Analysis of the Spatial Equity of Sustainable Transport in the City of Curitiba, Paraná, Brazil

Efectos de la dinámica antrópica en la degradación de los ecosistemas de manglar en el Haití

Abstract

Equity in distribution of accessibility is directly related to quality of life and sustainability. Accessibility measures gain ground in studies on social exclusion, especially in cities, since most of the world’s population is urban. This study focuses on Curitiba, where a mobility solution has emerged - the BRT - implemented since 1974, but which presents rapid growth in the peripheries and a modal matrix based on unsustainable transport - mainly the automobile - whose infrastructure favors higher income groups. Thus, an attempt was made to investigate how the spatial variation of access to opportunities through public and pedestrian transport to essential services is configured, proposing a composite index of sustainable accessibility, in order to contribute to the analysis of equity in the distribution of access to opportunities and its relationship with socioeconomic characteristics. The composite and partial indexes show that the values are far below what could be considered an equitable distribution.

Keywords:
Accessibility; public transportation; equity; environmental; sustainability; mobility

Resumo

A acessibilidade tem relação direta com qualidade de vida e sustentabilidade. Medidas de acessibilidade ganham espaço em estudos sobre exclusão social, principalmente nas cidades, já que a maioria da população mundial é urbana. Este estudo concentra-se em Curitiba, onde surgiu uma solução de mobilidade - o Bus Rapid Transit (BRT) implantado desde 1974, mas apresentando rápido crescimento das periferias e matriz modal baseada em transporte não sustentável - sobretudo o automóvel - cujas infraestruturas favorecem grupos de rendas mais altas. Assim, procurou-se investigar como se configura a variação espacial do acesso a oportunidades por meio de transporte público e pedonal aos serviços essenciais, propondo um índice composto de acessibilidade sustentável, a fim de contribuir à análise da equidade na distribuição do acesso às oportunidades e sua relação com características socioeconômicas. O índice composto e os parciais mostram que os valores estão muito aquém do que poderia ser considerado uma distribuição equitativa.

Palavras-chave:
Acessibilidade; transporte público; equidade; sustentabilidade; mobilidade

Resumen

La equidad en la distribución de la accesibilidad está relacionada con la calidad de vida y la sostenibilidad, por lo que medidas de accesibilidad ganan terreno en los estudios sobre exclusión social, especialmente en las ciudades, ya que la mayor parte de la población mundial es urbana. Este estudio se centra en Curitiba, donde ha surgido el BRT, que ha presentado un rápido crecimiento en periferias y una matriz modal basada en transporte insostenible - especialmente el automóvil - cuya infraestructura favorece a grupos de mayores ingresos. Así, se intentó investigar cómo se configura la variación espacial del acceso a las oportunidades a través del transporte público y peatonal, proponiendo un índice compuesto de accesibilidad sostenible, contribuir al análisis de equidad en la distribución del acceso y su relación con las características socioeconómicas. Los índices muestran que los valores están muy por debajo de lo que podría considerarse una distribución equitativa.

Palabras-clave:
Accesibilidad; transporte público; equidad; sostenibilidad; Movilidad

Introduction

Accessibility is directly linked to social equity, being associated not only with physical access to goods and services but also with quality of life (NORDBAKKE and SCHWANEN, 2015) and sustainability in its socioeconomic and environmental aspects. Besides mobility, accessibility also concerns the quality of transport services, their distribution, frequency, comfort, safety, reliability, and fare prices (LUCAS et al., 2016).

According to the United Nations, the full exercise of human rights includes the “universal right to mobility,” making it urgent to abandon the transport bias in planning and focus on the human right to equitable access to opportunities and sustainable transport. This means prioritizing public transport and active modes (UN HABITAT, 2013). The guarantee of equal opportunities is also mentioned in the “Sustainable Development Goals” (UN, 2021a) as part of the goal to reduce inequality within and among countries. Additionally, “providing access to safe, accessible, sustainable, and affordable transport systems for all” is part of the goal to make urban areas inclusive and sustainable by 2030 (UN, 2021b).

Given this context, accessibility measures have gained increasing importance in research on social exclusion and inequality, as spatial mobility is directly related to social mobility (KAUFMANN and BERGMAN, 2004). According to Páez, Scott, and Morency (2012), the two main components of accessibility measures are the travel cost, determined by the spatial distribution of travelers and opportunities, and the quantity/quality of opportunities. These two components unfold into various possible indices, depending on the characteristics and level of detail of the data.

