Urban form as a problem of performance

8/13/2019 Urban form as a problem of performance

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Urban form as a problem of performance:From indicators of urban features to systemic indicators of actual performance

Research paperUnder 6,000 words excluding abstract, tables, references and appendix

Vinicius de Moraes NettoEscola de Arquitetura e Urbanismo

Universidade Federal Fluminense (UFF)

R. Passo da Ptria, 156 - Campus da Praia Vermelha

Niteri, Rio de Janeiro 24210-240

Email: [email protected]

Ph.D in Advanced Architectural Studies (The Bartlett School of Graduate Studies, UniversityCollege London, UCL 2007), with Post-doctoral studies in Urban Performance (National

Programme for Postdoctoral Studies PNDP CAPES, Brazilian Government, 2009), Mastersin Urban Planning (Urban and Regional Planning Graduate Programme, Federal University of

Rio Grande do Sul, UFRGS 1999) and undergradute studies in Architecture and Urbanism

(UFRGS, 1997). Reader, School of Architecture and Urbanism (Federal UniversityFluminense, UFF), Vinicius carries research on in the Urban Configurational Systems

Research Group, linking many universities thorughout Brazil and led by Professor Romulo

Krafta. He is also a researcher linked to the National Council for Research (CNPq) with a

number of projects related to urban performance.

Romulo KraftaFaculdade de Arquitetura

Universidade Federal do Rio Grande do Sul

Rua Sarmento Leite 320, 5o andar

90050-170 Porto Alegre, RS Brasil

Email: [email protected]

Ph.D in Urban Science (Cambridge, 1992), with Post-doctoral studies in the Centre forAdvanced Spatial Analysis (CASA, University College London, UCL 2003), Masters in

Urban Design (Oxford Brookes University, 1992), and undergraduate studies in Architectureand Urbanism (Federal University of Rio Grande do Sul, UFRGS 1973). Professor (School of

Architecture and Urbanism, UFRGS), Romulo is the leader of the Urban ConfigurationalSystems Research Group, a member of the Scientific Commitee of the Brazilian Society for

Progress in Science, a consulting member of CAPES and CNPq.

Abstract: One of the major challenges in the urban sustainability debate is to consider

morphology not as an end in itself, but something caught in a fabric of relations embedded in

social, economic and environmental processes. Theory still faces the challenges of describing

the conditions of performance of cities, and developing instruments able to assess urban formas a problem of performance. The article brings a critique of usual indicators asserting that

most consist of feature indicators of absolute urban properties rather than performance

indicators able to assess the dynamic effects of properties on urban processes. Discussing

epistemological conditions of performance analysis and the question of causality, it introduces

new, systemic indicators intended to grasp urban form and dynamics as relational processes.

A framework is arranged as (i) performance indicators (spatial quality, urban equity,

efficiency and sustainability), and (ii) urban indicators (morphology, space-socioeconomic


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networks relations, thresholds in urban patterns, and city-environment relations). Key words:

sustainable urban form, performance analysis, systemic indicators.

1. IntroductionOne of the major challenges in the sustainable urban form debate is to consider morphology

not as an end in itself, but as something caught in a fabric of relations embedded in social,economic and environmental processes; a fabric where lines of causality might be found

within a maze of contingencies and unpredictability. In other words, theory still faces(perhaps more than ever) the challenges of describing the conditions of performance of cities.

Referring intimately to a deeper and more critical understanding of urbanisation, attention has

been given to the impacts of urban patterns on the workings of societies and the environment

itself. However, we shall observe below important theoretical and methodological gaps in the

analytical tools available to identify urban form as a problem of performance according to

rigorously defined criteria. Aiming to contribute to existing theories and methods to assess

urban performance, this paper argues that most indicators found in the literature have not been

able to grasp the city as a complex relational phenomenon. Accordingly, it proposes a

conceptual and methodological framework geared to take into account the effects of spatial

patterns over socioeconomic processes and environmental externalities.

In order to assess relational aspects of urban performance, the paper introduces a series ofindicators of a systemic type, i.e. indicators (a) based on a view of cities as complexes of

interaction between constitutive elements, morphological characteristics and socioeconomicand environmental implications; indicators which (b) take into account rather explicitly the

problem of changein those elements, characteristics and implications as active factors in theperformance of the city as a whole. The new indicators shall be developed along two lines of

approach: performance indicators (synthetic indicators grouped under well-knowndimensions in urban theory, namely spatial quality and urban efficiency, equity and

sustainability) and urban indicators (synthetic indicators geared to assess states of

morphology of built forms and street networks, space and socioeconomic networks,

thresholds in urban patterns, and city-environment relations). These two sets of systemic

indicators lay down the grounds for a truly relational analysis of the performance of cities.

The final section addresses the combinations of systemic feature indicators into performanceindicators and potential applications, whereas the appendix brings the mathematical definition

of key indicators developed for the framework.

2. Representing the urban systemThe analysis of urban performance brings along, on the one hand, the evaluation of active

relations in an urban system defined by durability, rigity, and opacity and, on the other hand, a

substantially elusive system made out of practices and interactions, socialities and networks.

