doing so, it is used a mobility approach, but in comparison with (Roca et al., 2011b) where it is not guaranteed that the
44 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
indentified sub-centres using the expression (1) can be an important nodes within the metropolitan system in terms of incommuting flows (IF) (if they can significantly attract flows from the whole of the metropolitan area and become an attractive node to work) and in comparison with (Marmolejo, Masip & Aguirre, 2011), where it is used a LTL threshold as expression (2) in order to identify the sub-centres but with the next two problems: defining a mass critic level by local knowledge is very subjective task and the results are very dependent on the threshold employed and then what is an is an appropriate cutoff for a metropolitan area and a year (e.g. in 2001) it is not a for a another one (e.g. in 1991), which makes it hard to compare results for the same metropolitan area over time (the case of the study); in this paper it is proposed that in order to identify sub-centres it is used apart from by expression (1); the condition that the sub-centres should be a dominant node within the whole of the metropolitan systems, so attracting more flows than the average of the metropolitan system according to the expression (3). Using the two previous conditions, at urban sub-system scale the identified sub-centres for each year are: 3 sub-centres in 1991: Sabadell, Rubí and Terrassa, 6 in 1996: apart from the three previous ones, Mollet del Vallès, Granollers and Martorell and finally in 2001 there were 8 sub-centres: the previous 6 and Sant Andreu de la Barca and Sant Boi de Llobregat. Referring to the protosystem scale, in 1991 there were 4 sub-centres: Sabadell, Terrassa, Rubí I Cornellà de Llobregat. In 1996, it is identified 4 more: Granollers, Cerdanyola del Vallès, Martorell and Sant Feliu de Llobregat. And finally in 2001 these 8 sub-centres have become into 12: the new sub-centres that it emerged are Parets del Vallès, Sant Andreu de la Barca, Sant Boi de Llobregat and Santa Perpètua de Mogoda.
In the second part, the polycentricity level is measured by using a morphological, functional and the “integrated” approach. Using all these approaches the results bring to the same conclusion: from 1996 to 2001 the Barcelona Metropolitan system has become a more polycentric region. Behind this such urban process towards polycentricity, two main reasons. On the one hand, the process of decentralization of population and employment that has led to an urban dynamics of concentrated decentralization: the number of sub-centres has increased as well as their dominance as attractive nodes within the metropolitan system. On the other hand, the growth of the metropolitan boundaries from 1991 to 2001 it has entailed the integration of significant nodes within the metropolitan system and the relations between the residential and labour markets have become more and more complex. As a consequence, although, the Barcelona Metropolitan System tends to polycentricity due to the concentrated decentralization from Barcelona to the new sub-centres and the reduction of the urban sprawl, the separation of the residential and labour market has increased what it could mean that at the time that the labour market tends to be more concentrated the residential markets tends to be more sprawled (figure 60-61).
Finally, in the third part, by using the mobility approach (in section 1) it is measured the complexity-hierarchy grade of the metropolitan system. By analysing in detail the process by means of which sub-system integrates among them to form the Barcelona metropolitan area for each analysed year: 1991, 1996 and 2001 it is possible to detect the level of complexity of the subjacent structure. Simple structures are formed by the direct incorporation of peripheral urban sub-systems to the central one. Complex structures are formed by the formation of branches in which medium-important sub-system capture others before gravitate towards the central sub- system in which the metropolitan CBD is contained in. From analysing the urban structure of the Barcelona metropolitan system in 1991 and its evolution to 2001, it is clear that it has become more complex and hierarchical (in 2001 there were more hierarchical sub-systems –potential urban sub-centres- than in 1991). Therefore, from having a longitudinal point of view, the results suggest that the biggest is the level of polycentrism (measured by using the morphological, functional or the integrated) the more complex is the structure and hierarchical integration of potential subcentres into the central one.
5. FURTHER RESEARCH STEPS In this paper, it is finding appropriate to include the work (in a draft form) which the author of this paper is developing at this moment. This work is close linked with the present study and it is based on the following point:: the identification of urban sub-centres by using methods based on density analysis (in section 1.2 it is only used functional approach) for the Barcelona Metropolitan System from 1991 to 2001 at the time that is estimated the urban dynamics for this time period in terms of urban structure (polycentrism level) for each used density method..
45 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
5.1. IDENTIFYING THE URBAN SUB-CENTRES BY USING DENSITY METHODS (1991-2001) AND MEASURING THE POLYCENTRISM LEVEL (1991-2001) The family, based on the analysis of density, is by far the most widespread. This family has four major methodologies: 1. The first criterion suggested by (McDonald, 1987) is based on the identification of employment density “peaks” (the author suggests that a sub-centre is the second peak beyond the CBD). This criterion consists of analysing density employment to detect local disruptions with the aid of a geographic information system (GIS). Alternatively, the employment/population ratio can be used to detect the areas that have higher relative concentrations of economic activity. (Gordon, Richardson & Wong, 1986) restricted the number of sub-centres to those areas with high t-values; this line of research was continued by (McDonald & McMillen, 1990) and (Craig & Ng, 2001). 2. The second approach consists of using upper and lower cut-offs. This line was originally proposed by (Giuliano & Small,1991), who considered sub-centres to be the contiguous census tracts with a density of more than 10 employees per acre and a total critical mass of at least 10,000 jobs. Therefore sub- centres must to meet density and critical mass criteria. The references of this method are, (Cervero & Wu,1997), (McMillen & McDonald, 1997), (Bogart & Ferry, 1999), (Anderson & Bogart, 2001), (Shearmur & Coffey, 2002) and (Giuliano & Readfearn, 2007). In this line, (García-López, 2007, 2008) and (Muñiz & García-López, 2009), suggested that sub-centres are zones with a density higher than the metropolitan average and at least 1% of metropolitan employment. (Hall & Pain, 2006) have defined “cores” in their Interreg IIIB Polynet Project, as NUTs 5 with 7 or more workers per hectare, and at least 20,000 workers in either single. 3. From an econometric perspective, there is a third methodology that identifies potential sub-centres by analyzing significant residuals in an exponential negative density model (McDonald & Prather, 1994) suggested several models for detecting sub-centres based on the identification of areas with positive residuals that are significant at a 95% confidence level. 4. The fourth approximation (derived from that presented in 3) is based on non-parametric models (e.g., locally or geographically weighted regression –L or GWR-) to detect “peaks” that locally adjust the density function and prioritize the effect of neighbouring municipalities on the adjustment process (McMillen, 2001b; Craig & Ng, 2001; Readfearn, 2007). The main advantage of this method is that it enables local gradients of density reduction to be determined across the metropolitan area. (Suarez & Delgado, 2009) develop a hybrid method, where once that peaks of density have been detected by means of GWR residuals, adjacent census tracks are added to comply with a threshold number of workers and density.
According to (McMillen, 2001b) approaches based on cut-offs are useful because enables a historical analysis of the sub-centre structure. Nevertheless, they excessively rely on local knowledge to calibrate the thresholds of critical mass and density, and this can be a problem when trying to compare different metro areas with different local experts. The work of (García-López, 2007) seems to give a steep forward by relativizing the critical mass threshold to 1% of metropolitan employment and minimum density to metropolitan average. Nonetheless, such a criterion, in the way operationalized by him, is flawed since the larger the number of spatial units in the metro area, the highest is the difficulty to reach the critical mass criterion, and the most homogeneous is the density function across units, the higher is the probability that a large number of units are above average density. Additionally, cut-offs approach have a more serious defect: they tend to prioritize as subcentres central areas, since they regret what is essential in the standard urban model (i.e. global density is determined by proximity to CBD). Some authors have tried to solve such a problem by manually removing what they consider is the CBD, other have established differentiated thresholds in relation to centrality. Econometric models have meant a significant advance, in conceptual terms, by controlling the influence on overall density exerted by the CBD, approaching in this way to the central theory behind density formation. Namely the functional form that has been extensively used is the negative exponential. By taking logs it can be formulated as follows:
LnDx k += BDcx (9)
In (9) D is the employment density at municipality x, K is the constant which is argued to be the density at CBD and D is the distance between CBD c and municipality x. Sub-centres from this perspective are sites which density is significant above to what is explained by their proximity to CBD. Therefore, one part of their density is endogenously explained, and this piece comes into play
46 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
in differentiating them from other sites. Nonetheless almost all of the econometric methods have failed in constraining the complexity of metropolitan areas to one dimension: the distance to CBD. Notably the density function is affected by specificities lying in three dimensions. Some studies have broken down this limitation by analysing metropolitan corridors, nevertheless the result of such analyses are difficult to be conjointly interpreted. Advances in spatial modelling have solved such an issue by explicitly introducing the effect of bi-dimensional space, like in the locally or weighted non parametric models.