Geurs and Van Wee (2004) proposed a classification for such indices using four main components: Individual component - considering individuals’ needs, abilities, and opportunities, as well as their perception of times, distances, and travel behavior, such as modal choices; Land use component - referring to the characteristics of origins, destinations, and possible competition generated, with the distribution of residences and opportunities (jobs and services) within this component; Transport component - considering services and infrastructures, with service frequency being an example of a factor in the transport component; and Temporal component - taking into account individuals’ time availability differences and the schedules of services and opportunities, with service operating hours being part of the temporal component.

Based on these components, Geurs and Van Wee (op. cit.) categorize measures into four types: “person-based,” considering personal characteristics such as capabilities and travel budgets; “infrastructure-based,” observing the performance of existing or simulated infrastructure, mainly in terms of speed and congestion; “utility-based,” analyzing the economic benefits of access to opportunities; and “location-based,” calculating accessibility from a geographical perspective, i.e., from one location to another.

The area chosen for this study is the municipality of Curitiba, globally known for being the first city to implement the Bus Rapid Transit (BRT) as an innovative urban mobility solution (UN HABITAT, 2013), and a typical Latin American metropolis with characteristics of rapid peripheral growth and a modal matrix based on private and motorized transport, with infrastructures tending to favor higher-than-average income groups (MEJÍA-DUGAND et al., 2013).

Despite having a very positive image regarding urban mobility, highlighted in a United Nations report as “one of the most sustainable and best-planned cities in the world” (UN HABITAT, 2013), the municipality has not seen enough innovations to keep up with the city’s growth, especially lacking public policy focus on socioeconomic inequalities in peripheral areas, with lower investments in infrastructure and equipment. However, as Seco (2016) points out, the city’s good reputation remains despite the urban problems faced by the population outside the structural axes, which, according to Souza (2001), were a way to ensure that public and private efforts were directed to already valued central areas and expand these valued spaces, which gain value not only from the environment’s configuration but also from the intensity of investments.

An example to consider is the low density of sidewalks in peripheral neighborhoods, where walking is essential due to low income and the inability to buy and maintain a car. This type of infrastructure, besides being basic for urban activities, can also be characterized as an equity indicator (BISE et al., 2018), but is often in poor condition, compromising pedestrian safety (GUIMARÃES et al., 2019).

As in other Brazilian metropolises, Curitiba has also seen an increase in individual transport expenses and a consequent decrease in public transport passengers, resulting from policies of wage increases, credit expansion, and tax incentives for the automotive industry (COCCO, 2016). Additionally, Pereira et al. (2021) highlight the role of inflation in household budgets, which had a stronger impact on public transport, leading to a migration to other modes, mainly cars, ultimately compromising the economic sustainability of the public transport system.

Given the above, the issue of equitable access in developing countries’ metropolises is a challenge, as public transport is operated by companies that invest little in the sector and still need government subsidies to continue operating (UN HABITAT, 2013). Moreover, these public transport systems gain monopoly characteristics, with each line operated by a single company that will prefer lines serving areas with higher population density, often leading to the merging, shortening, or even extinction of certain lines that do not provide sufficient profits for the companies (PRIMI and RODRIGUES, 2015).

This reflection on the equitable distribution of access to opportunities applied to the study area led to the following research question: How does the spatial variation of accessibility in Curitiba relate to access to job opportunities via public transport and pedestrian access to essential services such as education, health care, and grocery shopping?

Given the above, this study aims to analyze the equity in the spatial distribution of access to opportunities and its relationship with demographic and socioeconomic characteristics in Curitiba.

Methodology

To develop the accessibility measures and indices, we used data from the official cartographic base of the road network and companies in Curitiba and a layer of geospatial data containing the hexagonal network of the Institute of Applied Economic Research (IPEA) (PEREIRA et al., 2022) - with aggregated socioeconomic data from the 2010 Census of the Brazilian Institute of Geography and Statistics (IBGE). For public transport measures, General Transit Feed Specification (GTFS) data were used, provided upon request through the Curitiba city hall website, as well as the results of the 2017 Curitiba origin-destination survey (MOBILIDADE, 2017).

