1 Introduction

There is a gap in our current knowledge with regard to the relationship between (spatial) accessibility and spatial inequality. This is in part because accessibility is not a well-defined concept and no universally accepted single definition exists. When it comes to a specific discipline or field such as health studies, accessibility becomes more complex and context dependent (Aday and Andersen 1974). For example, Penchansky and Thomas (1981, p. 128) have defined five dimensions for access to health care systems: availability, accessibility, accommodation, affordability, and acceptability. These five dimensions are all relevant for a study defining access to urban facilities and services, the subject of this paper. Khan (1992) explicitly discusses the spatial and aspatial dimensions of accessibility. Using Penchansky and Thomas’s terminology, availability and accessibility are spatial in nature while accommodation, affordability, and acceptability are inherently aspatial. That said, it is important to note that these last three dimensions can have indirect spatial manifestation and effects.

Table 1 summarizes different dimensions of accessibility and some differences between ‘having access’ and ‘gaining access’ (Gulliford et al. 2002). Having access depends on the availability of facilities and services. However, gaining access means the individual requiring a resource has the ability to bypass financial, organizational, sociocultural, possibly geographical, spatial constraints or other forms of barriers to satisfy his or her need.

Table 1 Dimensions of access
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Availability means the number of facilities and services that individuals can select to use, and accessibility is the travel cost (in terms of distance and time) between the user (i.e., the consumer) and the location of the type of service needed (i.e., the provider). The quality of services and personal treatment are components of Accommodation. The service should have a minimum standard quality in addition to proper personal treatment for people. Affordability is defined by economic factors. There may be enough facilities in close proximity, providing high quality services, and accepting people without any restriction but these facilities may not be affordable for users; i.e., a user must be able to pay to receive services or have enough support from the social welfare system to (partially or completely) cover the costs. Acceptability is interwoven with socioeconomic dimensions of the city, such as gender, race, religion, etc. For example, a facility or service may be spatially close and potentially able to provide services and must provide these services without any preferences (i.e., religion or gender discrimination). The list of barriers and facilitators includes time, scale, context, geography, social welfare system, ethnicity, race, religion, gender, age, health condition, income, cultural settings, mental capacity, social position and expectation, cultural beliefs, and media and advertising.

Finally, spatial or geographical accessibility is arguably the most intuitive component of accessibility. Spatial accessibility is useful proxy for ‘potential accessibility’ as compared to ‘revealed accessibility’ (Joseph and Bantock 1982) or as Khan described, the availability of that service moderated by space or the distance variable (Khan 1992). Assuming that the following condition is true, "given a maximum range for the service being offered at a facility and assuming that every member of the population is a potential user of the service, the pattern of physical accessibility will depend only on the relative location of the population and the service facilities" (Joseph and Bantock 1982), then all members of a society should have no restrictions in using facilities or services. In addition, the facilities and services should easily provide services for all users without any restrictions on Penchansky and Thomas’s five dimensions of access. In the analysis for this paper, the accessibility dimension of access was prioritized, accepting the condition that there is no limitation on use of facilities and services by individuals. The accessibility dimension has the advantage of being mappable and thus facilitating the visualization of spatial inequality within a city.

1.1 Tehran

Tehran is an exemplar city for examining the challenges of, and adaptation to, spatial inequality in the context of rapid urban growth. Tehran is the capital and primate city of Iran, the second largest city in Western Asia, and with a population that has doubled within 25 years it has been one the fast growing cities in the Middle East and the developing world (Madanipour 2006; Zebardast 2006). Current population estimates place Tehran at approximately 9 million residents in the city and approaching 20 million in the wider metropolitan area, and thus it is among the largest cities in the world. Tehran’s rapid population growth and the spatial patterning of its residents is a function of historical, cultural, social, economic and spatial factors. It has been the capital city of Iran since 1796 when it was selected by Agha Mohammad Khan of the Qajar dynasty. It is the primate city, politically, culturally and economically; all central government functions are concentrated in Tehran and it is the main business and financial center. The ‘economic’ primacy of Tehran attract migrants with much of the recent population growth driven by interrelated processes related to rural to urban migration (urbanization), post-war migration (restructuring), and an influx of foreign migrants (globalization); see Fanni (2006). Several challenges have accompanied Tehran’s population growth; including housing and overcrowding, transportation and traffic congestion, water availability and pollution as well as natural disasters such as flooding and vulnerability to earthquakes. In addition the costs and benefits of population growth are not distributed evenly within the urban area; replicating historical patterns of inequality. One of the most important, clear, and sharp features of the city is a north–south disparity and socio-spatial gradient. Mirroring the physical terrain the northern part of the city has relatively affluent districts and neighborhoods (called Nahyeh) in the higher elevations while the southern section includes poor; predominantly at lower elevations. In addition, the northern part enjoys a more green environment while the southern part has high population densities and worse air pollution (Fig. 1).

