The rediscovery of accessibility and economic potential: the critical issue of self-potential

Transcription

1 Environment and Planning A 95, volume 27, pages The rediscovery of accessibility and economic potential: the critical issue of self-potential M E Frost, N A Spence Department of Geography, Kings College London, The Strand, London WC2R 2LS, England; also Mile End Road, London El 4NS, England Received 25 April 94; in revised form 4 August 94 Abstract. Economic potential measures of accessibility seem to have been rediscovered in the research literature recently, as well as in research that informs policy formulation. These new applications are using more and more sophisticated sources of data but are in large measure still operationalising the familiar concepts of market potential. Such potential is calculated for any zone by summing the representative economic mass of all other zones in the system each divided by some measure of the intervening travel impedance between that zone and every other zone. In this straightforward calculation it becomes necessary to incorporate the economic mass of the zone under consideration itself and to decide on the appropriate travel impedance. This apparently simple task is the focus of this paper. Most research of this type uses a weighting of the radius of the circle equalling the area of the zone in question to approximate the travel impedance. The purpose of this paper is to demonstrate that the choice of weighting is important in determining the nature of the resultant potential surface. Introduction One of the products of a growing emphasis on regional economic policies at a European rather than a national scale over the past decade has been a development of interest in the concept of peripherality. This interest at the continental scale has been underpinned by important, and still much quoted, research undertaken for the European Commission through the 80s (Keeble et al, 82; 88). It is currently being reinforced by the introduction of the Cohesion Fund as part of the Maastricht Treaty package, with the specific brief of investing heavily in infrastructural improvements in order to reduce the inaccessibility suffered by Greece, Spain, Portugal, and the Republic of Ireland as a result of their relative peripherality in comparison with the rest of the European Community. Even at the national scale these accessibility concepts still find important contemporary use. Within the United Kingdom, the recent review of areas eligible for regional assistance included (for the second time) measures of the relative peripherality of localities, alongside a range of the more obvious and well-known measures of economic disadvantage (DTI, 93). Most practical attempts to measure relative peripherality, including those mentioned above, have involved the long-established approach of using models of economic or market potential based on ideas first suggested in the late 40s (Stewart, 47). Within these, the economic potential of a place is measured by its access to markets, with markets in the early measures being represented by population. In practice, potential is calculated for any locality by summing the population of all other localities in the system and dividing these by some measure of their intervening distance. Over the years these measurements have become more sophisticated, with perhaps spending power (gross domestic product) replacing population and perhaps generalised transport cost replacing distance. The underlying structure of the models, however, has remained broadly the same. In this respect the sum of opportunities between an area / and all other areas j gives a potential value for area /. It is a measure of the relative strength of the

2 1834 M E Frost, N A Spence relationship between a given area and the markets and input sources which that area could either actually or potentially supply or be supplied by. The potential of zone /, P i9 is given by where Mj is a measure of mass in zone/, C tj - is a measure of the impedance or transport costs from zone / to zone /, and a is an exponent often assumed to be equal to 1. Such an approach is not without its detractors. Most criticism rests on the attempt to disentangle the complex economic relations which are mixed together in the aggregate attractions of population (or spending power) for economic activity. It is clear that different forms of activity respond differently to the economic landscape around them. For some, port access is important; for others, it is access to international air connections which is critical; whereas, for many, motorway or rail access within a national setting can be decisive. In addition, the nature of transactions varies: business connections dominate the interests of producer service activities, whereas access to distributed population-based markets might be expected to be crucial for the suppliers of some consumer goods. Further, Newman and Vickerman (93) stress that response to the economic landscape is likely to differ from one area to another as firms adjust their production technology to the opportunities they face. It is clearly optimistic to expect two simple terms of population and distance to be able to capture these complexities. In response, in some recent applications of accessibility-based measures, researchers have experimented by adapting the basic potential approach. In their review, Newman and Vickerman (93) identified several attempts to supplement 'traditional' potential models with: distances calculated for only selected networks of key links to ports or airports; destinations selected for business travel only; and composite indices produced for travel-time access to local as well as more distant centres, with a separately estimated local population effect. At the moment it seems that, in spite of the difficulties posed by the underlying model, research is still being conducted by taking an economic potential approach (Linneker and Spence, 92a; 92b; Spence and Linneker, 93). With the ambitious programme of the Cohesion Fund, containing within it a commitment to evaluation of its effects, the quantity of research seems set to rise. Almost all of the traditional and alternative approaches for assessing relative peripherality outlined above still follow the basic logic of including a populationrelated mass factor. This reflects the notion that access to population as both a potential market and a potential source of suitable labour is still significant for many forms of economic activity and that 'pure' accessibility in terms of network connections has few attractions in the absence of at least some population. So long as a mass factor is included, any potential model, however sophisticated its network structure, will still have to face the issue of estimating what has come to be known as the 'self-potential' of its zones. This factor is the contribution of the potential of the individual area itself to the total potential of that area in accessing the network of places in the system under consideration. Few studies include an examination of the sensitivity of their results to the way in which self-potential is estimated. One exception is the work of Owen and Coombes (83) who conducted a wide range of tests on their results, to judge the influence of external areas on the system under consideration, the ramifications of using different distance exponents, the effects of using air-line as opposed to

