Evaluating the Accessibility of Urban Public Open Spaces Based on an Improved 2SFCA Model: A Case Study Within Chengdu’s Second Ring Road

Abstract

The rational allocation of urban public open spaces (UPOS) is critical for creating a livable urban environment. Traditional Two-Step Floating Catchment Area (2SFCA) models often lack sufficient quantitative analysis regarding the supply of urban public service facilities and population demand. This study, taking the area within Chengdu’s Second Ring Road as an example, proposes a 2SFCA model that integrates both supply and demand improvements to evaluate UPOS accessibility. The accessibility results are further analyzed using hotspot analysis, and blind zone detection. In terms of supply improvements, the model incorporates additional indicators beyond the spatial area of UPOS, including service quality and the diversity of surrounding environmental service functions, to better evaluate the overall attractiveness of UPOS to residents. On the demand side, besides population size, the model incorporates the spatial distribution of residents and differences in social characteristics affecting UPOS demand. Results indicate that the improved 2SFCA model, which considers both the attractiveness of UPOS and residents’ demand, significantly enhances the accuracy of accessibility assessments. There are substantial differences in service quality among UPOS, while the diversity of surrounding environmental service functions remains generally high. UPOS demand follows a “high in the northeast—low in the southwest” spatial pattern. The spatial distribution of UPOS accessibility shows a “high in the west—low in the east” pattern, opposite to the demand distribution, indicating a supply–demand mismatch. UPOS accessibility identifies one hotspot cluster and four cold spot clusters, with large areas showing no significant characteristics. Additionally, 10.58% of the study area remains blind zones, requiring urgent attention. This study offers a more scientific method and framework for research on the spatial layout and supply–demand matching of UPOS.

1. Introduction

With the rapid urbanization of China and the formation of high-density urban development models, land resources available for urban greening and recreational activities are becoming increasingly scarce. Meanwhile, the national emphasis on high-quality urban development has heightened attention on the construction of environmentally friendly and ecologically livable cities. Urban Public Open Spaces (UPOS), comprising parks, green spaces, leisure plazas, and scenic areas, serve as key ecological and recreational spaces, playing vital roles in residents’ economic and leisure activities [1]. Rational spatial planning of these spaces is crucial to ensuring that urban residents can equitably and effectively access the services provided by UPOS [2]. However, as urbanization advances, environmental issues become increasingly prominent, and the residential segregation in urban areas has led to the uneven distribution of public service facilities, leading to spatial injustice [3]. Against this backdrop, investigating the efficiency and balance of the existing UPOS layout is essential for improving residents’ well-being.

Current evaluations of urban public service facilities typically rely on quota-based indicators such as coverage rates and per capita ratios, which fail to accurately reflect the rationality of planning and spatial layouts. The accessibility of UPOS refers to a quantitative measure of residents’ willingness and ability to reach UPOS from a given location, overcoming barriers such as distance, travel time, and cost. It is an effective method for assessing the spatial layout of UPOS [4]. In recent years, the concept of accessibility has been increasingly applied to the evaluation of urban public service facilities, employing methods such as the minimum proximity method [5], statistical indicators method [6], gravity model [7], and Two-Step Floating Catchment Area (2SFCA) method [8]. Among these, the minimum proximity method calculates accessibility independently from either a supply or demand perspective using Euclidean distance, which fails to accurately represent real-world travel conditions. Although the gravity model comprehensively considers multiple factors from both supply and demand sides, it involves subjective parameter definitions. The 2SFCA method improves on the gravity model by introducing the concept of “spatial thresholds” and applying it to spatial accessibility studies, accounting for supply, demand, and their interactions. Additionally, the 2SFCA method can be enhanced in various ways, such as by adjusting the distance decay function [9], optimizing the search radius [10], or incorporating different travel modes [11]. The Ga2SFCA model, proposed by DAI [12], incorporates a decay function and has been widely applied in evaluating the accessibility of urban public service facilities due to its better alignment with residents’ travel behaviors [13,14].

Although the 2SFCA model has been widely applied in spatial accessibility research, limitations exist in quantifying the supply of public service facility and population demand. Additionally, variations in travel costs and evaluation units can introduce calculation errors. Regarding supply, the traditional 2SFCA model typically uses spatial area as the sole evaluation criterion. The supply capacity of UPOS should comprehensively consider factors such as urban location, ecological quality, scale, supporting infrastructure completeness, and management efficiency [15]. In other words, existing research mostly focuses on the inherent attributes of space, such as area and geographic location [16], while less attention is given to the impact of internal service facilities, landscape design, and the diversity of surrounding environmental services on the service capacity. Generally speaking, UPOS with a higher-quality environment, more comprehensive facility configurations, better maintenance and management levels, and diverse surrounding environmental service functions will have greater service capacity [17]. On the demand side, traditional models mainly use population size to measure demand [18], while overlooking the spatial distribution of residents’ actual activities and variations in recreational needs, which can lead to spatial mismatches between supply and demand [19]. Additionally, variations in residents’ socioeconomic status can influence their demand for UPOS. Lower-income residents, constrained by financial limitations, are generally more inclined to use free public spaces, leading to higher demand for UPOS. In terms of travel costs between supply and demand points, traditional methods generally use Euclidean distance or city road network models to represent geographic space. These traditional, experience-based methods fail to account for real-time road conditions. In contrast, the integration of map service interfaces to obtain real-time data offers higher precision and has emerged as a new trend in related studies. Traditional studies typically divide spatial units into two categories: the first is based on administrative divisions within the study area, such as streets, communities, or residential blocks. Due to the irregular shapes of administrative areas, centroid points are often located within the search range, while large portions of the area remain outside, resulting in significant calculation errors. The second approach divides the study area into grids, using the geometric center of each grid as the demand centroid. However, this method often assumes an even population distribution within each grid [20], leading to discrepancies between the results and real-world conditions. To improve the accuracy of population statistics, a hexagonal grid system for evaluation units has been proposed by some scholars [21], and its effectiveness and scientific validity have been demonstrated [22].

