**1. Introduction**

As an important component of ecological products, urban parks serve not only ecological functions but also social functions, which can help cities enhance their environmental quality [1]. Numerous studies have proven that parks can improve physical health, reduce psychological stress [2–4], boost communication among residents [5], and improve residents' well-being [6]. In addition, as a third space, parks can meet the daily needs of inhabitants' for leisure activities, and positively promote the harmonious development of the urban social environment.

Park accessibility, a critical criterion for determining whether the layout of a park is balanced, is significant to the close integration of ecological civilization construction and urban development. Accessibility was originally presented as a notion in transportation geography, defined as the extent to which two nodes in a transportation network can communicate [7], and was later introduced into human geography [8]. Park accessibility refers to the proximity of a residential area to a park, in other words, residents' capacity to overcome travel expenses (time and distance) in order to visit the park [9].

**Citation:** Li, Y.; Xie, Y.; Sun, S.; Hu, L. Evaluation of Park Accessibility Based on Improved Gaussian Two-Step Floating Catchment Area Method: A Case Study of Xi'an City. *Buildings* **2022**, *12*, 871. https:// doi.org/10.3390/buildings12070871

Academic Editors: Yongjian Ke, Jingxiao Zhang and Simon P. Philbin

Received: 16 May 2022 Accepted: 16 June 2022 Published: 21 June 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

A number of studies have been conducted on measurement methods of park accessibility. Early, measurement techniques included the ratio methods [10] and buffer analysis methods [8]. The computation approach is simple and intuitive, as well as easy to implement in urban planning. The widespread application of GIS encourages the growth of the cost weighted distance model [11], the minimal nearest neighbor distance method [12], and the network analysis method [13,14]. By establishing a particular resistance value, this approach may represent the cost of reaching the park from various destinations depending on the actual road network and can accurately portray the park's accessibility, assuming the essential data are complete and the computational capability permits. Due to the fact that the potential model and the two-step floating catchment area (2SFCA) take into account the supply capacity of the park and the demand of residents, it has become a widely used calculation method. However, there are still some issues in the 2SFCA: while using the binary division approach to determine the search range according to the threshold, the search beyond the domain is fully inaccessible; all supply points in the search domain have the same attraction; ignoring the distance attenuation influence on demand points [15]. A number of improved models have been proposed in response to these flaws: kernel density two-step moving search method (K2SFCA) [16], variable width search method (VFCA) [17], three-step floating catchment area method (3SFVA) [18], and G2SFCA [19]. Among them, the G2SFCA is a more scientific accessibility measurement method by introducing the Gauss attenuation function to fit the changing relationship between park attractiveness and distance, which conforms to the travel characteristics of residents and considers the supply scale and population demand of the park. However, it did not take into account non-spatial factors. Therefore, to overcome shortcomings in classic accessibility models, several scholars incorporated new criteria gauging a park's attractiveness. Dony [20] assessed park accessibility by looking at the park size and on-site amenities. Xing [21] incorporated park size and function into the 2SFCA model in order to provide a more accurate assessment of park accessibility. According to several surveys, even if it is not the closest park, residents choose high-quality parks under the influence of non-spatial factors [22–26]. However, previous research did not adequately consider the park's quality, research that incorporates park level and park attractions into accessibility models is rare.

Most previous studies depend on census data at a sub-district level [27–29], or divide the research region into grids and distribute the population to each grid evenly. In recent years, the use of big data to modify traditional processed data has emerged as a new trend in geographic research [30], allowing for a finer scale of research. Guo [31,32] uses mobile phone signaling data to estimate area population density, but the cost of acquiring data is too high. The data on the number of households by the Anjuke platform can reflect the static population distribution and the precise demand for parks. In addition, the majority of traffic trip data are derived from network analysis results, but it is difficult to collect complete basic data. At the moment, major map providers can improve route time predictions for multiple means of transport, which has been establish by relevant research as accurate and reliable [33,34].