In this section 2 ways to detect sub-centres by density methods has been tested: 1. Using the classical approach, it is to say using the classic density (LTL/a) and functional form explained in (9) LnD k += BD x cx
In addition, in order to make comparable, the results by using the classical approach (expression 9) with the results of using other methodologies (for example the functional approach explained in section 1.2) it is decided to add a second condition, so the second classical approach is defined by:
( ) = LnDx k += BDcx 𝑢𝑢−𝑠𝑠𝑠𝑠𝑠𝑠 𝑖𝑖 𝑢𝑢−𝑠𝑠𝑠𝑠𝑠𝑠 𝐼𝐼𝐼𝐼 𝐷𝐷𝐷𝐷 𝑚𝑚𝑚𝑚 2. Using the cut-off approach in the way as has been𝐼𝐼𝐼𝐼 used by (García-López, 2007) LTL ≥ %1 LTL ≥ 𝑛𝑛 ∑ BMR ltl DD Average_ BMR
At the time that it is also used as previous the second condition (section 1.2)
( ) =
𝑢𝑢−𝑠𝑠𝑠𝑠𝑠𝑠 𝑖𝑖 𝐼𝐼𝐼𝐼 𝐷𝐷𝐷𝐷𝑢𝑢−𝑠𝑠𝑠𝑠𝑠𝑠 𝐼𝐼𝐼𝐼𝑚𝑚𝑚𝑚
𝑛𝑛 Sub-centres at Municipality territorial scale – (CL) and (CL) + (DI)-IF Dominance Index (way 1)
Figure 66: Regression Model. Barcelona Metropolitan System - 1991
47 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 67: Candidates to sub-centres (CL). Barcelona Metropolitan System - 1991
LnDx k += BDcx
Arenys Granollers de Munt Sant Iscle de Vallalta Sabadell Terrassa Canet de Mar
Arenys de Mar
Mataró Olesa de Montserrat Vilassar de Mar
Barcelona - CBD
10 candidates to sub-centres + CBD (Barcelona). The sub-centres ar e: A renys de M ar, A renys de Munt, C anet de M ar, G ranollers, M ataró, O lesa d e Montserrat, S abadell, S ant Iscle d e V allalta, Vilassar de Mar and Terrassa
Figure 68: Candidates to sub-centres (CL) + (DI)-IF Dominance Index. Barcelona Metropolitan System - 1991
LnD k += BD x cx
Granollers Sabadell Terrassa
Mataró
Barcelona - CBD
4 candidates to sub-centres + CBD (Barcelona). The s ub-centres ar e: G ranollers, M ataró, S abadell, and Terrassa
48 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 69: Regression Model. Barcelona Metropolitan System - 1996
Figure 70: Candidates to sub-centres (CL). Barcelona Metropolitan System - 1996
LnDx k += BDcx
Sabadell Breda Granollers
Terrassa
Martorell Mataró
Sant Sadurní d’Anoia Vilassar de Mar
Barcelona - CBD
Vilafranca del 20 candidates to sub-centres + CBD (Barcelona). Penedès The sub-centres are: Castellet I la Gornal, Castellvií de la Marca, Granollers, Martorell, Mataró, Polinyà, Sabadell, Sant C ugat S esgarrigues, V ilassar d e Mar, S ant M artí S arroca, S ant Q uintí de Mediona, Sant S adurní d’Anoia, S anta M argarida i els Vilanova i la Monjos, Terrassa, Vilafranca del Penedès, Vilanova El Vendrell Geltrú i la Geltrú, Breda, L’Arboç, Llorenç del Penedès, El Vendrell.
49 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 71: Candidates to sub-centres (CL) + (DI)-IF Dominance Index. Barcelona Metropolitan System - 1996
+= LnDx k BDcx
Sabadell Granollers
Terrassa
Martorell
Mataró
Polinyà
Barcelona - CBD
7 candidates to sub-centres + CBD (Barcelona). The s ub-centres ar e: Granollers, Martorell, Mataró, Vilafranca del Sabadell, T errassa, P olinyà a nd V ilafranca del Penedès Penedès.
Figure 72: Regression Model. Barcelona Metropolitan System - 2001
50 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 73: Candidates to sub-centres (CL). Barcelona Metropolitan System - 2001
LnDx k += BDcx
Sabadell Granollers Terrassa
Blanes
Martorell Pineda de Mar
Mataró Sant Sadurní d’Anoia
Barcelona - CBD
23 candidates to sub-centres + CBD (Barcelona). Vilafranca del The sub-centres are: Arenys de Mar, Calella, Canet Penedès de M ar, Castellví de la M arca, G ranollers, La Llagosta, Malgrat de Mar, Martorell, Mataró, Pineda Vilanova i la de Mar, Premià de Mar, S abadell, V ilassar de Mar, Geltrú Sant S adurní d’Anoia, S anta M argarida i els Monjos, Terrassa, Vilafranca del Penedès, Vilanova i la Geltrú, B lanes, Breda, Hostalric, Tossa de Mar, Salomó.
Figure 74: Candidates to sub-centres (CL) + (DI)-IF Dominance Index. Barcelona Metropolitan System - 2001
+= LnDx k BDcx
Sabadell Granollers
Terrassa
Martorell
Mataró
Barcelona - CBD
Vilafranca del Penedès 7 candidates to sub-centres + CBD (Barcelona). The s ub-centres ar e: Granollers, Martorell, Mataró, Vilanova i la Sabadell, T errassa, Vilafranca de l Penedès an d Geltrú Vilanova i la Geltrú.
51 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 72: Regressions Models. Barcelona Metropolitan System – 1991, 1996 and 2001
Measuring the polycentrism level at Municipality territorial scale – (CL) Figure 73: Measurement of the polycentrism level by using LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 2006
183 Municipalities
2001
YEAR - 163 Municipalities
1996
1991
PERIOD OF TIME
99 Municipalities
1986 2,40 2,60 2,80 3,00 3,20 3,40
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Urban Structure (Barcelona Metropolitan System) 1991 1996 2001
Number of munipalities 100 164 184 Barcelona (municipality - CBD) 1 1 1 Number of munipalities beyond CBD 99 163 183
LTL Entropy Index (Metropolitan System) 2,56466 3,00484 3,21571
Source: Own Elaboration
52 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 74: Measurement of the polycentrism level by using % LTL in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 30%
2001 1996 20% 1991
43,30% 40,34% LTL-CBD LTL-CBD 10%
LTL IN% SUBCENTRES 50,43% LTL-CBD
0% 2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Figure 75: Measurement of the polycentrism level by using % Dominance Index (DI) in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 24%
2001 1996
16%
1991 34,00% 31,05% DI-CBD DI-CBD 8%
40,01% DI-CBD
0% DOMINANCE % INDEX (DI) IN SUBCENTRES 2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40 LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Figure 76: Measurement of the polycentrism level by using % Population in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 25%
2001
20%
1996
1991
15% 33,23% 35,92% POP-CBD POP-CBD
10% 40,90% POPULATION % SUBCENTRES IN POP-CBD
5% 2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40 LTL ENTROPY INDEX (METROPOLITAN SYSTEM) 53 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 77: Urban structure dynamics at municipality scale 1991-1996-2001
Urban Structure (Barcelona Metropolitan System) 1991 1996 2001
LTL Entropy Index (Metropolitan System) 2,56466 3,00484 3,21571 Mean 0,02565 0,01832 0,01748 Median 0,01339 0,00696 0,00731 Std.Desv. 0,04251 0,03582 0,03386 Population Entropy Index (Metropolitan System) 2,82137 3,21005 3,44081 Mean 0,02821 0,01957 0,01870 Median 0,01156 0,00759 0,00837 Std.Desv. 0,04817 0,03861 0,03571 RW Entropy Index (Metropolitan System) 2,21876 2,60821 2,84885 Mean 0,02219 0,01590 0,01548 Median 0,00899 0,00517 0,00590