The analytical method proposed here considers independent ontological levels, yet interactiveand subject to mutual effects:

Material system Environmental system

Urban systemTechnical system

Social system Action systemAgents arranged in networks

Exogenous relations Macroeconomic flows

Regional relations


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Systemic indicators geared to grasp relational aspects of city dynamics operate within and

beween these levels. The material system is, composed of an urban system, a hardwarefounded in the rigidity and durability of space with immediate and active relations to an

environment, in turn both subject to externalities and a material resource for urban processes.The urban system is analysed in activities or attractors (buildings and their socioeconomic and

cognitive contents, arranged in plots, blocks etc.) and the network of public spaces (streets,squares and so on). The technical systemconsists of fixed, mobile and virtual artefacts and

technologies used to generate mobility and connectivity (Latour, 1993; Thrift, 2008) which,along with urban space and language, consist of a substantial part of how we keep social

systems together. The social system is constituted of actions and interactions of agents and

networks based on social interests, positions or economic role (arranged in the form of

groups, institutions, firms; as workers, consumers, suppliers of final or intermediary goods).

Figure 1: Ontological levels in urban sustainability: from social to spatial to environmental

systems - and back

Such distinctions allow direct investigations on the relationality in these systems and theanalysis of the role of cities as central in such relationality. This approach also allows an

account of the connections of the city to macroeconomic processes as inputs to growth.Furthermore, we propose the analysis of networks interacting in the city and competing for

location as a crucial dimension of performance from networks of social reproduction tonetworks of economic production and those engaged in the production of urban space:

i. Networks of non-instrumental social interaction

ii. Networks of Final supplier Consumer relations

iii. Networks of Intermediary Firms

iv. Networks of Firm Worker relations


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mobility as capacities in the generation of income and factors linked to transport costs,

interaction, and personal productivity. As certain locations and mobility levels potentialisethese capacities, the relation agent-urban structure is a relevant issue to social equity. If we

assume that an urban system benefits from increases in the average productivity of itsinhabitants, we may infer that the spatial conditions for agents to be equally productive are

also relevant aspects of urban efficiency. Overtly systemic indicators such as spatialopportunity (a property of locational advantage), accessibility (the influence of the street

network in reachability), and segregation (restrictions on social interaction due to spatiallocation and mobility), once combined, seem able to capture the impacts of spatiality over

levels of equity. The urban equity indicator proposed below relies on the spatial opportunity

indicator for work and facilities: when a particular social groups location is more privileged

than others, the indicator must point this out as a reduction of urban equity.Equity increases

with socially distributed mobilities, and the measure uses simple means to weigh different

transport forms.Accessibility, as we shall see below, captures the distance from every

residential location in the urban system from every other location, according to class. The

impacts of residential segregation are included in the urban equity indicator as the difference

between average topological distances between locations of different classes.

3.3. Urban efficiency

Paradigm in urban theory in the 1960s, the subject of efficiency has been recently broughtback by discourses on sustainability and resource management. We would like to approach it

as a problem of relations of urban form to socioeconomic networks. In principle, urbanefficiency has to do as much with the efficiency of elusive social dynamics under certain

spatial conditions as with the efficiency of spatial structures in supporting those dynamics.The first aspect involves the assessment of the network of agents connections as they are

mediated by the spatial network of physical linkages as factors of cost and efficiency ininteraction through graph-theoretic procedures i.e. relations mediated by distinct

accessibility levels between locations, in turn instrinsic to the grid. The second aspect

analyses how the urban structure performs in terms of allowing possible social and economic

interactions, comparing the current state of the network of paths and locations with potential

scenarios of connections between possibly complementary agents. The output here is a

measure of how the spatial network supports new interactions due to accessibility andinformational capacities intrinsic to its structure so that new interactions may easily come into

being. Locations which potentialise connections must be recognised (potential scenarios).

Both aspects are essential if we are to evaluate how agents immersed in syncopated

movements and interactions (workers, firms, consumers) are subject to spatial friction in their

potential to interaction. Other things being equal, distance tends to be a major aspect in the

choice amongst potential counterparts in future social or economic interactions. Movement

also depends on the distribution of activities and grids structured enough to minimise

distances a matter of urban form.

Despite all contingencies and local-dependencies, this is a universal problem: wherever citiesare found, there still seems to be a fundamental dependency of socioeconomic processes on

mobility of artefacts and people (mediated by space). Of course, we may say that citiesemerge as a solution to the problem of distance a common assertion in economic geography

(see Fujita and Thisse, 2002) and we may extend that idea to say that structures within citieshave exactly the same role: a collective and historical solution to the problem of relating and

connecting the actions of a changing number of diverse agents. However, cities can only

minimise the problem of distance through the distribution of potentials that take the form of

the hierarchies of accessibility and centrality within cities clearly in different extents in

different structures. Urban structures are at once a form of information of possibilities of