Therefore, Xi'an was chosen as a research area, and the iG2SFCA was proposed in this study using the Baidu map route planning interface based on the POI and population data. This paper aims to: (1) Compare two methods before and after improvement to test the practicability of the iG2SFCA (2) explore the accessibility of the park in Xi'an in 5-min, 15-min, and 30-min scenarios, under three trip modes (walking, cycling, and driving mode); (3) study the spatial equality of park distribution in Xi'an. This paper is structured as follows: The following section introduces the study area and data preparation. The third part introduces the G2SFCA and explains the iG2SFCA. The fourth section illustrates the assessment results. Specifically, the comparison between two methods and the accessibility features in various modes. The final section summarizes and discusses the findings of this research.

#### **2. Materials and Methods**

#### *2.1. Study Area*

Xi'an, the only mega city in northwest China, is the capital city of Shaanxi province. It possesses distinct historical and cultural genes and is home to numerous heritage parks. The city was named "National Forest City" in 2016. By 2020, the permanent population had reached almost 12.96 million, with 7.61 million urban residents. There are 117 parks in all, covering a total area of 3490.53 hm2. The built-up area has a green coverage rate of 39.32%. This study focuses on the area within the Xi'an City Ring Expressway, which encompasses six districts in the main city that serves as center area of the permanent population distribution.

#### *2.2. Data and Preprocessing*

In accordance with the definition in "Park Design Specification", the park data and the area of interest (AOI) in the Amap were collected and trimmed based on the 2 m image of Xi'an in 2019. There are 79 parks in all within the research area. Due to the length and narrowness of the Tang City Wall Heritage Park and the Ring Park, they were separated into sections in line with the main road, and serial numbers were applied to distinguish them so as to facilitate subsequent research. Ultimately, a total of 100 parks were recognized. According to the City Park Classification Standard DBJ61/T110-2015 and the green space system planning reports of Xi'an by urban planning department parks are divided into comprehensive park, theme park and community park, considering the grade, scale and facilities of parks. The spatial distribution of various parks is shown in Figure 1.

**Figure 1.** Distribution of parks within Xi'an Ring Expressway.

This project utilizes the Anjuke platform and python to collect residential district data within Xi'an City Ring Expressway. After data collection, 501 residential districts with no household data were deleted, with 4701 residential neighborhoods remaining as valid data. According to the 2020 statistical data of Xi'an (http://tjj.xa.gov.cn/tjnj/20 20/zk/indexch.htm, accessed on 10 August 2021), the average permanent population of each household in Xi'an is 3.0, hence the total population is calculated by multiplying the number of households in the community by 3.0.

Due to the fact that different demographic groups favored different modes of transport [21], we analyzed the accessibility of the park using the three modes of transport—walking, cycling, and driving. Among them, the transit time from the residential area to the park is obtained entirely through the Baidu Map API interface [35], which involves taking the residential area as the starting point and the park as the destination, constructing the OD matrix, and

then using python to request Baidu Maps' lightweight route planning service to obtain the transit time. This study recorded travel time in a week from 5 July 2021 to 11 July 2021. The travel time was gathered daily at 18:00, and the average time of seven days was used to determine the actual time taken from the residential area to the park.

#### *2.3. Methods*

#### 2.3.1. G2SFCA Method

Dai [19] presented the 2SFCA approach for evaluating the accessibility of green space in Atlanta, Georgia, the United States. The fundamental calculating idea is divided into two steps:

Step 1: Calculate the supply–demand ratio. Determine a distance threshold for each park in the research area, calculate the demand within the threshold range, and multiply it by the Gaussian function, and divide the park supply by the result of multiplication to obtain the supply–demand ratio.

Step 2: Calculate accessibility. For each demand point, search all parks within the threshold range, multiply the park's supply–demand ratio by the Gaussian function, accumulate the results, and obtain the accessibility *Ai* of each demand point.

$$A\_{i} = \sum\_{j \in \{d\_{kj} \le d\_{0}\}} G(d\_{kj}, d\_{0}) R\_{j} = \frac{S\_{j}}{\sum\_{k \in \{d\_{kj} \le d\_{0}\}} G\left(d\_{kj}, d\_{0}\right) P\_{k}} \tag{1}$$

$$G\left(d\_{kj}, d\_0\right) = \begin{cases} \frac{e^{-\left(\frac{1}{2}\right) \times \left(\frac{d\_{kj}}{d\_0}\right)^2} - e^{-\left(\frac{1}{2}\right)}}{1 - e^{-\left(\frac{1}{2}\right)}} \, & \text{if} \quad d\_{kj} \le d\_0\\ 0, & \text{if} \quad d\_{kj} > d\_0 \end{cases} \tag{2}$$

In the formula: *Sj* is the supply of the park *j*, *d*<sup>0</sup> denotes the distance threshold, *dkj* is the distance between the supply and the demand points, and *Pk* denotes the demand within the threshold range, which is frequently stated in terms of population. *G*(*dkj*, *d*0) is the Gaussian attenuation function.