Std.Desv. 0,04183 0,03510 0,03342 IF Entropy Index (Metropolitan System) 3,01530 3,37984 3,58361 Mean 0,03015 0,02061 0,01948 Median 0,01457 0,00790 0,00784 Std.Desv. 0,04446 0,03705 0,03466 OF Entropy Index (Metropolitan System) 3,47958 3,84786 4,08631 Mean 0,03480 0,02346 0,02221 Median 0,01689 0,01058 0,01174 Std.Desv. 0,04970 0,03804 0,03394 IF Entropy Index - OF Entropy Index (difference) -0,46428 -0,46802 -0,50269
Dominance Index 100 164 184
Mean 1 1 1
Median 0,24192 0,19202 0,21359 Std.Desv. 4,02645 4,44981 4,31867 BARCELONA (Municipality - CBD of the Metropolitan System) METHOD TO IDENTIFY SUB-CENTRES: Parametric model-CL Dominance Index 40,01323 55,75913 57,13453 % Dominance Index 40,01% 34,00% 31,05% LTL Entropy Information 0,34522 0,36244 0,36622 % LTL Entropy Information 13,46% 12,06% 11,39% LTL in CBD 740.037 639.981 747.905 % LTL in CBD 50,43% 43,30% 40,34% Population in CBD 1.643.542 1.508.805 1.505.325 % Population in CBD 40,90% 35,92% 33,23% Population Entropy Information 0,36566 0,36778 0,36610
% Population Entropy Information 12,96% 11,46% 10,64% SUBCENTRES (within the Metropolitan System) METHOD TO IDENTIFY SUB-CENTRES: Parametric model-CL Number of Subcentres 10 20 23 Dominance Index 8,36025 22,30881 27,92210 % Dominance Index 8,36% 13,60% 15,18% LTL Entropy Information 0,47101 0,65145 0,73693 % LTL Entropy Information 18,37% 21,68% 22,92% LTL in subcentres 188.444 241.227 328.101 % LTL in subcentres 12,84% 16,32% 17,70% Population in subcentres 553.072 663.752 814.578 % Population in subcentres 13,76% 15,80% 17,98% Population Entropy Information 0,49746 0,61573 0,74399
% Population Entropy Information 17,63% 19,18% 21,62%
REST OF THE METROPOLITAN SYSTEM METHOD TO IDENTIFY SUB-CENTRES: Parametric model-CL
Dominance Index 51,62652 85,93206 98,94338 % Dominance Index 51,63% 52,40% 53,77% LTL Entropy Information 1,74844 1,99095 2,11257 % LTL Entropy Information 68,17% 66,26% 65,70% LTL beyond nuclei 538.840 596.946 778.076 % LTL beyond nuclei 36,72% 40,38% 41,97% Population beyond nuclei 1.821.485 2.028.440 2.210.351 % Population beyond nuclei 45,33% 48,28% 48,79% Population Entropy Information 1,95825 2,22655 2,33072 % Population Entropy Information 69,41% 69,36% 67,74% Source: Own Elaboration
54 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Measuring the polycentrism level at Municipality territorial scale – (CL) + (DI)-IF Dominance Index Figure 78: Measurement of the polycentrism level by using % LTL in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 30%
20% 1996 2001 1991
10%
LTL IN% SUBCENTRES 43,30% 40,34% 50,43% LTL-CBD LTL-CBD LTL-CBD
0%
2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40
LTL ENTROPY INDEX (METROPOLITAN SYSTEM) Figure 79: Measurement of the polycentrism level by using % Dominance Index (DI) in sub-centres and LTL Entropy Index Evolution of Polycentrism Level (1991-2001)
24%
2001 16% 1996 1991
8% 34,00% 31,05%
40,01% DI-CBD DI-CBD
DI-CBD
DOMINANCE % INDEX (DI) IN SUBCENTRES 0% 2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Figure 80: Measurement of the polycentrism level by using % Population in sub-centres and LTL Entropy Index Evolution of Polycentrism Level (1991-2001)
25%
20% 2001 1991 1996
15%
33,23% 10% POP-CBD 40,90% 35,92% POPULATION % SUBCENTRES IN POP-CBD POP-CBD
5% 2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40 LTL ENTROPY INDEX (METROPOLITAN SYSTEM) 55 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 81: Urban structure dynamics at municipality scale 1991-1996-2001
Urban Structure (Barcelona Metropolitan System) 1991 1996 2001
LTL Entropy Index (Metropolitan System) 2,56466 3,00484 3,21571 Mean 0,02565 0,01832 0,01748 Median 0,01339 0,00696 0,00731 Std.Desv. 0,04251 0,03582 0,03386 Population Entropy Index (Metropolitan System) 2,82137 3,21005 3,44081 Mean 0,02821 0,01957 0,01870 Median 0,01156 0,00759 0,00837 Std.Desv. 0,04817 0,03861 0,03571 RW Entropy Index (Metropolitan System) 2,21876 2,60821 2,84885 Mean 0,02219 0,01590 0,01548 Median 0,00899 0,00517 0,00590
Std.Desv. 0,04183 0,03510 0,03342 IF Entropy Index (Metropolitan System) 3,01530 3,37984 3,58361 Mean 0,03015 0,02061 0,01948 Median 0,01457 0,00790 0,00784 Std.Desv. 0,04446 0,03705 0,03466 OF Entropy Index (Metropolitan System) 3,47958 3,84786 4,08631 Mean 0,03480 0,02346 0,02221 Median 0,01689 0,01058 0,01174 Std.Desv. 0,04970 0,03804 0,03394 IF Entropy Index - OF Entropy Index (difference) -0,46428 -0,46802 -0,50269
Dominance Index 100 164 184
Mean 1 1 1
Median 0,24192 0,19202 0,21359 Std.Desv. 4,02645 4,44981 4,31867 BARCELONA (Municipality - CBD of the Metropolitan System) METHOD TO IDENTIFY SUB-CENTRES: Parametric-CL+ DI-IF Dominance Index 40,01323 55,75913 57,13453 % Dominance Index 40,01% 34,00% 31,05% LTL Entropy Information 0,34522 0,36244 0,36622 % LTL Entropy Information 13,46% 12,06% 11,39% LTL in CBD 740.037 639.981 747.905 % LTL in CBD 50,43% 43,30% 40,34% Population in CBD 1.643.542 1.508.805 1.505.325 % Population in CBD 40,90% 35,92% 33,23% Population Entropy Information 0,36566 0,36778 0,36610
% Population Entropy Information 12,96% 11,46% 10,64% SUBCENTRES (within the Metropolitan System) METHOD TO IDENTIFY SUB-CENTRES: Parametric-CL+ DI-IF Number of Subcentres 4 7 7 Dominance Index 7,72379 19,21894 22,48635 % Dominance Index 7,72% 11,72% 12,22% LTL Entropy Information 0,41056 0,51493 0,53529 % LTL Entropy Information 16,01% 17,14% 16,65% LTL in subcentres 174.235 205.261 264.988 % LTL in subcentres 11,87% 13,89% 14,29% Population in subcentres 500.850 552.960 627.563 % Population in subcentres 12,46% 13,16% 13,85% Population Entropy Information 0,42035 0,47191 0,51008
% Population Entropy Information 14,90% 14,70% 14,82%
REST OF THE METROPOLITAN SYSTEM METHOD TO IDENTIFY SUB-CENTRES: Parametric-CL+ DI-IF
Dominance Index 52,26298 89,02193 104,37912 % Dominance Index 52,26% 54,28% 56,73% LTL Entropy Information 1,80888 2,12747 2,31421 % LTL Entropy Information 70,53% 70,80% 71,97% LTL beyond nuclei 553.049 632.912 841.189 % LTL beyond nuclei 37,69% 42,82% 45,37% Population beyond nuclei 1.873.707 2.139.232 2.397.366 % Population beyond nuclei 46,63% 50,92% 52,92% Population Entropy Information 2,03536 2,37036 2,56463 % Population Entropy Information 72,14% 73,84% 74,54% Source: Own Elaboration
56 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Sub-centres at Municipality territorial scale – (GL) + (DI)-IF Dominance Index (way 2)
Figure 82: Candidates to sub-centres. Barcelona Metropolitan System - 1991
LTL ≥ %1 LTL ∑ BMR ≥ ltl DD Average_ BMR
Sabadell Granollers
Mataró
Badalona Esplugues de Llobregat Santa Coloma de Gramanet
Barcelona - CBD
8 candidates to sub-centres + CBD (Barcelona). The s ub-centres are: B adalona, C ornellà de Hospitalet de Llobregat, E splugues d e Ll obregat, G ranollers, Cornellà de Llobregat Hospitalet de Llobregat, Mataró, Sabadell and
Llobregat Santa Coloma de Gramanet.