In summary, the traditional 2SFCA model incorporates relatively few factors in the quantification of supply and demand. Using the area within Chengdu’s Second Ring Road as a case study, this paper proposes an improved 2SFCA accessibility evaluation model and research framework. This model views the relationship between individuals’ subjective choices and the prioritization of UPOS as the foundation for accessibility evaluation. The aim is to provide a generalizable approach for accessibility studies of urban public facilities while offering scientific guidance for the optimal layout of UPOS in Chengdu.

2. Study Area and Data

2.1. Study Area

Chengdu, the capital of Sichuan Province and one of the core cities in the Chengdu-Chongqing Twin City Economic Circle, is primarily characterized by flat terrain and commonly known as the “Land of Abundance”. This study focuses on the area within Chengdu’s Second Ring Road (Figure 1), which includes the five main urban districts: Jinniu, Qingyang, Wuhou, Jinjiang, and Chenghua. The study area encompasses 36 streets, covering a total area of approximately 60.38 km². The area within the Second Ring Road constitutes the most densely built-up and developed region in Chengdu. Although there are numerous UPOS in this region, most are relatively small and outdated, highlighting a growing mismatch with the daily needs of the increasing permanent population. Therefore, this study examines the current distribution of UPOS in this area and evaluates the alignment between supply and demand, providing scientific guidance for future UPOS planning, layout, and site selection.

2.2. Data and Source

2.2.1. Basic Data Collection

(1)

Remote sensing images of the study area for 2024 (data source: https://earth.google.com (accessed on 15 June 2024)).

(2)

Chengdu’s Comprehensive Land Use Plan (2021–2035) (data source: Chengdu Municipal Bureau of Planning and Natural Resources).

(3)

Point of Interest (POI) data (data source: https://lbs.amap.com/ (accessed on 18 June 2024)).

(4)

Residential community POI data, including community names, housing prices, total number of households, and latitude/longitude coordinates (data source: https://cm.lianjia.com (accessed on 18 June 2024)).

(5)

Construction quality data of UPOS (data source: review data from social media platforms such as Amap (https://ditu.amap.com/ (accessed on 25 June 2024)), Ctrip (https://www.ctrip.com/ (accessed on 25 June 2024)), Dianping (https://www.dianping.com/ (accessed on 25 June 2024)), and field survey data).

2.2.2. UPOS Data Acquisition and Processing

UPOS data were obtained through the Baidu Maps API, selecting vector data with secondary categories of leisure plazas, parks, and scenic areas. These data were rigorously calibrated and verified using multiple sources, including Chengdu’s Comprehensive Land Use Plan (2021–2035) for green and open spaces, remote sensing satellite images, and Baidu online maps. Further corrections were made through street view analysis and field surveys, excluding UPOS that are inaccessible, require fees, or are affiliated with enterprises or institutions. Ultimately, 54 UPOS were identified (Figure 2), comprising 23 leisure plazas, 25 parks, and 6 scenic areas. An example of their basic information is shown in

Table 1. Example of basic information for UPOS within Chengdu’s Second Ring Road (Area: hm²).

Grade	District	Street	Name	Address	Type	Area
Class 1 parks or scenic areas (11)	Qingyang	Caotang	Huanhua creek park	No. 9 qinghua road	Park	30.71
	Qingyang	Wangjiaguai	People’s park	No. 9 citang street	Park	13.51
	Qingyang	Shaocheng	Kuanzhai alley	No. 127 changshun upper street	Scenic area	7.37
	......
	Chenghua	Mengzuiwan	Chenghua park	No. 22 mengzuiwan street	Park	7.15
	Jinjiang	Shuyuan	Running water park	No. 5 huaxing road	Park	2.61
Class 1 leisure squares (10)	Jinjiang	Jingguanyi	Taikoo Li east square	Taikoo Li east square, zhongshamao street	Leisure square	5.81
	Qingyang	Wangjiaguai	Tianfu square	No. 86 renmin southroad, section 1	Leisure square	5.05
	Qingyang	Xiyuhe	Kaila square	No. 306 shuncheng street	Leisure square	1.21
	......
	Jinniu	Fuqin	Weimin square	No. 28 weimin road	Leisure square	0.61
	Qingyang	Caoshi	Babao square	No. 56 wanhe garden, babao street	Leisure square	0.58
Class 2 parks or scenic areas (20)	Qingyang	Funan	Shiren park	No. 2 shiren north road	Park	1.90
	Qingyang	Caoshi	Suihan garden	Approximately 90 m east of wuding bridge and wudu road intersection	Scenic area	1.55
	Jinjiang	Chunxi road	Binjiang park	Binjiang park, xiaotianzhu binjiang west road	Park	1.34
	......
	Qingyang	Caoshi	Jiafu garden	No. 2 xiti north road	Scenic area	0.20
	Qingyang	Caotang	Zuimei garden	South of baihuatan road and qingyang main street intersection	Park	0.13
Class 2 leisure squares (13)	Jinjiang	Jingguanyi	Dongsheng square	No. 253 dongsheng street, unit 102	Leisure square	0.23
	Wuhou	Wangjiang road	Funan River music square	Phase 3, No. 1 jiangtian road	Leisure square	0.22
	Jinniu	Renmin north road	Jinxi square	No. 2-2-103 yingsha north street, xijin international plaza	Leisure square	0.20
	......
	Jinniu	Simaqiao	Chinese medicine culture square	West of the intersection of shubei street and shubei lane	Leisure square	0.16
	Wuhou	Fangcao	Fangcao cuiyuan square	No. 7 Yuhong Lane	Leisure square	0.13

. Based on differences in size and popularity, the service radius of these UPOS was classified into two categories: class 1 includes prominent parks or scenic areas larger than 2.6 hm² and leisure plazas larger than 1.23 hm², while all others are categorized as class 2.