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action, and a form of restriction; a form of increasing accessibility and reachability, and limit

free movement in any direction, and an initial friction to agents knowledge of other agents.This approach to efficiency relates essentially to the examination of degrees of influence of

space over the generation of possibilities of interaction and over choices amongst possibleinteractions. Sustainability, in this sense, would relate to diversity and longevity in the

generation of possibilities of interaction and in the actualisation of interactions. The typicalurgency of daily exchanges in the city, the centrality of spatial conditions adequate to

maximise mobilities and actualise interactions, and the problem of costs and time in transportassert the need to assess urban efficiency. Urban efficiency is a way of searching the economy

of means, productivity gains and functionality in a city. In that sense, it is a property of states

of urban systems: (i) the efficiency of a pattern of location of activities and relative distances

for potential interactions, and the degree of interactivity itself so that interactions may emerge

with less material costs; and (ii) the degree of intensity of exchanges in instances of material

production and social reproduction.

A synthetic way to assess urban efficiency is through the potential to connections in a social

network namely, in the passage from connection possibilities between potentially

complementary agents to the network of actual connections, a passage mediated by internal

hierarchies in the spatial network (grid and locations). An efficient city would have a network

of physical linkages connecting a pattern of locations in a way to render that passage fluid.High degrees of dispersion of materially dependent agents imply greater distances and less

efficiency in the management of resources and time, affecting the socioeconomic performanceof the urban system with negative externalities over the workings of the city such as

negative externalities and decreases in productivity. The analysis of urban efficiency includesmeasuring topological relations between pairs of agents locations and their distances

compared to a graph of ideal locations where every agent would be one topological step fromany other. This ideal locational set show how close the actual system is to offering minimal

distance between potentially interactive agents. Space always means distance between agents

in a social network, so the problem is to assess how spatial patterns may impose difficulties in

network connectivity. It also takes into account the size of the urban system as a factor that

can be methodologically normalised, as the efficiency of spatial patterns (grid and locations)

is relativised especially for comparisons of different cities. There are other applications: The analysis of urban efficiency may focus on specific networks (say, between

intermediary firms in a certain sector) considering the topological distance between locations

and comparing to the ideal graph of one-step distance locations. Hierarchies of future

locations may be simulated, considering specific complementarities and how much agents

would benefit from certain locations or ignore the advantages of better locations an

application potentially useful in zoning.2

It may also show efficiency as effects of (i) increases in accessibility and mobility

due to improvements in the spatial network or changes in location patterns; (ii) increases incompacity and centrality; and (iii) increases in spatial information of possible counterparts in

interaction (namely, in the hierarchies of location and accessibility) assessed in simulatedscenarios.

3.4. Urban Sustainability

Precisely because of the extension of variables involved and the resulting indefinition inconcepts largely used, sustainability is a category of difficult treatment. Notions that

encompass the city are frequently associated with ideas of management of resources and

2Other advances in the measurement of urban efficiency may include other, more usual, items: the efficiency in

coverage of infrastructure and transport (usual indicator) in relation to the degrees of reachability between

agents.


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negative externalities of urban form and processes (e.g. Ratti et al, 2003; Stone et al, 2007). In

this approach, we shall consider urban sustainability as a meta-indicator of forms of assuringthe continuity of urban systems which take into account the continuity of other systems

environmental, social, economic, and so on.

Usual hypotheses regarding the relation of urban form and sustainability have pointed outthat: (a) up to certain thresholds, compact cities tend to be more sustainable (e.g. Johnson,

2001; Chen et al, 2008). On the other hand, some have argued against oversimplifications,considering that both fragmentation and compacity are processes temporally implicated in the

continuity of cities (Polidori and Krafta, 2004). Research on urban sustainability has focused

on the analysis of states rather than processes related to self-organised solutions to

fluctuations in time. The problem at hand whether to assess instability as a threat to

sustainability or the opposite, a sign of urban vitality. These two possibilities shed some light

on the nature of the debate over sustainability: the opposition of a view on sustainability as a

process of reduction of pace in urban development to a view geared to reassert the capacity to

solve problems brought about exactly by development. Instability is an instrinsic component

of urban processes, and change lies at the heart of the urban. Among its central factors lie: (i)

changes in urban processes subject to exogenous forces brought about by the connections

between city, region, and the macroeconomy (Krugman, 1994; Fujita and Thisse, 2002); and

(ii) the problem of thresholds in structuration process, and the recursive consolidation andchange of urban patterns. Such processes operate in time throughout different (and related)

scales and frequencies whose discontinuities point to transitions from one scale to another.The problem of change, essential to understanding the real conditions of urban sustainability,

implies the question of localised thresholds in different processes, structures and scalesconnected to changes of global patterns in a city (Bak et al., 1988; Batty and Xie, 1999).

Thresholds have to do with the capacity of urban form to absorve change: the capacity to self-organisation becomes a key part of continuity. Urban sustainability therefore includes:

(1)Efficiency in socioeconomic networks supported by city structures, assessed in

time, and including the analysis of the nature of evolution in its continuity;

(2)The structural capacity of urban form (thresholds), generation and change of

spatial patterns and the possibility of changes in urban areas. The capacity toabsorve change in its structure would assure ways adequate or not into

continuity. The analysis of thresholds of growth, urban patterns and the capacities

of interaction that follow are key issues in urban sustainability analysis, and relate

to limits to both urban sprawl and internal densification.

