Introduction

With the continuous acceleration of urbanization processes, cities are experiencing significant growth and expansion, leading to increased demand for well-planned urban areas. When it comes to developing or reactivating urban areas, gaining useful insights into complex processes, like the residents’ movement or the supply of basic needs, is crucial for successful urban planning. A focus of recent research has been on analyzing and planning urban green spaces (UGSs), as they fulfill important ecological, social, and recreational functions for the public (Oehrlein et al., 2019; De la Barrera et al., 2016; Zhang et al., 2020). Since they usually do not generate direct revenue but instead create costs, e.g. through maintenance, they are often overlooked, not sufficiently sized, or not well distributed. As a prerequisite for improving the situation, urban planners and decision-makers must have the right computational methods, implemented as software tools, to monitor and evaluate the increasing demand for and the available supply of public green spaces. Developing such methods and tools is challenging; however, since the assessment of green spaces should not only depend on their sizes but also their overall quality and their spatial distribution within the urban context.

One type of method that considers the spatial distribution of green spaces is based on computing an assignment that maps every resident of a city to a green space. Once computed, the assignment can be assessed with quantitative indicators. For example, a simple and pragmatic approach is assigning every resident to the green space with the smallest Euclidean distance to the resident’s home (Sister et al., 2010). Based on the resulting assignment, the distance between a resident and the corresponding green space averaged over all residents can be used as a quantitative indicator. Hence, the assignment enables an assessment of the green spaces on the scale of a whole city. Moreover, an assignment between residents and green spaces enables fine-grained analyses, such as an assessment of the importance of an individual green space based on the number of residents assigned to it.

Despite the general advantages of assignment-based methods, their validity depends on how realistically the computed assignment reflects the actual usage of the green spaces by the residents. In particular, assigning every resident to the nearest green space leads to unrealistically large numbers of residents being assigned to relatively small green spaces. To overcome this shortcoming, Oehrlein et al. (2019) introduced an optimization method that computes an assignment of residents to green spaces under the constraint that for each green space, the number of assigned residents does not exceed a prescribed capacity. More in detail, the method computes an assignment that respects the capacities of the green spaces and that maximizes a function expressing the overall “happiness” of a city’s population. For this, it is assumed that a resident’s happiness is one (perfect happiness) if that resident is assigned to a green space at a distance of zero. Consequently, only when the UPGS is located within a city block does the highest level of citizen happiness occur. The resident’s happiness decreases linearly with an increase of the distance in the road network to the corresponding green space such that, at a certain distance \(d_{\textrm{max}}\), happiness of zero is reached (no supply of that resident). The happiness of a city’s population is simply the sum of the happiness scores for all residents. The method is general enough to compute an optimal assignment for arbitrary capacities, but in their experiments, Oehrlein et al. simply defined the capacities of the green spaces proportional to their sizes. The capacity of green space is thus directly related to a constant area of green space required for each resident, which is called “per-capita demand”. For example, if the per-capita demand is 25m\(^2\), a green space of 1000m\(^2\) has a capacity of 40 residents. Again, this overly simplistic definition leads to unrealistic assignments, since in reality, the number of residents a green space can supply depends on multiple criteria, such as the type of green space and the facilities it provides. Therefore, in this article, we aim to define the capacities of green spaces in a way that leads to more realistic assignments.

To summarize, this article aims to identify different criteria that help to understand the distribution of residents in the available green spaces. The identified criteria are incorporated into a definition of capacity that is applied to compute an assignment between the residents and the green spaces of an urban area using the optimization approach of Oehrlein et al. (2019). By providing a method for computing more realistic assignments, we want to give decision-makers, urban planners, and researchers a more realistic model for assessing the green space supply of a city.

Developing the enhanced capacity measure of an urban public green space is not trivial. Different studies have evaluated UGSs from a variety of perspectives, highlighting their multifaceted importance in urban environments. These aspects include, but are not limited to, Environmental impact (e.g., Diener and Mudu, 2021; Zhang and Qian, 2024; Edeigba et al., 2024), Physical and Mental Health benefits (e.g., Dadvand et al., 2016; Van den Berg et al., 2016; Geneshka et al., 2021), and Social and recreational utility (e.g., Zhou and Parves Rana, 2012; Mensah et al., 2016; Hunter et al., 2019; Ghavimi et al., 2025). Several studies have attempted to take a more comprehensive approach that encompasses a wide range of different aspects (e.g., Daniels et al., 2018).

Based on the literature review, we define ten qualities of a green space that we use to describe its recreational capacity. These ten qualities are responsiveness, safety and security, variety of activity, social interactions, perception, facilities, symbolic value, water body, aesthetics, and connectivity. We use social data, which is publicly available data generated by social media users, to measure each quality in our study area, the urban region of Bonn. We give an overview of the nature of social data. In particular, we discuss the existing data types by assessing value and possible barriers or pitfalls. Based on this review, we narrow down the data types that we use in this work to two types of information, i.e., points of interest (POIs) in green spaces and the popularity of green spaces. We exclude other types of data, e.g., photos or text. Then, we briefly discuss existing data platforms. In the end, we select OSM and Flickr as appropriate platforms for obtaining relevant data for the enhanced capacity of green space. We also explain the appropriate method for obtaining data from them.

To evaluate whether the resulting assignments are realistic, we compare them with statistics on user ratings from Google Maps. In particular, we consider the number of Google ratings for an individual green space as an interesting variable since it reflects actual visits to that green space. Although this variable provides a rather inaccurate estimate of the number of visits by residents to the corresponding green space, we interpret a positive correlation between the number of Google ratings and the number of residents assigned by the automatic method as a hint that the computed assignment is realistic.

In the following, we review related work (“Background and Related Work” section), introduce our new definition of the capacity of green space (“Enhanced Capacity of UPGSs” section), present the experiments that we conducted (“Experiments” section), and conclude the article (“Conclusion and Future Work” section)

Background and Related Work

Given the extensive advantages UGSs confer to a city and its citizens, diligent research has been invested in evaluating these green spaces’ supply within urban environments. Numerous studies probe into this realm from varying perspectives. While some research in the US has highlighted the environmental implications of UGSs (e.g., Barah et al., 2021), other studies have shifted their focus to examine the impact of these spaces on the lives and well-being of urban residents (e.g., Mitchell and Popham, 2008; Maas et al., 2006; Twohig-Bennett and Jones, 2018). Notably, Mitchell and Popham (2008) study focused specifically on England, while the others addressed the topic without a regional focus.