Potential Accessibility

The potential accessibility indicator is one of the most used in the literature dedicated to studies of this nature because it attempts to represent the behavior of economic agents in choosing existing opportunities in a territory. Thus, this indicator simulates that, given a set of opportunities, agents will choose those that are more important (due to their size, importance, variety, among other factors) and that are closest to their origin.

In potential accessibility measures to work destinations, considering the well-documented importance of motorized transport for home-work commuting, it is important to analyze the use of collective motorized transport, as most people do not have a job in the immediate vicinity of their homes, making public transport an essential means for workers, especially those with low income (LUCAS, VAN WEE, and MAAT, 2016). The responses to the Curitiba origin-destination survey also show this trend, with work destinations being the ones where people spend the most time commuting compared to other destinations.

The accessibility measure used here is the “gravity-based” type, which considers the attractiveness level of the destination, represented in this case by the number of companies and considering the travel cost in terms of time. It is important to note that the location of company headquarters does not necessarily mean a job position, as the registration may have been done at an address different from where the workers actually perform their duties, but it is considered here as an estimate, which was compared with the “work” destination responses in the Curitiba origin-destination survey, showing a great similarity between the data.

To put the public transport network in the analysis, GTFS data were used, providing information on all bus lines managed directly by Curitiba, with data on routes, stops, and schedules. The next step in obtaining the potential accessibility measure was to create an origin-destination cost matrix, using the centroids of the IPEA hexagon layer as origins and the centroids of the IBGE census tracts layer as destinations.

Next, the potential accessibility calculation was performed. The equation used followed the description by Iacono, Krizek, and El-Geneidy (2008) on Hansen’s (1959) potential accessibility model, which is:

$A_i=\sum _j{O}_{j}f\left(C_{ij}\right)$ (1)

where Ai​ is the potential accessibility of the origin; iandj are, respectively, the origin and destination points ∑j​Oj​ represents the sum of opportunities at the destination (number of companies); and f(Cij​) is the distance decay function, obtained from equation (2).

The distance decay parameter measures the relationship between interaction patterns and distance, considering all other interaction factors as constants (FOTHERINGHAM, 1981). This means that the greater the distance between origin and destination, the lower the intention to make a trip. The parameter β is inversely proportional to accessibility; the higher the parameter value, the lower the accessibility and travel distance (DALVI and MARTIN, 1976). This equation takes the form of a negative exponential function, using the relation:

$f_{ij}=e^{\left(-\beta C_{ij}\right)}$ (2)

where: β is the parameter representing the magnitude of distance decay obtained from linear regression, using the natural logarithm of the trip count originating from the residence and the median travel time; and Cij​ is the impedance, in this case, the total travel time fromitoj.

This procedure was repeated for each hour of the day, choosing a Tuesday as the standard day to avoid the atypical flows of weekends and the first and last working days of the week - Monday and Friday. The final step is to join this table to the hexagonal grid layer, cartographically representing the potential accessibility for each origin to the census tracts weighted by the number of companies.

Cumulative Opportunities and Average Time to the Three Nearest Destinations

The measure of cumulative opportunities, according to Koenig (1980), results from an equation that is a particular case of equation (1), considering a travel timeT:

$\begin{array}{c}f\left(C_{ij}\right)=\mathrm{1,}{C}_{ij}\le T\\ f\left(C_{ij}\right)=\mathrm{0,}{C}_{ij}>T\end{array}$ (3)

This means that all opportunities within a defined time or distance threshold have the same level of accessibility in this measure, while no opportunities are considered outside this limit. The author notes that, from a common-sense perspective, the greater the number of accessible opportunities, the higher the probability of finding one that best meets an individual’s needs and desires.

Given the various proposals found in the literature on reasonable thresholds for pedestrian travel (CHEN et al., 2011; LEE and GOULIAS, 1997), in this study we decided to use the travel times from the origin-destination survey of Curitiba, as these data come from actual trips made by a sample of the population. For each type of destination analyzed, the median travel times were used, as the survey responses tend to be very disparate, thus avoiding under- or overestimated thresholds that would occur if the mean were used, which is heavily influenced by extremes.