(3)The dependency of cities on energy resources, and thresholds in resources

available for urban development.

(4)Negative externalities of urban processes over the environment of cities, which

might bring potential impacts back over urban continuity (the city-environmentrelation).

(5)Urban performance regarding equity, with close relations to urban efficiency.

Urban sustainability is, therefore, a meta-dimension of performance that incorporates previousones. Its assessment involves comparative analyses of the evolution of urban states, and the

study of alternative scenarios based on parameters found in a particular city.

4. Meta-indicators and the empirical dimensions of the city

The analysis of performance faces the problem of diversity: the complexity of urban processes

might imply a number of indicators nearly as big as the number of variables possibly

identified. Key methodological steps, therefore, are selection, combination and synthesis:the


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ability of indicators to address and relate in a powerful and meaningful way features, relations

and processes actually ongoing in our cities. Urban indicators may be grouped in a number ofways. We proposed to do so firstly according to dimensions found in the history of urban

theory and methods. We would like to suggest now a second way of assessing urbanperformance: a set of indicators geared to address directly well-known dimensions of cities.

Thus, morphology indicators refer to spatial features whose measurement may give hints intothe workings of the city; space and socioeconomic networks indicators should capture

relations between the spatial system and agencies; and city-environment indicators address themutual impacts of urban functions and environmental context and resources.

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4.1. Urban morphology indicatorsMorphology indicators are certainly a key class of indicators: planners should closely know

the spatial characteristics of a city and their implications in its workings. In this framework,

morphology indicators are perfectly analogous to the property synthetically defined above as

spatial quality. Nevertheless, we propose three related levels of investigating and assessing

morphology: global configuration (the city as a whole spatial system), the level of spatial

informationderived from spatial structures (useful for cognitive and bodily navigation in the

city and essential for social practices to come into being), and local morphology (forms of

occupation of space and building patterns) as an expression of tendencies seen globally in the

city, having effects back into global structures and processes. Grasping mutual scale effects isextremely important in a systemic approach to performance.

Indicators of urban configuration

They address properties divided in subgroups according to the approach to urban form:according to absolute geometry characteristics of urban form (areas, volumes, and metrical

distances) and to topological ones (connectivity in the spatial network, topological distance,etc.).

Building morphology

a. Compacity has recently found enormous attention in the sustainability debate, due to its

relation to internal distances in the city, sprawl and impacts on car dependence, fuel

consumption and so on. Current indicators are based on metrical measures, generallyaddressed through three relations (also related to density see Churchman, 1999): (i) built

area and total urban area; (ii) occupied area and total urban area; (iii) population and area

(which assumes that areas more densely populated are also more spatiall compact). However,

these indicators do not grasp precisely what spatial compacity really means to urban

performance: the point is not so much the geometrical property as such, or sheer numbers of

people, but what these spaces support in terms of socioeconomic activity. Similar spatialities

may have quite different forms and intensities of occupation and activity. Usual measures say

little about the potential to socioeconomic interactivity lying in urban space: how spatialdensity matters for practices which depend on proximity, and how agencies occupy space in

order to potentialise their interactivity.Therefore, the number of spatial units that supportthese agencies may be a better way to tackle how compacity matters in urban performance.

We propose a measure of compacity geared to grasp the city as a system of spatial units,socially and economically active and irregularly distributed as an indicator to the compression

of residential and economic units per area or street segment. This way we may redefine moreprecisely the notion of compacity in a more rich measure naturally related to other systemic

3Many feature indicators brought together in this framework were developed in previous works by the authors;

new feature indicators are introduced, along with the synthetical urban performance indicators; others are found

in the best available literature on systemic indicators, and are indicated below. Mathematical definitions of our

indicators are found in the appendix.


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indicators defined to capture urban form and dynamics as relational processes. A step

forward, there is the problem of thresholds of compactity: the effects of compacity might haveunintended consequences such as lowering habitability.

b. Built form continuity:relation of built form extension and the extension of streets,assuming that buildings support activities and faades are their interfaces to the public realm

of the street. Faades support the pedestrian appropriation of streets, potentially stimulatingmicro-economic exchanges and urban life.

Street network morphology

a. Accessibility: topological measure for every segment in the street network in

relation to every other segment. Every segment has an average distance in relation to all

others, which expresses the accessibility to this unit. Averages define an accessibility rank and

a measure of spatial differentiation. Notably, accessibility is central to urban efficiency, equity

and sustainability.

b.Depth:classic measure of topological distance in the urban grid (e.g. Hillier, 1996).

Deeper spatial networks tend to imply longer distances, which may have effects on costs and

time travel in socioeconomic interaction. They also may be related to segregation. A way of

measuring depth is the the sum of all shortest paths connecting every pair of street segments.