2.2.3. Population Data Acquisition and Processing

The granularity of population study units directly affects the accuracy of accessibility analysis results. This study uses fine-grained residential community aggregation points as research units, obtaining 2024 POI data for residential communities within Chengdu’s Second Ring Road. Previous research has demonstrated that regular hexagonal grids, due to their equal distance from the centroid in all directions, can reduce sample bias caused by grid shape boundary effects [23] and are more suitable for spatial analysis (Figure 3). Therefore, this study employs regular hexagons with a side length of 100 m, creating a polygonal hexagonal grid in ArcGIS 10.8 to serve as the residential grid units (Figure 4a). Residential community points within each hexagon are aggregated at their coordinate centroids, resulting in a total of 1757 residential points (Figure 4b). The total population for each residential point is calculated based on the aggregated number of households, using the following formula:

$$P_k={\displaystyle \sum _{i\in A_k}{B}_i\times \overline{M}}$$

(1)

where $P_k$ represents the total population at a specific point $k$, $A_k$ denotes the hexagon in $k$, and $B_i$ indicates the total number of households in the residential community within $A_k$. The average number of people per household, $\overline{M}$, is obtained from the Chengdu Statistical Yearbook 2023, which reports an average household size of 2.764 persons in the five main districts within Chengdu’s Second Ring Road. The results were validated using resident population data from the same yearbook for various streets, confirming that the aggregated population data accurately reflect the actual population situation.

2.2.4. Walking Time Data and Time Thresholds

According to a survey on transportation modes of residents in Chengdu’s main urban areas [24], walking is the predominant mode of transport. Therefore, this study evaluates UPOS accessibility under walking conditions. In the context of developing a “15 min living circle” in Sichuan Province, a walking time threshold of 15 min is established. For higher-level UPOS, the walking time threshold is set at 30 min according to existing literature. Actual walking times from residential areas to UPOS are calculated using the route planning interface of the Amap API. To mitigate the impact of road traffic congestion on route collection, data are collected between 15:00 and 16:00 on weekdays.

3. Methods

The study includes three main aspects (Figure 5): (1) developing an improved model based on the traditional 2SFCA model; (2) using the area within Chengdu’s Second Ring Road as a case study to assess UPOS walking accessibility with both the traditional and improved 2SFCA models, followed by a quantitative comparative analysis; (3) conducting hotspot and blind zone analyses of the UPOS accessibility results, and ultimately providing recommendations for optimizing UPOS layout based on the research findings.

3.1. UPOS Service Range

To establish the UPOS search thresholds, this study references the service population and service radius guidelines outlined in the “Chengdu 15-Minute Community Happiness Circle” construction guide. The search radius for class 1 UPOS is defined as 30 min of walking time, while for class 2 UPOS, it is set to 15 min of walking time. The actual service range is calculated based on the defined UPOS service radius. The route planning API provides travel routes and times between two points by inputting the travel mode and the latitude and longitude coordinates of the start and end locations. The traditional 2SFCA model designates the geometric centroid of a location as the supply point. However, in practice, individuals are considered to have accessed the public facility once they reach its entrance or exit. Therefore, this study designates the entrance or exit of UPOS as the supply point. For different levels of UPOS, buffers are established with the park entrance or exit as the center, using 15 min and 30 min walking distances as radii. Since the straight-line distance between two points is the shortest path, any endpoint reachable within the set threshold time will fall within the buffer zone, with points created at 100 m intervals as endpoints. Walking times from the start to the endpoint are obtained using the Amap API, and isochrones for 15 min and 30 min are extracted through spatial interpolation to represent the actual service range of the corresponding UPOS.

3.2. Model Improvement

3.2.1. Traditional 2SFCA

The 2SFCA model was originally proposed by John Radke and later modified by Luo and Wang, who subsequently named it the 2SFCA method [25]. The principle of the 2SFCA model for calculating accessibility involves conducting two distinct searches centered around UPOS and residential points, respectively. The calculations for the traditional 2SFCA model are represented by Equations (1) and (2):

$$R_j={\displaystyle \frac{S_j}{{\displaystyle {\sum }_{k\in \left\{d_{kj}\le d_0\right\}}{D}_k}}}$$

(2)

$$A_i={\displaystyle {\sum }_{j\in \left\{d_{ij}\le d_0\right\}}{R}_j}$$

(3)

where $i$ and $k$ represent demand points, $R_j$ denotes the supply–demand ratio, and $S_j$ is the total supply. The variable $d_{kj}$ indicates the service cost between supply point $j$ and demand point $k$, while $D_k$ is the total demand from all demand points where $d_{kj}\le d_0$. Additionally, $d_{ij}$ represents the service cost between demand point $i$ and supply point $j$. The accessibility of point $i$, denoted as $A_i$, is calculated with a higher value of $A_i$ indicating better accessibility.

3.2.2. Construction of the Improved 2SFCA Model

Building on the traditional 2SFCA model, this study makes improvements from both the supply and demand perspectives. In terms of supply, in addition to the area of UPOS, the service quality index and diversity of surrounding environmental service functions index are introduced as additional parameters for measure. Regarding demand, besides population size, the spatial distribution and social characteristics of residents are considered to account for differences in UPOS demand.

(1)

Supply improvement: Differences in the quality of UPOS construction directly affect its attractiveness to residents. To efficiently and accurately obtain data on UPOS construction, this study utilized a combination of social media data and field survey data. Social media data, with their vast volume, extensive coverage, and ease of access, have become an important data source for urban spatial analysis [26]. Data from travel apps such as Amap, Ctrip, and Dianping were collected, including user reviews and images from the past two years, which were manually searched and analyzed. For UPOS with numerous reviews, online searches were conducted, while for those with limited online data, field surveys were carried out to ensure data authenticity and timeliness.