The survey data table was filtered to always consider the origin as the residence and the chosen mode as pedestrian, resulting in a median travel time of 10 minutes for the destination “education” (public elementary and high schools) and 15 minutes for the destinations “health care” and “grocery shopping.”

The time threshold was obtained by considering it as a function of distance, estimating that a person walks 4 km in 1 hour, using the following equation:

$T_{(\min )}=\left[D_{(km)}\times 60\right]/4$ (4)

The reason for considering only pedestrian access in this measure is that it is more commonly used for the listed activities and should be encouraged for sustainable mobility reasons. Therefore, the road network was used instead of the public transport network generated with GTFS data, as schedules and days of the week were not considered, assuming these factors do not significantly influence pedestrian accessibility.

Based on these parameters, two categories of accessibility measures were obtained:

1. Cumulative Opportunities Measure: Based on the average travel time equal to or less than the established threshold (10 minutes for education-related destinations and 15 minutes for health and food shopping destinations). This measure includes all destinations within a threshold defined by the isochrone line from the origin.

2. Average Time to the Three Nearest Destinations: In this measure, accessibility to opportunities is measured according to the average time it takes to reach the three nearest services on foot. Therefore, in this measure, accessibility is higher the lower the average time.

These two mapped measures were overlaid with the population layer, obtaining results on the population served and excluded from the threshold, and for the latter, the average time to reach the destinations. These spatial variation measures of accessibility were later combined with potential accessibility measures to obtain a composite sustainable accessibility index, knowing the percentage of each of the three components of the index.

Composite Sustainable Accessibility Index

Once the accessibility diagnosis from the different perspectives presented in the previous indices was made, the aim is now to obtain a single indicator of sustainable accessibility for Curitiba. For this index, the modes of transport considered sustainable by UN Habitat (2013) were used, classifying non-motorized and public transport as sustainable. Thus, this composite index includes the following indicators: Potential accessibility to work by public transport, Cumulative Opportunities and Average time to the three nearest destinations.

The latter indicator consists of three indicators (health care, education, and grocery shopping purposes), requiring the arithmetic mean of the three partial indicators to obtain a global indicator of average time to essential services. After this procedure, an inverse function was obtained so that shorter times indicated better access.

Composite indices are useful tools for integrating large amounts of data into more comprehensible forms for scientific evaluation and use as public policy tools and in comparing different areas. Due to the subjective nature of their formulation, involving data selection, aggregation models, and data gap treatment, these indices should be developed and analyzed with caution, as they can mask or contribute to the manipulation of results according to the needs of those who develop them (CHERCHYE et al., 2008).

Therefore, it is important that each step is evaluated, especially regarding the choice and weight of variables (FREUDENBERG, 2003). The development of composite indices follows the general formula:

$I={\sum }_{i=1}^n{W}_i{X}_i$ (5)

where Xi​ is the normalized variable, Wi​ is the weight ofXi​ (0 ≤Wi​ ≤ 1); and i = 1,…, n.

According to the manual for developing composite indicators (OECD, 2008), ten steps should be followed to create a composite index: 1. Theoretical framework; 2. Data selection; 3. Imputation of missing data; 4. Multivariate analysis; 5. Normalization; 6. Weighting and aggregation; 7. Uncertainty and sensitivity analysis; 8. Back to the data; 9. Links to other indicators; 10. Visualization of results.

Steps 1 to 4 were previously completed during the development of procedures for obtaining accessibility measures. From here, the data normalization process began. All values of the partial indices were normalized using the MIN-MAX statistical method, based on the formula:

$X_{Norm}=\frac{X-X_{Min}}{X_{Max}-X_{Min}}$ (6)

where Min​ = Lowest value in the series; XMax​ = Highest value in the series.

After this step, the normalized data were aggregated by neighborhood, initially using a simple average. In the next step, the data were aggregated by neighborhood, resulting in a composite accessibility index for each of the 75 neighborhoods in the municipality.

Results and Discussion

Potential Accessibility

The results showed that the highest potential accessibility values are located around the central region. The only time when the periphery has values closer to those of the Central Business District (CBD) is at 5:00 AM, when the first services of the public transport system start. After this time, the differences between the CBD and the periphery only increase, due to the greater number of opportunities in the CBD and the shorter time its residents would take to access them. It is also possible to notice a tentacular characteristic of accessibility values along the BRT lines, as they are the main public transport routes (Figure 1).