The measure relates to questions like what is the effect of increases in topological depth in a

particular urban system (say, due to peripheral growth or sprawl) to internal distances anditems such as fuel consumption, or the economic sustainability of interactions (say, within a

particular economic sector)? However, the indicator may be of little use if not related toothers, or if not normalised against the size of the urban system: a large morphological

structure may have more beneficial effects over socioeconomic interactivity than one withless topological depth, if the former has more compacity.

c.Distributivity:property associated with the number of alternative paths between anypair of locations allowed by the level of connectivity and geometry of the network. A network

is not distributive when there is only one possible path between two locations. One way to

measure distributivity is through the number of cycles within a network compared with that of

regular grid (as the most usual spatial structure, although not optimal in terms of

distributivity). This is a key quality of urban structures: grids whose geometry allows multiple

paths with similar internal distances naturally offer more mobility, supporting daily trafficmore efficiently.

d. Permeability:a metric indicator related to the potential to mobility in an urban area,

it also provides a look into the interface between private built form and public open space in

turn related to the possibility of exchanges between them. The former aspect relates to

distributivity in the network; the second relates to the functional foundation of the city as a

place for interaction between private and public realms. Low permeability means difficulties

to movement and efficient access to urban activities increasing local distances that impose

difficulties especially on pedestrians. On the other hand, networks with too much permeabilitymight imply inefficient occupation of urban space, and dispersion of pedestrian and vehicular

movement to lower levels than those required to sustain microeconomic activities linked topublic spaces. A simple form to assess permeability is the ratio of areas invested in

occupation (blocks) and the extension of the corresponding street network. However, this isproblematic since a city may have parts with big blocks and low permeability and other parts

with small blocks and high permeability, finding the same average as a city with a goodbalance of grid and block sizes. The indicator also requires the definition of adequate ratios of

permeability in a particular city, in order to define thresholds of high and low permeabilities.

Spatial information


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The property addresses cognitive relations between agent and urban morphology, and implies

levels of intelligibility inherent to the network of streets and built forms. On the one hand,differences in accessibility found in different streets mean more facility to navigation; we tend

to understand the city through them, and relate the information retrieved from them to otherspaces with their own levels of information (structural information). On the other hand, built

forms also contain informational differentials related to practices they support; they arecarriers of social information, which in turn inform about possibilities of action. Information

indicators are relevant in the analysis of the capacity of agents to appropriate urban space, asaspects of interaction to urban efficiency and sustainability. Performance analysis must take

into account the property of spaces containing and potentially diffusing information:

a. Identity:analyses the extension of spaces in the spatial network that are part of the

informational core of the city (spaces with higher level of structural and semantic

information) in relation to the grid as a whole assuming that this core anchors navigation

and efforts to relate to space in order to retrieve social information.

b. Information: property of spaces containing and potentially diffusing information

useful for navigation, or about activities and practices. The first aspect relates to street

network topologies and probabilities of reach (Rosvall et al, 2005) whereas the second relates

to built form (semantic information) and their informational capacities and roles of different

spaces.

4.2. Indicators of space-socioeconomic networks relations

A series of indicators allow the analysis of the role of space in agents interactions. Theyaddress states in a localised socioeconomic system whose interactions are mediated by space,

in order to assess how space is part of its potential to connectivity. State indicators aretriggered in every iteration and associated with sequences of urban scenarios, in comparative

analyses.a. Centrality finds a number of interpretations in urban theory. We define as levels of

spatial differentiation in the urban structure related to the intensity of activities supported,

including the effects of scale and diversity of land uses and the accessibility of spatial

networks. It grasps the spatial conditions for the interactivity of agents in different intensities.

b. Spatial opportunity: indicator of privilege of residential locations in relation to

services or jobs location: it analyses the relation between each agents residential location toservices/jobs, taking topological distance and attraction as features in the relation. It is a key

operation regarding the analysis of urban equity and efficiency: it describes how easy or

difficult is to reach useful locations in a city. The city is methodologically disaggregated in

spatial locations (in segments of streets corresponding to blocks, or their corners), and

services are considered individually or in categories according to scale, attraction potential,

complexity, and type of activity. Analysis also involves a selective graph (i.e. origins and

destinations are specified), along with thresholds of mobility of agents and attraction for each

service.c. Convergence: indicator of locational privilege for a number of services regarding

the location of potential consumers, calculated through agraph which only takes into accountpairs of spatial units that have residential location as origins and selected services as

destinations. It is geared to inform about the potentials inherent to every service location inattracting consumers heterogeneously distributed in space.

d. Polarity means the effects of a certain activity on the pattern of centrality of a city.The indicator takes into the account the potential relationships of a particular attractor to all

potential consumers, weighing the spaces in the street network between them.

e. Interactivity:the intensity, diversity and scale of potential interactions in an urban

system are key aspects of the spark to economic processes. The indicator relates to

connectivity, density and cohesion in selected networks (based on functional complementarity


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or not) through usual measures in Social Network Analysis, along with intensities of

exchanges (see Friedkin, 2004; on directed relations in networks, see Grannis, 2010; recentapproaches have included space-depency on neighbourhood effects, see Savitz and