The survey focuses on evaluating the landscape environment, supporting facilities, and infrastructure of UPOS, collecting data on construction quality. Facilities were counted in two ways: presence and type. Facilities counted by presence were marked as 1 if present and 0 if absent, while type-based scoring evaluated the diversity and service functions of facilities. For example, if a UPOS includes both a football field and a basketball court, it would receive a score of 2 for sports facilities. Furthermore, the Analytic Hierarchy Process (AHP) was applied to calculate the weights of various indicators, and the service quality index for each UPOS was calculated according to Equation (4). The details of the scoring criteria and indicator weights are provided in

Table 2. UPOS service quality evaluation.

Primary Indicator	Secondary Indicator	Evaluation Criteria	Scoring Method	Weight
Landscape environment	Water feature	Presence of water features or proximity to rivers	by presence	0.358
	Plant landscape	Rich plant configurations	by presence
	Sculpture	Sculptures with memorial or cultural significance	by presence
	Cultural elements	Cultural elements related to the design theme	by presence
Supporting facilities	Sports facilities	Courts for sports like basketball, table tennis, etc.	by categories	0.443
	Leisure facilities	Lawns available for camping	by categories
	Fitness facilities	Fitness trails and equipment	by categories
	Educational facilities	Memorials, museums, cultural walls	by categories
	Recreational facilities	Dedicated children’s play areas	by presence
	Event space	Spaces for special events and performances	by presence
Infrastructure	Lighting system	Well-developed lighting system	by presence	0.199
	Stores/convenience stores	Presence of shops and convenience stores	by presence
	Parking lot	Availability of parking	by presence
	Public restrooms	Standard public restrooms	by presence
	Public seating	Sufficient public seating	by presence
	Pavilion/arbor	Spaces for rest and communication	by presence
	Visitor center/police office	Visitor center and police station for emergencies	by presence

.

$$M_j=C_a{P}_a+C_b{P}_b+C_c{P}_c$$

(4)

where $M_j$ represents the total service quality score for each UPOS. $C_a$, $C_b$, and $C_{\mathrm{c}}$ denote the weights for landscape environment, supporting facilities, and infrastructure, respectively. $P_a$, $P_b$, and $P_c$ indicate the scores for the landscape environment, supporting facilities, and infrastructure of UPOS, respectively.

The attractiveness of UPOS is influenced not only by its own services but also by the service functions of the surrounding environment. Research indicates that the richness of surrounding environmental functions is positively correlated with spatial visit rates [27]. POIs, including geographical coordinates and addresses, provide timely and detailed data [28]. To reflect the service functions of the environment surrounding UPOS within Chengdu’s Second Ring Road, this study collected relevant POI data and categorized it into 13 types: transportation facilities, sports and recreational services, shopping services, educational and cultural services, daily living services, scenic spots, medical care services, government and social organizations, dining services, financial and insurance services, corporate services, public facilities services, and accommodation services. The Shannon–Wiener Diversity Index (SWDI), originally used to measure species richness, has recently been adapted to quantify the diversity of research subjects [29]. This study applies the SWDI formula to calculate the service function diversity within the service range of UPOS, using the POI data.

$$H_j=-{\displaystyle {\sum }_{i=1}^m{P}_{ji}}\ln (P_{ji}).$$

(5)

where $H_j$ represents the service function diversity within the service area of public open space $j$. $\mathrm{m}$ is the number of POI categories; $i$ denotes a specific POI category; and $P_{ij}$ is the percentage of POI of category $i$ within the total number of POI in the service area of public open space $j$. A larger $H_j$ indicates a higher diversity of service functions around the UPOS.

By integrating the traditional 2SFCA model with supply improvements, the overall attractiveness $S_j$ of public open space $j$ will be determined by three factors: the area of the UPOS, service quality, and the diversity of service functions in the surrounding environment.

$$S_j=\left({\gamma }_A{\displaystyle \frac{{S^{\prime }}_j}{{\displaystyle \sum {}_j{S}^{\prime }_j}}}\right)+\left({\gamma }_B{\displaystyle \frac{{M^{\prime }}_j}{{\displaystyle \sum {}_{j}M_j}}}\right)+\left({\gamma }_C{\displaystyle \frac{{H^{\prime }}_j}{{\displaystyle \sum {}_{j}H_j}}}\right)$$

(6)

where ${\gamma }_A$, ${\gamma }_B$, and ${\gamma }_C$, respectively, reflect the importance of the public open space area (${S^{\prime }}_j$), service quality ($M_j$), and surrounding environmental service function diversity ($H_j$) to the overall attractiveness $S_j$ of the public open space, with ${\gamma }_A={\gamma }_B={\gamma }_C=0.3$.

(2)

Demand improvement: The demand for UPOS is influenced by residents’ spatial distribution and social characteristics [30]. In terms of population distribution density, numerous studies have shown that the distribution of public facilities closely aligns with population distribution. The spatial distribution pattern of urban populations significantly influences the layout of public facilities. Therefore, population density can be inferred from the distribution characteristics of public facilities. This study selects six types of POI data as factors influencing population distribution: public transportation stations, residential areas [31], educational facilities (e.g., primary and secondary schools), office facilities [32] (e.g., companies and enterprises), cultural and recreational facilities (e.g., cinemas, shopping malls, libraries, and sports arenas), and medical facilities (e.g., hospitals and health institutions). Regarding social characteristics, factors influencing residents’ socioeconomic status include physiological aspects, such as age and gender, and economic aspects, such as income and housing. Given data availability, this study uses socioeconomic level as a proxy of residents’ social characteristics. Research indicates a positive correlation between residents’ income and housing prices [33]; thus, housing prices in residential areas serve as a relevant factor for socioeconomic status.

The seven categories of POI data influencing UPOS demand are linked to evaluation units, with each category undergoing statistical analysis, reclassification, and rasterization. Figure 6 shows the spatial distribution of these factors, and

Table 3. Weights of population demand influencing factors.