Figure 1:
Potential Accessibility to Jobs

The maximum potential accessibility value was observed at 6:00 AM (46279.28), with a minimum of 0.00 at 1:00 AM, when GTFS data do not record bus departure times. The highest average value was observed at 6:00 AM (9791.46), followed by 9692.23 at 7:00 AM, which, according to the origin-destination survey report, is the morning peak hour.

The comparison of potential accessibility measure values with demographic and socioeconomic data was grouped to obtain the sum of the population and subsequently the percentage share of each in relation to the quartile of frequency values. Income values were represented in Brazilian reais (BRL), and income quintiles were grouped by median.

The results of potential accessibility by public transport compared with socioeconomic data show that the population in the 5th income quintile, i.e., the highest income, has the best performance, representing only 0.03% of the total population. Generally, potential accessibility values decrease as income values also decrease.

The population with the highest share of the best performance was of Asian origin, with 60.30% in the 3rd quartile of potential accessibility. The ethnicity with the worst performance was Indigenous, with 11.67%, followed by Black, with 10.71% of the population having the minimum accessibility value, also representing the 1st income quintile. This result is expected, as these ethnicities historically show evident social exclusion in social indices and spatial distribution in urban areas in Brazil.

Cumulative Opportunities

To analyze the results of this measure (Figure 2), the hexagons with the number of cumulative opportunities were aggregated by summing the population and calculating the average income, based on aggregated data by IPEA hexagon, containing the total population, White population, Black population, Indigenous population, and Yellow population, represented by Asian descendants. The average income was represented in BRL. Finally, the income quintiles were represented as 1 (poorest), 2, 3, 4, 5 (richest). To better understand the proportion of the population within the time thresholds, the data were converted to percentages of the total within each ethnicity.

Figure 2:
Cumulative Opportunities for a) Health care, b) Grocery Shopping, and c) Education purposes

For the “health care” destination, five classes of cumulative opportunities were obtained, including zero, where no opportunity is found within the established pedestrian travel time threshold. It was observed that 40.43% of the population is located outside the 15-minute walking distance to a health service, with this proportion being higher among the Asian population (54.66%). This can be partly explained by some of this population living in rural areas or higher-income neighborhoods. The highest income values had accumulated opportunities between 0 and 1, which can be partly explained by the study being based on public services, with greater distribution in areas farther from the center and with lower average income.

It is important to note that approximately 84% of the total population has up to 1 accumulated opportunity, which, despite being an opportunity, shows that there is no choice for a large part of the population. In the case of health care services, which require specialties, most people probably have to travel to more distant districts to have their needs properly met. Although the lowest incomes reached a relatively high value of opportunities, this represents only 2.08% of the population.

For the “grocery shopping” destination, represented by supermarkets and open markets, 20 classes were presented, ranging from no opportunity to a maximum of 19 opportunities. Here, it was found that 32.71% of the population was outside the 15-minute walking threshold to the destination, with this proportion being higher among the Indigenous population (40.32%). This can be partly explained by this population being distributed in lower-density areas, which may be a factor of disinterest for entrepreneurs in opening new businesses due to logistical difficulties and low demand. The lowest income values are found in the first classes, between 0 (none) and 1 opportunity within the time threshold. These values increase relatively until reaching a maximum of 16 opportunities, with the population of the hexagons presenting an income quintile value of 5 (maximum), showing a trend of food trade establishments being closer to areas where the population has a higher average income.

For the “education” purposes destination, only public schools were used as a reference, resulting in 37.86% of the population being outside the 10-minute pedestrian travel threshold from their residence. This 5-minute faster pedestrian travel time threshold compared to health and food shopping destinations can partly be explained by the fact that students are, on average, younger than people who need to travel to hospitals, health centers, open markets, and supermarkets. Additionally, travel to health locations is often done with a person with reduced mobility (child or elderly), and the return from supermarkets and open markets is added with the weight of purchases, which reduces speed, especially for the elderly.

The group with the largest share outside the thresholds was the Asians, representing 42.83% of this population, which again may be due to the higher average income in this group, allowing them to live closer to private schools in higher-standard neighborhoods. The hexagons with the lowest income values accumulated the highest number of opportunities - 5 in total - which can be explained by the distribution of public schools in peripheral neighborhoods, where the population cannot afford private school fees, car ownership is low, and there are more offers of cheaper land for government purchase.