3 Accessibility and economic potential 1835 shortest-route distance measures, the variations induced by the use of geometric centroids compared with more functional centroids, and the effects of using different spatial scales of base units as well as different mass factors. Additionally, they also tested the sensitivity of what they term the 'multiplicative factor' in the intraarea distance calculation (self-potential). The range of values for their multiplicative factors were chosen on the basis of contemporary applications rather than within a theoretical framework. Our purpose in this paper is to explain with the aid of simple examples some of the mathematical bases of alternative approaches to the self-potential problem, to illustrate the effects of different estimates on a potential model of Britain, and to examine the implications of the results for the meaning of the accessibility measures which these models produce. The origins of the concerns for the self-potential problem Established practices of measuring the self-potential of zones have their roots in Stewart's (47) original work. He introduced the approach of representing each zone as a circle of equivalent area and estimating intrazonal distance from some transformation of the radius, r, of that circle. Self-potential is, then, the mass of the zone divided by its estimated intrazonal distance. He argued that the effects on overall potentials of the particular choice of transformation applied to the radius were likely to be small, and he went on to suggest a value of 0.5 r, based on the physical analogy that the electrical potential of a circular disc at its centre was proportional to half its radius. He did not, however, explain the implications of applying this analogy to systems of human interaction. In spite of some varied approaches to the self-potential problem in the 50s and 60s, with authors adding fixed values to the diagonal of the distance matrix to allow for intrazonal effects (Anderson, 56; Houston, 69; Ray, 65). Stewart's general approach survived, although with the additional suggestion that values of less than half of the radius could allow for the peaking of population towards the centre of zones (Rich, 78; 80a; 80b). The logic of reducing the internal distance used, thereby increasing the magnitude of the self-potential effect, to allow for the peaking of population towards the centre of zones is supported by a finding reported by King (69). The reasoning was based on an unpublished paper (Court, 66), not seen by the present authors, and is that the self-potential created by a uniformly distributed mass over a circle is only two thirds of that imposed by either a conical or Gaussian distribution. The mechanisms by which any particular radial weight is selected seems, within the literature, to be shrouded in mystery. However, from this broad range of research Owen and Coombes (83) found that a value of 0.33r has emerged and is frequently used. Owens and Coombes also considered the effects of taking both 0.25 r and 0.5 r on their potential surfaces. They recognised from their sensitivity tests that the smaller the radial weight used the more important the influence of the employment within the area. They indicated that total potential is extremely sensitive to the different measures used, but conclude that 0.33 r is a reasonable empirical compromise. The rationale for the selection of this particular range of radial weights was not discussed, in common with many previous applications of these models. In this paper we try to fill this gap by offering a simple illustration of the mechanics of self-potential, and their implications, before proceeding to investigate the sensitivity of potential models to alternative estimates of self-potential.

