Evaluating policy effectiveness and equity of access to urban green spaces in Karaj, Iran (2007–2017): a fine-grained G2SFCA analysis

In recent decades, rapid urbanization and increasing population have transformed land use and demographics in cities across Asia and the Middle East, especially in developing countries (Kanbur and Zhuang, 2014; Wang et al., 2020). This expansion is expected to continue (United Nations, 2019), often without proper planning, leading to sprawl and fragmentation (Sun et al., 2019). These trends exacerbate disparities in access to essential land uses such as urban green spaces (UGSs) (Pandey et al., 2022).

UGSs, including parks, recreational areas, and other public green spaces in urban environments, are essential for cities, providing numerous environmental and societal benefits (Eizenberg and Jabareen, 2017). They conserve natural resources, support ecosystems, provide clean air, purify water (Konijnendijk et al., 2013; Yang et al., 2015), prevent flooding (Song et al., 2020) and reduce noise pollution (Dzhambov and Dimitrova, 2015). In addition to improving urban vitality and livability, UGSs enhance health, mental well-being and lower stress (Dong et al., 2022; Malekzadeh et al., 2023). They also reduce the risks of diabetes, obesity and heart disease through social and physical recreation (Doubleday et al., 2022). Additionally, UGSs foster community engagement, lower crime rates and enhance neighborhood satisfaction by promoting social cohesion and safe environments (Jennings et al., 2016). Therefore, policymakers and urban planners must ensure equal access to UGSs to improve public health and promote environmental and social equity (Huang et al., 2022; Wang et al., 2021).

Despite these recognized benefits, accessibility to UGSs is frequently unevenly distributed across urban neighborhoods. Such inequalities exacerbate existing socio-economic disparities and reduce the effectiveness of UGS provision as a planning tool (Rigolon, 2016). These challenges are particularly pronounced in developing cities experiencing rapid urbanization and land-use change, such as Karaj, Iran, where population growth, informal development and policy implementation gaps intensify pressures on green-space provision and distribution. Here, breakneck population growth, coupled with financial constraints and speculative land markets, often outpaces planning efforts, leading to a persistent mismatch between the supply of green infrastructure and the demands of a growing urban populace (Dadashpoor et al., 2024; Hosseini and Hajilou, 2019; Rahmati and Hanaei, 2024). In response, municipal governments frequently enact comprehensive plans with ambitious policies aimed at expanding green space provision and improving spatial equity.

However, a critical gap remains in our understanding of the long-term effectiveness of these planning policies in improving equity of access over time (Wu et al., 2023; Zhou et al., 2025). While numerous studies provide valuable cross-sectional snapshots of accessibility patterns, they cannot capture whether policy interventions kept pace with shifting demand (population growth and spatial redistribution) (Huang et al., 2022; Zhang et al., 2021). This gap is especially pronounced in developing contexts such as Iran, where limited evidence exists on whether government strategies have successfully improved equitable access over time (Heo et al., 2021; Rao et al., 2022).

In this paper, we aim to evaluate the effectiveness of UGS accessibility policies implemented in Karaj, Iran, between 2007 and 2017, with a focus on addressing the unequal distribution of UGS. Specifically, we will (1) assess UGS accessibility by car and pedestrian access at the building block scale for the years 2007 and 2017, using the G2SFCA and Gini index, Palma ratio and Foster–Greer–Thorbecke (FGT) index methods; (2) identify changes in both population and UGS accessibility during this period and explore the relationship between these changes using Bivariate Local Moran's I; and (3) contextualize these results by comparing them with the city's stated planning goals and policies, in order to highlight the key factors that contributed to successes and failures in promoting equitable access to UGS.

A growing body of research has examined accessibility and equity in UGSs, drawing on concepts from transport geography, environmental justice and urban planning. This literature spans multiple dimensions, from conceptual frameworks of accessibility to methodological advances in measuring access to empirical evaluations of spatial equity. Given this diversity, the following review is organized into three main strands: (1) accessibility components and measures, (2) measuring equity in accessibility and (3) empirical evidence on equity in UGS accessibility. This structure enables a systematic synthesis of theoretical foundations, methodological approaches and empirical findings, while also highlighting existing gaps relevant to the present study.

Accessibility is a core concept in urban studies, transport geography, and environmental justice research, broadly defined as the ease with which individuals can reach desired destinations and services within the urban environment (Geurs and van Wee, 2004; Hansen, 1959). The concept is inherently multidimensional. Geurs and van Wee (2004) conceptualize accessibility through four key interacting components: (1) land-use, which describes the amount, quality and spatial distribution of opportunities as well as demand and resulting competition; (2) transport, which concerns the performance of the transport system, including travel time, cost, reliability and comfort; (3) the individual component, which refers to socio-demographic and economic characteristics (e.g., age, income and physical ability) and resource constraints that shape a person’s ability to travel; and (4) the temporal component, which reflects the time constraints on both the availability of opportunities (e.g., opening hours) and the individual’s schedule. These components interact in complex ways, and a disadvantage in one dimension can potentially be compensated for by creating an advantage in another (Lucas et al., 2016). While comprehensive frameworks incorporating these dimensions have been proposed, empirical studies often focus on selected aspects due to methodological and data constraints (El-Geneidy et al., 2016; Karner et al., 2024). Over the past decades, various methods have been developed to evaluate UGS accessibility, each with distinct methodological assumptions and limitations.

Accessibility measures are commonly grouped into two broad categories: place-based and people-based approaches (Neutens et al., 2010). Place-based approaches (e.g., container/coverage counts, cumulative-opportunity and gravity models) evaluate accessibility from fixed spatial units, offering straightforward implementation and transparent results. However, they mask individual heterogeneities and may underestimate equity gaps in service delivery. By contrast, people-based approaches incorporate individual space–time constraints and provide a more behaviorally realistic assessment of access. Although theoretically superior, their application requires detailed microdata such as activity schedules, which are rarely available for large populations or longitudinal studies, particularly in developing contexts (Marwal and Silva, 2022; Neutens et al., 2010). Consequently, place-based measures remain widely applied in planning practice due to their transparency and compatibility with commonly available spatial data (Geurs and van Wee, 2023).