Figure 83: Candidates to sub-centres. Barcelona Metropolitan System - 1996
LTL ≥ %1 LTL ∑ BMR ≥ ltl DD Average_ BMR
Sabadell Granollers
Terrassa
Mataró Martorell
Badalona
Santa Coloma de Gramanet
Barcelona - CBD Esplugues de Llobregat
Hospitalet de Llobregat
El Prat de Llobregat
Sant Boi de Cornellà de Llobregat Llobregat 12 candidates to sub-centres + CBD (Barcelona). The s ub-centres are: B adalona, C ornellà de Llobregat, E splugues d e Ll obregat, G ranollers, Hospitalet de Llobregat, M artorell, M ataró, Prat de Llobregat, Sabadell, S ant B oi de Llobregat S anta Coloma de Gramanet and Terrassa
57 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 84: Candidates to sub-centres. Barcelona Metropolitan System -2001
LTL ≥ %1 LTL ∑ BMR ≥ ltl DD Average_ BMR
Sabadell Granollers
Terrassa
Martorell Mataró
Badalona
Santa Coloma de Gramanet
Barcelona - CBD
Hospitalet de Llobregat
El Prat de Llobregat Cornellà de Llobregat 11 candidates to sub-centres + CBD (Barcelona). Sant Boi de The s ub-centres are: B adalona, C ornellà de Llobregat Llobregat, Granollers, Hospitalet de Llobregat, Martorell, Mataró, Prat de Llobregat, Sabadell, Sant Boi de Llobregat S anta C oloma de Gramanet and Terrassa
Figure 85: Cut-off s: 1% Employment & Average density employment. Barcelona Metropolitan System – 1991, 1996 and 2001
58 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Measuring the polycentrism level at Municipality territorial scale – (GL) + (DI)-IF Dominance Index Figure 86: Measurement of the polycentrism level by using % LTL in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 40%
1996 2001 30%
1991
20% 43,30%
50,43% LTL-CBD 40,34% LTL-CBD LTL-CBD
LTL IN% SUBCENTRES 10%
0% 2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Figure 87: Measurement of the polycentrism level by using % Dominance Index (DI) in sub-centres and LTL Entropy Index
Evolution of Polycentrism Level (1991-2001) 40%
1996 2001 30% 1991
20% 34,00% 31,05% 40,01% DI-CBD DI-CBD DI-CBD 10%
% DOMINANCE % INDEX (DI) IN SUBCENTRES 0% 2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40
LTL ENTROPY INDEX (METROPOLITAN SYSTEM)
Figure 88: Measurement of the polycentrism level by using % Population in sub-centres and LTL Entropy Index Evolution of Polycentrism Level (1991-2001)
40%
1996 35% 2001 1991
30%
35,92% POP-CBD 33,23% POP-CBD 25% 40,90%
POPULATION % SUBCENTRES IN POP-CBD
20% 2,40 2,50 2,60 2,70 2,80 2,90 3,00 3,10 3,20 3,30 3,40 LTL ENTROPY INDEX (METROPOLITAN SYSTEM) 59 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
Figure 89: Urban structure dynamics at municipality scale 1991-1996-2001
Urban Structure (Barcelona Metropolitan System) 1991 1996 2001
LTL Entropy Index (Metropolitan System) 2,56466 3,00484 3,21571
Mean 0,02565 0,01832 0,01748 Median 0,01339 0,00696 0,00731 Std.Desv. 0,04251 0,03582 0,03386 Population Entropy Index (Metropolitan System) 2,82137 3,21005 3,44081 Mean 0,02821 0,01957 0,01870 Median 0,01156 0,00759 0,00837 Std.Desv. 0,04817 0,03861 0,03571 RW Entropy Index (Metropolitan System) 2,21876 2,60821 2,84885 Mean 0,02219 0,01590 0,01548 Median 0,00899 0,00517 0,00590 Std.Desv. 0,04183 0,03510 0,03342
IF Entropy Index (Metropolitan System) 3,01530 3,37984 3,58361
Mean 0,03015 0,02061 0,01948 Median 0,01457 0,00790 0,00784 Std.Desv. 0,04446 0,03705 0,03466 OF Entropy Index (Metropolitan System) 3,47958 3,84786 4,08631 Mean 0,03480 0,02346 0,02221 Median 0,01689 0,01058 0,01174 Std.Desv. 0,04970 0,03804 0,03394 IF Entropy Index - OF Entropy Index (difference) -0,46428 -0,46802 -0,50269 Dominance Index 100 164 184 Mean 1 1 1 Median 0,24192 0,19202 0,21359
Std.Desv. 4,02645 4,44981 4,31867 BARCELONA (Municipality - CBD of the Metropolitan System) METHOD TO IDENTIFY SUB-CENTRES: Cutoff- GL
Dominance Index 40,01323 55,75913 57,13453 % Dominance Index 40,01% 34,00% 31,05% LTL Entropy Information 0,34522 0,36244 0,36622 % LTL Entropy Information 13,46% 12,06% 11,39% LTL in CBD 740.037 639.981 747.905 % LTL in CBD 50,43% 43,30% 40,34% Population in CBD 1.643.542 1.508.805 1.505.325 % Population in CBD 40,90% 35,92% 33,23% Population Entropy Information 0,36566 0,36778 0,36610 % Population Entropy Information 12,96% 11,46% 10,64%
SUBCENTRES (within the Metropolitan System) METHOD TO IDENTIFY SUB-CENTRES: Cutoff- GL
Number of Subcentres 8 12 11
Dominance Index 19,98907 44,07009 45,14543
% Dominance Index 19,99% 26,87% 24,54% LTL Entropy Information 0,70446 0,97578 1,27523 % LTL Entropy Information 27,47% 32,47% 39,66% LTL in subcentres 288.830 390.647 454.566 % LTL in subcentres 19,68% 26,43% 24,52% Population in subcentres 1.100.465 1.380.223 1.334.620 % Population in subcentres 27,39% 32,85% 29,46% Population Entropy Information 0,88161 1,11972 1,01880 % Population Entropy Information 31,25% 34,88% 29,61% REST OF THE METROPOLITAN SYSTEM METHOD TO IDENTIFY SUB-CENTRES: Cutoff- GL
Dominance Index 39,99770 64,17078 81,72005 % Dominance Index 40,00% 39,13% 44,41%
LTL Entropy Information 1,51498 1,66662 1,57426
% LTL Entropy Information 59,07% 55,46% 48,96% LTL beyond nuclei 438.454 447.526 651.611 % LTL beyond nuclei 29,88% 30,28% 35,14% Population beyond nuclei 1.274.092 1. 311.969 1.690.309 % Population beyond nuclei 31,71% 31,23% 37,31% Population Entropy Information 1,57410 1,72256 2,05591 % Population Entropy Information 55,79% 53,66% 59,75% Source: Own Elaboration
60 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
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61 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
• Greene, D.L. (1980). Recent trends in urban spatial structure. Growth and Change, 11, pages 29-40. • Griffith, D.A. (1981a). Evaluating the transformation from a monocentric to a polycentric city. Professional Geographer, 33, pags 189-196. • Griffith, D.A. (1981b). Modelling urban population density in a multicentered city. Journal of Urban Economics 9,pags. 298-310. • Hagget, P. (1965). Locational analysis in Human Geography. London: Edward Arnold. • Hall,P.; Pain,K. (2006). The Polycentric Metropolis.Learning from mega-city regions in Europe.Earthscan. • Heikkila, E.; Gordon, P.; Kim, J.I.; et al. (1989). What happened to the CBD-distance gradient?. Land values in a polycentric city. Environment and Planning A (21), pages. 221-232. • IGEAT (2007). Espon project 1.4.3. Study on Urban Functions. • Indovina, F. (1990). “La cittàpossible” en la città di finne milenio. Milano, Franco. • Julien, P. (2000). Mesurar un universo urbano en expansion. Rev. Economie et Statistique, nº336; págs. 3-33. • Kloosterman,R.; Musterd,S. (2001). The polycentric urban region: towards a research agenda, Urban Studies, 38 (4), pp. 623-633 • Marmolejo, C.; Aguirre,C.; Ruiz,M.; (2010). ¿Hacia un sistema de metrópolis españolas policéntricas?: caracterización de su estructura metropolitana?.6CTV Mexicali 2010. • Marmolejo, C.; Masip.J.; Aguirre, C. (2011-forthcoming). Policentrismo en el sistema urbano español: un análisis para 7 áreas metropolitanas. Ciudad y Territorio. Estudios Territoriales. Ministerio de Fomento. • Martinotti, G. (1991). La población de la nueva morfología social metropolitana. En Borja, J. et alia Las Grandes ciudades en la década de los noventa, págs..65-141. Madrid, Ed, Sistema. • Masip,J. (2011-forthcoming). Polycentrism and emerging sub-centres in the restructuring of metropolitan systems. The case of Barcelona Metropolitan Region (RMB). 