4 1836 M E Frost, N A Spence Self-potential: its mechanics and implications The bases of our illustration are set out in figure 1. Following the generally accepted practice, it is assumed that the zone for which self-potential is being assessed is a circle. For our illustration this circular zone is divided into five subzones an inner circle and four bands each of which is one unit apart. The area of each subzone can be calculated readily as the subzones form a group of concentric circles (see figure 1). Area of inner circle = Jtr 2 = n units 2 Area of band 1 = nr -nr? = 3 n units 2 Area of band 2 = Jtr 3 2 -Jtr 2 2 = 5 n units 2 Area of band 3 = jrr 4 2 -jtr 3 2 = 7 jt units 2 Area of band 4 = nrl-nr? = 9Jt units 2 Figure 1. The study zone (radius = r 5 ) and the area of each of the subzonal regions. Note: each band is one unit apart, that is, r x = 1 unit, r 2 = 2 units, r 3 = 3 units, and so on. Figure 2 shows the areas converted into measures of potential. Stewart's original physical analogy holds only if population (or some other measure of mass) is evenly distributed across the subzones. This is shown as a horizontal line in the diagram and is labelled case (a). In these circumstances potential is contributed equally by each subzone, as shown by the calculations in figure 2. In this case it is assumed that the total population of the zone is 25 which yields a constant density, the value of which is given by the reciprocal of JT per unit area. This results in a value of 1 person in the inner circle; 3 people in band 1; rising to 9 people in band 4. Given these population mass factors and distance values arising from the various radii, we obtain a total potential for the zone of units (figure 2). It can be seen arithmetically that the self-potential of the total system can be calculated from the total population divided by half of the radius, 0.5 r 5. The more that the population within the circle is concentrated towards the centre, the smaller the weight applied to the radius needs to become to produce an equivalent result. Clearly, there are many distributions of population that could generate a value close to 0.33 r. One such distribution is illustrated in figure 2, labelled as case (b), with average densities declining from 2 persons per unit area in the inner circle to 1.5, 1.0, 0.5, and 0.3 persons per unit area in successive outer rings. These weights can be used directly in the arithmetic, as set out in figure 2, so that the population of the inner circle becomes 2; in band 1 it becomes 4.5, continuing out to band 4 with 2.7. In this form the total population falls to 17.7,

5 Accessibility and economic potential 1837 but the total potential, derived from dividing the population by the radial distances and summing, increases slightly from that in case (a) ( units) to.6 units. This combination yields a result of population divided by 0.334r 5. The diagrams in figures 1 and 2 are highly simplified, but it can be seen that the shape of the intrazonal population distribution implied by the 0.33 r approach is not an unreasonable representation of many urban population density profiles. However, an important feature of these models that requires some emphasis is that the potential value produced by this arithmetic holds only for the central point of the circle. Any points lying away from the centre will have lower values within the enclosed system as the distance needed to connect them to all other points in the circle increases. Some of the implications of this can be gauged from the approaches used in interaction modelling where the concern is focused on interactions taking place across a zone as well as journeys concentrated on the centre. Two results are of interest. The first result is closely related to Stewart's original proposition. In a widely quoted but unpublished paper, Bonsall (75) states that, for a circular zone with 2.0 -i Case (b) a & Case (a): Inner circle: Band 1: Band 2: Band 3: Band 4: Pntpntial Subzone JtXjr Potential = T! 3jtxjr Potential = _1 = 2 O.Sfo + r, " 5jtxjt Potential = _1 = 2 0.5(/- 3 +r 2 7jtXjr Potential = _1 0.5(r 4 + r 3 9JTX3T" 1 0.5(r 5 +r 4 ) Case (b): Inner circle: Band 1: Band 2: Band 3: Band 4: Jtx2jr" _ Potential 0.5/-J ~ Potential = 3JTX1.5JT" 1 = 3 0.5(72+7-,) Potential = 5jtxl.Qjt" 1 0.5(7-3 + r 2 ) Potential = 7JIXQ.5JT" 1 = 1 0.5(r 4 + r 3 ) 9jtxQ.3jt" 1 Potential = = (r 5 + r 4 ) Figure 2. Profiles of the population density (in persons per unit area) of the study zone (see figure 1) and the potential in the cases where (a) population is spread evenly per unit area and thus population is directly proportional to area, and (b) population density decreases with distance from the centre of the zone and thus population is given by area multiplied by density. Note: potential is equal to the population divided by intrazonal distance [the distance from the centre of the zone to a point midway between the inner and outer limits (rings) of the subzone under consideration] and is given here in persons per unit length; units are not shown in the calculations.