Traditional place-based approaches, such as container-based and coverage-based methods, measure accessibility by counting or calculating the area of services within administrative boundaries or fixed-distance buffers (Richardson et al., 2010; Zhang et al., 2019). While simple and interpretable, they are prone to the modifiable areal unit problem (MAUP) and edge effects, and implicitly assume that residents rely exclusively on the nearest facility (Huang et al., 2022; Kelobonye et al., 2020; Xiao et al., 2017). The cumulative opportunity model improves on these methods by counting the number of destinations within a specified time or distance threshold, offering straightforward calculation and ease of interpretation (Ashik et al., 2020; Hansen, 1959; Marwal and Silva, 2022). However, its precision is undermined by the arbitrary choice of thresholds and the assumption that all destinations are equally attractive, regardless of type or quality (Marwal and Silva, 2022; Vickerman, 1974).

Gravity-based models represent another advancement, as they integrate the distance–decay effect and the relative attractiveness of each destination (Dai, 2011; Li et al., 2021a, b). They provide a more realistic assessment and consider the possibility of multiple choices but often neglect supply–demand balance, leading to biased estimates where populations and facilities are unevenly distributed (Huang et al., 2022; Wu et al., 2020). As the relevant research progresses, it is believed that the use of accessibility to discuss equity issues must consider both supply and demand, because the distribution of public service resources is fair only in terms of the spatial distribution based on population demand (Zhang et al., 2021). The Two-Step Floating Catchment Area (2SFCA) method was introduced to overcome this shortcoming, balancing supply and demand within catchments and offering a more robust framework for evaluating accessibility (Lin et al., 2021; Xing et al., 2020). Despite its advantages, the original 2SFCA method assumes equal accessibility for all individuals within a catchment, failing to reflect the gradual decrease in accessibility as distance increases (Ashik et al., 2020; Delamater, 2013). Addressing this issue, several enhanced versions of 2SFCA have been proposed, including the Gaussian-based 2SFCA (G2SFCA), which applies a continuous, distance–decay weight following a Gaussian distribution to more accurately model accessibility patterns and better capture spatial inequalities (Li et al., 2021a, b).

The choice of accessibility measure can substantially affect conclusions about equity outcomes (Neutens et al., 2010). Method selection should therefore be aligned with research objectives, data availability and scale, striking a balance between analytical rigor and feasibility (Geurs and van Wee, 2023; Marwal and Silva, 2022). In this study, the aim is to evaluate whether UGS provision in Karaj kept pace with population change at the building-block scale (2007–2017). While people-based approaches could, in principle, provide richer insights, their data demands and methodological complexity make them infeasible in this context. Accordingly, we adopt the G2SFCA method, which offers a robust yet practical solution, compatible with available block-level population and land-use data. By integrating both supply–demand balance and distance–decay effects, G2SFCA represents an effective trade-off between analytical robustness and data feasibility, and has demonstrated superior performance in UGS accessibility studies (Wu et al., 2021; Zhang et al., 2019).

Spatial equity is another critical aspect of UGS studies (Crooks and Andrews, 2016). It has emerged as a central concept in urban planning and environmental justice, referring to the state in which facilities and services are distributed impartially and uniformly across a given area, regardless of scale, in alignment with population density (Seyedashraf et al., 2022; Yuan et al., 2017). In UGS research, spatial equity ensures that all residents, irrespective of their location or socio-economic status, have reasonable access to environmental and recreational resources (Rigolon, 2016). Scholars typically assess spatial equity using two conceptual approaches: horizontal equity, which calls for equal distribution of services among all social classes, and vertical equity, which allocates resources based on the specific needs of different groups or areas (He et al., 2020; Murray and Davis, 2001). In this study, we primarily adopt a horizontal equity perspective, since detailed socio-economic data for residents in the study area were not available, which precluded a vertical equity analysis. However, in line with recent literature, we also draw on sufficientarian concepts, which emphasize that all individuals should achieve a minimum acceptable threshold of access, regardless of inequalities above that level (Karner et al., 2024). This view is especially relevant in UGS planning, where policies frequently define minimum per-capita provision or maximum distance thresholds as benchmarks for equity (Rigolon, 2016; Wolch et al., 2014). By explicitly addressing whether residents fall below such thresholds, sufficientarian measures complement horizontal equity frameworks and provide actionable insights for policy evaluation.

Measuring equity in UGS accessibility typically involves assessing the degree of inequality in the spatial distribution of parks relative to population needs (Talen, 1997). The Gini coefficient remains a widely used metric to quantify inequality in UGS accessibility, valued for its simplicity, intuitive interpretation and ability to summarize distributional inequality in a single, standardized number (Li et al., 2021a, b; Martin and Conway, 2025; Yang et al., 2020). Its broad applicability in urban studies and compatibility with spatially aggregated data make it a practical tool for UGS policy evaluation and planning (Chen et al., 2022). While it provides a robust overall measure of distributional inequality, it alone does not fully capture disparities among the most underserved or marginalized groups, and it can overlook local variations hidden in aggregate patterns (Karner and Golub, 2015). To overcome these shortcomings, alternative indices offer distinct advantages. The Palma ratio is a tail-focused indicator defined as the ratio of the mean outcome for the top 10% of the distribution to the mean outcome for the bottom 40% (Cobham and Sumner, 2013; Karner et al., 2024). In the context of UGS accessibility, this tail-focus is valuable because it highlights cases where a small share of the population captures a disproportionate share of accessible park area or high-quality UGS, while a substantial segment remains underserved, an aspect that aggregate measures can obscure (Karner et al., 2024; Liu et al., 2021). The FGT index, originally developed for poverty measurement (Foster et al., 1984), has been increasingly adapted in accessibility and transport equity studies to capture “accessibility poverty” (Karner et al., 2024; Tiznado-Aitken et al., 2018). The FGT family provides a sufficientarian framework that identifies not only the proportion of residents falling below a policy-defined accessibility threshold but also the depth and severity of their shortfall (Foster et al., 1984; Karner et al., 2024; Tiznado-Aitken et al., 2018). This makes it particularly advantageous for UGS equity analysis, as it enables policymakers to assess whether interventions achieve minimum acceptable access levels and to prioritize improvements for the most deprived areas. Compared with distributional indicators such as the Gini, which summarizes overall dispersion, and the Palma ratio, which highlights tail concentration, the FGT index explicitly operationalizes a policy threshold and yields actionable metrics for monitoring sufficiency over time or across neighborhoods. Accordingly, combining the Gini coefficient with complementary indices such as the FGT index and Palma ratio allows for a more comprehensive and policy-relevant assessment of accessibility inequality.