58th Annual North American Meetings of the Regional Science Association International (NARSC-RSAI) and 2nd Conference of the Regional Science Association of the Americas. Miami, 9-12 November • McDonald, J.F. (1987). The identification of Urban Employment Subcenters. Journal of Economics, 21, pages 242-258. • McDonald, J.; McMillen, D. (1990). Employment Subcenters and Land Values in a Polycentric Urban Area: the Case of Chicago, Environment and Planning A, 22, pp. 1561-1574. • McDonald, J.F.; Prather, P.J. (1994). Suburban Employment centres: the case of Chicago. Urban Studies 31:2, pages 201-218. • McMillen, D.P.; McDonald, J.P. (1998). Population density in Suburban Chicago: A bid-rent approach. Urban Studies, 35:7, pages 1119- 1130. • McMillen, D. (2001). Non-Parametric Employment Subcenter Identification, Journal of Urban Economics, 50, pp. 448-473. • McMillen,D. (2003). 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Local Labour markets. Written for the Handbook of Labor Economics. • Murphy, P. 2003. Preliminary 2006 Census Metropolitan Area and Census Agglomeration Definition. Statistic Canada, Geography Working Paper Series; nº2003-2002. • Nel·lo, Oriol (2001). Ciutat de ciutats . Barcelona, Ed. Empúries. • NUREC (1994).Atlas of Agglomerations in the European Union. Part of an Integrated Observation System. Volume I, Volume II, Volume III.Network on Urban Research in the European Union. Duisburg 1994. • OMB (2000).Office of Management and Budget. Part IX. Standards for Defining Metropolitan and MicropolitanStadistical Areas; Notice, Federal Register. • Parr, J. (2004). The polycentric urban region: a closer inspection, Regional Studies, 38(3). pp.231-240 • Readfearn, C. (2007). The topography of metropolitan employment: Identifying centers of employment in a polycentric urban area. Journal of Urban Economics 61, pages 519-541. • Roca, J (2004): La explosión urbana: presente y futuro de las metropólis. Ciudad y Territorio. Estudios Territoriales, nº 141-2; pp. 501-503 • Roca, J.; Moix, M. (2005). The Interaction Value: Its Scope and Limits as an Instrument for Delimiting Urban Systems , Regional Studies, 39, pp. 359-375. • Roca, J.; Burns, M.; Moix, M. (2005). Las Áreas Metropolitanas Españolas. Evolución 1991-2001. CPSV. UPC. Barcelona. • Roca, J.; Marmolejo, C.; Moix, M. (2009). Urban structure and Polycentrism. Towards a redefinitation of the Sub-centres concept. • Roca, J.; Arellano,B.; Moix,M. (2011a-forthcoming): Estructura urbana, Policentrismo y Sprawl, los ejemplos de Madrid y Barcelona. Ciudad y Territorio. • Roca, J.; Moix,M.; Arellano,B. (2011b-forthcoming): El sistema urbano en España. Scriptanova. Revista Electrónica de geografía y ciencias sociales. Universidad de Barcelona. • Roca, J.; Arellano, B. (2011c). 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• Salvador, N.; Mora, C.; Salvat,E. (1997). “La regió urbana funcional de Barcelona en el contexteuropeu”. Revista Econòmica de Catalunya, nº33. • Serra, J.; Otero, M.; Ruiz,R. (2002). “Grans aglomeracions metropolitanes Europees”. IERMB. • Sforzi, F. (1987). L’identificazione spaziale en Giacomo Becattini (ed). Mercato e forze locali: il distretto industrial. Bologna. Pages. 143- 167. • Shearmur, R.; Coffey, W.J. (2002). A tale of four cities: Intrametropolitan employment distribution in Toronto, Montreal, Vancouver and Ottawa-Hull, 1981-1996. Environment and Planning A, 2002, vol.34, pages 575-598. • Small, K.A.; Song, S. (1994). Population and Employment Densities: Structure and Changes. Journal of Urban Economics, 36 pg. 292-313 • Smart, M.W. (1974). Labour Market Areas. Uses and Definition. Progress in Planning, Vol.2; part 4; pages 238-353. • Transnational Interactions. The American Journal of Sociology. Vol 84, nº5, pages 1096-1126. • Song, S. (1994). Modelling Worker Residence Distribution in the Los Angeles Region. Urban Studies, 31:9, pages 1533-1544. • Suarez,M.; Delgado, J. (2009). Is Mexico City Polycentric? A trip attraction capacity approach, Urban Studies, Volume 46(10), P 2187- 2211.
63 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
7. ANNEXES In this section, it is presented in a more detail the next urban structure analysis: the evolution from 1991 to 2001 of the analyzed spatial units (sub-systems and protosystems; not municipalities due to the functional approach used in this paper to identify urban sub-centres at municipality scale does not work to identify them). By analyzing the following four tables, the results bring to confirm for example, the conclusion that the urban dynamics from 1991 to 2001 towards a higher degree of polycentricity, it is consequence of the growth of the metropolitan boundaries as well as the integration of new nodes or the strengthening of others. These are the cases of Granollers, Martorell, Mollet del Vallès and Rubí at sub-system scale or the cases of Martorell, Cerdanyola del Vallès, Rubí, Granollers and Sant Boi de Llobregat at protosystem scale. Finally, observing that both at sub-system and protosystem scale, although the self-containment and self-sufficiency have significantly decreased from 1991 to 2001, that it was not mean a urban process to monocentricity or urban sprawl: as it was proved in the paper (section 2), the Barcelona Metropolitan system in the analyzed period of time it has characterized as a metropolitan area that has experimented a process towards a more polycentric structure.
64 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
01 ‐ ‐ ‐ 2,88% ‐ 7,29% ‐ 4,34% ‐ 7,60% ‐ 9,82% ‐ 7,88% ‐ 0,43% ‐ 1,30% ‐ 4,22% ‐ 7,08% ‐ 4,98% ‐ 0,02% ‐ 10,62% ‐ 16,34% ‐ 11,58% ‐ 11,54% 91 Self sufficiency ‐ ‐ ‐ ‐ ‐
72,22% 77,88% 88,98% 47,50% 73,27% year) ‐ sufficiency
(2001 or last Self ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
78,78% 71,51% 65,53% 50,23% 32,62% 76,17% 73,98% year) ‐ sufficiency (1991 or org. Self
‐ ‐ 1,21% 70,28% 67,40% ‐ 4,35% 91,33% 84,03% ‐ 6,70%‐ 9,35% 72,02% 89,84% 55,68% 85,51% ‐ 7,59% 73,07% 61,49% ‐ 9,34% 63,23% 55,64% ‐ 5,03% 62,05% 54,17% ‐ 1,63% 89,73% 89,29% ‐ 5,30% 75,36% 71,13% ‐ 1,24% 80,14% 73,06% ‐ 4,72% 54,73% 66,46% 11,73% ‐ 7,11% 85,78% 80,80% ‐ 2,12% 79,74% 79,72% ‐ 15,71% 89,96% 79,34% ‐ 11,61% 60,32% 48,78% ‐ 15,49% 37,30% 52,63% 15,33% Self 01 ‐ 91 containment ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
53,06% 59,27% 88,10% 70,67% 70,95% 69,09% 55,64% 57,39% 54,98% 2,66% 59,16% 49,34% 68,15% 51,23% 54,80% 69,29% 71,22% 70,17% 81,11% 0,07% 76,86% 75,56% 73,99% 70,50% 0,81% 86,49% 86,56% 0,07% 58,76% 74,04% 73,33% 86,53% 65,86% 51,00% ‐ containment Self (2001 or last year) ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
54,28% 74,98% 92,45% 77,36% 80,30% 76,68% 64,98% 69,00% 52,32% 55,52% 54,73% 54,76% 61,54% 66,72% 59,83% 72,85% 75,47% 59,98% 81,05% 75,22% 69,69% 63,49% 81,14% 75,45% 67,49% 51,12% ‐ containment Self (1991 or org. year) ‐ ‐ ‐ ‐ ‐
0,53% 1,55% 1,07% 0,08% 0,16% 1,95% 0,21% 0,40% 1,70% 0,69% 1,88% 1,31% 0,40% 0,92% 0,15% 0,59% 1,26% 0,23% ‐ ‐ ‐ ‐ 11,51% ‐ % LTL 01 ‐ 91 ‐ ‐ ‐ ‐ ‐ ‐ ‐
9.773 9.204 7.312 7.401 2.680 2.835 54.012 70.589 12.014 59.999 15.537 13.827 59.834 40.445 54.026 20.502 34.871 24.350 68.522 16.988 72.953 10.931 LTL year) 154.924 1.030.553 (2001 or last
‐
‐
‐
‐
‐
984
4.868 9.638 1.322 29.844 21.265 14.509 LTL year) (1991 or org.
‐
‐ ‐ ‐ ‐
‐ ‐
‐ ‐
‐
‐ ‐
0,63% 6.981 0,08% 5.108 0,81%0,27% 20.491 55.277 0,55% 34.917 1,39% 16.624 0,02% 7.956 0,04% 12.145 1,60% 13.366 0,34% 33.134 2,33% 26.169 0,39% 6.077 0,19% 3.587 1,20% 17.746 0,65% 7.704 1,21% 11.575 0,09% 54.316 1,14% 139.838 ‐ ‐ ‐ 13,00% 998.893 ‐ 01 ‐ 91 % Population ‐ ‐ ‐ ‐ ‐ ‐ ‐
4.897 8.537 28.628 30.810 31.985 17.863 98.282 40.410 28.831 57.438 94.287 17.451 54.241 29.618 54.983 year) 202.973 123.086 120.717 236.664 383.721 105.704 116.128 192.483 2.450.517 Population (2001 or last
‐
‐
‐
‐
‐
year) Population (1991 or org.