Raudenbush, 2010).e. Mobility: capacity to reach places in the urban grid. It relates to a number of

variables, from morphological to technical systems. The former relates to distributivity,accessibility, internal distances and residential location; the latter relates to transport modes,

costs and coverage, and travel times. Mobility are different for socially different agents.f. Segregation in networks: the level of overlapping of different social networks

(according to class, social groups or other categories selected) in urban space. Social networks

are modelled through categorisation of residential, services, consumption and job locations

(and facilities such as transport services) according to different social groups or classes. It

includes locations, accessibility and patterns of mobility in order to generate maps of

movement and appropriation of distinct social groups, in order to acess how convergent they

are in spaces of the city.

4.3. Indicators of thresholds in urban patterns

A set of indicators is introduced to assess the capacity of urban systems to absorb changes in

the face of instabilities in built form, location and accessibility patterns or fluctuations in their

interactions with the environment, region or macroeconomy. Of course, these processes arehighly context-dependent. Threshold indicators operate with measures such as centrality,

related in a way to grasp the signs of global or local morphology and location patterns facingexhaustion or reaching thresholds.

a. Tension: a measure of intensity of urban activity geared to capture thedifferentiation between accessibility patterns in street networks and activity distribution

patterns as urban centralities. A high superimposition of these patterns would be expected,and may consist of an ongoing trend of self-organisation in a city. Differences mean that

tensions are found and changes in patterns may be near or underway. The indicator calculates

the correlation between positions in both patterns, and the degree to which they overlap a

measure particularly useful to understand cities with an ongoing, intensive growth.

b. Thresholds: specific indicators assess (i) the consolidation of patterns (Bak et al,

1988) in urban areas, e.g. centralities; (ii) limits to densification due to progressive built formsubstitution; and (iii) limits to mobility accessibility and modes of transportation (coverage

and capacity) regarding estimated demands of vehicular movement distributed over the street

network, in turn assessed as a function of centrality values.

4.4. Indicators of city-environment relationsSpecific indicators are also developed in order to assess the level of dependence and

unintended consequences of urban production and reproduction over the status of:

a. Negative externalities generated along with interactions in the localisedsocioeconomic system namely, pollution generated by industrial activities, vehicular

movement, and so on. The indicator operates as relations between numbers of socioeconomicunits, the internal (topological and metrical) distance between them, estimated levels of fuel

consumption associated, and externalities measured as the sum of average emissions;b.Natural resourcesemployed in the reproduction of urban activities i.e. employed

in production industries, sevices and homes namely, natural geographies consumed inurbanisation, energy and water, and overall quantities of raw materials in relation to the

availability of resources, measured by a simple mathematical ratio. The indicator operates

with estimated quantities of a resources considered, distance from resource areas and

estimated quantities of materials deployed in socioeconomic units. It requires data on such

variables.


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5. Conclusions: combining feature indicators systemically intoperformanceindicatorsIndicators grouped in the present method of analysis of urban performance were defined in

order to allow their application in different possibilities. The framework allows to assess aspecific problem (e.g. the impacts of changes in a street network over the level of global

accessibility in a city), a specific urban dimension (e.g. the state of morphology, or the effectof increasing accessibility on location patterns and, by extension, on the potential to

connectivity within an economic network, or between workers and job locations) or adimension of performance (such as potential increases of urban efficiency related to those

former changes). Systemic indicators allow combined applications. In turn, the combination

of indicators of different orders from indicators of states of patterns to states in iterations

within urban dynamics to states of performance seem to advance the definition of real

performance indicators. Instruments of this kind should allow the planner or researcher to

obtain relatively straightforward answers to key questions like how changes in compacity in

a certain proportion or rate observed or simulated in a temporal sequence of scenarios would

affect spatial quality, or the sustainability of a particular urban system?

The synthesis of indicators of relational dynamics of cities is achieved through simple

mathematical operations, such as harmonic average of specific indicators (tables 1 and 2;

appendix). These operations shall be refined as work progresses.

Urban

Dimension: Morphology

Space-

socioeconomic

networks

Thresholds in

urban patterns

City-environment

relations

Feature

indicators

Compacity

Built formcontinuity

AcessibilityDepth

Distributivity

Permeability

Identity

Information

Centrality

OpportunityConvergence

PolarityInteractivity

Segregation

Mobility

Tension

Thresholds

Morphology

Centrality

Mobility

Resource

consumpExternalities

Urban

indicators)/1/(

1

n

n

i

MindnMorph

)/1/(1

n

n

i

SSNindnSSN

)/1/(1

n

n

i

TindnThr

)/1/(1

n

n

i

CEindnCityEnv

Table 1 Urban dimensions as meta-indicators composed of systemic feature indicators.