For evaluating whether a city meets the needs of its residents, most studies focus on accessibility, while some also add additional criteria. For example, studies by Kuta et al. (2014) and Comber et al. (2008) conducted in the UK, utilized GIS-based network analysis to investigate UGS accessibility for different demographic groups. The first study assessed accessibility for socio-economically deprived groups, focusing on factors such as unemployment and housing. The second study concentrated on greenspace access for various ethnic and religious groups, examining spatial distribution and accessibility disparities. Both studies used distances ranging from 300 to 5000 meters to evaluate greenspace access. They highlight the crucial role of spatial analyses in uncovering inequities in greenspace distribution, stressing the need for targeted urban planning to ensure equitable access for diverse communities.

Another approach is adopted by Chang and Liao (2011). This study was conducted in Taiwan, focusing on accessibility and mobility to evaluate public facilities distribution. It adopted a methodology incorporating both street networks and straight-line distances to better assess accessibility, highlighting regional differences in mobility and access patterns in the context of spatial equity. An approach that combines multiple criteria on accessibility, economic, and environmental influences is given by Baycan-Levent et al. (2009). The study assessed the ’green performance’ of 24 European cities by evaluating the heterogeneous supply of UGSs using a multi-criteria evaluation framework. Key dimensions included the quantity, availability, and planning of green spaces, as well as financial and performance indicators. Oehrlein et al. (2019) briefly described in “Introduction” section analyzes the quantity of green space in terms of area and accessibility in an integrated way. The overall score of an optimal assignment serves as a quantitative measure of the quality of a city’s supply of UGSs. Since we extend the method in this paper, we review it in more detail in the following.

Let R be a set of residential areas, with I(r) representing the number of residents in each \(r \in R\). Let G be a set of green spaces, with C(g) indicating the capacity of each \(g\in G\), which is the number of residents the green space can serve. In the model of Oehrlein et al. (2019), the capacity is proportional to the green spaces’ area, i.e., \(C(g) = \text {area}(g) / k\). This is termed area-proportional capacity. The parameter \(k \in \mathbb {R}_{> 0}\) represents the per-capita demand, or the area of green space needed for one resident. This value is usually set by local urban planners and varies by country (e.g., Wüstemann and Kalisch, 2016; Beiranvand et al., 2013; Fuller and Gaston, 2009). For Germany, Schröter (2021) recommends \(k = 22\)m\(^2\).

To assign residents from a residential area to a green space, the model of Oehrlein et al. (2019) introduces triplets \((r, g, i) \in R \times G \times \mathbb {R}_{\ge 0}\) which indicate that i residents from area r are assigned to green space g. To take distances into account, they introduce a parameter \(d_{\text {max}} \in \mathbb {R}_{>0}\) as the maximum distance between a green space g and a residential area r such that a resident from r can be assigned to g. A set A of such triplets is called a valid assignment if it fulfills

$$\begin{aligned} \sum _{(r,.,i) \in A} i&\le I(r) \hspace{3em}&\text {for every}~ r \in R~\text {and} \end{aligned}$$
(1)
$$\begin{aligned} \sum _{(.,g,i) \in A} i&\le C(g) \hspace{3em}&\text {for every}~g \in G. \end{aligned}$$
(2)

In other words, a valid assignment A respects the demand of the residential areas and the capacity of the green spaces. In order to distinguish and rate multiple valid assignments, a rating h(r, g) is used. The higher the value of h(r, g), the more a resident of residential area r prefers to be assigned to g. As a basic model, Oehrlein et al. (2019) suggest to use \(h(r,g) = 1 - \ \frac{d\left( r,g\right) }{d_{\text {max}}}\), where d(r, g) denotes the distance between r and g in the road network. Consequently, \(h(r,g) = 1\) for distance \(d(r, g) = 0\) and \(h(r,g) = 0\) for distance \(d(r, g) = d_\textrm{max}\). Based on this, the optimization objective is to maximize the overall score, which is formally defined as follows.

$$\begin{aligned} \text {Maximize} \quad \sum _{(r,g,i)\in A} h(r,g) \cdot i \hspace{3em} \text {over all valid assignments~} A. \end{aligned}$$
(3)

Note that h(r, g) attains negative values for \(d(r,g) > d_\textrm{max}\). However, a triplet (r, g, i) with \(d(r,g) > d_\textrm{max}\) will never be selected for an optimal assignment since it will be more profitable to keep the residents in r unassigned.

Computing the optimal assignment can be reduced to finding a maximum flow in a complete bipartite graph and solved via linear programming. To this end, for every pair \((r, g) \in \) \(R \times G\) the variable \(x_{r,g} \ge 0\) is introduced, which models the number of residents of r who are assigned to g. Then, finding an optimal assignment can be reformulated as follows.

$$\begin{aligned} \text {Maximize} \quad \sum _{r\in R}\sum _{g\in G}{h\left( r,g\right) \cdot x_{r,g}} \end{aligned}$$
(4)

under the constraints

$$\begin{aligned} \sum _{g\in G}{x_{r,g}\ \le \ I(r)} \hspace{3em}&\text {for every}~r\in R~\text {and}\end{aligned}$$
(5)
$$\begin{aligned} \sum _{r\in R}{x_{r,g}\ \le \ C(g)} \hspace{3em}&\text {for every}~g \in G. \end{aligned}$$
(6)

In the end, we call the \(\sum _{r\in R}{x_{r,g}}\) of a green space g the used capacity of g.

For more details on the linear programming formulation, more general objectives, and experiments, we refer to Oehrlein et al. (2019). We incorporate our work on enhanced green space capacities into their framework. This is a major enhancement since they modelled the capacity proportional to the green spaces’ sizes.

From an algorithmic point of view, the above-stated problem is closely related to the transportation problem, which is a classic problem of operations research. More precisely, with a simple transformation, the maximization objective (4) can be turned into a minimization objective, which is commonly assumed for the transportation problem. The transportation problem and one of its variants, the bounded transportation problem, have been applied by Green et al. (1980) to assign patients to medical facilities to analyze their locational efficiency. While in this study and other similar studies, the capacity of a medical facility is usually well defined, e.g., with the number of hospital beds, defining the capacity of green space is more challenging. Concerning the application of methods from operations research to the analysis of green spaces, Chen et al. (2023) have recently published a method for optimizing the distribution of green spaces over the different blocks of a city to achieve more spatial justice based on accessibility. In contrast, our focus is on assessing the quality of the existing green spaces of a city and integrating these qualities in the allocation task.