6 1838 M E Frost, N A Spence evenly distributed population, the mean length of trips joining the centre to all possible points within the circle will be 0.66 r. Reconciling this with Stewart's result throws an interesting light on the workings of the potential approach. The divergence arises from the implicit assumption in Bonsall's statement that the probability of an individual making a trip to (or from) the centre is not affected by the position of the origin (or destination) of the trip. In other words, trips will be generated in direct proportion to population. The effects of this can easily be demonstrated by using the simple five-zone model outlined above for case (a). In that model the five subzones moving out from the centre have populations in proportions of 1, 3, 5, 7, and 9, respectively. These can be thought of as the number of people originating in each of the zones, travelling distances of 0.5 units, 1.5 units, 2.5 units, 3.5 units, and 4.5 units from the inner circle and bands 1-4, respectively. Arithmetic shows the average journey length of the whole group to be 3.3 units, which is exactly 0.66 r. The contrasting logic of the potential model translated into interaction terms would be that the probability of movement declines with increasing distance from the centre, thus leading to a lower estimate of intrazonal distance. The second result rests on more complicated mathematics that defies translation into a simple arithmetic example. Once again, an even distribution of people (points) is assumed across the circle, all with an equal propensity to travel. It can be shown that the average length of connection between all possible points across the circle is equivalent to 0.905r (Kendall and Moran, 63). This reflects an intuitively straightforward conclusion that, once the constraint of a central origin or destination is relaxed, longer cross-zone trips will be possible which increase overall travel distance. The choice of transformation for the radius, therefore, rests partly on the degree to which it is assumed that zones are internally unicentric with respect both to travel patterns and to a declining propensity for interaction from locations situated away from a central position. Clearly, such an assumption will suit some population configurations more than others. An isolated town in the middle of a largely rural zone would have its concentration of potential interaction underestimated by values as low as 0.33 r. For a conurbation whose built-up area extends to the boundary of the zone, it is more difficult to rationalise that access and potential interaction will not have strong cross-zonal components, suggesting a higher value. In either case it is difficult to justify peak levels of potential, estimated for the central point of each zone, as being representative of general levels of potential across the whole area. In these terms, the potential of Croydon is likely to be very different from the value obtained by concentrating all of the self-potential of the London system on a traditional central point such as Charing Cross. All of this discussion would be of only peripheral interest were the size of the self-potential effect, as Stewart suggested, small and largely inconsequential in relation to total potentials generated by access to more distant zones. This assumption was challenged by Rich (80a, page ), who stated that "self potential often contributes a significant proportion of total potential of particular zones" but unfortunately did not give any guidance on what 'significant' meant. Clearly, the particular balance of importance will vary as zone sizes vary and as the nature of their intrazonal population distributions vary. Our purpose in the next section of this paper is to take as an example a 'typical' potential model applied to areas within Britain and examine the strength and variability of its self-potential components.