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Performance

dimension:

Spatial quality Equity4 Efficiency Urban

Sustainability

Feature

indicators

Acessibility

Depth

DistributivityPermeability

CompacityBuilt form

continuityIdentity

Information

Opportunity

Acessibility

MobilitySegregation

Acessibility

Centrality

OpportunityConvergence

InteractivityCompacity

Mobility

Spatial Quality

Equity

Efficiency

Thresholds

City-Environment

Performance

indicators)/1/(

1

n

n

i

QindnSQual

)/1/(

1

n

n

i

EqindnEquity

)/1/(1

n

n

i

EfindnEff

)/1/(

1

n

n

i

SindnSust

Table 2 Performance indicators.

This method of performance analysis relies heavily on the passage from conceptual toquantitative tools. It does so in order to render urban properties and problems objectifiable

something hardly achieved through an exclusively discoursive approach. Of course, it is not a

matter of reifying quantitative methods, but recognising their potential to throw light on

substantive problems largely constituted by the problem of intensity, such as those brought

about by recent concerns with urban sustainability. These indicators are operationalised as a

computational model based on previous models developed by the authors a Planning

Support System also developed to explore the extent of causalities and contingencies in the

relation of stimulating factors to the plethora of possible effects and directions undertaken by

an urban system, as exemplified in the hypotheses below (table 3). The first two lines in the

table show possible effects of increases in compacity over other systemic properties graspedby meta-indicators of urban and performance states. The third line shows the effects of

reaching the threshold in compacityfor a given area (the number of spatial units or activitiesin a collection of streets or blocks) in terms of habitability (accessibility to natural agents,

assessed through parameters of natural ventilation and lighting see Ratti et al, 2003). Thetrade-off between habitability and other properties beneficially implied by compacity (e.g.

centrality or interactivity) may also reach a point where urban sustainability is compromised,despite partial positive effects.

4See appendix.


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Feature indicator Dependent

feature indicator

Urbanindicator Performance

indicator

increasingcompacity

anIcomp a

n

i

/1

-- increasingvalues for

morphology

)/1/(

1

n

n

i

MindnMorph

increasingspatial

quality

)/1/(

1

n

n

i

QindnSQual

increasingefficiency

)/1/(1

n

n

i

EfindnEff

increasing

sustainability

)/1/(1

n

n

i

SindnSust

increasingcompacity

anIcomp a

n

i

/1

increasingcentrality

jiijaac

increasingvalues forspace-socioeconomic

networks relations

)/1/(1

n

n

i

SSNindnSSN

increasingefficiency

increasing

sustainability

compacity threshold

atIcomp a

T

i

T /1

decreasing

habitability

decreasingvalues for

morphology

decreasingspatial

quality

decreasing

sustainability

Table 3 Hipotheses concerning partial causal relations captured by specific feature

indicators and their effects on performance dimensions.


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References

Bak, P; Tang, C.; Wiesenfeld, K. (1988) Self-organizing criticality. Physical Review A38(1), 364-375.

Batty, M. and Xie, Y. (1999) Sel-organized criticality and urban development.DiscreteDynamics in Nature and Society,Vol. 3, pp. 109-124.

Batty, M. (2007) Planning Support Systems: progress, predictions, and speculations on theshape of things to come. CASA Working paper series.

Bertuglia, C.; Clarke G.; Wilson, A. (1994)Modelling the City: Performance, Policy andPlanning. Routledge, London.

Burton, E. (2002) "Measuring urban compactness in UK towns and cities"Environment and

Planning B: Planning and Design29 (2) 219 250.

Chen, H., Jia, B., Lau, S. (2008) Sustainable urban form for Chinese compact cities:

challenges of a rapid urbanized economy.Habitat Internations 32,2840.

Chin, N. (2002) Unearthing the roots of urban sprawl: a critical analysis of form, function

and methodology. CASA Working paper series, 47.

Churchman, A. (1999) Disentangling the concept of density.Journal of Planning Literature

13(4), 389-411.

Ewing, R. (1994) Characteristics, causes and effects of sprawl: a literature review.

Environmental and Urban Issues. FAU/FIU Joint Center.

Friedkin, N. (2004) Social cohesion.Annual Review od Sociology 30:40925.Fujita, M.; Thisse, J-F (2002)Economics of Agglomeration.University Press, Cambridge.

Grannis, r. (2010) Paths and semipaths: reconceptualizing structural cohesion in terms ofdirected relations. Sociological Methods 39 (1), 117-150.

Harvey, D. (1973) Social Justice and the City. John Hopkins University Press, Baltimore.Hillier, B. (1996) Space is the Machine. University Press, Cambridge.

Johnson, M. P. (2001), Environmental impacts of urban sprawl: a survey of the literature andproposed research agendaEnvironment and Planning A 33(4), 717-736.

Krugman, P. (1994) Complex landscapes in economic geography.American Economic

Association, Papers and Proceedings 84, 412-416.

Latour, B. (1993) We have never been modern. Harvard University Press, Cambrigde Mass.

Martin, L.; March, L. (1972) Urban Space and Structures.Cambridge University Press,

Cambridge.Polidori, M.; Krafta, R. (2004) Environment urban interface within urban growth In:

Proceedings DDSS.