Enhanced Capacity of UPGSs

Based on the literature review, we define ten qualities of a green space that we use to describe its recreational capacity. We model the ten qualities of a green space g with ten score functions \(q_i :g \mapsto [0,1]\) with \(i \in \{1,\hdots ,10\}\). The score function design was an iterative process based on the available data and the definition of that quality. Therefore, the final score functions are designed with some trial and error and influenced by the characteristics of the data. We design the enhanced capacity \(C^*\) of green spaces based on the ten score functions. In particular, assume we are given the capacity C(g) of a green space g such that C(g) is proportional to the area of g. Then, we define \(C^*(g) = (4/5(\sum _{i=1}^{10} q_i(g)/10)+0.2) \cdot C(g)\). Since \(0 \le q_i(g) \le 1\) for \(i \in \{1,\hdots ,10\}\). In our approach, the enhanced capacity \(C^*\) of a UPGS is calculated with weighted factors - the 4/5 term stressing the significance of the quality score and the 0.2 terms ensuring a baseline capacity. Therefore, the enhanced capacity \(C^*\) of a UPGS will be less than or equal to its maximum capacity C in the basic approach by Oehrlein et al. (2019) unless the UPGS’s overall quality is at its optimum value - thereby reflecting the nuanced reality of UPGS capacity. This method allows us to capture a more realistic representation of a UPGS’s capacity, factoring in its varying degrees of quality rather than relying solely on its maximum theoretical capacity.

For modelling the ten score functions \(q_1,\dots , q_{10}\), we use social data. Relevant social-media platforms are, for example, Twitter, flickr, and OpenStreetMap (OSM). After reviewing the type of data that was accessible, we narrowed down the data types that we use in this work to two types of information, i.e., points of interest (POIs) in green spaces and the popularity of green spaces. We exclude other types of data, e.g., photos or text. Considering the existing data platforms, we select OSM and Flickr as appropriate platforms for obtaining relevant data for the enhanced capacity of green space.

In the following, we provide a review of social data, social media platforms, and urban green space qualities. From this, we synthesize the definition of an enhanced capacity measure for UGSs.

Measuring UPGSs Qualities

The evaluation of UPGSs is multifaceted. In our research, we emphasize the recreational capacity of these spaces. Recognized studies in this field, such as those conducted by Shuvo et al. (2021); Ahirwal (2020); Haq et al. (2011); Kruize et al. (2019); Jennings and Bamkole (2019), and recently Ghavimi et al. (2025) explored these dynamics in-depth, providing valuable frameworks and insights. Drawing from the existing literature, this study suggests a model to estimate the recreational capacity of UPGSs, to help decision-making for a more realistic assignment of PGSs in urban areas.

The main focus of this article is on those UPGS recreational qualities that can be measured using social data. We limit the data to two types: data about POIs and the frequency of photographs taken in each green space. Therefore, selected UPGS qualities are water body, aesthetics, perceptual value, symbolic value, social interaction, facilities, variety of activities, security, connectivity, and responsiveness. In addition to these ten qualities, accessibility and spaciousness are two other qualities that are considered in the experimental part of the research but not directly measured by data extracted from the selected platforms. As previously discussed, accessibility is already considered and integrated into the assignment tool designed by Oehrlein et al. (2019). Spaciousness refers to the perception or subjective experience of having ample space or roominess within a given UPGS. The people’s perception has been taken into account as one of our ten qualities, and the size, which is the only attribute of green spaces that is considered in the existing model, is integrated with ten other qualities. More precisely, in order to measure the qualities, the number of POIs, categories of the POIs, and the number of taken photos are extracted from social data in this research. In Table 1, the used platforms and extracted data types for each of the UPGS qualities are listed.

Table 1 Platform and data type for each UPGS’s quality
Full size table

To standardize the quality measures, we design all of them to lie in the range [0, 1]. Some of them are more difficult to quantify. To limit their influence on the result, we design them to lie in the range [0.5, 1].

In our approach, we distinctly consider external environmental factors like air quality and climate separately from the intrinsic recreational qualities of the UPGSs. Our tool is designed for city-region scale applications; these external variables are assumed to be reasonably constant across this scale. This assumption allows for a more precise focus on the variation in the inherent UPGS qualities during the assessment.

Within the scope of our study, our primary objective was to construct a tool capable of estimating the capacity of UPGS utilizing VGI and social network data. Although we recognize the importance of qualities such as biodiversity in the comprehensive study of UPGS, our focus was strictly on those attributes that could be adequately measured with the specified data sources. We believe that our approach offers a tangible and practical tool to guide UPGSs analysis while leaving the window open for future studies to incorporate additional variables, as data availability and methodologies evolve.

Also, it should be noted that the allocation of weights in our study resulted from in-depth discussions and multifaceted considerations. The weightings were derived from an iterative process, striving for the most realistic approximations of the capacity, refining our innovative method, and anchoring it in local realities.

We do not claim the completeness of the criteria we have identified or the perfection of their mathematical modelling. Our goal, however, was to formalize the quality and enhanced capacity in such a way that individual model components can easily be replaced by more accurate measures and additional criteria can easily be added.

Responsiveness

With the quality measure responsiveness, we describe how well a green space meets people’s needs. This measure is highly significant, as emphasized by numerous scholars (e.g., Carmona, 2015; Ives et al., 2017; Rahman and Zhang, 2018), due to its direct effect on the capacity of the UPGSs to serve people. One main concern in UPGS management is equity and equality in addressing different groups’ needs, which is also a key challenge for smart development strategies and is one of the pillars of good spatial governance (Du et al., 2022). UPGS should be able to support social and cultural diversity and serve users of different groups (Herman et al., 2018; Rahman & Zhang, 2018). This social diversity indeed adds to the value of the UPGS and its recreational capacity. We distinguish between five different groups of people emphasized in the literature (e.g., Madanipour, 2013a): the elderly, the youths, the children, families, and the deprived people. We model responsiveness as a function \(q_1\) that maps each green space \(g \in G\) to \(0,\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5}\) or 1, such that a larger value corresponds to more groups being responsive to the green space. For example, \(q_1(g)=\frac{2}{5}\) means that the green space g suits two groups. We consider a green space to be responsive for a group if it contains at least two POIs that support the group’s needs. For deciding which POIs are relevant for which group, we used the detailed descriptions of the POIs and associations from the literature between POIs and groups (e.g., Radaelli et al., 2011; Burke, 2005; Abbasi et al., 2016; Lak et al., 2019). In particular, we used this association for all of the following qualities that use POIs. As an example of such responsiveness, relevant POIs are benches and shelters for elderly people.

$$\begin{aligned} q_1(g)= \frac{1}{5} \cdot \text {number of responsive groups for }g \quad \in \Biggl \{0,\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5},1\Biggr \} \end{aligned}$$
(7)

Safety and Security

Safety and security of a UPS is one of the most explicitly mentioned qualities by many scholars (e.g., Stålhammar and Brink, 2021; Maas et al., 2009; Hong et al., 2018). Safety refers to conditions that could cause harm to individuals, such as unsafe pathways or hazardous playground equipment. On the other hand, security pertains to measures that protect individuals from deliberate acts like theft or assault. In this text, while we refer to both safety and security aspects, we will use ‘security’ as an overarching term for convenience.