Indicator Level	Influencing Factor	Score Values	Weight
Population distribution	Residential area	1, 2, 3, 4, 5	0.3185
	Public transportation and subway stations	1, 2, 3, 4, 5	0.2154
	Educational facilities	1, 2, 3, 4, 5	0.1132
	Office facilities	1, 2, 3, 4, 5	0.076
	Cultural and recreational facilities	1, 2, 3, 4, 5	0.0525
	Medical facilities	1, 2, 3, 4, 5	0.0421
Social status of population	Average housing prices	1, 2, 3, 4, 5	0.1823

presents the factor weights determined using the AHP method. Applying Equation (7), differences in spatial distribution and social characteristics of the population across evaluation units are calculated. This comprehensive evaluation of UPOS demand incorporates population size, spatial distribution, and social characteristics within each unit. Ideally, higher-rated areas would have denser populations and provide higher levels of UPOS service. This integration of population distribution and social characteristics into the 2SFCA model proceeds as Equation (8).

$$P_i={\displaystyle {\sum }_{j=1}^m{v}_{ij}\times w_j}$$

(7)

$$G\left(t_{ij},t_0\right)=\left\{\begin{array}{c}{\displaystyle \frac{e^{-(1/2)\times {(t_{ij}/t_0)}^2}-e^{-(1/2)}}{1-e^{-(1/2)}}},\\ \begin{array}{ccc}\begin{array}{cccc}& & & \end{array}& & 0,t_{ij}>t_0\end{array}\end{array}\right.t_{ij}\le t_0$$

(8)

In Equation (7), $P_i$ represents the spatial distribution and social characteristics of the population within the evaluation unit $i$.$j$ represents a specific category of POI. $V_{ij}$ denotes the reclassified results of the $j$ category of POI within evaluation unit $i$, and $W_j$ is the weight of the $j$ category of POI.$m$ represents the number of POI categories. In Equation (8), $t_{ij}$ is the time cost between evaluation unit $i$ and $j$; $t_0$ is the time threshold. The Gaussian function $(G)$ represents the distance decay effect of time.

3.2.3. Accessibility of UPOS Based on the Improved 2SFCA Model

(1)

The improved supply-to-demand ratio is calculated by integrating UPOS service quality, the diversity of surrounding environmental service functions, and the spatial distribution and social characteristics of the population:

$$R_j={\displaystyle \frac{S_j}{{\displaystyle {\sum }_{i\in \left\{t_{ij}\le t_0\right\}}{P}_i{D}_{i}G(t_{ij},t_0)}}}$$

(9)

where $R_j$ represents the supply-to-demand ratio for public open space $j$; $S_j$ denotes the overall attractiveness of UPOS; $P_i$ refers to the spatial distribution and social characteristics of the population; $D_i$ is the population count for each hexagonal grid $i$; $t_{ij}$ is the road distance between location $i$ and location $j$ obtained from Amap API routing service; and $t_0$ is the maximum acceptable search radius for residents traveling to the UPOS.

(2)

The supply-to-demand ratio is weighted using the spatial distribution and social characteristics of the population. After applying these weights, the weighted sum is calculated to determine the accessibility for each residential point:

$$A_i={\displaystyle {\sum }_{j\in \left\{t_{ij}\le d_0\right\}}{P}_{ij}}{R}_{j}G(t_{ij},t_0)$$

(10)

The improved 2SFCA model in this study integrates travel time impedance, UPOS service quality, surrounding environmental service diversity, and the spatial distribution and social characteristics of the population.

3.3. Local Spatial Autocorrelation Analysis

Local spatial autocorrelation primarily assesses the spatial relationships between local areas in the study region and their neighboring areas. The hotspot analysis (Getis-Ord Gi*) is widely employed to identify significant hot and cold spots in the data [34]. The results of the Gi* index include the Z-score (multiples of standard deviations), the p-value (probability), and the confidence interval (Gi_Bin field). A higher absolute Z-score indicates a more significant clustering effect, reflecting a stronger aggregation of hot or cold spots. A Z-score close to 0 indicates the absence of significant spatial clustering. Z-scores and p-values test the statistical significance, determining whether the null hypothesis should be rejected for each element. A high positive Z-score coupled with a low p-value indicates a hotspot, while a low negative Z-score with a low p-value indicates a cold spot. The confidence interval (Gi_Bin field) reflects the level of statistical significance: +3 to −3 represents a 99% confidence level, +2 to −2 represents a 95% confidence level, +1 to −1 indicates a 90% confidence level, and a confidence interval of 0 indicates no statistically significant clustering in the area. The formula for calculation is as follows:

$$G_i^{*}={\displaystyle \frac{{\displaystyle \sum _{j=1}^n{w}_{i,j}{x}_j-\overline{x}{\displaystyle \sum _{j=1}^n{w}_{i,j}}}}{s\times \sqrt{\frac{n{\displaystyle \sum _{j=1}^n{w}_{i,j}^2-\left({\displaystyle \sum _{j=1}^n{w}_{i,j}}\right)}}{n-1}}}}$$

(11)

$$\overline{x}={\displaystyle \frac{{\displaystyle \sum _{j=1}^n{x}_j}}{n}}$$

(12)

$$s=\sqrt{{\displaystyle \frac{{\displaystyle \sum _{j=1}^n{x}_j^2}}{n}}-{\overline{x}}^2}$$

(13)

where $w_{i,j}$ represents the spatial weight between feature $i$ and $j$; $x_j$ is the attribute value of feature $j$; $n$ is the number of features.

3.4. Blind Zone Analysis

Identifying accessibility blind zones is crucial for optimizing UPOS distribution to ensure service coverage across all urban areas. Blind zones of accessibility can be categorized into two types: explicit and implicit [35]. Explicit blind zones refer to areas entirely outside the coverage of UPOS, where the accessibility index ($A_i$) is zero. Identifying explicit blind zones is essential for guiding improvements in UPOS layout. Implicit blind zones, on the other hand, exist within the service radius of UPOS, where the accessibility index is greater than zero. However, due to high population density exceeding the carrying capacity of the UPOS, many residents are unable to effectively utilize the public facilities within these spaces. Therefore, identifying implicit blind zones necessitates a comprehensive assessment of the accessibility index and population density pattern.