7 Accessibility and economic potential 1839 A model of economic potential in Britain based on employment mass factors and road-travel generalised cost impedance The model chosen for this experiment is broadly similar to that used by the Department of Trade and Industry to assess peripherality in its recent review of Assisted Areas. The model is based on the concept of market potential and is calibrated at the spatial scale of travel-to-work areas (TTWAs). The mass factor, reflecting the total economic activity in each TTWA, was in fact taken to be the population in employment (the total number of employees in employment and the total number of self-employed) in 89. The impedance restricting the interaction between areas also needs to be estimated. Impedance may take the form of distance, time, or a generalised transport cost between zone-centroid origins and destinations. In the research presented here we have taken estimates of the quickest (not shortest) routes between origins and destinations, and the generalised transport costs have been derived from the Service in Information and Analysis (SIA) road network model operated for the Department of Transport (DoT). SIA operates the DoT's computer record of the British road network (SIA, 92). One piece of available software the Routefinder model is a computer program capable of selecting the quickest routes between over named origins and destinations in Great Britain. Journey times for cars are calculated through realistic estimates of fluctuations in daytime off-peak speeds on different classes of road (motorways, A roads, and B roads). Trip routes are selected on the basis of a computer record of the 1:50000 large-scale Ordnance Survey maps, taking into account the rural, urban, and suburban environment, road alignment, complex junctions, town-centre traffic flows, gradients, and one-way streets. As a result of problems in estimating journeys through London, travel-time estimates through London are based on actual measured speeds. Although the Routefinder model does estimate travel time and distance for trips between the mainland and the Isle of Wight and the Isle of Skye it does not make such estimations for the Western Isles, the Orkney Isles, or the Shetland Isles. As a result, in the subsequent calculations these locations (incorporating TTWAs) were assumed to be represented by their nearest mainland ports plus the straight line distance to the representative TTWA location and the journey time taken by sea. The SIA model of the British road network as of April 92 was used to calculate the quickest journey time and distance values of the road network between each origin and destination selected. For each of the 322 TTWAs a representative place was selected, usually on the basis of size. Time and distance data for the 322 x 322 matrix of geographical areas selected in this research were combined, and this made it possible to estimate the generalised transport costs for every trip in the matrix. Accessibility variables based on generalised transport costs were calculated from the estimated zonal population given in employment data (the number of employees in employment and of self-employed) for 91. Accessibility values, based on generalised transport costs for car trips only, are reported on in this research. The Mathematical Advisory Unit of the Department of the Environment (Nichols, 75) has suggested that, for modelling purposes, generalised transport costs can be estimated from a costs formulation based upon time and distance, of the form G = a D D + b T T. where G is the generalised transport cost, D is the distance in kilometres, T is the time in hours, a D is the distance coefficient, calculated from vehicle operating costs per kilometre, and b T is the time coefficient. The distance coefficient can be

8 1840 M E Frost, N A Spence calculated from the DoT vehicle operating-cost formula (DoT, 89). This can be used to calculate the perceived vehicle operating costs in pence per kilometre for 89 at 88 prices. These measures contain a fuel and nonfuel component and take the general form O = a c 0 v, v where O is the operating cost in pence per kilometre, v is the average vehicle speed in kilometres per hour, and a 0, b 0, and c 0 are operating-cost coefficients for vehicles. For cars in 89 (pence per kilometre at average 88 prices) the operating cost is given by O = , v 2. v The average vehicle speeds for every origin-destination trip in the matrix can be calculated from the time and distance data, and thus the distance operating-cost coefficient for every trip in the generalised transport-costs formula can be derived. However, and this is the principal focus of the paper, because the time and distance data so generated were from each zone-centroid origin to each zone-centroid destination, the intrazonal time and distance values still need to be estimated. To do this, first a hypothetical zonal radius in kilometres was derived from the actual area of each TTWA. The second stage in the estimation concerns the use of DoT (92a; 92b) data on the daytime off-peak average traffic speeds on all roads inside and outside London from surveys carried out in 91. For cars, these speeds were km h" 1 and km hr 1 for inside and outside London, respectively. From the zonal radius (variously weighted; see below) and the average speed data it was possible to estimate intrazonal travel times and distances for the study areas inside and outside London. In addition to the vehicle operating cost per kilometre there is a time component involved in trips in the generalised transport-cost formula. From average vehicle occupancies the DoT (89) published resource values of time per vehicle in pence per hour. The 89 value of time per vehicle (88 prices) for working cars was pence h" 1. The results of the economic potential model under a variety of measures of self-relative potential The above model is thus not an artificially simplified example but represents an up-to-date model based on a sophisticated representation of the road network through which a generalised cost function is used to assess travel times. All experimental runs were performed for the complete set of 322 TTWAs in Great Britain, and in the figures to follow we illustrate some of the results. However, for compactness, the detailed numerical results are tabulated only for a selection of 25 areas which are designed to show a range of zone sizes and regional contexts. The radial transformation used first is the popular 0.33 r value. The full potential surface is illustrated in figure 3, which is fundamentally a map of road-based, generalised-cost accessibility to the location of population in employment in Britain. The areas with highest accessibility on this surface are, as expected, London (with the contiguous TTWAs of Heathrow, and Watford and Luton), Manchester, and Birmingham. These locations represent the peaks on a general southeast-tonorthwest rectangular axis of high accessibility in England. Modest extensions of