Many scholars have mentioned security as an expected core quality of any UPGS (e.g., Carmona, 2019; Ives et al., 2017; Hoyle et al., 2017). It is important to consider green space’s (perceived) security when assessing its capacity since people avoid unsafe places. Hence, an unsafe green space cannot serve as many people as a safe green space.

For modelling the security \(q_2(g)\) of a green space g, we first count all POIs in g that support the security. Examples of such POIs are activities or places that normally collect people, such as sports or playgrounds, police, and surveillance cameras. Since this quality measure is rather difficult to quantify, we aim for \(q_2(g) \in [0.5,1]\) for all green spaces g. Let \(p_{\text {security}}(g)\) be the number of security-supporting POIs in green space g. Let \(p'_{\text {security}}\) be the maximum of \(p_{\text {security}}(g)\) over all green spaces g. Then, the normalized number of security-supporting POIs of a green space g is given by \((p_{\text {security}}(g) / p'_{\text {security}})\in [0,1]\). We believe that the presence of these POIs in a UPGS would enhance security, but it does not necessarily imply that the UPGS would be inherently less safe in the case of their absence. Therefore, to ensure a balanced and comprehensive assessment, we have restricted our index to a range between 0.5 and 1 by dividing it by two and adding 0.5. This approach allows us to account for the potential benefits of POIs while maintaining a cautious perspective on the overall safety evaluation.

$$\begin{aligned} q_2(g) = \frac{1}{2} \cdot \text {normalized number of security POIs of } g + 0.5 \hspace{4em} \in [0.5,1] \end{aligned}$$
(8)

Variety of Activities

How various the activities inside a UPGS are is one of the most emphasized qualities by scholars (e.g., Schipperijn et al., 2013; Madanipour, 2013b; Baycan-Levent et al., 2009; Picavet et al., 2016; Ghavimi et al., 2025). It is part of the UPGS’s capacity to serve people. Therefore, the most capable UPGSs are the most flexible for a variety of activities. Notably, a thematic UGS is more capable than one with limited activities, but not more capable than a more diverse UGS, as it supports fewer varied visits. For modelling the variety of activities \(q_3(g)\) of a green space g, all activity-related POIs (e.g., sports, tourism, and picnics) are extracted from the OSM API using multiple queries. The centroids of activity-related polygon features are also added to the extracted points. The number of these points inside each of the UPGSs is counted and normalized to be considered as the rank for this quality.

$$\begin{aligned} q_3(g) = \frac{1}{2}\cdot \text {normalized number of activity-related POIs of }g + 0.5 \hspace{3em} \in [0.5,1] \end{aligned}$$
(9)

Social Interactions

It is essential that a UPGS is capable of serving residents according to their important need for social interaction and can provide opportunities for communication as a friendly conversation, meeting new people, etc. (e.g., Kemperman and Timmermans, 2014; Vierikko et al., 2020; Carmona, 2019; Rasidi et al., 2012; Peters and De Haan, 2011; Aram et al., 2019). The better a green space supports such social interactions, the more people can be served by the green space.

For modelling this quality \(q_4(g)\) of a green space g, different POIs that can support the social interaction including some activities (e.g., gaming center and art center), services (e.g., food-related services), and facilities (e.g., charging station and bench), are extracted from the OSM API. The number of these points inside each of the UPGSs is counted and, in the end, the normalized number of them is considered as the final rank for this quality.

$$\begin{aligned} q_4(g) = \text {normalized number of social interaction supporting POIs of }g \hspace{3em} \in [0,1] \end{aligned}$$
(10)

Residents’ Perception

Residents’ perception of a UPGS is key to its quality (Kothencz et al., 2017; He et al., 2022; Ghavimi et al., 2025) and, consequently, its capacity. It determines how positively people perceive a UPGS (e.g., its security and aesthetics) and, hence, how many people can be served (Zhang et al., 2018). It also refers to how people perceive being invited to PUGS (Gehl, 2013). People prefer to go to positively perceived spaces and avoid others. Therefore, residents’ perception of a UPGS is part of its capacity.

Since aesthetics is one of the most perceptual qualities of a UPGS and since we consider photo taking as a sign of aesthetics, for modelling this quality \(q_5(g)\) of a green space g, we use the number of photos taken in each green space. For each UPGS, a query with the Flickr API was performed to get the number of photos taken inside it. We contend that a large UPGS with the same number of photos as a smaller one is inherently less attractive, or at least not all parts of it are appealing. Our belief stems from the notion that a larger UPGS inherently offers a greater range of landscape opportunities, providing people with a diverse array of scenic vistas and captivating elements to capture. The spatial density of the photographs is calculated by dividing the number of photos captured inside each UPGS by its area. After normalizing this density, the outcome is regarded as the quality’s ultimate value.

$$\begin{aligned} q_5(g) = \text {normalized}\left( \frac{\text {number of photos taken inside } g}{\text {area} (g)} \right) \hspace{3em} \in [0,1] \end{aligned}$$
(11)

Facilities

To bring people to the UPGS and create a pleasant perception of the space, facilities for their main needs should be provided. This is essential for UPGSs’ capacity to serve residents. Here we use the term facility for all physical amenities and infrastructure provided within UPGSs to enhance visitor experience, comfort, and usability. These facilities are designed to support various recreational, social, and practical activities in green spaces. Some common examples are toilets, benches, bins, shelters, playgrounds, lighting or sports facilities. Considering this definition, facilities available in UPGS and the quality of these facilities are another criterion mentioned by scholars (e.g., Schipperijn et al., 2013; Peters and De Haan, 2011; Kruize et al., 2019; McCormack et al., 2010). Facilities are typically aligned with the primary goal of UPGS and therefore, naturalness and is less prioritized than Facilities by citizens (Stessens et al., 2020). Many facilities are even important to wilderness-oriented visitors who prefer unspoiled natural areas (Lehto et al., 2024).