Fig. 1
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Locator map of Tehran, and its Nahyeh (neighborhoods)

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The case of Tehran is of interest in its own right but the approach adopted in this paper can be used and tested in other Middle Eastern and Western Asia cities with similar socio-spatial settings such as Riyadh, and Delhi and well as other world cities such as Accra, Bogata, Caracas, Jakarta, Lagos, and Mexico City. Moreover, as geospatial databases are proliferating and increasingly available for international contexts we will likely see many more applications of GIS and spatially explicit studies of urban social problems in developing city contexts (Weeks et al. 2013), including Iran (Tayyebi et al. 2011; Reshadat et al. 2015). Much of the necessary geospatial data and statistical information for a study of accessibility are available for Tehran.

2 Measuring Accessibility

How is accessibility measured? There are several established methods for measuring accessibility. Some of them are theoretically and mathematically simple while others are more complex (Koenig 1980; Handy and Niemeier 1997; Talen 1998, 2003). Each method captures different aspects of accessibility but are highly dependent on the method of measurement (Talen 1998). In this paper accessibility is calibrated as a distance or spatial proximity measure.

Accessibility can be studied from two independent points of view: topological accessibility and contiguous accessibility (Rodrigue et al. 2009). From the topological accessibility point of view, accessibility is measured based on the transportation network through nodes and paths. In contrast, contiguous accessibility is measured across a continuous surface. To measure spatial accessibility to facilities and services, the second concept was applied in this study.Footnote 1 This method can be used to produce a composite indicator of objective spatial accessibility to various types of services in an urban area, considering limitation of available data for the city. The model, including the justification of weighting systems used, is introduced below.

2.1 Minimum Distance Model

Travel cost is often the best measure to accessibility, approximating the real mobility scenarios facing individuals within a city. Travel cost can be decomposed into travel time and travel distance and both factors can be used as a proxy for spatial accessibility. Travel distance (or Euclidean distance) was used for measuring spatial distance to urban centers that serve the people. While Euclidian distance does not consider physical barriers and travel impedance (e.g., travel speed or travel time), it requires fewer data inputs and is applicable in cases that lack detailed data on the transport system and network (Delamater et al. 2012). Spatial distance to facilities and services is measured through spatial analysis functions that when operationalized assume that all people are treated the same way, all attractive factors (size, capability, the cost of services, and quality of the services) are similar and the only variable is distance (i.e., the friction distance). In addition, it is assumed that all people have the knowledge about where is the nearest facility they need. The topological accessibility or network distance would provide a more robust measure of spatial accessibility, but in this paper the minimum distance model was used due to the lack of information about the transportation network in Tehran. Acquiring detailed and accurate data on the transport system data for Tehran is desirable but was not available at the time of writing and thus beyond the scope of the current study. While there is considerable elevation variation within the city (over 500 m) the street pattern is fairly dense with several major north–south and east–west major thoroughfares facilitating movement in all directions within the city. Future work will attempt to compare Euclidian versus network based distances.

3 Data and Methodology

3.1 Data

All the data and resultant maps were updated in 2002 and provided by Tehran municipality ICT (Information and Communication Technology) organization that maintains a comprehensive listing of facilities and services. Table 2 shows the list urban facilities and services used in this paper (all geospatial data are in ESRI shapefileFootnote 2 format, used the WGS84 projection). ArcGIS 10.x. was used for all spatial analysis and mapping.

Table 2 Urban facility and services maps
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3.2 Methodology

Figure 2 is an example of one of the typical maps of (point specific) services available to the project; in this instance ambulance services. Due to the lack of information about the geographical area that urban facilities can serve and support, all facilities were considered as point specific services. It is important to note that some services require the individual user to come to them (e.g., schools) whereas other services are provided at the individuals residence, a kind of outreach service, such as the ambulance service (Knox and Pinch 2009).

Fig. 2
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Geographical Distribution Ambulance Service Centers in Tehran

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Subsequently, spatial distance maps were produced for all available facilities and urban services. Figure 3 is an example of a map that visualizes the nearest spatial distance to facility/service points (e.g., ambulance) within Tehran’s official border and Nahyeh. The distance function represents the distance between each cell in the map and the nearest target of a set of features. The output is a raster map, with the value of each pixel showing the distance to the nearest service. In this example, the darker green color shows higher accessibility to each urban facility or service.

Fig. 3
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Distance to the Nearest Ambulance Services Center

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As the range of values of the distance map is based upon on the number of facilities and its geographical distribution (spatial configuration), they are rescaled to facilitate comparison between all produced distance maps. For rescaling, raster values were transformed using a normal distribution function; i.e., using a linear scaling to re-scale every distance map to a standard range between zero and one (0 and 1). There are many other methods and functions to normalize data (De Smith et al. 2015).