Accessibility to UGS has become a central concern in recent scholarship, as spatial and socio-economic disparities continue to shape who benefits from environmental and recreational resources. Recent studies increasingly highlight spatial and socio-economic disparities in UGS access. Rigolon (2016) identified systematic inequities affecting racial, ethnic and low-income groups in developed countries, shaped by urban form and segregation. Zhang et al. (2011) proposed the Population-Weighted Distance (PWD) metric, revealing notable urban–rural disparities in the United States. Similarly, Wei (2017) applied a gravity-based model in Chinese cities, showing widening inequalities amid urban expansion. Li et al. (2021a, b), using an enhanced 2SFCA model integrating travel modes and park quality, confirmed persistent spatial inequities in Nanjing. Perry et al. (2018) emphasized that proximity alone is insufficient without usability and inclusive infrastructure, while El Murr et al. (2023) demonstrated discrepancies between perceived and GIS-based park access, advocating for integrating subjective perceptions.

Despite these advancements, limited research has evaluated the long-term effectiveness of UGS accessibility policies. Rigolon and Németh (2020) evaluated urban greening policies across 10 US cities, finding that new park developments enhanced accessibility but often triggered green gentrification, disproportionately benefiting affluent residents and displacing marginalized groups. Similarly, Wolch et al. (2014) explored strategies to expand green spaces in US and Chinese cities, finding a paradox: while intended to improve equity and health, these strategies can raise property values and cause gentrification, displacing residents. They recommend that urban planners focus on policies that are “just green enough” to avoid unintended consequences. Wu et al. (2018) evaluated Beijing's 2016 policy of dismantling fences around gated communities, finding it slightly improved UGS accessibility but exacerbated inequities, as wealthier neighborhoods benefited more. Using the Gini coefficient, the study highlights how such interventions can widen socio-spatial disparities. This underscores the need for equitable UGS policy design. As is evident, most studies focus on developed cities, short-term policy effects and basic accessibility measures, such as Euclidean or network-based service areas, without accounting for supply-demand imbalances and distance–decay effects.

Despite these contributions, some gaps remain. UGS accessibility and equity are affected by regional urbanization level, UGS policy and population growth. However, few studies have explored the dynamic changes in UGS accessibility and equity on a time scale (Wu et al., 2023; Zhou et al., 2025) and further evaluated the effectiveness of these policies. It often remains unclear whether the policies introduced by city governments and planners have achieved their intended outcomes, or, if not, why they have fallen short. Additionally, more research is needed to examine how UGS accessibility and equity have evolved over time, reflecting broader urban development processes. Most studies have adopted a cross-sectional approach, often overlooking the longitudinal relationship between accessibility changes and demographic shifts, such as variations in population size or income, over time (Huang et al., 2022). A better understanding of these dynamics would enable policymakers to adjust policies based on empirical evidence (Chen et al., 2017; Qian et al., 2015). For instance, if certain neighborhoods experience a decline in UGS accessibility despite a growing population, this could signal a need for reassessment of zoning regulations or reallocation of resources. It is also worth noting that most research on UGS access equality has focused on cities in the US and Europe, while cities in developing countries, particularly in the Middle East, have received comparatively little attention (Heo et al., 2021; Rao et al., 2022).

Karaj, the capital of Alborz Province in northwestern Iran, is part of the Tehran metropolitan area and has experienced rapid urban growth due to migration from Tehran (Figure 1). Covering 134 km², the city's population grew from 1.3 million in 2007 to 1.6 million in 2017, with the highest population growth rate in Iran (Statistical Center of Iran, 2021). This growth has led to significant challenges in the distribution and accessibility of UGSs. Despite efforts, Karaj’s park area per capita remains below the national average, with 2.32 m² per person in 2017 compared to the recommended 6 m² (Supplementary Materials - Table S1). This urban expansion and population density increase make access to UGS critical for residents’ well-being, especially migrants. For further details, refer to Supplementary Materials 1.

The urban development of Karaj has been formed by its proximity to Tehran, favorable climate and increasing population. Historically, the city comprised agricultural lands, gardens and villa estates. However, urban expansion has resulted in the transformation of a significant portion of these green spaces into residential, industrial and educational areas. Given the importance of preserving green spaces in this rapidly expanding urban environment, several key policies and goals have been outlined in Karaj's comprehensive and detailed plans (City of Karaj Urban Planning Department, 2007), as follows. These represent all the major UGS goals and strategies explicitly stated in the city's plans that are directly relevant to accessibility and distribution.

Preservation of gardens and agricultural lands: One of the main priorities is the preservation of existing gardens and agricultural lands to maintain the city's environmental quality and prevent the subdivision and conversion of these areas for other purposes. The preservation of these zones is crucial for environmental sustainability and to prevent further reduction of green spaces.

Increase in per capita green space: A critical issue raised in the comprehensive and detailed plans is the severe shortage of parks and green spaces in Karaj. One of the goals set in these plans was to increase the per capita green space from 1.38 square meters in 2007 to 6 square meters by 2026. This goal was established to address the severe shortage of green spaces and improve access for the growing population.

Creation of green corridors: A key strategy outlined in the comprehensive plan is the integration of green spaces along the branches of the Karaj River. In this context, recreational and green zones have been defined along the three main branches of the river, with an emphasis on connecting these areas to form green corridors running from the north to the south of the city. This strategy also emphasizes continuous pedestrian access to these green spaces and the preservation of the natural landscape along the river (Figure 2).