We model this quality \(q_6(g)\) of a green space g based on the number of POIs that are related to facilities. We query the POIs obtained from OSM for keywords that we assume to be facilities, e.g., barbeque, bicycle parking, toilet, and bench. Then, the normalized number of facilities inside each UPGS is considered as the final value for this quality.

$$\begin{aligned} q_6(g)= \text {normalized number of facility POIs of }g \hspace{3em} \in [0,1] \end{aligned}$$
(12)

Symbolic Value

Green spaces with high symbolic value are considered to be attractive to a wider range of people (Ives et al., 2017; Huang, 2024; Bayramova et al., 2021). When a UPGS is or has been a place for events and has a monument or a common meaning attached, it has a high symbolic value. This value is largely concerned with the experience this space offers people (Vierikko et al., 2020) and consequentially with the meaning that attaches to it over time (Carmona, 2015). This is because UPGSs provide social, cultural, and recreational services (Loughran, 2020), and citizen use these spaces to reproduce their identity and enhance the sense of place (Low et al., 2005).

Generally, the symbolic value of an UPGS derives from cultural significance, physical symbols, memorable associations, and public events occurring within it. This value can be quantified through VGI, using the presence and frequency of specific POIs. These POIs, which represent historical sites, cultural landmarks, community centers, and distinctive architectural features, serve as tangible indicators, reflecting the rich mix of historical and social elements that characterize the symbolic value of the UPGS.

For modelling this quality \(q_7(g)\) of a green space g, let S(g) be the number of cultural, symbolic, artistic, touristic, and historical POIs that could have a positive effect on the symbolic value of the green space g. Then, we model \(q_7(g)\) such that if there is no symbolic, cultural, or historic POIs, it is zero. If it has at least one of these POIs, it is a number between 0.5, and 1.

$$\begin{aligned}&\text {If S=0} \hspace{2em}&q_7(g)=0 \hspace{3em} \in [0,1] \end{aligned}$$
(13)
$$\begin{aligned}&\text {otherwise}\hspace{2em}&q_7(g) = \frac{\text {normalized}\ S}{2} + 0.5 \hspace{3em} \in [0,1] \end{aligned}$$
(14)

Water Body

People have a preference to be near water. Water bodies can enhance physical and mental health (Geneshka et al., 2021; White et al., 2021; Zhou et al., 2017), enhance the variety of activities in the UPGSs, add to the aesthetic value, and therefore make the UPGSs more attractive and capable of serving people (Kurochkina, 2020; Baycan-Levent et al., 2009; Zhou et al., 2017; Kruize et al., 2019; Börger et al., 2021). A water body refers to any significant natural or artificial expanse of water (Wang et al., 2022; Ghavimi et al., 2025; Grinham et al., 2018). Such therapeutic landscapes are especially crucial in UGSs where natural blue spaces are limited (Vaeztavakoli et al., 2018).

For modelling this quality \(q_8(g)\) of a green space g, all features that could be perceived as a type of water body are selected from different queries and keywords from the OSM API and the number of different water features inside each UPGS is counted. Then, the score function is set in a way that for green spaces with at least two different waterbody types, the value 1 and for green spaces with exactly one water body type the value 0.5 is assigned. Other green spaces receive the value zero. Let W(g) be the number of different water body types of green space g.

$$\begin{aligned}&\text {If W(g)=0} \hspace{2em}&q_8(g)=0 \hspace{3em}\in \{0, 0.5, 1\}\end{aligned}$$
(15)
$$\begin{aligned}&\text {If W(g)=1} \hspace{2em}&q_8(g)=0.5 \hspace{3em}\in \{0, 0.5, 1\}\end{aligned}$$
(16)
$$\begin{aligned}&\text {otherwise}\hspace{2em}&q_8(g) = 1 \hspace{3em} \in \{0, 0.5, 1\} \end{aligned}$$
(17)

Aesthetic Value

GSs are by their nature a source of aesthetic perception (Gupta et al., 2012). Nature-related beauty (incl. especially water bodies) is one of the motivations for citizens to visit UPGS. Surveys on UPGSs have shown that many citizens choose UPGSs based on aesthetic values, which are highly associated with biodiversity, water bodies, natural landscape, greenery density, and space design (Peters & De Haan, 2011). In addition to the higher satisfaction in more beautiful UPGSs (e.g., Gozalo et al., 2019), the recreational opportunity is closely related to aesthetics and perceived aesthetics (Sang et al., 2016; Wang et al., 2021). Scenic beauty generally increases the site’s recreation potential (Derkzen et al., 2015). The aesthetic value of a UPGS supports the attraction of people to it, its variety of activities, responsiveness to aesthetic needs, and hence the the recreational capacity of the space.

For modelling this quality \(q_9(g)\) of a green space g, data from both platforms OSM and Flickr are used. In particular, we count the number of water bodies from OSM data and the number of photos from Flickr. We assume that the number of photos indicates the beauty of the green space. From the literature, it is known that water bodies have an aesthetic effect (e.g., Kurochkina, 2020). We design the quality such that for a green space which has no water body (i.e., \(q_8(g) = 0\)) the aesthetic rank is proportional to the number of photos taken in it and for green spaces with at least one water body (i.e., \(q_8(g)= 0.5\) or \(q_8(g) = 1\)) the aesthetic value is calculated based on both water bodies and photos taken inside the UPGS, so that the value is at least 0.5 and at maximum 1. For this purpose, we have added 1 to the value of the quality of the residents’ perception (\(q_5(g)\)) and divided the result by 2.

$$\begin{aligned} R_{q_9g_i}= & \text {Normalized}\ Pp (R_q{}_5) \ \ \ [0, 1]\ \ \ \text {UPGS with no Water Body}\end{aligned}$$
(18)
$$\begin{aligned} R_{q_9g_i}= & (R_q{}_5 + 1)/2=(\text {Normalized}\ Pp+1)/2 \ \ \ [0.5, 1] \ \ \ \text {UPGS with Water Body}\nonumber \\ \end{aligned}$$
(19)

Connectivity

Connections between urban public spaces (UPSs), including UPGSs, help them to support each other (Paumier, 2004) and make it possible to combine activities in a set of connected urban spaces (Hillier, 1996). This will undoubtedly lead to an increase in the capacity of these spaces to be used in daily life. Although the broad concept of connectivity includes more concepts such as simple connection and clear connection (e.g., Paumier, 2004), in this study we narrowed it down to only the proximity of UPSs to take advantage of social data. Therefore, this quality in our research checks if the UPGS is in proximity to other main UPSs. Based on the literature, we consider two places to be near if their Euclidean distance is at most 300m (e.g., Wüstemann and Kalisch, 2016; Ghavimi et al., 2020). Then, even if the network distance is twice the Euclidean distance, the distance between the UPSs is walkable.