4. Result and Analysis

4.1. Analysis of UPOS Supply and Residential Population Demand

Figure 7 illustrates the differences in UPOS service quality and the diversity of surrounding environmental service functions within Chengdu’s Second Ring Road, while

Table 4. Ranking of UPOS supply within Chengdu’s Second Ring Road (Area: hm²).

Top 7 UPOS by Service Quality
Type	District	Street	Name	Address	${\mathbf{M}}_{\mathbf{j}}$	Area
Park	Chenghua	Xinhong road	Xinhua park	No. 87 shuanglin road	5.93	9.72
	Qingyang	Caotang	Huanhua creek park	No. 9 qinghua road	5.48	30.70
	Chenghua	Mengzuiwan	Chenghua park	No. 22 mengzuiwan street	5.48	7.89
	Qingyang	Caotang	Du Fu thatched cottage	No. 37 qinghua road	5.04	15.55
	Wuhou	Yulin	Wangjiang Lou park	No. 30 wangjiang road	5.04	13.61
	Qingyang	Caotang	Baihuatan park	No. 5 fanglin road	5.04	8.12
	Qingyang	Wangjiaguai	People’s park	No. 9 citang street	5.04	14.02
Leisure Plaza	Qingyang	Caoshi	Wenshu fang	No. 66 wenshu yuan street	3.8	5.87
	Qingyang	Wangjiaguai	Tianfu square	No. 86 renmin southroad, section 1	3.11	5.19
	Wuhou	Jiangxi	Ximianqiao cultural plaza	Intersection of ximianqiao street and ximianqiao cross street	3	3.00
	Jinniu	Fuqin	Weimin square	No. 28 weimin road	2.76	2.76
	Jinjiang	Chunxi road	Zhongshan square	North section of chunxi road	2.56	2.56
	Qingyang	Caoshi	Babao square	No. 56 wanhe garden, babao street	2.56	2.56
	Jinniu	Simaqiao	Chinese medicine culture square	West of the intersection of shubei street and shubei lane	2.56	2.56
Top 7 UPOS by Diversity of Surrounding Environmental Services
Type	District	Street	Name	Address	${\mathbf{H}}_{\mathbf{j}}$	Area
Park	Qingyang	Caotang	Cultural park	No. 73 qintai road	2.30	12.69
Scenic Area	Wuhou	Caotang	Ya cultural garden	About 1 east from the intersection of dashidong road and jinli riverside road	2.26	0.64
Park	Chenghua	Fuqing road	Sandong ancient bridge park	No. 217 sanyou road, annex 1	2.25	4.94
	Qingyang	Wangjiaguai	People’s park	No. 9 citang street	2.23	14.02
	Jinjiang	Chunxi road	Binjiang park	Xiaotianzhu binjiang west road	2.23	1.38
	Qingyang	Caoshi	Wenshu fang	No. 66 wenshu yuan street	2.22	5.87
	Qingyang	Wangjiaguai	Jushuang garden	No. 2 wenweng road	2.22	0.61
Leisure Plaza	Wuhou	Hongpailou	Wuhou life plaza	No. 2 section 1, second ring road	2.21	1.32
	Jinjiang	Jingguanyi	Dongsheng square	No. 253 dongsheng street, unit 102	2.21	0.28
	Jinjiang	Jingguanyi	Taikoo Li east square	Taikoo Li east square, zhongshamao street	2.20	6.28
	Wuhou	Hongpailou	Biyun Plaza	No. 1 Biyun Road	2.19	1.23
	Jinniu	Renmin North Road	Jinxi square	No. 2-2-103 yingsha north street, xijin international plaza	2.17	0.20
	Qingyang	Wangjiaguai	Tianfu square	No. 86 renmin southroad, section 1	2.14	5.19
	Jinjiang	Chunxi Road	Zhongshan Square	Chunxi Road North Section	2.14	0.32

lists the top-ranked UPOS. Notably, People’s Park, Tianfu Square, and Zhongshan Square stand out for having both high service quality and diverse surrounding environmental services. The average service quality score for UPOS is 2.77, with 38.89% of UPOS scoring above this average. Ten UPOS scored highly (≥4.15), most of which are large, well-known class 1 parks, with the exception of Shiren Park. A majority of UPOS, totaling 26, fall into the medium score range (2.15–4.15). Because of less comprehensive facilities, leisure squares generally have lower service quality compared to parks, with a significant shortage of high-quality leisure squares. Although some UPOS, such as Shahe Park, Biyun Square, and Wuhou Life Square, are relatively large, they exhibit lower service quality due to inadequate facilities. The average diversity score for the surrounding environmental service functions is 2.12. Given the high economic level, population density, and commercial development in this area, the overall diversity of surrounding environmental services is relatively high, with approximately 51.85% of UPOS scoring above average. Despite some UPOS, such as Ya Culture Park, Jushuang Park, and Jinxi Square, being smaller in areas and having lower service quality, their surrounding environments are rich in services, leading to high visitation rates from residents.

The population density within Chengdu’s Second Ring Road exhibits a “high in the northeast, low in the southwest” distribution pattern (Figure 8a). The central and northeastern regions show higher population densities, with the central area encompassing Yanshikou, Chunxi Road, Taisheng Road, Hejiangting, and Caoshi subdistricts, and the northeastern area including Lianxin, Niushikou, Shuangziqiao, Shuijingfang, and Simaqiao subdistricts. In contrast, the southwestern region, which includes Caotang, Jiangxi Street, and Wangjiang Road subdistricts, exhibits relatively low population density. The spatial distribution of the population and its social characteristics gradually decreases from the urban center outward, following a northwest–southeast axis (Figure 8b). The study reveals that although some grids lack residential areas, they still exhibit high levels of population spatial distribution and social characteristics, likely due to increased work and recreational activity, which leads to higher visitation rates. Thus, these areas still require a certain level of UPOS to meet the public’s daily leisure and recreational needs. To accurately reflect the comprehensive demand for UPOS, the study assigns an average population count to cells with zero residential population but high spatial distribution and social characteristics (levels 3–5), representing potential demand for UPOS in these areas. The overall UPOS demand assessment results are shown in Figure 8c. The schematic diagram of the evaluation results (Figure 8d) indicates that the demand for UPOS within Chengdu’s Second Ring Road predominantly follows a northwest–southeast axis. Demand is higher on the northern side of the axis and lower on the southern side. A large high-demand concentration area and several sub-high-demand zones are present, while low-demand areas are relatively scattered and smaller in coverage.

