EL BALONCESTO EN LAS CATEGORÍAS DE FORMACIÓN ESTUDIADAS ESTUDIADAS

Where:

p = proportion of individuals or objects in a category

N = number of categories.

Equation 3: Density-Diversity

Where:

p = proportion of individuals or objects in a category

N = number of categories.

In summary, urban function is a vital dimension for understanding urban spatial structure. Functional diversity has an important role in policies encouraging local travel patterns, whilst functional specialisation is linked to agglomeration economies. Measures of function vary from basic live-work classifications to more sophisticated employment and property measures which can be used to calculate specialisation and diversity indices. Functional measures are highly dependent on the classification system used.

4.6.3 Urban Centrality: Identifying Monocentric and Polycentric Forms

This sub-section addresses the research aim of developing a methodology for the empirical identification of polycentric forms. The spatial dimensions of

accessibility- are interrelated aspects of urban centrality, and urban centrality is the basis for the empirical measurement of monocentric and polycentric forms.

The quantitative spatial analysis of urban centrality is needed to locate and define intra-urban centres, and to analyse their properties. This analysis requires the consideration of scale dependence and urban hierarchies as discussed below.

The definition of urban centres is a long-running concern of geographical analysis. Murphy and Vance (1954) classically defined the Central Business District of cities in the USA based on the concentration of retail and office premises, high land values, and the intensity of pedestrian and vehicular activity. To this list we could add many other elements, such as transportation accessibility, concentrations of services, civic centres and landmark buildings.

A particular challenge for defining the urban centres of contemporary cities is that newer centres at the urban fringe often contrast with the traditional centres, being relatively low density and with a narrower range of functions. One of the most straightforward and commonly used means of defining urban centres is to analyse employment clusters (Giuliano and Small, 1991; Wang, 2000). This approach is clearly of direct relevance to economic geography and commuting, and is applied in this thesis in Chapter 5. Giuliano and Small (1991) define employment centres as groups of adjacent zones where: 1) each individual zone exceeds an employment density threshold; and 2) the collective employment total for the zones exceed a total employment threshold. Clearly the limitation with such an approach is the arbitrary thresholds, which influence the number of centres identified. Threshold values can be defined according to a global cut-off value or a local regional value, which is useful for contexts where sub-centres vary across the city-region (as is found in the London region study area).

More sophisticated approaches to identifying employment centres include locally weighted regression models (Redfearn, 2007), and the use of clustering statistics, as described below.

A key consideration in the analysis of centres is the existence of urban centre hierarchies. Earlier in Section 2.1 we explored the hierarchies or networks of urban centres that exist from the perspective of central place and economic location theory. These hierarchies result from the interplay of transportation

costs, agglomeration economies, dispersion forces and economic specialisation.

Urban hierarchies can be found for many functions including retail, public-service and office activities, and exist to varying degrees at intra-urban and regional scales in all cities. It is highly improbable for a city to be entirely monocentric with absolutely all economic activities in a single centre; whilst similarly no real-world city has a pure polycentric pattern with activities exactly distributed across multiple centres. Instead the terms monocentric and

polycentric are used to describe the relative dominance of centres within a city;

they are trends in a spectrum of spatial activity hierarchies.

The existence of urban centre hierarchies is directly related to the scale dependence of urban centrality measures. Essentially the pattern of urban centres display fractal properties (Batty and Longley, 1994), and the number of centres measured will be influenced by the scale of analysis. The extent of the analysis is also significant as potentially a city could be monocentric at the intra-urban scale while being part of a larger polycentric network at the regional scale. Urban decentralisation trends are increasingly blurring distinctions between these scales, as greater mobility draws neighbouring settlements into functionally unified urban regions (see Section 1.2).