Ratti, C.; Raydan, D.; Steemers, K. (2003) Building Form and Environmental Performance:

Archetypes, Analysis and an Arid Climate.Energy and Buildings,35 (1), 49-59.

Razin, E.; Rosentraub, M. (2000) Are fragmentation and sprawl interlinked? North American

evidence. Urban Affairs Review 35(6), 821-836.

Rosvall, M.; Minnhagen, P.; Sneppen, K (2005) Navigating networks with limited

information Navigating networks with limited information. Physical Review E 71,111-116.

Savitz, N.; Raudenbush, S. (2010) Exploiting spatial dependence to improve measurement ofneighborhood social processes. Sociological Methods 39 (1), 151-183.

Talen, E. (1998) Visualizing fairness: equity maps for planners.Journal of the AmericanPlanning Association64 (1), 22-38.

Talen, E.; Anselin, L. (1998) Assessing spatial equity: an evaluation of measures ofaccessibility to public playgrounds.Environment and Planning 30 (4), 595-613.

Thrift, N. (2008)Non-Representational Theory: Space, Politics, Affect. Routledge, London.

Wilson, A. (2008) Urban and regional dynamics 1: a core model. CASA Working paper

series 128.


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APPENDIX:FEATURE INDICATORSANDPERFORMANCE INDICATORS

This section brings some of the systemic indicators developed for the method of performanceanalysis. Equations derived from previous formulations not shown here; indicators found in

the literature are not listed; the complete set of equations may be obtained from the authors.

FEATURE INDICATORS:

Compacity: anIa

n

icomp

/1

n is the number of activity units in the street segment or blocka

Continuity in built form: UbfUbfcont llUI /)(

: l is the total length of streets and the built fraction of that lenght

Acessibility: 1/)( nodijiIn

i

acc

iis the spatial unit belonging to a system U with nunits.

Depth in the grid 1/)( ndijUIn

i

depth

grid

depth

U

depth

rel

depth IIUI /)(

dis the shortest path between any pair ijbelonging to a system U

nis the total number of spatial units in the urban system

Distributivity: )1( NAC gridU

distrCCUI /)(

Cis the cyclomatic number,A is the number of lines,Nthe number of

nodes

Permeability:

ALUIn

i

perm /)( )(/)()( iIjIUI permpermrel

perm

Lis the total length of streets andAthe area being considered

jrepresents an area within the urban systemi represents an area within the urban system where permeability is

maximum

Identity:UU

epident llUI /)( 1

lUis the total length of streets in the street network

lep+1Uis the length of the subsystem 1 in its primary structure

Centrality: jiij aac ...,,

...,,

isrji uaa

n is the tension between between any pair of spatial units tijaiand ajare atributes of these pairsur, us, ui,etc. are land uses (residential, service, retail, and so on)

, , , are parameters defined according to attractivity of each landuse

Atributes aie ajmay be unfolded in as many land uses as one intends to

disaggregate the urban activity system, producing a sum for every

attribute, weighed according to the equation below


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Segregation in networks: )/()/)(( MSNaPI mnnnsegr

segrI is the dynamic segregation in the urban system

mS is the total segregation level in the grid

na is the segregation level in the street segment n

nP is the segregation level in the atractor nn is the parameter for forms of contact in the street segment n

Mis the number of activities in the urban system

Nis the number of street segments in the urban system

PERFORMANCE INDICADORS

Meta-indicators consist of relations of feature indicators. We include here, as an example of

this procedure, the combination of feature indicators for the performance indicatorEquity.

Where:

pcprO / (Opportunity): relation between location of residents in class x and their places

of consumption/leisure

opEq (Equity of opportunity):measure for the harmonic average of opportunities per

class.

accEq (Equity of Acessibility): level of accessibility for each inhabitant per class in

relation to the urban system as a whole. It takes into account the average depthlevel of each inhabitant.

mobEq (Equity of Mobility per class): value for mobility, dependent on transport form

used per class (private car, underground, bus, pedestrian and so on).

Mob (Mobility): the measure synthesises morphological properties like distributivity,

accessibility, internal distances and residential location, and weightens

different levels of mobility dependent on transport form. An is the proportion

of car users in the class x; Cn stands for bus or underground; Pn for

pedestrians.

)/1/(

)/1.../1/1/1/1/(

/)]1()2()3[(

)/1/(

)/1/(

)/1/(

2/)]}/1/([]/1/({[

1

1

1

1

1 1

n

n

i

urb

nsegrmobaccopurb

nnn

n

n

i

mob

n

n

ai

segr

n

n

i

acc

n

i

n

n

i

nop

EqnEquity

EqEqEqEqEqnEquity

npcaMob

MobnEq

SegrnEq

IaccnEq

OpcnOprnEq


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segrEq (Equity regarding residential segregation): levels of accessibility and spatial

proximity between classes, dependent on the level of concentration between

pairs of residential locations of a same social class and dispersion betweenpairs of residential locations of distinct classes

urbEquity (Urban Equity): general level of equity for the urban system, all factors

considered.

Urban form as a problem of performance

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