4.2. Spatial Analysis of UPOS Walking Accessibility

The study assessed the walking accessibility of UPOS within Chengdu’s Second Ring Road using both traditional and improved 2SFCA models, with results normalized (Figure 9). A comparative analysis indicates that while both models show similar overall spatial distribution characteristics, with a clear “high in the west, low in the east” pattern, notable differences emerge in the detailed results. The traditional 2SFCA model produces relatively coarse results, displaying a clustered distribution centered around UPOS. In contrast, the improved 2SFCA model provides a more nuanced view, showing a gradual decrease in accessibility from west to east. The traditional model tends to overestimate accessibility in certain areas, such as the densely populated People’s North Road street. Despite the smaller area and lower service diversity of UPOS such as Suihan Garden, Xiangxue Garden, and Xiti Garden, the traditional model still indicates high accessibility. In contrast, the improved model, which incorporates residents’ choice probabilities and spatial attractiveness, reflects lower accessibility that more accurately aligns with actual conditions. In the southern junction of Jiangxi Street and Yulin Street, there are small strip-like UPOS such as Binjiang Park, Ginkgo Garden, and Jushuang Garden. The traditional model shows higher accessibility in these low-quality UPOS areas, which does not align with residents’ actual preferences. Additionally, in the southeastern areas such as Wangjiang Road Street and Longzhou Road Street, which feature medium-sized, high-quality UPOS such as Wangjiang Tower Park and Xiangshulin Riverside Park, the traditional model underestimates accessibility. In contrast, the improved model more accurately reflects the higher accessibility experienced by residents. In summary, the improved 2SFCA model incorporates the comprehensive attractiveness of UPOS into the accessibility evaluation and accounts for residents’ needs comprehensively, resulting in a more accurate and realistic assessment of walking accessibility.

4.3. Local Spatial Autocorrelation Analysis

A hotspot and cold spot analysis was conducted based on the accessibility evaluation results from the improved model (Figure 10). The results indicate the presence of one hotspot cluster and four cold spot clusters within the study area, while the remaining areas exhibit no significant spatial features. The hotspot areas are located on the western side of the Second Ring Road, encompassing regions such as Caotang Street, Guanghua Street, and Wangjiaguai Street. These areas have moderate population densities and feature high-capacity UPOS with strong service provision, such as Du Fu Thatched Cottage, Huanhua Creek Park, Cultural Park, Baihuatan Park, and People’s Park, which significantly enhance residents’ willingness to visit. The largest cold spot cluster is located in the southern part, encompassing Yulin Street, Parachute Tower Street, Fangcao Street, and Xiaojiahe Street. These areas have high population densities but are served by only a few small recreational squares resulting in inadequate public open space resources. Xiaojiahe Street also suffers from low road network density and poor road accessibility, which further contributes to its lower accessibility. Two cold spot clusters are located in the northern part, specifically in Fuqin Street and Hehua Pool Street. Fuqin Street has a dense residential distribution but is served by only three small UPOS with limited service quality and functions, which are insufficient to meet residents’ needs. The adjacent Hehua Pool Street has high population density but sparse network coverage, leading to a severe shortage of UPOS resources. Additionally, Lianxin Street in the southern area is another cold spot region with low accessibility. Overall, the accessibility of UPOS within Chengdu’s Second Ring Road shows a clear imbalance, with higher accessibility in the western hotspot areas, while the four cold spot regions face supply shortages due to insufficient UPOS quantity, area, and unreasonable distribution in high-density population areas.

4.4. Accessibility Blind Zone Analysis

In terms of quantity, the walking accessibility blind zones for UPOS within Chengdu’s Second Ring Road account for 10.58% of the total residential area in aggregated zones. Spatially, explicit blind zones, characterized by an accessibility index of 0, are clustered into three small groups: the northern area of Hehua Pond Street, the southern junction of Yulin Street and Parachute Tower Street, and the southwestern area of Lianxin Street (Figure 11). Field surveys reveal that these areas are predominantly older neighborhoods with sparse road networks and a shortage of UPOS resources, resulting in no nearby UPOS reachable within a 15 min walking radius. While these areas have numerous commercial streets that meet residents’ daily consumption and shopping needs, there is still a need to enhance recreational activities and urban green spaces. Implicit blind zones are identified by overlaying areas with a population density exceeding 43,800 people/km² and a high overall demand (levels 4–5) with regions where accessibility is less than 0.13 m²/person. These implicit blind zones are relatively scattered, with higher density in the northeast compared to the southwest. Due to the higher population density and relatively scarce UPOS resources in the northeast, public open space per capita is insufficient, leading to the formation of implicit blind zones.

5. Discussion

5.1. Advantages of This Study

The improved 2SFCA model overcomes the limitations of traditional models in quantifying public service facilities and actual demand. A comparative analysis of the accessibility evaluation results of UPOS within the Second Ring Road of Chengdu before and after the improvement shows that the modified model yields more realistic results. Several optimizations are introduced in this study compared to previous research: (1) UPOS accessibility evaluation is improved by incorporating both supply and demand aspects. On the supply side, in addition to considering spatial area, service quality indicators such as landscape environment, supporting facilities, and infrastructure and the diversity of surrounding environmental service functions are integrated. On the demand side, in addition to population size, the actual spatial distribution of populations and social characteristics is considered, accounting for differences in UPOS demand. (2) By integration of new internet technologies, residential community POI data are obtained via web scraping from the Lianjia housing transaction platform to obtain real population data for various residential areas. Additionally, the Amap API path planning interface is employed to obtain actual walking travel times for residents. (3) The adoption of cellular grids as the research unit effectively mitigates statistical errors caused by the irregular shapes of residential units. This approach enables more detailed comparisons of the spatial patterns, differences, and causes of UPOS accessibility. (4) Hotspot and blind zone analyses are conducted based on the accessibility evaluation results, providing direct guidance for future UPOS planning, layout, and site selection.