‐ ‐ ‐
‐ ‐
‐
‐ ‐
‐
‐
‐
‐
1 0 1 28.206 1 0 0 68.240 0 0 1 1 0 0 121.280 0 1 1 23.439 1 1 1 2.695.745 0 1 0 18.218 11 1 1 1 1 54.821 169.053 1 1 1 12.809 0 0 1 1 1 0 20.423 1 1 1 87.120 1 1 1 51.186 1 0 0 19.873 0 1 0 4.672 0 1 1 90.435 0 0 1 0 0 1 1 1 1 167.147 1 1 1 89.342 0 1 1 8.848 0 1 1 44.004 0 1 1 17.648 0 1 0 4.089 1 1 1 386.256 0 0 1 0 1 1 41.956 0 1 1 22.219
d'Anoia i Plegamans 1 1 1 27.140 del Vallès del Penedès i la Geltrú (El) de Llobregat
(La) de Mar de Rei del Vallès del Vallès Subsystem (name) 1991 1996 2001 Boi Andreu de la Barca 1 1 1 19.458 Sadurní Martí Sarroca Celoni Garriga Cardedeu Barcelona ‐ CBD Arenys Molins Martorell Mataró Malgrat de Mar Gavà Piera Montornès Granollers Parets Pineda de Mar Palau ‐ solità Mollet Sant Rubí Blanes Breda Vilanova Sabadell Sant Hostalric Arboç (L') Terrassa Sant Vendrell Vilafranca Sant Sant Source: Own Elaboration
65 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
‐ 0,19% ‐ 2,67% ‐ 0,51% ‐ 0,45% ‐ 0,27% ‐ 0,64% ‐ 0,40% ‐ 1,02% ‐ 0,49% ‐ 0,79% ‐ 1,57% ‐ 3,70% ‐ 0,16% ‐ 0,31% ‐ 0,52% Index 01 ‐ 91 % OF Entropy
‐ 1,16% ‐ 0,09% ‐ 0,34% ‐ 0,73% ‐ 0,67% ‐ 0,27% ‐ 0,26% ‐ 0,52% ‐ 3,40% ‐ 0,77% ‐ 0,81% ‐ 0,12% Index 01 ‐ 91 % IF Entropy ‐ 0,94%‐ 2,02% ‐ 0,26% 0,09% ‐ 1,29% 0,55% ‐ 0,33% ‐ 0,94% ‐ 0,46%‐ 2,79% ‐ 0,59% 0,01% ‐ 0,97% ‐ 1,13% ‐ 6,23% ‐ 0,23% ‐ 3,14% ‐ 0,28% ‐ 0,28% Index 01 ‐ 91 % RW Entropy
Index ‐ 0,77% ‐ 2,27% ‐ 0,28% ‐ 0,97% ‐ 0,20% ‐ 0,79% ‐ 0,43% ‐ 2,66% ‐ 0,45% ‐ 0,98% ‐ 1,29% ‐ 5,53% ‐ 0,15% ‐ 2,49% ‐ 0,25% ‐ 0,30% 01 ‐ 91 % Population Entropy ‐‐‐‐ ‐‐‐‐ ‐‐‐‐ ‐‐‐‐ ‐‐‐‐
4,15% 2,28% 1,72% 0,21% 3,45% 4,28% 0,04% 0,23% 2,63% 0,55% 4,98% 0,95% 1,36% 3,20% 0,45% 1,75% 1,65% 5,05% 1,10% 1,12% 1,66% 6,91% 2,73% 4,52% 4,84% 1,80% 1,69% 2,85% 2,17% 7,94% 7,17% 0,61% 2,76% 0,38% 17,12% 10,77% Index % Population Entropy ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ (2001 or last year)
1,87% 4,24% 4,02% 2,52% 1,93% 6,01% 1,53% 1,33% 7,65% 2,44% 1,57% 9,58% 3,18% 5,49% 0,50% 6,13% 1,94% 0,45% 1,90% 1,84% 9,65% 5,01% 0,86% 3,06% 19,39% 16,30% Index % Population Entropy (1991 or org. year)
‐ 0,68% ‐ 1,98% ‐ 0,18% ‐ 0,67% ‐ 0,30% ‐ 0,29% ‐ 0,80% ‐ 2,23% ‐ 0,45% ‐ 0,70% ‐ 5,48% ‐ 0,84% ‐ 0,18% ‐ 2,49% ‐ 0,43% ‐ 0,20% Entropy Index 01 ‐ 91 % LTL ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
1,72% 2,62% 1,92% 6,42% 0,50% year) Entropy last % LTL ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ Index (2001 or
5,80% 1,22% 0,41% 0,32% 2,42% 3,34% 4,49% Entropy org. year) % LTL Index (1991 or
‐ 1,16%‐ 0,04% 19,16% 1,64% 17,18% 1,46% ‐ 0,35% 2,90% 2,11% ‐ 0,12% 1,44% 1,15% ‐ 1,23%‐ 0,17%‐ 0,15% 8,93% 3,44% 4,63% 6,70% 2,99% 3,93% ‐ 5,44% 16,40% 10,92% ‐ 0,07% 1,78% 1,59% ‐ 0,18% 9,04% 6,55% ‐ 0,40%‐ 0,06% 0,95% 2,46% 0,52% 2,26% % IF Dominance Index 01 ‐ 91 ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
0,80% 0,54% 0,73% 4,40% 0,34% year) last % Dominance Index (2001 or ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
org. year) % Dominance Index (1991 or ‐ ‐ ‐ ‐ ‐ 1 0 1 0,38% 0,46% 0,08% 2,07% 1,39% 0 0 1 10 1 1 1 1 40,67% 0,81% 39,51% 0,76% 1 1 1 4,41% 5,55% 1,13% 6,51% 5,84% 1 0 0 2,97% 00 1 0 0 1 0,54% 0 0 1 10 10 10 1 1 1 1 1 4,59% 0 1,59% 1,04% 3,36% 0,12% 1,43% 0,90% 0 0 1 0 1 1 0,47% 0,48% 0,01% 1,46% 1,16% 1 1 1 0,88% 0,76% 0 1 0 0,10% 1 1 1 2,69% 5,75% 3,06% 4,37% 5,42% 1,06% 11 1 1 1 1 5,90% 16,17% 5,94% 10,74% 0,04% 6,27% 5,42% 1 1 1 3,19% 7,28% 4,09% 3,72% 5,83% 2,12% 1 11 1 1 2,64% 0 2,46% 2,25% 0 0 1 1 0 0 3,44% 1 0 00 3,63% 1 1 0,61% 0,53% 0 1 1 0,63% 0,23% 0 1 1 0,61% 0,55%
d'Anoia i Plegamans 1 1 1 2,26% 1,91% del Vallès
del Penedès i la Geltrú (El) de Llobregat (La) de Mar de Rei del Vallès del Vallès
Subsystem (name) 1991 1996 2001 Boi Sadurní Andreu de la Barca 1 1 1 3,93% 4,60% 0,67% 3,13% 4,39% 1,26% Celoni Martí Sarroca Arenys Barcelona ‐ CBD Cardedeu Granollers Malgrat de Mar Garriga Blanes Sant Gavà Palau ‐ solità Piera Pineda de Mar Sant Terrassa Vilafranca Vilanova Breda Rubí Sabadell Sant Martorell Hostalric Mollet Parets Sant Sant Mataró Montornès Arboç (L') Vendrell Molins Source: Own Elaboration
66 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
01 ‐ ‐ ‐ 0,43% ‐ 6,12% ‐ 4,98% ‐ 1,17% ‐ 6,82% ‐ 4,71% ‐ 2,37% ‐ 8,34% ‐ 6,53% ‐ 6,33% ‐ 3,79% ‐ 7,88% ‐ 0,57% ‐ 1,12% ‐ 7,08% ‐ 6,01% ‐ 0,31% ‐ 9,02% ‐ 6,34% ‐ 4,58% ‐ 0,24% ‐ 4,00% ‐ 13,96% ‐ 11,34% ‐ 22,18% ‐ 16,90% ‐ 11,54% 91 Self sufficiency ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
88,98% 61,08% 72,22% 75,81% 64,99% 29,65% 47,50% 50,40% 78,52% year) ‐ sufficiency (2001 or last Self ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
61,82% 78,21% 51,79% 73,98% 42,27% 60,66% 64,71% 65,65% 61,22% year) ‐ sufficiency (1991 or org. Self