The cumulative opportunities measure, combined with socioeconomic data, allowed for the correlation of spatial exclusion with social exclusion, considering income levels and ethnicity, which are the available data for this level of aggregation. It was proven, based on the measures, that most of the population, including the poorest, is located outside the reasonable reach of services that meet basic needs for a better quality of life.

Average Time to the Three Nearest Destinations

The average time to the three nearest destinations was mapped in hexagons for the various service categories, as seen in Figure 3.

Figure 3:
Average Time to the Three Nearest Destinations: a) Health care, b) Grocery Shopping c) Education

To create the tables with average times, we used the grouping by quartiles of the average times recorded for each hexagon. This resulted in five classes, ranging from the minimum value, passing through 25%, 50%, and 75% of the values, corresponding respectively to the 1st, 2nd, and 3rd quartiles, ending with the maximum value.

The analysis of the “health care” destination showed that the highest-income group was only in 3rd place, with a time value more than double that of the first-place group. However, the lowest-income group was in the last quartile, with a travel time exceeding the first-place group by more than 42 minutes and more than 24 minutes of average travel time compared to the immediately preceding group.

Additionally, the largest proportion of the population is within the first group, with 46.66% of the total. The population with the best time result is the Black population, with 56.85% within the group with the lowest average travel time. The population with the worst performance for this destination was the Yellow (Asian) population. The fact that the 3rd income group represents 46.66% of the population and is in the best-performing position may indicate a more equitable distribution of public health services in the municipality, locating public facilities in neighborhoods where the population is more in need of this service.

For the “grocery shopping” destination, it was observed that the shortest time to the nearest destinations was obtained by the group with the highest average income, corresponding to the 3rd income quintile, meaning these people have a monthly income above the median income of the municipality’s population. Conversely, the worst results were found in the group with the lowest income, corresponding to the 1st income quintile. The population classified as “yellow” (Asians) by IBGE had the best performance, with 60.71% of its population within the category of the lowest average time. The group with the largest share within the worst-performing group was the Black population, with 3.86% of this population.

For the “education” purpose, it was observed that the best performance was not achieved by the highest-income population group, ranking only 3rd in this regard. This phenomenon can be partly explained by the large portion of the student population that does not yet have an income, and those who do must spend more time on transportation. The worst performance was observed in the lowest-income population, representing a travel time more than four times that of the best performance.

The average time to destinations, not presenting a rigid time threshold as in the case of cumulative opportunities index, showed better indices regarding the equitable distribution of opportunities, highlighting the limiting factor of choosing a threshold for index development. Despite this, the numbers are far from what could be considered an equitable distribution.

Composite Index of Sustainable Accessibility

The normalized results of the accessibility measures presented earlier were aggregated by district, resulting in the composite sustainable accessibility index, as shown in Figure 4.

Figure 4:
CISA aggregated by district

Analyzing the composite index from the disaggregated results of the partial indices, it is found that the central region districts have the best results, with the Center in the first position, while the districts in the 10 worst positions are all in the city’s periphery, bordering other municipalities (Figures 6 and 7). Part of this phenomenon can be explained by the border effect, which could be minimized using data from neighboring municipalities. However, these did not have data such as GTFS and company locations available. Despite this methodological limitation, the results align with the positive correlation between accessibility and average districts income.

Regarding the partial indices, the potential accessibility index for job destinations had the best results in the central region districts, with Centro (CBD) again performing the best. Conversely, the districts with the lowest potential accessibility results were in the periphery, especially those along the municipality’s borders. This effect was expected, as indicated in the methodology section for developing the potential accessibility measure, considering the border effect. Additionally, these peripheral areas have a lower concentration of companies and a lower density of public transport lines. Since the potential accessibility measure considers public transport and is weighted by the number of companies, the results in peripheral neighborhoods performed poorly, as expected.

The districts with the best cumulative opportunities indices are also located in the central region, with the CBD in the first position. The worst positions in the index are the neighborhoods closest to the periphery. It is important to note that the accumulated opportunities indices did not reach 1 due to the average made between the three chosen destinations - health care, education, and grocery shopping. These performance differences in the cumulative opportunities index can be partly explained by the decreasing population density towards the periphery, leading to less representative services in space, especially regarding the “grocery shopping” destinations, as these, being private companies, benefit from agglomeration economies.