The main challenge for modelling this criterion is to determine the main UPSs in the study area. In this research, we decided to use the concept of Areas of Interest (AOIs). Urban AOIs are based on people’s perceptions (Hu et al., 2015) and cannot be defined by clear boundaries (Ghavimi, 2020). Main UPSs in an urban area are public spaces that are the center of residents’ daily activities and needs. We derive the AOIs from the POI data as follows.

Fig. 1
figure 1

Selected POIs related to main UPSs in the urban region of Bonn. The dataset contains more than 52k points. Background map data obtained from OSM - published under ODbL

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As our dataset, we utilize all points of interest (POIs) within the urban region of Bonn see Fig. 1, extracted from OSM that are related to daily shopping, daily needs, third places, and the daily walking trip (e.g., Van Diepen and Musterd, 2009; Harani et al., 2021; Oldenburg and Brissett, 1982). Then, to derive areas, we first cluster the POIs with DBSCAN (Khan et al., 2014); see Fig. 2a. DBSCAN has two parameters to define a minimum density threshold; the search radius (\(\epsilon \)), and the minimum number of points within the search radius (k). At those locations where the density of POIs is greater than the specified threshold, the clusters are recognized. We use \(\epsilon =200\)m as the maximum distance and \(k=50\). In this research, the clustering parameters are defined so that the number of clusters reduces to the limited number of very main UPSs in the study area and excludes other UPSs in the area.

Fig. 2
figure 2

Computation of AOIs from POIs. Background map data obtained from OSM - published under ODbL

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We selected the DBSCAN method since, compared to other clustering methods, such as K-Means or K-Medoids, it does not require a predefined number of clusters. In this study, the number of clusters is equal to the number of AOIs, which was initially unknown and is part of the findings of this study. Further, DBSCAN is good at detecting clusters in various shapes. AOIs in cities also do not have a specific shape. They depend on the perception of residents and can be in any shape. DBSCAN identifies clusters based on the density of connected points instead of their distance from the center. Finally, DBSCAN is strong against potential data noise (Hu et al., 2015, p.9). The resulting set of areas created by these clusters can be evaluated by the general information about these urban spaces; see Fig. 2b. After clustering, we can compute the AOIs as the concave hull for each cluster (Moreira & Santos, 2007; Li et al., 2021). Alternatives to the concave hull are convex hulls, KNN-based concave hulls, X-shape concave hulls, etc. (Li et al., 2021; Zhong & Duckham, 2017; Moreira & Santos, 2007). The advantage of the concave hull is the flexibility in its shape, which avoids the inclusion of adjacent areas that are not indicated by the data.

Fig. 3
figure 3

UPGSs in walkable distance (300 m) to the main UPSs highlighted in yellow. Other UPGSs are shown in dark green and UPSs shown in purple. Background map data obtained from OSM - published under ODbL

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We model the quality \(q_{10}(g)\) of a green space g so that if the UPGS has at least one main UPS in the walking distance of 300m, then \(q_{10}(g)=1\) as it can be part of a resident’s daily walking trip, and otherwise \(q_{10}(g)=0\); see Fig. 3.

$$\begin{aligned}&\text {If no main UPS is in the walkable distance of { g}} \hspace{2em}&q_{10}(g)= 0 \hspace{3em} \in \{0,1\} \end{aligned}$$
(20)
$$\begin{aligned}&\text {otherwise}\hspace{2em}&q_{10}(g)= 1 \hspace{3em} \in \{0,1\} \end{aligned}$$
(21)

Enhanced Capacity

In the following, we introduce the enhanced capacity. First, we introduce the quality Q(g) of a green space as

$$\begin{aligned} Q(g)= \frac{1}{10}\sum _{i= 1}^{10}q_i(g)\hspace{3em} \in [0,1]. \end{aligned}$$
(22)

Then, the enhanced capacity is

$$\begin{aligned} C^*(g) = \Biggl (\frac{4}{5} Q(g)+0.2\Biggr ) \cdot C(g) \hspace{3em} \in [0.2\cdot C(g),C(g)]. \end{aligned}$$
(23)

Note that the enhanced capacity is less than or equal to the area-proportional capacity. We decided on this design because only when all qualities have full rank it is probable that all parts of the UPGS have the capacity to serve people. Then, it is reasonable to consider the whole size of the green space. On the other hand, if the quality of green space is very low, then it is more probable that most parts of the UPGS do not have the full capacity to serve people. We pay attention to the fact that some green spaces may not have some criteria, such as a water body, but still, most of their parts are usable and attractive to people. However, we still consider our approximation valid and necessary, especially for large green spaces. The descriptive statistics for each quality metric are presented in Table 2. To optimize computational efficiency, we subdivided all PGS polygons into 20,653 partitions, applying rankings to each polygon segment accordingly. As illustrated in the table, only a small number of PGS segments achieved a \(> 0.9\) rank under our proposed methodology for assessing qualities. These descriptive statistics offer valuable insights into the distribution of PGS qualities within the area, highlighting how each quality significantly impacts the model’s results and contributes to the enhanced capacity of PGSs.

Table 2 Descriptive statistics of PGSs’ qualities
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Platform Selection

In recent years, “social data” has been increasingly used for research, planning, and decision-making (e.g., Hu et al., 2016; De Jong et al., 2014; Vann and Garson, 2001). Social data is data generated by users of social media platforms that are publicly shared (Silva et al., 2014; Olteanu et al., 2019). Such platforms are, e.g., social networks (e.g., Twitter, Flickr, Instagram, Facebook, etc.), collaborative sites (e.g., Wikipedia), search platforms (e.g., Google), and also data from citizen organizations (Conrad & Hilchey, 2011; Jiménez, 2008). Social data is characterized by its collective, user-generated, and user-driven nature (Olteanu et al., 2019).

Data about points of interest (POIs), semantic data, and data from photos are some of the main types of data related to UPGS studies and are extractable from social data sources (e.g., Yang et al., 2021; Liu et al., 2023; Sun et al., 2021). A POI is known as a specific point location that someone may find useful or interesting. The emergence of location-based social networks (LBSNs) such as Instagram and Google Maps, location-based social media (LBSM) such as Twitter, and collaborative mapping platforms has contributed to the availability of POIs in urban areas. They offer the opportunity to build personalized POI recommender systems. Recommender systems mainly recommend three items: tags, friends, and location (Gao & Liu, 2014). A GPS point of interest specifies, at minimum, the latitude and longitude of the POI. Examples of POIs related to UPGSs are parks, park facilities, zoological gardens, and ticket offices of the park (Chen et al., 2018), ice cream parlors, food shops, and different facilities inside or in the very vicinity of the UPGSs. Some global POI sources used in the reviewed literature so far are the location-based social network Foursquare (e.g., McKenzie et al., 2014), Gowalla (e.g., Scellato et al., 2011), OSM, and Weibo. Data from social media can also be used to define the popularity of UPGSs. Studies have shown that social media platforms can relatively well reveal the popularity of the UPGSs (Tenkanen et al., 2017). The number of check-ins (if provided by the platform API), posts (e.g., Twitter, Facebook, Instagram), photos taken inside a place (e.g., Instagram and Flickr), or geotagged contents of these platforms can all can be used to define the popularity of UPGSs. In this study, after listing all used platforms in urban studies from the reviewed literature and their characteristics, we select the two platforms, OSM and Flickr.