Development of small, decentralized parks: The detailed plan prioritizes the creation of smaller, dispersed parks throughout the city, rather than large, centralized green spaces, to ensure more equitable access to green spaces for all residents.

Conversion of private gardens into public parks: One of the policies in the comprehensive plan is the transformation of private, inaccessible gardens (owned by private or governmental entities) into public parks. This initiative aims to rapidly increase citizens' access to green spaces within the urban area.

The population data, which capture the spatial distribution of residents at the building block scale, were sourced from the Statistical Centre of Iran. These data are crucial for assessing demographic shifts and their implications on the accessibility to UGSs. The land use data, detailing the spatial distribution and the size of UGSs at the parcel scale, were obtained from the Information and Communication Technology Organization of Karaj Municipality. These datasets are instrumental in evaluating changes in land use over the study period and in calculating the accessibility of parks from residential areas with high precision. Road network data were acquired from (OpenStreetMap, 2022), which is essential for determining realistic access routes to UGSs. Given the limited availability of road network data, with the oldest dataset dating from 2017, this study assumes that no significant changes in the road network occurred between 2007 and 2017. This assumption is necessary to maintain the consistency of the analysis across the two time points.

It should be noted that the national census takes place every ten years in Iran, and the 2007 and 2017 datasets are the two latest census datasets for population and land use. Also, the scale of all analyses in this study is at the building block (enclosed area of land that is surrounded by roads) scale, which has an average area of 14.7 km².

We used the Gaussian-based Two-Step Floating Catchment Area (G2SFCA) method (Alford et al., 2008), where a Gaussian function serves as a distance decay function to quantify the accessibility to UGSs. The G2SFCA model has been frequently used in UGS accessibility evaluation research to obtain more accurate results (Zhou et al., 2023).

Accessibility measurement based on the G2SFCA method can be realized with two steps. The first step is to determine the ratio of supply to demand (⁠$Rj$⁠), which applies as follows Eq. (1):

where $Sj$ is the area (in $m2$⁠) of the park (⁠$j$⁠), $Pi$ indicates the total population of the building blocks (⁠$i$⁠) located in the catchment area, $dij$ is the shortest network distance from the building block (⁠$i$⁠) to the park (⁠$j$⁠) and, $d0$ is the threshold distance. $G(dij)$ represents the Gaussian function that is determined by employing Eq. (2).

Finally, the accessibility value, $Ai$ in $m2/person$⁠, of each building block (⁠$i$⁠) is determined in the second step, measured by the sum of (⁠$Rj$⁠) multiplied by $G(dij)$ Eq. (3):

The determination of accessibility to green space relies significantly on the threshold distance (d₀), making it a vital and influential factor in accessibility calculations. Many studies adopt specific time or distance thresholds to represent reasonable walking access to urban parks. For example, Rojas et al. (2016) demonstrate the use of adaptive thresholds based on urban context, while Laan and Piersma (2021) test fixed radii ranging from 300 m to 1,500 m for different park types and population densities. Recent research by Jasso Chavez et al. (2024) aligns this practice with the “15-minute city” framework, using a 15-minute walking threshold combined with sufficiency standards such as a minimum of 10 m² per person. In the absence of explicit time or distance targets in Karaj's master plans, which specify only per capita goals, we adopt a time threshold of 15 minutes for pedestrian accessibility in this study. This choice aligns with international practice and ensures realistic representation of typical walking behavior in the local context (Hu et al., 2020; Wang and Dong, 2022). Moreover, based on previous studies, we picked 5 and 25 km/h for walking and driving speeds, respectively (Huang et al., 2022). All geoprocessing and accessibility measurements were performed using ArcGIS Pro 3.3.2 and Python scripts. Due to data limitations, micro-level factors such as slope variation, intersection delays and traffic conditions were not included in the distance or time calculations, which is acknowledged as a limitation of this study.

Spatial equality is a critical aspect of the UGS studies (Crooks and Andrews, 2016). Spatial equality refers to the state in which facilities and services are distributed impartially and uniformly across a given area, regardless of scale, based on population density (Seyedashraf et al., 2022). In this study, we use the Gini, Palma ratio and FGT indices to measure the equality of UGS accessibility. The Gini coefficient is mainly employed as an economic index to evaluate income inequality among residents (Wu et al., 2020). However, in recent years, to evaluate the inequitable distribution of accessibility to UGSs, researchers have expanded the use of the Gini coefficient (Cheng et al., 2021). Therefore, to estimate the equality of UGS accessibility in each period and each mode of accessibility, we employed the Gini coefficient. A Gini coefficient value of 0 represents perfect equality, while 1 represents complete inequality. Currently, there is a widespread acceptance of certain thresholds for interpreting Gini coefficient values. A coefficient below 0.3 is commonly regarded as “good,” and a range of 0.3–0.4 is considered “normal,” while values exceeding 0.4 are deemed “poor.” A coefficient surpassing 0.6 is labeled as “dangerous,” indicating a potential risk of significant social discontent (Wu et al., 2020). The Gini coefficient is determined using Eq. (4):

where $n$ indicates the number of building blocks, $Bi$ represents the cumulative index of the ratio of accessibility to UGSs of the building block $i$ to the total accessibility to UGSs, and $ai$ is the population ratio of the building block $i$ to the overall population. Additionally, we employed the Lorenz curve using Microsoft Excel as a convenient graphical method to display the relationship between the rate of accessibility to UGSs and the population, the proportion of the population that possesses a certain level of accessibility to UGSs.