Each urban facility and service was classified into two groups: positive and negative. The positive services (maps) were those facilities and services where proximity is generally regarded as positive and favorable to the individual. Conversely, the negative facilities and services were those that are generally regarded as having negative externalities for those individuals living nearby. In reality some facilities and services are complex, such as when they can been seen as having both positive and negative effects on an individual; for example, in an extreme case proximity to an airport or transportation hub is a double-edged sword. From the accessibility point of view, it is good to be close to these hubs but from an environmental perspective, it is the opposite due to noise pollution and congestion. In our model there are both positive and negative values assigned.

3.2.1 Weighting System and Analytical Hierarchical Process Approach

Different facilities and services do not have the same priority in urban life. For example, access to sport fields or clubs is not as important as access to health care facilities such as hospitals. In order to insert the functional priorities into the model, a weighting system was used to assign weights to each facility and services. An Analytical Hierarchical Process (AHP) approach was implemented. AHP is a structural, mathematical and philosophical decision process developed by Saaty (1988) that has been applied in many contexts for decomposing decision systems and problems. This technique decomposes the decision problem into a hierarchy of simpler and easier to understand problems. It compares different criteria (i.e., factors) and then assigns weights to them, according to their role and effect on the decision or problem. Nyerges and colleagues write, ‘‘The AHP incorporates a confidence index to test whether the continuity between all comparisons corresponds with the pattern exhibited in the data.’’ (Nyerges et al. 2011). It is worth noting that, “… user-defined weights are inherently subjective and biased by personal opinion, thus challenging the validation of an unbiased effect or the extent that their value represents meaningful depictions of the data.” (Ibid, p. 148)

This weighting system can be applied using two methods: subjective and objective weighting. In the subjective method, the researcher assigns weights based on his or her knowledge or based on other studies (i.e., on facility preference and their importance in urban life). In objective method, weights are assigned according to the preference of experts. To evaluate the preference of people for accessibility to urban facilities and services, a questionnaire was designed and respondents were asked to assign weights to each variable on a scale -3 (extremely negative) to +3 (extremely positive); see Table 3. The implementation of the weights to facilities and services are listed in “Appendix”.

Table 3 Weighting system
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4 The Composite Index of Spatial Accessibility

The composite index of spatial accessibility was produced using the raster calculator and weighted overlay in ArcGIS. Figure 4 visualizes the spatial accessibility service within the city border; with areas of higher spatial accessibility to all facilities and services having higher values shown in the darker color. Based on the composite measure the western, and to a lesser extent the south-eastern, parts of the city have low levels of spatial access to urban facilities and services. The northern extreme seem to fair better than other areas of similar distance from the central city. The central area, not surprisingly, has high levels of spatial accessibility.

Fig. 4
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The composite Index of Spatial Accessibility in Tehran

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5 Population Weighted Distance Map

Accessibility index can decompose and reveal hidden structures of the city and the society;

[…] accessibility is a good indicator of the underlying spatial structure since it takes into consideration location as well as the inequality conferred by distance. Due to different spatial structures, two different locations of the same importance will have different accessibilities (Rodrigue et al. 2009).

That is, the spatial configuration of facilities is relative to the spatial configuration of the population. Many factors affect the accessibility to services, but physical supply and population demand are the most important (Huff 1963, 1964). Balancing between these two factors is as an essential objective in urban planning and social policy studies. As Fig. 5 indicates, accessibility is highly dependent on the spatial structure of services and population. It explains how accessibility in the city increase or decrease according to the spatial configuration and structure of the city.

Fig. 5
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Source Geography of transportation (Rodrigue et al. 2009)

Accessibility and Spatial Structure,

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Overlapping the population map on the generated composite spatial accessibility map facilitates the creation of a new map that better represents the lived conditions in urban areas. This process can define a new map for spatial accessibility and identify shortage in each Nahyeh of Tehran; since more population means more pressure on the services and less opportunity for services for people who live in that Nahyeh or neighborhood. To consider the impact of geographical distribution of population on spatial accessibility in different part of the city the output of the composite index of spatial accessibility (Fig. 4) was calibrated based on population map (Fig. 6), derived from census data using kriging to generate a raster surface.

Fig. 6
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Population surface of Tehran

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Tehran, like all cities, has an uneven population densities, ranging at the district level from between 3000 and over 40,000/km2. The calibration formula is:

$$ {\text{PWA}} = ({\text{A/P}}) $$
(1)

where PWA is population weighted (spatial) accessibility; A is accessibility; P is population.

The output of this process is a map (Fig. 7) that underlines spatial accessibility to urban facilities and activities based on potential demand and pressure on these facilities and centers. It denotes that different parts of the city do not have the same levels of spatial accessibility.