9 Accessibility and economic potential 1841 this axis are to be found into Hampshire, Bristol, and South Wales. Glasgow has the highest potential value in Scotland. In figure 4 (see over) we depict self-potential as a percentage of the total potential for each TTWA. It is immediately clear that the notion that self-potential is of little consequence is untenable. Although it seems that the highest contributions of self-potential do arise in the centres of highest employment, it is certainly not the case that figure 4 replicates the pattern of figure 3. Figure 3. Accessibility of travel-to-work areas in Britain, measured by total potential. The numerical range of contribution that self-potential makes to the total potential of each selected TTWA is shown in table 1, together with the contribution made by some other arbitrary distance bands. London has the highest total potential value, but some 60% of this potential is contributed by its own self-potential. Although the local mass is important it is not the only influence on the relative magnitude of this figure. Glasgow shows an overall potential value of about half that seen in London but has an employment level that is only 11% that of the capital city of England. Its relatively isolated regional position, however, helps to give a reliance on self-potential that is only a few percentage points less than that seen in London.

10 1842 M E Frost, N A Spence Figure 4. The self-potential as a percentage of the total potential of travel-to-work areas in Britain. In general, a 40% threshold captures all of the main conurbations, with the exception of Leeds. The smaller centres in the South East of England show the opposite effects, where proximity to a larger centre reduces the relative importance of self-potential. The low contributions of self-potential for these TTWAs are strongly related to the place of London in the system. This can be seen in the potential value broken down by distance bands, the 'London effect' producing a distinct bulge in the profiles (table 1). A more important question, however, is the degree to which changes in radial transformation influence the role played by self-potential. In table 2 we show the effect of adjusting the radius through a range of values from 0.33 r to a maximum of 1.0 r. The impact on the proportions of total potential accounted for by self-potential is clearly substantial. In most cases, a change from a weight of 0.33 r to 1.00 r produces a reduction in the proportion of total potential contributed by self-potential of about 50% or more. This is clearly important, but its particular importance lies in the effects which this has on the total potential of a zone, given that there are wide differences in the relative contributions made by the self-potential term.