In addition to the Gini coefficient, this study employs the Palma ratio and FGT indices to provide a more comprehensive assessment of accessibility inequality and insufficiency. The Palma ratio focuses on the extremes of the distribution and is defined as the ratio of the mean accessibility of the top 10% of the population to that of the bottom 40%:

where $A̅Top10%$ and $A̅Bottom40%$ represent the average accessibility scores of the respective groups. A higher Palma ratio indicates greater inequality concentrated at the tails of the distribution (Cobham and Sumner, 2013; Karner et al., 2024). The FGT indices, adapted from poverty analysis, are used to evaluate the share, depth and severity of insufficient access relative to a defined threshold. The general form is:

where: N is the total population; q is the population with accessibility below the threshold z; x_i​ is the accessibility score for individual or unit i; and α is a parameter indicating the order: α = 0 (FGT0) is the proportion below the threshold (headcount ratio); α = 1 (FGT1) is the average proportional shortfall (gap index); and α = 2 (FGT2) captures the severity of insufficient accessibility by squaring the shortfall, which gives greater weight to individuals or areas with the largest gaps (severity index).

In this study, the threshold z is set at the 40th percentile of G2SFCA scores for each mode and year, ensuring consistency with the Palma ratio cut-off. FGT values are calculated using population weights to accurately reflect the number of residents experiencing insufficient access. This approach provides a multi-dimensional view of accessibility inequality, addressing both distributional extremes and the sufficiency of access levels (Karner et al., 2024).

In order to evaluate whether changes in UGS accessibility between 2007 and 2017 corresponded with shifts in population (demand), we quantified the differences in accessibility and population using the subsequent equations (Eqs (7) and (8)):

where $ΔAi$ is the accessibility difference, $ΔPi$ is the population difference, and $Ai$ and $Pi$ represent accessibility and population of the building block $i$⁠, respectively,

We employed Bivariate Local Moran's I to evaluate the inequality in UGS access over ten years (2007–2017). The bivariate local Moran’s I is widely employed for determining the spatial relations between two variables (Hu et al., 2020). Therefore, to identify clusters exhibiting disparities between accessibility and population changes, we employed bivariate local Moran’s I using Eq. (9) (Anselin, 1995; Talen and Anselin, 2016):

where $Wij$ is the spatial weight matrix computed using a distance-based approach, $Zxi$ and $Zyj$ represent the standardized values of the population difference (x) and accessibility difference (y) of areas $i$ and $j$⁠, respectively.

The car and pedestrian accessibility levels to UGSs for each building block in the city of Karaj in 2007 and 2017 are illustrated in Figure 3. In 2007, Districts 10, 8, 2 and 3 (Figure 3a), and in 2017, Districts 6, 3, 10, 8 and 2 (Figure 3b) had higher pedestrian accessibility to UGSs due to the greater number and total area of parks. The average pedestrian accessibility to UGSs increased from 1.94 $m2/person$ in 2007 to 2.57 $m2/person$ in 2017, indicating a 32% increase. In 2007, District 8 (Figure 3c), and in 2017, Districts 8, 10, 7, 1, 9 (Figure 3d) had higher car accessibility to UGSs. The average car accessibility to UGSs increased from 1.98 $m2/person$ in 2007 to 2.75 $m2/person$ in 2017, indicating a 39% increase.

When visually comparing pedestrian and car accessibility, it becomes evident that pedestrian accessibility had a more uniform geographical spread in both years, unlike car accessibility, which remained concentrated in Districts 8, 1, 10 and 7. Despite the overall increase in accessibility, areas with lower accessibility did not experience a significant improvement, highlighting constraints of urban planning in the city of Karaj regarding geographical inequality and equitable UGS distribution.

Pedestrian accessibility to UGSs improved significantly in Districts 6, 10 and 2, while Districts 3 and 5 experienced a decline (Figure 4a). The average increase in pedestrian accessibility to UGSs among building blocks was 0.4 (20%).

Car accessibility remained stable across most of the city, except for district 8, which saw a decline (Figure 4b). Districts 7, 6 and 3 showed moderate increases in car accessibility. The average increase in car accessibility to UGSs among the blocks was 0.55 (27%).

Districts 7, 5, 4 and part of 6 experienced significant population growth (Figure 4c), while the eastern areas had no significant demographic changes. The largest population reductions occurred in larger blocks.

We observe that the Gini coefficient for pedestrian accessibility to UGSs decreased from 0.6 in 2007 to 0.51 in 2017, representing a reduction in inequality of about 15% (Figure 5). This improvement can be due to the increased number and size of parks in Karaj, which have enhanced pedestrian accessibility. Additionally, Gini coefficient for car accessibility to UGSs decreased from 0.60 in 2007 to 0.55 in 2017, equivalent to a reduction in inequality of a roughly 8% (Figure 5). Despite this improvement, both pedestrian and car accessibility to UGSs remain inequitable, exceeding the 0.4 threshold established by Wu et al. (2020). The Lorenz curves indicate that roughly 60% of both pedestrian and car accessibility are concentrated within only 20% of the population in both 2007 and 2017.

To complement the Gini index, the Palma ratio and FGT indices were calculated to provide a more detailed understanding of the distributional extremes and the prevalence and severity of insufficient accessibility (Table 1). The results indicate that in 2007, the Palma ratio was significantly higher for pedestrian accessibility (83.70) compared to car accessibility (14.45), revealing substantial disparity between the top 10% and bottom 40% of the population. By 2017, the Palma ratio decreased for both modes, falling to 29.67 for pedestrian and 5.75 for car access. These reductions suggest improvements over time, although inequalities remained more pronounced in pedestrian access than in car access when measured across the population distribution.

The FGT indices further illustrate the extent of under-service. In 2007, 42.1% of the population had car accessibility below the acceptable threshold (FGT0 = 0.421) with an average shortfall of 11% (FGT1 = 0.111) and a severity index of 4.2% (FGT2 = 0.042), indicating that the largest accessibility gaps contributed disproportionately to overall inequality. For pedestrian accessibility, while the share below threshold was lower at 35.2%, the average shortfall (20%) and severity (14.6%) were substantially higher, showing that the underserved experienced deeper and more intense gaps. In 2017, the proportion below the threshold decreased slightly for car access (40.4%) and remained stable for pedestrian access (35.9%). However, the average shortfall and severity remained greater for pedestrian access than car access, indicating that while overall inequality decreased, the depth and intensity of insufficient pedestrian accessibility persists. These findings confirm and reinforce the patterns identified by the Gini index.