Fig. 7
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Population-weighted (spatial) accessibility map

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6 Herfindahl–Hirschman Index (HHI)

To define the geographical distribution of urban facilities and services in each Nahyeh, the Herfindahl–Hischman Index (HHI) was calculated. This index, similarly to Simpson Diversity Index used in ecology, defines in our context the geographical distribution of urban facilities and services in each Nahyeh.

The, formula is:

$$ H = \sum\limits_{i = 1}^{N} {s_{i}^{2} } $$
(2)

where si is the share of market for facility/services i; N is the number of facilities/services; The range of HHI is between 1/N to one.

The HHI index was calculated for thirty facilities and services within Tehran, based on Nahyeh administrative divisions of the city. Results are presented in Fig. 8 that reveals a significant difference in the distribution of facilities and urban services by type of service.

Fig. 8
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HHI index for Urban Facilities and Services in the Urban Area Based on Nahyeh Administrative Districts

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Figure 9 is the reclassified map of accessibility index produced and presented in Fig. 7. The map was classified into five classes of accessibility. The higher values mean higher levels of accessibility to urban services, and are represented by light and dark green color (classes 4 and 5). The areas that have medium levels of accessibility are shown in yellow, class 3. Finally, places that have low level of accessibility are shown in light and dark red color classes, 2 and 1. This final map can be used in plans for addressing the problem of unequal access to urban facilities and infrastructure. They define the condition in Tehran in terms of accessibility into urban facilities and services and help identify areas with high priority for implementing accessibility development plans and projects.

Fig. 9
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Reclassification of accessibility

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Figure 10 is the histogram of accessibility index; in this figure, the horizontal axis is the value of the pixel (accessibility value), and the vertical axis is the number of pixels. The distribution of values indicate that a large number of pixels are at low and medium values which is another ample criterion for existing unequal spatial accessibility in Tehran and for its habitants.

Fig. 10
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Histogram of accessibility

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Table 4 is the reclassification of population and area based on proposed 5-class spatial accessibility index for Tehran. This table reveals that the majority of Tehran’s residents have low level of accessibility to urban amenities (i.e., class 1 and class 2), while less than four percent of the residents (i.e., those in class 4 and class 5) have the highest levels of accessibility. High levels of uneven accessibility thus exist within the city.

Table 4 Reclassification of population and city area based on accessibility
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As Fig. 8 illustrates the HHI for urban facilities and services varies across Nahyeh within Tehran. Some urban facilities and services, for example, schools are ubiquitous across the city and other are relatively well dispersed (disaster management centers), and others again are poorly distributed (e.g., sewage). The HHI can provide invaluable information for urban managers and researchers interested in different service applications (e.g., spatial budgeting, location and allocation analysis. These data and visual representation can help decision makers to allocate budgets and plan and/or determine the location (site selection) of urban facilities and services.

7 Discussion

In this paper, we calculate and examine the urban spatial inequality in terms of spatial accessibility in the global city of Tehran. The analysis confirms that Tehran, a complex city, is one with spatial unevenness in accessibility to urban facilities and services. Tehran is a rapidly growing city and accommodating change in population and providing sufficient and necessary infrastructure will be a continuing challenge. By identifying areas of unequal access to facilities and services this paper provides one perspective and approach that can help planners and policy makers prioritize decisions. Further, these data can have academic use in fields related directly to demography, health and urban services. Increasingly, large-scale urban health studies are being implemented in cities around the globe, including in Tehran (Asadi-Lari et al. 2010; Kassani et al. 2016; Kiadaliri et al. 2015; Nedjat et al. 2012), and our study can hopefully raise awareness regarding the potential use of geospatial data more generally as well as the ability to generate contextual variables for subunits in the city (e.g., Nahyeh) that can be combined with health outcomes studies to examine the role of place characteristics in health disparities.

This methodology is not without limitations. The approach is based on specific data, not always complete or perfect for the task at hand. We were unable to incorporate urban public transportation system data and available transportation modes in the city, and by its very nature the approach we use focuses on the spatial dimensions of accessibility and not the aspatial measures. That is, our approach does not measure availability, accommodation, affordability, and acceptability nor is such data easily available. The proposed model could also benefit from further testing, validation, and refinement. Testing and validation of this methodology in similar rapidly growing cities in emerging market economy countries will facilitate a better understanding of the mechanism generating and maintaining spatial inequality in such cities.

Spatial inequality, specifically in terms of spatial access to urban amenities, is highly related to economic factors driving inequality. In emerging market economy countries, recent neoliberalism urban policies are important factors in locating and providing urban services by both the private and public sector. Tehran and Iran have been at the edge of neoliberal policies during the last decade, but as the maps show the city is faced with serious problem regarding spatial accessibility to main urban facilities. Monitoring and modeling spatial accessibility in these cities using time series analysis and change detection techniques can improve our knowledge about future spatial effects of neoliberal urban policies such as privatization of public services and private and public investment in mega projects.