Other data platforms are not considered due to a variety of reasons such as being restricted (e.g., Instagram, Facebook, Mapillary), being more appropriate for some parts of the world instead of global coverage (e.g., Baidu, Weibo, Tencent), or lacking relevant or useful information for the purpose of this research (e.g., Swarmapp, TripAdvisor, Yelp).

Our study focuses on the urban region of Bonn, which is relatively well-populated and benefits enough data on platforms such as OSM and Flickr. OSM is maintained by a large, active community that regularly updates data, making it one of the most current sources of VGI (Wang et al., 2013; Mooney et al., 2017), and Flickr’s platform allows for continuous user uploads, meaning the underlying data is constantly being updated (Höpken et al., 2020; Spyrou & Mylonas, 2016). Since the study area does not include rural or sparsely populated regions, we assume that the VGI data used are reasonably representative of the actual conditions in this context. However, we acknowledge that this assumption may not hold in some other areas and further validation would be necessary when applying our methodology elsewhere.

Experiments

In order to assess the enhanced capacity and whether it leads to realistic assignments we performed a case study for the city of Bonn, Germany. We obtained the data on green spaces and residential areas from Urban Atlas 2012Footnote 1. In particular, each residential area is extracted as a simple polygon that typically corresponds to a housing block and contains information on the number of residents as can be seen in Fig. 4a. Similarly, each green space is a simple polygon in the city or its surroundings; see Fig. 4b. For computing the distances between the green spaces and residential areas, we used the road network obtained from OSM.

Fig. 4
figure 4

The study area. Data obtained from Urban Atlas 2012 - ©European Union, Copernicus Land Monitoring Service 2018, European Environment Agency (EEA). https://land.copernicus.eu/. Background map data obtained from OSM - published under ODbL

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For the area-proportional capacity as defined by Oehrlein et al. (2019), we set the per-capita demand to \(k = 22\)m\(^2\) as recommended by Schröter (2021). As a result, the equation for the area-proportional capacity can be described as

$$\begin{aligned} C(g) =\frac{\text {area}(g)}{22\text {m}^2}. \end{aligned}$$
(24)

Based on C(g) we compute the enhanced capacity \(C^*(g)\) as described in Eq. 23. We incorporate the enhanced capacity into the framework of Oehrlein et al. (2019) by replacing C with \(C^*\).

Fig. 5
figure 5

POIs from Google Maps classified by the number of ratings. Background map data obtained from OSM - published under ODbL

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In order to assess the enhanced capacity, we use additional data on green spaces from Google Maps. on Google Maps any visitor can rate the place, including tourists who have experienced it. Although many of these UPGSs may not be tourist destinations, it is reasonable to assume that the majority of reviewers are local residents due to our familiarity with the area. Regardless of who the reviewers are, the number of reviews and the average ratings provide valuable insights into how these spaces are perceived and evaluated by individuals seeking recreational opportunities. In detail, we extract all relevant POIs that lie in a green space in the study area; see Fig. 5. Some of these POIs are UPGSs themselves. Further, we extract the average rating of each POI and the number of ratings for each. The rating is a number between 1 and 5 and the number of ratings is an integer larger than zero. Overall, we extracted 123 POIs, with 4.4 ratings on average. For our evaluation, we focused on all UPGSs that contain at least one POI, which are 79 UPGSs in our study area. We introduce the number of ratings of a UPGS as the summation of the number of ratings of all its contained POIs and similarly, the average rating of a UPGS as the average of all average ratings of the contained POIs; see Fig. 6.

For the maximum travel distance \(d_{\text {max}}\) between a resident and its associated green space, we test different values ranging from 1500m to 5000m, and find that all residents in an optimal allocation are assigned to green spaces for \(d_{\text {max}} = 4650\text {m}\); see Fig. 7. Below this distance, not all residents are assigned to a green space. Oehrlein et al. (2019) conducted experiments on the same data but with different values for the parameters k and \(d_{\textrm{max}}\), i.e., the per-capita demand and the maximum distance to the assigned green spaces, respectively. The results show that with a distance of \(d_{\text {max}}=2500\)m, and a per-capita demand of \(k=50 \text {m}^2\) all residents are assigned to the green spaces. With the same parameter values and our enhanced capacity model, the method assigns \(71.5\%\) of all residents. However, when using the per-capita demand of \(k=22 \text {m}^2\) recommended for Germany and maximum distance of \(d_{\text {max}} = 4650\text {m}\), all residents were assigned with the proposed enhanced capacity model. This is due to the definition of enhanced capacity, which implies \(C^*(g)\le C(g)\).

Fig. 6
figure 6

GoogleMaps data on POIs mapped to UPGS. For UPGSs that are colored green there does not exist any GoogleMaps data. Background map data obtained from OSM - published under ODbL

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Fig. 7
figure 7

Satisfied residential areas and participating UPGSs of the city area of Bonn ranked by the used capacity (\(d_\textrm{max} = 4.65\)km and \(k = 22\)m\(^2\)). Data obtained from Urban Atlas 2012 - ©European Union, Copernicus Land Monitoring Service 2018, European Environment Agency (EEA). https://land.copernicus.eu/

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In the following, we give a comparison of the different capacity models with real-world data. We consider the area-proportional capacity C(g) and the enhanced capacity \(C^*(g)\) as theoretical models for the capacity as well as the overall value of the UPGS’s quality Q(g). For capacity models, we set the per-capita demand to \(k= 22\)m\(^2\) and the maximum travel distance to \(d_{\text {max}}=4650\)m. We compare the allocations obtained from the two models to the average rating and the number of ratings of each green space derived from Google Maps data. The correlation test is used to compare the two models. Before selecting the correlation test, we check our data for outliers and non-normal distributions. The Shapiro–Wilk test is one of the most widely used methods to test the normality of the data and is an appropriate method for small sample sizes although it can also handle larger sample sizes (Mishra et al., 2019). The Shapiro-Wilk Test of normality for both the average ratings and the number of ratings for the 79 UPGSs show significant departures from normality (respectively \(W = 0.91278\), \(p = 4.895\cdot 10^{-5}\) and \(W = 0.33628\), \(p = 2.2\cdot 10^{-16}\) for average ratings and the number of ratings). Since the p-values in the Shapiro-Wilk test are less than 0.05, the departure from normality is significant, and the null hypothesis \(H_0\) that the variable is normally distributed is rejected. Corresponding histograms and QQ plots are shown in the Figs. 8 and 9. The two data sets’ non-normal distribution is indicated by the considerable deviation of the two sets’ histograms from a bell shape and QQ plots from a diagonal line.