‐ ‐ 1,63% 89,73% 89,29% ‐ 7,11% 85,78% 80,80% ‐ 3,72% 49,11% 42,30% ‐ 3,76% 79,74% 75,02% ‐ 8,54% 64,86% 62,49% ‐ 8,62% 71,80% 57,84% ‐ 9,34% 63,23% 56,70% ‐ 9,23% 59,16% 52,83% ‐ 6,58% 71,24% 49,06% ‐ 3,97%‐ 5,03%‐ 3,95% 74,64% 62,05% 72,37% 70,85% 54,17% 71,80% ‐ 1,24% 80,14% 73,06% ‐ 4,02% 85,84% 79,83% ‐ 2,56% 70,30% 61,28% ‐ 4,72% 54,73% 66,46% 11,73% ‐ 3,71% 65,18% 61,18% ‐ 4,57% 71,51% 81,31% 9,80% ‐ 15,22% 76,17% 67,84% ‐ 18,07% 90,68% 79,34% ‐ 12,80% 37,30% 36,19% ‐ 12,51% 76,39% 76,08% ‐ 10,53% 87,20%‐ 11,57% 80,87% 50,23% 45,65% ‐ 13,41% 66,99% 50,09% ‐ 11,61%‐ 15,32% 60,32% 32,62% 48,78% 32,38% Self 01 ‐ 91 containment ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
71,22% 74,04% 81,28% 2,07% 74,16% 75,32% 1,17% 36,90% 50,76%71,68% 10,07% 55,92% 72,27%46,28% 16,35% 43,00% 1,44% 2,41% 55,67% 64,22% 49,54% 63,05% 45,33% 2,48% 44,46%36,50% 45,63% 1,17% 52,27% 68,45% 55,64% 59,27% 43,95% 9,00% 60,45% 63,44% 2,99% 70,50% 0,81% 86,49% 86,56% 0,07% 70,61% 44,27% 54,80% 72,42% 53,92% 41,33% 0,71% 52,50%86,53% 55,73% 3,23% 35,33% 73,99% 85,52% 76,44% 43,09% 49,97% 35,56% 58,76% 34,95% 57,39% 44,65% 49,85% 50,18% 37,23% 68,15% 71,01% 42,99% 41,91% 65,86% 42,97% 43,44% ‐ containment Self (2001 or last year) ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
72,85% 81,14% 79,21% 40,62% 40,69% 75,45% 44,84% 40,59% 42,86% 45,03% 67,49% 77,08% 64,98% 77,34% 34,95% 69,69% 77,19% 48,24% 59,83% 76,37% 66,72% 40,62% 47,84% 75,22% 89,54% 86,97% 52,32% 61,54% 38,11% 63,49% 48,36% 69,00% 59,98% 41,49% 53,57% 55,26% 30,95% 41,90% 51,12% 54,76% 43,27% 55,04% 51,27% 39,22% ‐ containment Self (1991 or org. year) ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
0,11% 0,23% 0,18% 2,25% 0,70% 0,63% 0,02% 0,10% 0,14% 0,05% 0,13% 0,01% 0,03% 1,18% 0,37% 0,66% 0,24% 0,01% 0,02% 0,00% 0,30% 0,02% 0,03% 0,04% 0,05% 0,06% 0,01% 0,02% 0,02% 1,87% 0,01% 0,15% 0,09% 0,11% ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 11,31% ‐ % LTL 01 ‐ 91 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
135
9.165 4.582 1.477 1.766 7.312 9.204 1.945 3.189 1.754 2.680 1.225 2.766 7.401 8.587 2.835 3.170 4.008 7.828 34.871 72.953 24.215 20.502 55.344 67.297 43.495 33.983 44.606 16.988 47.238 17.375 54.026 21.343 11.331 12.014 12.073 19.827 12.223 21.287 51.737 15.537 18.720 LTL 111.429 932.639 year) (2001 or last
‐
‐ ‐ ‐ ‐ ‐ ‐ ‐
‐
68
984 783 460 294
3.882 2.684 29.234 17.039 LTL year) (1991 or org.
‐
‐ ‐ ‐
‐
‐ ‐
‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
0,18% 26.169 0,00% 7.704 0,09%0,21% 54.316 16.669 3,09% 20.276 0,41% 24.187 0,01% 1.322 0,08% 5.108 0,05% 7.145 0,55% 8.320 0,03% 1.062 0,49% 17.650 0,03%0,05% 8.868 811 0,05% 9.638 0,21% 11.575 0,34%0,05% 20.031 6.053 0,34%0,18% 33.134 13.366 0,08% 4.226 0,06%0,09% 610 1.651 0,03% 16.624 0,51% 48.175 0,18% 14.509 0,04% 5.919 0,10% 33.266 0,03% 6.077 1,56% 115.651 0,02% 3.587 0,03% 43.075 0,04% 12.145 0,09% 4.868 ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 10,71% 904.055 01 ‐ 91 % Population ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
677 5.568 6.446 5.725 5.737 4.897 7.253 8.537 5.568 57.438 24.050 15.680 53.564 17.863 30.810 12.252 31.985 34.685 65.546 77.418 31.359 36.358 87.328 17.451 25.305 54.983 75.302 35.141 29.997 10.453 58.996 28.831 30.362 15.727 22.182 105.704 192.483 112.743 155.122 231.096 116.128 270.978 year) 131.690 2.182.836 Population (2001 or last ‐
‐ ‐ ‐ ‐ ‐ ‐
‐
‐
year) Population (1991 or org. ‐
‐
‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐
‐
‐ ‐
‐
‐ ‐ ‐ ‐
0001 1 1 90.435 0 1 1 22.219 110 1 1 1 10 1 1 167.147 1 17.286 40.795 1 4.672 1 1 1 12.809 0 1 01 4.089 1 1 83.394 1 0 1001 1 25.143 1 1001 158.214 001 1 10 11 10 36.040 11 1001 1 1 1 0 4.704 001 80.962 101 1.937 1 49.079 1 0 1 1 0 1 32.581 15.083 3.063 001 1 1 1 81.284 001 0 1 1 17.648 1 1 1 20.423 1 1 1 2.366.458 1 0 0 11.971 11 1 1 1 1 52.994 29.061 001 111 1 1 1 1 1 1 89.342 302.862 19.458 1 1 0 118.804 11 1 0 1 1 2.476 5.836 1 1 1 51.186 0 1 1 41.956 1 1 10 117.930 1 0 302 1 0 0 50.954 0 1 1 8.848 1 0 0 1.827 11 10 1 1 1 1 27.140 0 19.873 1.272 0 1 1 18.218 0 1 1 18.735
a r s
t t s t t t
(name) 1991 1996 2001 Hort de Mogod r r r r r r d'Anoia de Vilamajo i Plegamans del Vallès del Vallès del Penedès de Llobrega i la Geltrú (El) de Llobrega de Llobrega (El) de Ma (La) de Ma de Ma de Rei del Vallès del Vallès Perpètua Protosystem Celoni Cugat Sesgarrigue Pol de Ma Vicenç de Montal Boi Martí Sarroca Sadurní Feliu Andreu de la Barca Vicenç dels Antoni Vilanova Blanes Sant Terrassa Vallirana Vilafranca Breda Garriga Sant Sant Sant Sant Sant Cerdanyola Vilassar Hostalric Granollers Malgrat de Ma Gelida Montornès Sant Barcelona Montgat Sant Vendrell Cornellà Martorell Masnou Pontons Rubí Sabadell Sant Sant Arboç (L') Sant Gavà Santa Begues Bigues i Riells Mollet Mataró Molins Mura Premià Bruc (El) Palau ‐ solità Parets Pla del Penedès (El) Piera Cardedeu Corbera de Llobrega Pineda de Ma Arenys Source: Own Elaboration
67 RSAI – 58th Annual North American Meetings of the Regional Science Association International & Second Conference of the Regional Science Association of the Americas. Miami (9th – 12th November 2011)