We used Bivariate local Moran’s I to identify clusters where accessibility changes negatively correlate with population changes. These clusters exhibit the highest UGS access inequality, as population growth over ten years coincided with decreased accessibility.

Clusters with significant population growth and declining accessibility are classified as high-low and highlighted in red, representing areas where demand has exceeded supply (Figure 6). For pedestrian accessibility, these clusters are primarily located in Districts 5, 3 and 8 (Figure 6a). Meanwhile, for car accessibility, they are positioned in Districts 5 and 8 (Figure 6b). The larger extent of these clusters in Figure 6b indicates that spatial mismatches between population growth and car accessibility are more pronounced, reflecting stronger clustering of underserved areas in car access compared to pedestrian access. These spatial mismatches point to localized inequities in UGS provision, highlighting that car accessibility has lagged behind population growth more severely than pedestrian accessibility.

This section provides a contextual comparison between the planning goals outlined in Karaj's comprehensive and detailed urban plans and the observed outcomes. While not a direct statistical result, this comparison helps situate the empirical findings within the broader policy framework. The results of this analytical study provide a comprehensive comparison between the projected goals and policies outlined in the comprehensive and detailed plans of Karaj and the actual achievements in terms of access to and distribution of UGSs from 2007 to 2017. These plans, with an ambitious vision, emphasized enhancing environmental sustainability and ensuring equitable access to green spaces for all residents. The key goals and policies included increasing the per capita green space, preservation of gardens and agricultural lands, creation of green corridors, developing small, decentralized parks and converting private gardens into public parks. In our analysis, we evaluated the numerical per capita target based on the calculated green space per capita in 2007 and 2017. For the other supportive policies, we assessed the extent of their implementation by examining the available land use data and observing the changes between 2007 and 2017. The findings of this study reveal that these goals have not been fully achieved, and significant discrepancies exist between planning and actual outcomes.

Increase in per capita green space: While the comprehensive plan aimed to increase the per capita green space to 6 square meters by 2026, by 2017, this figure had only reached 2.32 square meters, a modest improvement from the 1.38 square meters in 2007. This gap between target and reality reflects significant challenges in turning policies into action, as well as financial constraints and managerial weaknesses in urban governance.

Preservation of gardens and agricultural lands: Despite the emphasis in the comprehensive and detailed plans on the necessity of preserving gardens and agricultural lands, the results of this study show that this goal has not been realized. Many of these areas have been converted into residential, commercial and other uses. A key factor contributing to this transformation could be rising land values and the municipality's dependence on revenue from land sales, driven by the absence of stable and sustainable income sources, an issue explicitly acknowledged as a structural weakness in the comprehensive plans and broadly documented in Iranian municipal finance studies (Yazdani and Roya, 2023).

Creation of green corridors: Despite the emphasis on establishing green and recreational zones, including interconnected green spaces along the branches of the Karaj River to form a green corridor, the expansion and integration of these spaces have not been sufficient to meet the policy objectives. The study shows that only a portion of the proposed green spaces have been developed, and many of these areas lack the necessary connectivity, resulting in isolated green areas, limiting their overall accessibility and utility, particularly for pedestrians. This is evident when comparing the actual park distribution in Figure 1 (2017) with the planned green space zoning presented in Figure 2, which highlights the discrepancy between the intended interconnected corridors and the fragmented reality on the ground.

Development of small, decentralized parks: One of the key objectives of the detailed plan was the development of small and dispersed parks throughout the city to enhance equitable access to green spaces. However, in practice, the newly developed parks have predominantly been larger and concentrated in specific areas, mostly near major roads and affluent districts. While these larger parks are easier to manage, they are less effective in addressing local needs and improving equal access. This finding is supported by Figure 6, which presents the Bivariate Local Moran's I maps highlighting spatial clusters of accessibility driven by the location of larger parks, and by Supplementary Table S1, which indicates a 34% increase in the average area of UGSs between 2007 and 2017.

Conversion of private gardens into public parks: One of the few successful policies of the comprehensive plan has been the conversion of private gardens into public parks. Over the decade, several previously inaccessible private gardens have gradually been turned into public parks. This observation is based on a spatial overlay of 2017 park locations with the 2007 land use map (Figure 1 and Supplementary Material Figure S1), which reveals multiple instances where private garden parcels were converted into public parks over the study period.

In conclusion, many of the policies proposed in Karaj's comprehensive and detailed plans have not been fully implemented, and the current status of green spaces in the city falls significantly short of the initial goals.

This study evaluated the effectiveness and equity of UGS accessibility policies in Karaj, Iran, from 2007 to 2017. Using the G2SFCA method at the building-block scale, we assessed pedestrian and car accessibility, incorporating equity metrics such as the Gini coefficient, Palma ratio and FGT indices. Longitudinal changes in population and accessibility were examined via Bivariate Local Moran's I to identify spatial mismatches. The findings were further interpreted in relation to the objectives of the study.

Addressing the first objective of this study, to assess UGS accessibility by car and pedestrian access between 2007 and 2017, the findings show clear contrasts between pedestrian and car access to UGSs. Both car accessibility and pedestrian accessibility experienced overall improvements from 2007 to 2017, as the number and size of parks in Karaj increased. The study indicates that areas with high accessibility to UGSs are predominantly near arterial roads. The eastern part of the city exhibits higher car accessibility to UGSs, due to a greater number and size of parks, along with better road network connections compared to the west. The improvement in pedestrian access to UGSs in the central part of the city is mainly due to the conversion of old private gardens into public parks in 2017 (Karaj Municipality, 2022). Similarly, establishing a large park in the northwest, District 6, has significantly enhanced local accessibility for pedestrians. Pedestrian accessibility displays a more balanced geographical distribution due to the more uniform placement of local parks but suffers from deep local shortfalls where park provision is lacking and where high-density areas lack nearby green spaces. Although car accessibility shows slightly higher average accessibility values than pedestrian accessibility, it remains more spatially concentrated. This concentration of car accessibility carries important implications. While it benefits residents with private vehicles and proximity to large green spaces, it simultaneously exacerbates disparities by privileging higher-income or better-connected districts and leaving peripheral or densely populated areas underserved. Similar patterns have been documented in other contexts, where motorized access to parks reinforces socio-spatial inequalities and limits equitable exposure to green benefits (Li et al., 2021a, b; Wolch et al., 2014) .