11 Accessibility and economic potential 1843 A measure of the variability of this effect can be gauged from table 3. An adjustment of the radial transformation from 1.00 r to 0.33 r increases the potential value for London by 68% whereas it increases that of Oxford by only 11%; Birmingham's total increases by 30% whereas the smaller but more isolated centres of Glasgow and Edinburgh increase by 63% and 49%, respectively. The full picture of the sensitivity of total potential to this variation in the way self-potential is measured is provided in figure 5 (see over). Here it can be seen that the pattern shown does not simply replicate that of figure 4. The resultant pattern of sensitivity is an outcome of a complex set of forces dependent on employment size and density and on relative location. In addition, table 3 shows that a relatively modest adjustment from 0.50r to 0.33 r as a transformation value can also have significant effects. In London's case this raises its total potential by 25% yet increases the value seen in many other centres by less than %. Table 1. Percentage composition of total potential (the self-potential is based on a radial transformation of 0.33) for selected travel-to-work areas (TTWAs). TTWA Total potential (absolute) Selfpotential Nearest 64 km Next 64 km Rest of study zone Crawley Guildford and Aldershot Hertford and Harlow Medway and Maidstone Oxford Southend Watford and Luton Heathrow London Bristol Birmingham Coventry and Hinkley Dudley and Sandwell Leicester Nottingham Bradford Leeds Sheffield Liverpool Manchester Wirral and Chester Newcastle upon Tyne Cardiff Edinburgh Glasgow The relative effects of these changes for interzone comparisons can be seen in the ranked positions of total potential levels, given in table 4. Although there are no dramatic changes between the rankings for each of the alternative radial transformations, some major centres change position quite significantly. With a radial weight of 1.00 the effects of local mass are relatively low, but the effects of roadnetwork accessibility are relatively high. In these calculations, London has only the sixth highest potential score whereas both Heathrow and Watford score higher as a

12 Table 2. Self-potential (based on various transformations of the radius, r) as a percentage of total potential for selected travel-to-work areas (TTWAs). TTWA 1.00 r 0.66 r 0.5 r 0.33 r Crawley Guildford and Aldershot Hertford and Harlow Medway and Maidstone Oxford Southend Watford and Luton Heathrow London Bristol Birmingham Coventry and Hinkley Dudley and Sand well Leicester Nottingham Bradford Leeds Sheffield Liverpool Manchester Wirral and Chester Newcastle upon Tyne Cardiff Edinburgh Glasgow Table 3. Percentage change in total potential according to different measures of self-potential (based on various transformations of the radius, r) for selected travel-to-work areas (TTWAs). TTWA l.oor to 0.33r 0.5r to 0.33r Crawley Guildford and Aldershot Hertford and Harlow Medway and Maidstone Oxford Southend Watford and Luton Heathrow London Bristol Birmingham Coventry and Hinkley Dudley and Sandwell Leicester Nottingham Bradford Leeds Sheffield Liverpool Manchester Wirral and Chester Newcastle upon Tyne Cardiff Edinburgh Glasgow

13 Accessibility and economic potential 1845 result of their superior access to the national motorway network. At this radial adjustment, Dudley outscores London, as Dudley's proximity to the West Midlands and its access to the motorway system taken together outweigh its relative lack of local mass. Changing the radial weight to 0.33 we start to place a heavier emphasis on local mass. London rises to the top of the ranks, with Manchester ranked second. Watford slips from second to sixth, and Liverpool shows the greatest improvement, from sixteenth to eighth, as its size starts to outweigh its relatively disadvantageous physical location with respect to the rest of the urban system. Figure 5. The magnitude of the percentage change in total potential caused by changing the self-potential by altering the radial weight from 1.00 to Conclusions In this brief paper we have shown that, at least at the spatial scale which potential models are being currently applied within Britain for policy purposes, the role of self-potential is far from small and inconsequential. In addition, adjustment of the manner in which this self-potential is estimated can be seen to have noticeable effects on the total potential of an area and on its potential in relation to other places in the national system.