#### 2.3.2. iG2SFCA Method

Although the G2SFCA assesses park accessibility from both supply and demand perspectives, there are still deficiencies. This paper is enhanced in two aspects as follows.

Firstly, consider the contrasts in park quality and park attractiveness factors. In addition to spatial features, park size, and nearby facilities also have a significant effect on park accessibility [10,36,37]. As a result, we assign attraction weights of 0.6, 0.4, and 0.2 to the three levels of classification. With an appropriate walking distance of 800 m [38], we take the normalized quantity of POI within the 800 m buffer outside the park as an indicator of attractiveness. The normalized quantity is calculated as the attractiveness factor. This article focuses on five types of POIs that are closely related to leisure and entertainment [39]: catering services, shopping services, sports and leisure services, scenic places, and scientific, educational, and cultural services; with a total of 77,089 POIs retrieved.

Secondly, the distance threshold is replaced with the time threshold. Due to the advancement of big data technology, it is possible to utilize a Baidu map to acquire travel time under multiple travel modes, which facilitates the analysis of the park's spatial accessibility and reveals the accessibility variations under different traffic modes [10]. Consequently, this study used three modes of transportation—walking, riding, and driving—to examine the accessibility change characteristics at various time thresholds.

The revised calculating formulas are as follows:

$$A\_{\rm ij} = \sum\_{j \in \{t\_{kj} \le t\_0\}} G(t\_{kj}, t\_0) R\_j = \frac{W\_{\rm j} S\_{\rm j}}{\sum\_{k \in \{t\_{kj} \le t\_0\}} G\left(t\_{kj}, t\_0\right) P\_k} \tag{3}$$

$$\mathcal{W}\_{\dot{\jmath}} = \mathcal{N}\_{\dot{\jmath}} \times A\_{\dot{\jmath}} \tag{4}$$

$$G\left(t\_{kj\prime}, t\_0\right) = \begin{cases} \frac{e^{-\left(\frac{1}{2}\right) \times \left(\frac{t\_{kj}}{t\_0}\right)^2} - e^{-\left(\frac{1}{2}\right)}}{1 - e^{-\left(\frac{1}{2}\right)}}, \text{if } \quad t\_{kj} \le t\_0\\ 0, & \text{if } \quad t\_{kj} > t\_0 \end{cases} \tag{5}$$

In the formula, *Aij* represents the accessibility of park *j* under traffic mode *i*, *Rj* represents the park's supply–demand ratio, *Sj* represents the area of park *j*, *Wj* represents the attractiveness of park *j*, expressed as the product of the normalized index *Nj* of the number of POIs within an 800 m buffer and the park's type weight *Aj*, *Pk* represents the population, *t*<sup>0</sup> represents the time threshold, *tk*<sup>j</sup> represents the transit time between the park and the community, and *G*(*tkj*, *t*0) is the Gaussian attenuation function.

#### 2.3.3. Location Quotient

The location quotient is the ratio of the park area enjoyed by a street's population to the per capita park area in the research area, which can indicate the equity of street parks distribution [40]. Typically, the location quotient is compared to 1. When it is greater than 1, it implies that the street's park distribution level is greater than the average value of the study area. The greater the location quotient is, the greater the degree of street park distribution level is. The calculation formula for location quotient is:

$$LQ\_i = (\frac{A\_i}{P\_i}) / (\frac{A}{P}) \tag{6}$$

In the formula, *LQi* denotes the location quotient of street *i*, *Ai* and *Pi* denotes the park area and population of the street *i* respectively, and *A*, *P* respectively represent the total area and population of the park in the study area.