In line with the first objective, this section interprets inequality measures, including the Gini coefficient, Palma ratio and FGT indices, to provide a deeper understanding of the distributional fairness of UGS access across the population. The Gini coefficient declined for both pedestrian and car accessibility to UGSs between 2007 and 2017, indicating reduced inequality among population units; nevertheless, values exceeding 0.4 signify ongoing inequity, a trend consistent with findings from Chinese cities, where rapid UGS expansion lowered Gini values but persistent disparities remained due to concentrated spatial development and land-market pressures (Rao et al., 2022; Song et al., 2021). This suggests that inadequate UGS distribution planning and the effects of land speculation, as observed in Karaj, mirror dynamics reported in China and other urban contexts. The Palma ratio highlights sharp improvements in reducing disparities between the extremes of the distribution (64.6% reduction for pedestrian accessibility and 60.2% for car accessibility), suggesting that UGS policies during the study period were particularly effective in alleviating severe deprivation among the bottom 40% of the population. Similar dynamic reductions of Palma ratios have been documented in Beijing, where residential exposure to green space inequality, as measured by Palma, declined significantly over decades, though spatial heterogeneity persists (Cao et al., 2023). However, the persistence of relatively high Palma values, particularly for pedestrian accessibility, indicates that tail-end disparities remain a significant challenge.

The FGT indices provide a sufficientarian perspective by assessing not only how many residents fall below the accessibility threshold but also the depth and severity of their deprivation. From 2007 to 2017, the share of residents below the threshold (FGT0) declined slightly for car access, while it remained constant for pedestrian access. For car accessibility, both depth (FGT1) and severity (FGT2) increased, suggesting that although fewer residents were deprived, those who remained underserved faced deeper and more severe shortfalls, due to population growth and the concentration of large parks in limited districts. In contrast, for pedestrian access, FGT1 and FGT2 decreased, indicating that while the proportion of deprived residents remained stable, the intensity and severity of deprivation eased. Notably, FGT1 and FGT2 were consistently higher for pedestrian access than for car access, meaning that although fewer people lacked sufficient access by foot, those deprived faced deeper and more severe shortfalls. These findings align with evidence from related domains, where FGT indices have been applied to transport equity: Tiznado-Aitken et al. (2018) showed that accessibility poverty can persist or even deepen for specific groups despite overall improvements in access, underscoring the value of FGT in revealing the depth and severity of shortfalls beyond average measures. Taken together, the Gini and Palma results highlight persistent inequalities in the distribution of UGS access, while the FGT indices add a sufficientarian lens by showing that these disparities are not only widespread but also deeper and more severe for particular groups. Overall, this dual evidence underscores that equity-oriented policies must move beyond aggregate improvements: they should both redistribute access more evenly across neighborhoods and directly target the depth of deprivation. In practice, this means that expanding parks or green infrastructure in currently underserved locations, enhancing connectivity in peripheral areas and reducing reliance on private vehicles are essential steps to prevent overall gains from masking persistent or worsening shortfalls among the most disadvantaged.

Addressing the second objective, examining the spatial relationship between population growth and changes in accessibility, the Bivariate Local Moran's I analysis identified high–low clusters (highlighted in red in Figure 6), indicating areas where rapid population growth coincided with declining UGS accessibility, reflecting a mismatch in which demand exceeded supply. These clusters were larger for car access, showing that motorized accessibility favors well-connected districts while rapidly densifying areas remain underserved. From a planning perspective, such clusters highlight priority locations for UGS development, where interventions can both reduce severe gaps and maximize equality gains. This aligns with previous applications of Bivariate Local Moran's I, which translate spatial mismatch analysis into actionable planning insights (Luo et al., 2022; Pan et al., 2021). Targeting these areas allows policies to move beyond aggregate improvements and directly address localized inequalities, supporting sufficientarian goals of minimum acceptable access for all residents.

Addressing the third objective, contextualizing the empirical results through a comparison with Karaj's stated planning goals and policies, this section evaluates the effectiveness of Karaj's UGS policies, identifying the key factors that contributed to both successes and failures in promoting equitable access. Based on the findings of this study, despite the ambitious goals set out in Karaj's Comprehensive and Detailed Urban Plans, the city has struggled to fully realize its green space development objectives between 2007 and 2017. Among the key goals, the conversion of private gardens into public parks stands out as relatively successful, as several previously inaccessible private parcels were turned into public parks, enhancing access in some districts. In contrast, the goal to increase per capita green space to 6 m² has not been met; by 2017, the city had only reached 2.32 m² per person. The preservation of agricultural land and gardens has also largely failed, with many such areas being repurposed due to rising land values and the municipality’s dependence on revenue from land sales. Similarly, the creation of green corridors along the Karaj River has seen limited progress, with incomplete implementation and fragmented green areas that do not support continuous pedestrian connectivity. Finally, while the plan prioritized small, decentralized parks to ensure equitable access, the actual pattern of green space development has favored larger parks in higher-income districts, undermining this decentralization goal. These shortcomings are largely attributable to a lack of sustainable municipal revenue, pressure from land speculation, poor alignment between planning and population changes, and the absence of an integrated green space strategy tailored to Karaj's evolving urban context.

A second key issue is the insufficient consideration of population distribution and uneven growth across different areas. The initial urban plans did not adequately account for demographic changes, leading to a mismatch between the demand for green spaces and their supply in various districts. While efforts to create green corridors were commendable, they were not aligned with the city’s demographic shifts, contributing to persistent inequalities in UGS accessibility. This is evident in the Bivariate local Moran's I red clusters, which highlight areas that experienced a significant population increase alongside declines in UGS accessibility (Figure 6). The third reason for the policy failures is the lack of cohesive green space planning and a comprehensive green space plan tailored for Karaj. The city’s policies regarding green spaces are limited in scope and lack integrated short-term or long-term strategies for maintaining and expanding UGS access.