‐ 0,33% ‐ 0,48% ‐ 0,01% ‐ 1,03% ‐ 2,64% ‐ 0,75% ‐ 0,02% ‐ 0,10% ‐ 2,16% ‐ 2,27% ‐ 0,09% ‐ 0,15% ‐ 0,03% ‐ 0,48% ‐ 0,89% ‐ 0,07% ‐ 0,38% ‐ 0,08% ‐ 0,19% ‐ 0,19% ‐ 0,07% Index 01 ‐ 91 % OF Entropy
‐ 0,21% ‐ 0,11% ‐ 2,10% ‐ 0,06% ‐ 0,22% 0,30% ‐ 0,21% ‐ 1,84% ‐ 3,57% ‐ 0,27% ‐ 0,15% ‐ 0,70% ‐ 0,57% 0,38% ‐ 0,40% ‐ 0,01% ‐ 0,01% ‐ 0,65% ‐ 0,35% ‐ 1,23% 0,27% ‐ 0,41% ‐ 0,44% Index 01 ‐ 91 % IF Entropy ‐ 0,54% 0,20% 0,31% ‐ 0,68% ‐ 0,29% 0,04% ‐ 0,20% 0,04% ‐ 0,12% 0,05% 0,04% ‐ 1,82% ‐ 0,18%‐ 0,31% ‐ 2,10% 2,13% 0,25% ‐ 0,05% ‐ 1,91% ‐ 0,05% 0,18% 0,17% ‐ 4,38% ‐ 0,25% 0,10% ‐ 1,88% ‐ 0,22% ‐ 0,73% ‐ 0,11% ‐ 0,30% ‐ 0,29% 0,00% 0,07% ‐ 1,60% ‐ 0,41% ‐ 0,05% 0,06% 0,14% ‐ 0,70% ‐ 0,30% ‐ 0,18% ‐ 0,30% Index 01 ‐ 91 % RW Entropy
Index ‐ 0,29% ‐ 0,64% ‐ 0,12% ‐ 0,49% ‐ 0,03% ‐ 2,04% ‐ 0,23% ‐ 0,35% ‐ 1,29% ‐ 0,12% ‐ 2,10% ‐ 3,48% ‐ 0,17% ‐ 1,53% ‐ 0,08% ‐ 0,64% ‐ 0,45% ‐ 0,15% ‐ 1,08% ‐ 0,24% ‐ 0,01% ‐ 0,48% ‐ 0,01% ‐ 0,11% ‐ 0,27% 01 ‐ 91 % Population Entropy ‐‐‐‐ ‐‐‐‐ ‐‐‐‐ ‐‐‐‐ ‐‐‐‐ ‐‐‐‐ ‐‐‐‐ ‐‐‐‐ ‐‐‐‐
2,58% 0,29%0,39%6,39% 0,23% 0,04%2,93% 2,12% 0,24% 0,07% 0,01% 2,83% 0,36% 0,05% 0,26% 0,36% 0,11% 0,06% 1,33% 0,01% 0,00% 0,11% 2,87% 0,35%0,59% 0,10% 0,07% 0,04% 0,01% 0,22% 2,21% 0,12% 0,05% 1,43% 3,95% 1,17% 3,87% 1,10% 4,86% 1,59% 4,33% 1,63% 7,09% 0,90% 5,65% 0,92% 2,38% 1,40% 0,00% 0,83% 0,67% 1,47% 1,57% 0,35% 1,45% 3,69% 3,20% 1,22% 0,06% 2,25% 0,11% 0,04% 0,04% 0,02% 0,43% 0,35% 1,35% 2,33% 1,41% 0,50% 0,83% 0,31% 14,81% Index % Population Entropy ‐ ‐‐‐‐ ‐ ‐‐‐‐ (2001 or last year) ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐ ‐ ‐‐‐‐
2,29% 0,35% 4,27% 2,92% 0,30% 3,10% 0,25% 0,51% 2,09% 1,72% 4,59% 1,29% 4,36% 1,12% 6,91% 1,93% 5,62% 1,75% 0,16% 1,07% 1,14% 7,17% 0,19% 0,99% 3,00% 0,31% 3,01% 1,40% 1,27% 3,84% 4,28% 0,94% 1,46% 0,03% 5,65% 2,14% 0,35% 1,83% 1,42% 0,60% 1,10% 0,11% 16,91% 10,57% Index % Population Entropy (1991 or org. year)
‐ 0,43% ‐ 0,17% ‐ 0,05% ‐ 0,34% ‐ 0,05% ‐ 1,87% ‐ 0,11% ‐ 0,22% ‐ 1,59% ‐ 2,08% ‐ 4,13% ‐ 0,12% ‐ 1,46% ‐ 0,18% ‐ 0,68% ‐ 0,22% ‐ 0,32% ‐ 0,17% ‐ 1,02% ‐ 0,45% ‐ 0,01% ‐ 0,53% ‐ 0,60% ‐ 0,27% ‐ 0,32% Entropy Index 01 ‐ 91 % LTL ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
0,48% 1,42% 1,42% 0,29% 2,11% 0,03% 0,42% 2,16% 0,41% year) Entropy last % LTL ‐‐ ‐‐ Index (2001 or ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
0,19% 0,90% 2,96% 0,23% 0,14% 0,66% 4,46% 0,02% 0,08% Entropy org. year) % LTL Index (1991 or
‐ 1,71% 6,42% 4,55% ‐ 0,08% 1,47% 1,35% ‐ 4,88% 17,08% 15,00% ‐ 4,18% 11,46% 7,33% ‐ 0,74% 6,98% 5,52% ‐ 0,25% 2,90% 2,23% ‐ 0,07% 2,45% 2,23% ‐ 0,16% 0,96% 0,64% ‐ 0,26% 1,89% 1,44% ‐ 0,02% 2,27% 1,74% ‐ 0,70% 2,61% 2,01% ‐ 0,22% 0,70% 0,43% ‐ 0,20% 0,90% 0,58% % IF Dominance Index 01 ‐ 91 ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
0,24% 0,64% 0,56% 0,12% 2,66% 0,01% 0,26% 0,43% 0,27% year) last % Dominance Index (2001 or ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐ ‐‐
org. year) % Dominance Index (1991 or ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ ‐ 1 1 10 1 4,00% 1 4,72% 0,38%1 0,72% 0,44% 1 4,90% 1 0,05% 4,47% 2,46% 1,31% 4,18% 1,14% 1,72% 3,87% 3,82% 1 0 1001 1 0,21% 1 1001 0,36% 7,80% 0,15% 6,08% 1,48% 1,14% 001 1 10 11 10 11 0,67% 1001 1 1 1 0001 0,96% 0,10% 10 2,84%11 1 0,11% 0,29% 0,14% 0 3,12% 3,55% 1 1 0 1,68% 0,03% 1 3,52% 0,71% 1,03% 0,47% 1,90% 0,25% 0,09% 0,40% 3,39% 0,96% 0,22% 0,31% 0,11% 3,04% 5,22% 0,06% 0,01% 3,18% 1,84% 0,14% 0,24% 0,25% 0,01% 1 1 1 40,72% 35,83% 1 1 1 10,16% 5,98% 1 1 1 3,41% 2,67% 0 1 1 0,50% 0,58% 0,07% 1,06% 1,00% 111 1 1 1 1 1 1 1,83% 0,57% 1,75% 4,58%001 0,63% 1,89% 2,75% 0,06% 0,13% 3,35% 1,30% 5,93% 4,06% 1,08% 0 4,33% 0,70% 1 0 0,06% 1 0 0 2,13% 0 1 1 0,30% 0,38% 0,08% 1,08% 0,96% 1 1 1 2,16% 1,91% 111 1 0 0 1 1 0 0,05% 0,17% 0,05% 0,06% 0,30% 0,01% 0,13% 0,19% 0,44% 0,21% 0,47% 0,02% 0,04% 1 1 1 2,67% 2,59% 1 1 1 0,48% 0,32% 1 1 1 0,60% 0,60% 0,01% 1,13% 0,95% 001 1 0 0 0,41% 0 1 1 1,06% 1,14% 0,08% 2,42% 2,46% 0,04% 1 1 1 1,53% 1,27% 1 1 0 2,03% 0001 1 1 0,66% 0,71% 0,05% 3,41% 3,24% 1 1 1 2,98% 3,58% 0,60% 4,91% 3,89% 0 1 0 0,01% 0 1 1 0,08% 0,11% 0,03% 0,30% 0,29% 1 1 1 1,53% 1,52% 001 1 1 1 3,11% 2,41% 0 1 1 0,34% 0,14% 0 1 1 0,40% 0,18% 0 1 0 0,03% 0 1 1 0,38% 0,43% 0,05% 1,81% 1,87% 0,05% a r s t t s t t t (name) 1991 1996 2001 Hort de Mogod r r r r r r d'Anoia de Vilamajo i Plegamans del Vallès del Vallès del Penedès de Llobrega i la Geltrú (El) de Llobrega de Llobrega (El) de Ma (La) de Ma de Ma de Rei del Vallès del Vallès solità Perpètua Protosystem Celoni Pol de Ma Cugat Sesgarrigue Feliu Vicenç de Montal Boi Martí Sarroca Vicenç dels Sadurní Andreu de la Barca Antoni Rubí Sant Sant Cerdanyola Barcelona Sabadell Sant Terrassa Sant Sant Cardedeu Corbera de Llobrega Arenys Cornellà Garriga Martorell Masnou Mataró Molins Pontons Sant Sant Sant Vilassar Mollet Sant Begues Bigues i Riells Bruc (El) Sant Santa Vallirana Gelida Premià Montgat Sant Vilafranca Montornès Palau ‐ Gavà Vilanova Blanes Granollers Malgrat de Ma Mura Breda Hostalric Parets Arboç (L') Piera Pla del Penedès (El) Pineda de Ma Vendrell Source: Own Elaboration 68