The partial index of average time to the three nearest destinations was the only one where the CBD was not the best-performing district, with a peripheral district appearing among the top 10 for the first time. This can be partly explained by the distribution of public schools and public health service units being slightly farther from the CBD, including in districts with lower average income. However, the 10 worst performances in this index were in peripheral districts, in the city outskirts, where population and service densities are lower.

When analyzing the indices with predominant values in each district, it is found that the partial potential accessibility index predominates only in the CBD, probably due to the number of public transport lines and the higher number of companies. In all other districts, the average time index to the three nearest destinations predominated. The cumulative opportunities index did not achieve the highest result in any district, partly explained by the low average value compared to the other indices.

As observed in the scatter plot of data aggregated by neighborhoods (Figure 5), there is a positive correlation between accessibility and income, indicating that the benefits of access in Curitiba are not equitable and do not benefit the part of the population that most needs sustainable mobility, precisely because they do not have sufficient purchasing power to acquire and maintain motorized vehicles.

Regarding the distribution of accessibility, the Gini coefficient for the CISA was 0.46, showing a better result than its intermediate indices, such as Potential Accessibility (Gini=0.52), Cumulative Opportunities (Gini=0.48), and Average Time to the Three Nearest Destinations (Gini=0.48). Although these values indicate significant inequality in the distribution of accessibility, the composite index improved these values by adding more possibilities to the studied areas, as districts with relatively poor public transport service distribution could have their value compensated by good accessibility to certain services by pedestrian mode.

Figure 5:
Income vs CISA

Conclusions

As the world becomes increasingly urban, improving quality of life largely means focusing efforts on cities. The daily commuting flow is influenced by various factors, from individual constraints to infrastructure, including the quality of transport services and land use. These aspects make the study of accessibility increasingly relevant, as access to various opportunities is a determinant of equity levels and, consequently, social mobility.

The use of various types of data, from surveys to open data like GTFS, was crucial in forming a methodological framework to capture diverse characteristics in the study of accessibility in the study area, both by pedestrian mode and public transport. Understanding th ese data can indicate the areas of the city that most need certain types of services.

The origin-destination survey conducted by the municipality of Curitiba, based on individual responses regarding actual trips, proved extremely important by providing data on completed trips, which served as parameters to assist in validating other types of measures, such as potential accessibility and cumulative opportunities. Additionally, the survey data provide socioeconomic and demographic information that can be related for equity analysis.

On the other hand, the location-based potential accessibility index proved to be a good complement to the origin-destination survey. While the latter analyzes only the trips that were possible, excluding those not made due to some constraint, the potential accessibility measure shows the level of accessibility for the entire study case area - and, consequently, the entire population - all weighted by the attractiveness of destinations, in this case, the number of companies accessed by public transport.

The cumulative opportunities index inherently includes a spatial equity analysis, despite the limitation of chosen thresholds, which give the measure an “all-or-nothing” character, immediately excluding all individuals outside it and considering all individuals within as equal. However, this measure based on pedestrian travel showed more spatially diverse results than others, with higher values in the central region, showing a greater variety of access to services for the population closer to the city outskirts. This brings an important field of analysis, as urban sprawl is a reality, especially in Latin American metropolises.

Finally, the Composite Index of Sustainable Accessibility (CISA), developed from the normalized data of potential accessibility measures, cumulative opportunities, and average time to the three nearest destinations, showed a spatial equity disparity between central and peripheral districts. The disaggregation of the index revealed which indices were most important within each district. This type of result points to possibilities for increasing urban socio-environmental sustainability.

Future research aims to aggregate data from neighboring municipalities to mitigate the border effect (MAUP), assuming the metropolitan character of Curitiba and its surrounding region. For the composite index of sustainable accessibility, it is also intended to include data on accessibility to public transport stops, weighted by service frequency, and data from other active modes, especially bicycles.

References

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Publication Dates

• Publication in this collection
  07 July 2025
• Date of issue
  2025

History

• Received
  13 Mar 2024
• Accepted
  28 Nov 2024