14 1846 M E Frost, N A Spence Certainly, it is clear that no area has been transformed from 'peripherahty' to 'centrality' or vice versa by a technical adjustment to the calculating formula such as the one made in this paper. This finding echoes the conclusion of Owen and Coombes (83) that the essential features of the potential surface are maintained in spite of adjustments to the underlying models. However, potential models are increasingly being used not only to identify these essential features but also to position areas in relation to one another. Any major change in rank order, such as that shown in table 4 by Liverpool, as the radial weight changes is important when one of the stated aims of the recent review of Assisted Areas was to identify the 'worst third' of the country by using economic potential as a component in the ranking system (DTI, 93). Table 4. Changes in total potential and the ranking of areas based on this quantity according to different measures of self-potential (based on various transformations of the radius, r) for selected travel-to-work areas (TTWAs). TTWA 1.00 r 0.5 r 0.33 r Crawley Guildford and Aldershot Hertford and Harlow Medway and Maidstone Oxford Southend Watford and Luton Heathrow London Bristol Birmingham Coventry and Hinkley Dudley and Sandwell Leicester Nottingham Bradford Leeds Sheffield Liverpool Manchester Wirral and Chester Newcastle upon Tyne Cardiff Edinburgh Glasgow potential rank potential rank potential rank Additional concern about the policy application of these methods is raised by the magnitude of the self-potential contribution. Within large cities, with London being a clear example, it has been seen that self-potential can account for one half or more of an area's total, sometimes resulting in large overall values. These high values, however, are really only representative of the positions of the central points of these areas. In London's case the implication is that Central London has high levels of radial access to the substantial London labour market, that it can perform as a centrally focused point for the service provision to the city, and that it has access in all directions to economic interactions and exchange throughout the city. Such a position can reasonably be viewed as one of high economic potential.

15 Accessibility and economic potential 1847 The position of suburban subcentres within the London area, however, is far less clear. Noncentral locations, such as Bromley or Stratford, have access to only a much smaller labour market. Additionally, the difficulties of travelling within cities means that travel from one side of a large city to the other can frequently take longer than travel to surrounding 'free-standing' cities. The central peak of economic potential has little relevance to such noncentral locations and yet the simple implication of the potential models illustrated above is that all parts of the zone under consideration display the same (high) level of potential. For areas of cities suffering from long-term economic hardship at a level of economic potential significantly lower than that of the central area of such cities, this poses a considerable problem when these models are used in the distribution of policy support. In a situation where it is clear that there is no obvious theoretical basis for favouring one radial weight over another, one way forward for these types of applications might be to reduce to the minimum possible the size of the zone used in the calculation. The computer software and the data embodied in the approach to the measurement of travel time and distance between specified points detailed in this paper opens up the possibility of generating fine-grained tables of interzonal distance and time impedance. With more than nodes on the current Routefinder system, the main constraint on the detail of a potential surface is the size of area for which measurements of the mass factor is available. With many population and employment measures available for research purposes at the level of census wards, this, too, does not appear to be much of a problem. Even if the focus of policy interest is at the level of local authority districts or counties, or even NUTS II regions (standard regions in the United Kingdom), a fairer path to the measurement of economic potential would be to estimate a potential surface based on a detailed or aggregated ward unit and then to read from the surface the range of values found within any particular configuration of a spatially larger administrative unit. Only by doing this can the potentially dominating effect of self-potential be translated into a direct measure of a locality's accessibility to the rest of an urban or regional system. References Anderson T R, 56, "Potential models and the spatial distribution of population" Papers of the Regional Science Association Bonsall P, 75, "Approaches to the prediction of intra-zonal interactions", WP-65, Institute for Transport Studies, University of Leeds, Leeds Court A, 66, "Population distributions and self-potential", mimeograph, Department of Geography, San Fernando State College, San Fernando, CA DTI, 93, "Regional policy review of the assisted areas of Great Britain. Background document on the new assisted areas map", Department of Trade and Industry, 1- Victoria Street, London SW1 DoT, 89, "Values of time and vehicle operating costs for use in economic appraisal", Highways Economic Note 2, Department of Transport, 2 Marsham Street, London SW1P 3EB DoT, 92a, "Vehicle speeds in Great Britain", Department of Transport, 2 Marsham Street, London SW1P 3EB DoT, 92b London Traffic Monitoring Report 92 Department of Transport (HMSO, London) Houston C, 69, "Market potential and potential transportation costs: an evaluation of the concepts and their surface patterns in the USSR" Canadian Geographer Keeble D, Owens P L, Thompson C, 82, "Regional accessibility and economic potential in the European Community" Regional Studies Keeble D, Offord J, Walker S, 88 Peripheral Regions in a Community of Twelve Member States (Office of Official Publications, European Commission, Luxembourg)

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