To address the ongoing challenges, certain efficacious strategies and UGS policies can improve the inequality in accessibility to UGS. The findings of this study highlight the necessity of establishing sustainable financial models. To mitigate urban speculation and prevent further loss of green spaces due to financial pressures, the municipality must explore alternative and sustainable revenue streams to reduce its reliance on land sales. Implementing policies such as green taxes or public-private partnerships for green space development can provide long-term financial support for the preservation and expansion of these areas (David and Venkatachalam, 2019; Taxwerx, 2021).

Our research also reveals that a major contributor to unequal UGS accessibility is the misalignment between UGS distribution and population changes. To address this issue, we propose equality-focused planning by revising zoning policies. Specifically, the green space zones, currently concentrated along river branches (Figure 2), should be reallocated to high-low (red) clusters identified in Figure 6, where significant population growth coincides with sharp declines in accessibility, areas of highest inequality. This approach ensures that UGS expansion and distribution directly respond to the spatial distribution of the population and its changes, better addressing community needs.

Another key recommendation is to improve the quality of UGSs to compensate for quantity limitations. Based on the works of Haaland and van den Bosch (2015) and Wu et al. (2022), in urban areas experiencing densification and rapid urbanization, where financial constraints and limited land availability hinder the creation of new parks, investment in enhancing the quality of existing UGSs can effectively offset the lack of quantity. High-quality green spaces can provide a broader range of benefits and improve user satisfaction, even in areas with limited UGS coverage.

Moreover, increasing the number of small UGSs and pocket parks is crucial in high-density areas with limited construction space, such as the western part of Karaj, Districts 5 and 6 (Fan et al., 2021; Zhang et al., 2021). In contrast, in the southeastern part of the city, Districts 8 and 2, with greater land availability and lower population density, we recommend a mix of large and small UGSs to improve access and reduce inequalities. Based on McConville (2021) and Nesbitt et al. (2019) studies, an innovative strategy for addressing green space shortages could be the creation of pop-up parks, temporary green spaces developed in vacant or underutilized urban areas. Pop-up parks provide quick solutions to green space shortages and offer opportunities to test new concepts and engage the community in planning.

To promote equality in accessibility to UGSs, it is crucial to improve walkability and enhance connectivity to ensure better access to parks (Li et al., 2021a, b; Rojas et al., 2016). This can be achieved through measures such as upgrading sidewalks, constructing new pedestrian and bicycle paths, and enhancing other pedestrian facilities (Wu et al., 2020). Finally, by implementing these recommendations and adopting a comprehensive green space plan that considers spatial distribution, community demand and the development of diverse park spaces, alongside monitoring and evaluating policies and projects, policymakers can take significant steps toward achieving equitable access to UGSs for all residents.

There are limitations in this research that require further investigation. First, demographic factors, including income, ethnicity and age, significantly impact accessibility (Shi et al., 2020; Zhang et al., 2021). Recent research highlights that socioeconomically disadvantaged groups and ethnic minorities have limited UGS access (Kronenberg et al., 2020; Li et al., 2021a, b). In our study, due to data access constraints, we could not include demographic indicators (such as income, ethnicity, age and disability) in our assessment of UGS access equality. Future studies could incorporate demographic stratification variables to more comprehensively examine accessibility equality to UGSs using our methodology.

Second, our assessment of accessibility only focuses on UGS size. Research on the qualitative aspects of UGSs provides valuable insights, exploring how environmental factors impact target groups and identifying effective intervention strategies (Huang et al., 2022; Macintyre et al., 2019). Future studies could incorporate UGS qualitative features to evaluate accessibility to UGSs. Moreover, while Karaj has very limited bicycle infrastructure and lacks openly available data on public transit networks, integrating multimodal accessibility analyses that include cycling and public transportation modes can enrich the evaluation. Finally, integrating road quality as a crucial factor in assessing accessibility is innovative. Particularly within developing or underdeveloped countries, this could be a crucial factor in choosing a UGS, as poor road conditions leading to UGSs can influence people’s choices, as they may prefer traveling longer distances to access UGSs via higher-quality roads (National Recreation and Park Association, 2014), emphasizing road quality as a determining aspect.

The main contributions of this study include assessing the effectiveness of policies related to green space access in urban plans and analyzing the reasons for their success or failure. Additionally, it evaluates the relationship between changes in access to UGSs and population changes over a ten-year period (2007–2017), aiming to identify areas experiencing the greatest inequalities in access.

The findings show that many of the policies and goals outlined in Karaj's Comprehensive and Detailed Plans were not fully realized. While the conversion of old gardens into new parks contributed to an increase in UGS access, an analysis of the relationship between access and population changes revealed mismatches in certain areas. Despite a reduction in inequality over time, significant inequalities in access to UGS still exist, with 60% of UGS access concentrated among just 20% of the population. Key reasons for the failure to implement the proposed policies include the lack of sustainable financial resources for the municipality, land speculation and insufficient consideration of population distribution and uneven growth in different areas.

To address these inequalities, we propose two main strategies aimed at improving equitable access to UGS. First, sustainable financial models must be developed to reduce the municipality's reliance on land sales, which is seen as a fundamental solution to the failures of past policies. Second, we emphasize equality-focused planning, prioritizing areas with the greatest inequalities in UGS access, as identified by high-low clusters in the Bivariate Moran's I analysis.

The method employed in this study can serve as a model for evaluating spatial equity in other urban contexts and public services. By identifying areas where access to UGS remains inequitable, policymakers and urban planners can make informed decisions to address these inequities. Equitable access to UGS should be a central goal of urban development, ensuring that all citizens, regardless of location, benefit from the diverse advantages that green spaces provide.

The supplementary material for this article can be found online.