Monocentric and polycentric spatial distributions can be defined empirically using two linked measures of spatial concentration: centralisation and clustering (Anas et al., 1998). Centralisation describes the degree of concentration around a single centre at the metropolitan scale, whilst clustering analyses number and size of sub-centres. By combining these two measures of centralisation and clustering a matrix of idealised urban centre hierarchies can be postulated, as illustrated diagrammatically in Figure 4.10.

Clustered

Dispersed

Figure 4.10: Urban-Centre Hierarchy Patterns, Defined by Spatial Clustering and Centralisation

In the centre of the figure we have a pattern of centres corresponding to a standard central-place hierarchy. The models in the four corners represent acute variations in the hierarchy of centres; namely of centralised-clustering,

decentralised-clustering, centralised-dispersion and decentralised-dispersion.

Monocentricity refers to the spectrum of structures between the central-place hierarchy and the centralised-clustered model. Polycentricity refers to the spectrum of structures between the hierarchical city and decentralised-clustered model. The bottom row of models illustrates dispersed forms lacking spatial clustering, resembling population catchment type distributions.

To apply the above framework empirically we need a statistical measure of spatial concentration. The most commonly used statistic is the Moran‟s I statistic of spatial autocorrelation, which measures the probability that a distribution is randomly formed. The Moran‟s I statistic was found to be

Decentralised Centralised

Monocentricity Polycentricity

relatively ineffective in distinguishing between varied patterns of urban centres shown in Figure 4.10. An alternative global spatial clustering index, the Getis-Ord General G statistic, is shown in Equations 10 and 11. The statistic measures the degree to which high or low values are clustered, based on the product of proximal values (Getis and Ord, 1992). This statistic was found to successfully capture the different urban clustering patterns shown in Figure 4.11 and be largely unaffected by the varying sample sizes of urban functions, thus making it suitable for quantifying agglomeration patterns as applied in Chapter 5.

Equations 10 & 11: Getis-Ord General G Statistic. Source: Getis and Ord (1992).

Where:

xi = value of variable at location i Wij = spatial proximity weights matrix

E [G] = Expected value of G for a random distribution

In summary the terms monocentric and polycentric are scale-dependent terms that describe the relative dominance of centres within a city-region hierarchy or intra-urban network of centres. The combined spatial analysis of clustering and centralisation provides an empirical test of monocentric and polycentric spatial distributions. Monocentricity describes processes of centralised-clustering in the hierarchy of urban centres, whilst polycentricity describes processes of

decentralised-clustering. The empirical analysis of these concepts requires statistical measures of spatial concentration, of which the Getis-Ord General G statistic was found to be most effective.

4.7 Techniques for the Analysis of Accessibility and Travel Sustainability

We now turn to spatial analysis techniques for the accessibility and travel pattern indicators. Firstly accessibility measures are detailed, and then we consider the analysis of travel time. Finally the methodology for calculating the intra-metropolitan CO2 emissions indicator is presented.

4.7.1 Measures of Geographical Accessibility

Geographical accessibility indicators describe the ease of which actors (e.g.

residents, firms) can access opportunities (e.g. people, jobs, shops, parks) through transport networks. Accessibility has fundamental relationships with travel demand (see Chapter 3) and urban form (see Chapter 1). Measures of accessibility in urban geographical theory generally consist of two parts: a transportation (or resistance/impedance) element and an attraction (or

motivation/activity) element (Handy and Niemeier, 1997), as shown in Equation 4. Accessibility measures are generally composite indices that sum accessibility values from one zone to all other zones. Different forms of the impedance function result in three general classes of accessibility measure: cumulative opportunity measures, gravity-based measures and utility-based measures.

Cumulative measures or threshold measures total the opportunities within a given travel cost, for example the total population within 45 minutes travel time.

In the cumulative case the impedance function is binary, either being 1 if the opportunity is within the threshold or 0 if it is beyond the threshold. The

advantage of cumulative measures is in their simplicity, both for calculation and for communication to stakeholders. On the other hand the arbitrary cut-off value is a poor reflection of travel demand relationships.