5.2. Implications for Urban Planning

Based on the research findings, the southern areas of Chengdu’s Second Ring Road, including Yulin Street, Parachute Tower Street, Fangcao Street, and Xiaojiahe Street, have been identified as regions with the most significant UPOS supply gaps. These areas urgently require an increase in both the quantity and quality of UPOS. In densely built areas where expanding UPOS is not feasible, optimizing existing spaces is recommended. For instance, in the northern region, such as Fuqin Street, existing UPOS (e.g., Jinniu Square and Jiulidi Park) have limited areas and provide low service quality and functionality. Prioritizing the enhancement of the supply capacity of these spaces is advisable. Additionally, in areas like Hehua Pond Street, where population density is high but UPOS for daily leisure is lacking, increasing the quantity and quality of facilities and introducing refined management models are recommended to improve the UPOS capacity and service provision. For larger UPOS with low service quality (e.g., Shahe Park, Biyun Square, and Wuhou Life Plaza) or low service diversity (e.g., Baihuatan Park, Jiulidi Park, and Rongde Sports and Leisure Plaza), prioritizing improvements in internal construction quality or surrounding service diversity should be emphasized to increase visitor attractiveness. Furthermore, attention should be paid to accessibility blind zones to improve the overall layout and accessibility of UPOS in the region. Explicit blind zones can be addressed through exploration of existing spaces and urban micro-renewal measures, while implicit blind zones can be improved by increasing road network density, adding pedestrian bridges, enhancing park entrances, and adding small UPOS along roads.

5.3. Limitations and Future Research

Although this study has made positive progress in UPOS accessibility evaluation through the improved 2SFCA model, it still has some limitations, which can be further refined and expanded in future research. Firstly, this study primarily focused on walking as the sole mode of transportation for residents accessing UPOS. Future research could incorporate actual public facility usage data to evaluate accessibility across multiple transportation modes, such as bicycles, buses, and cars, to provide more valuable insights for optimizing UPOS layout. Second, this study did not investigate the varying needs of different demographic groups for UPOS. Future research could examine the specific needs of different demographic groups, including the elderly, children, and individuals with disabilities, to provide a more detailed accessibility evaluation. Additionally, as a complex system, urban livability is influenced by a wide range of social, economic, ecological, and cultural factors. Relying solely on the spatial distribution and scale of UPOS is insufficient to fully reflect the service quality and livability levels of different districts. Therefore, future research should focus on the construction of livable urban environments, exploring how to integrate more diverse influencing factors into models and spatial analysis, such as users’ subjective perceptions of space, the spatial characteristics of social interactions, and the alignment of spatial functions with cultural contexts. This approach will not only enhance the scientific rigor and comprehensiveness of accessibility evaluations but also provide practical guidance for the development of livable urban environments.

6. Conclusions

This study, using Chengdu’s Second Ring Road area as a case study, conducted a quantitative analysis of UPOS accessibility by applying an improved 2SFCA model combined with internet mapping services. UPOS supply was assessed based on its spatial area, service quality, and the diversity of surrounding environmental services, while demand was evaluated using population size, spatial distribution, and social characteristics. The study also conducted cold and hotspot analysis, providing new research insights and methods for the rational layout of UPOS and its supply–demand relationships, and offering scientific evidence for UPOS site selection. The study’s conclusions are as follows:

(1)

UPOS supply and demand: The study area contains 54 UPOS, with large UPOS primarily concentrated on the western side of the Second Ring Road, while fewer are located on the southern side. Overall, the diversity of service functions surrounding UPOS is high, but there are significant differences in service quality. Population density exhibits a “higher in the northeast, lower in the southwest” pattern, with population spatial distribution and social characteristics decreasing from the city center outward. The comprehensive demand for UPOS follows a “northwest–southeast” axis pattern, with higher demand on the northern side of the axis than the southern side.

(2)

Accessibility: The improved 2SFCA model outperforms the traditional model in quantifying both supply and demand, providing a more accurate assessment of UPOS accessibility. UPOS accessibility within the Chengdu Second Ring Road follows a “higher in the west, lower in the east” spatial distribution pattern. High accessibility areas are concentrated in the west, where population density is moderate, the transportation network is well-developed, and UPOS offers high service levels and capacity, such as around Caotang Street, Guanghua Street, and Wangjiaguai Street. Lower accessibility areas are found in the south, such as Yulin Street, Parachute Tower Street, Xiaojiahe Street, and Fangcao Street, mainly due to a shortage of UPOS resources and sparse road network.

(3)

Cold and hotspot distribution: The overall accessibility of UPOS within Chengdu’s Second Ring Road includes one hotspot cluster and four cold spot clusters. The hotspot cluster is located on the west side, where UPOS service levels and residents’ willingness to visit are higher. The largest cold spot cluster is in the south, followed by cold spots in the north, particularly in Fuqin Street and Hehua Pool Street. These cold spot areas suffer from a shortage of UPOS, insufficient space, and unreasonable distribution, resulting in low accessibility in densely populated and high-activity zones, creating a mismatch between supply and demand.

(4)

Blind zone analysis: UPOS walking accessibility blind zones account for 10.58% of the total residential area within the aggregated zone. Explicit blind zones include three small clusters located in the north at Hehua Pool Street, in the south at the intersection of Yulin Street and Parachute Tower Street, and the southwest at Lianxin Street. Implicit blind zones are more dispersed, with a higher concentration in the northeast compared to the southwest.