Fig. 8
figure 8

Distribution analysis of the number of ratings for the 79 UPGS

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Since we have data sets with ordinal scale (average ratings), with non-normal distribution (both average rating and the number of ratings), and including outliers (number of ratings), the Kendall rank correlation is an appropriate tool to test the correlations. The Kendall rank correlation is a non-parametric test, meaning it can be tested on data that does not follow a normal distribution and as an alternative to Spearman’s correlation if weak dependencies are shown. In principle, the Kendall rank correlation answers the question of whether two data sets are correlated or not and determines the correlation direction and the size of the effect (Sullivan & Feinn, 2012). Equation 25 defines the Kendall rank correlation (Sprent & Smeeton, 2016).

$$\begin{aligned} \text {Kendall's}\ \tau&= \frac{\text {Concordant pairs}-\text {Discordant pairs}}{\text {Concordant pairs}+\text {Discordant pairs}} \nonumber \\&= \frac{2(\text {Concordant pairs}-\text {Discordant pairs})}{n(n-1)} \end{aligned}$$
(25)

To determine the Kendall rank correlation coefficient for the results of our models, we normalize the capacities, used capacities from model results, and the real-world average ratings and the number of ratings so they range between zero and one. Since for some UPGSs only very few user ratings are available and the corresponding average ratings will not be reliable and may result in a false conclusion, we excluded those with less than 6 ratings from the rating data set before normalizing to produce more reliable results. We pair-wise compare each of the results to the real-world average ratings and the number of ratings. The correlation coefficient \(\tau \) indicates the correlation strength by using a range of adjectives from perfect to negligible correlation as described by Botsch (2009) and Akoglu (2018):

$$\begin{aligned}< 0.1 \quad&\text {negligible correlation} \\ 0.1 -< 2 \quad&\text {weak correlation} \\ 0.2 -< 3 \quad&\text {moderate correlation} \\ 0.3 -< 5 \quad&\text {strong correlation} \\ 0.5- < 1 \quad&\text {very strong correlation} \\ 1 \quad&\text {perfect correlation} \end{aligned}$$
Fig. 9
figure 9

Analysis of the distribution of ratings for the 79 UPGSs

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Table 3 Kendall rank correlations
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The results of the correlation test can be seen in Table 3 and indicate moderate correlations (respectively \(\tau = 0.2087\) and \(\tau = 0.2393\), \(p<.05\)) with the number of ratings and average ratings for the area-proportional capacity defined by Oehrlein et al. (2019). Our enhanced capacity, on the other hand, shows strong correlations with both average ratings and the number of ratings (respectively \(\tau = 0.3061\) with \(p<.01\) and \(\tau = 0.3351\) with \(p<.001\)). This indicates that our approach to the definition of capacity is more in accordance with reality.

We also investigated the correlations for the number of residents served by each green space, which we refer to as used capacity in the two model assignments, in order to evaluate and compare the two models more directly. Results show that there is no significant correlation between used area proportional capacity and average ratings (\(p>.05\)) and there is a moderate correlation between used area proportional capacity and the number of ratings (\(\tau = 0.2129\), \(p<.05\)). While used enhanced capacity has a strong correlation with the number of ratings (\(\tau = 0.3364\), \(p<.001\)) and a moderate correlation with the average ratings (\(\tau = 0.2950\), \(p<.05\)). This finding shows that our enhanced capacity approach is substantially better in line with the actual usage of UPGSs and can reflect the distribution of residents on available green spaces better than the area-proportional capacity approach.

The Kendall rank correlation test also indicates a strong correlation between the UPGS’s overall quality (Eq. 22) and the number of ratings (\(\tau = 0.3642\), \(p=.001\)) as can be seen in Table 3. Here we had a rather small sample with some average ratings resulting from a few numbers of ratings. We think that a larger quantity of average ratings with a considerable number of ratings may result in a significant correlation between average ratings and the UPGS’s overall quality.

Conclusion and Future Work

The capacity of a green space, i.e., the number of residents that can be served by it, is modelled so far proportionally to its size. In this work, we introduce a new capacity model, which consists of ten quality scores. We provide a model for each quality measure and explain how to derive each quality based on social data. Then, we show how to incorporate the enhanced capacity into the introduced framework by Oehrlein et al. (2019) that assigns residents of an urban area to green spaces. In our experimental evaluation, we compare the area-proportional capacity, the enhanced capacity, the used area-proportional capacity, the used enhanced capacity, and the UPGSs’ overall quality to the average rating and the number of ratings of each green space obtained from user ratings. The statistical tests indicate significantly better correlations for the enhanced capacity than the area-proportional capacity.

Regardless of who has participated in creating the social data used in this research and whether they are all citizens or tourists, the rankings based on Google Maps indicated people’s preferences for using UPGSs. Therefore, our enhanced capacity, as measured by the integration of UPGS qualities, aligns more closely with people’s preferences in reality.

Our proposed enhanced capacity evaluative framework consistently results in a value that is less than or equal to the area-based proportional capacity. This approach is predicated on the rationale that a PGS can fully serve the community with its entire area only when it attains the highest ranking across all qualities. Within our overall PGS quality equation, as well as individual assessments for each quality, the impact of each aspect is evident. For instance, a large forest lacking key attributes such as water bodies, facilities, and safety measures cannot adequately serve diverse population groups across its full expanse. This result can assist planners and decision-makers in making more informed decisions regarding UPGSs, providing them with a framework to enhance UPGS capacity based on the introduced qualities and corresponding measurement indexes.

We neither make claims about the perfection of our mathematical modeling nor the completeness of the criteria we have established. However, our objective was to establish a formalized framework for assessing UPGS’s quality and enhanced capacity, allowing for the easy substitution of individual model components with more accurate measures and the straightforward incorporation of additional criteria. One limitation of this study is that our model components for each quality may not encompass the entirety of the criteria associated with that quality. Here, we focused on using social data and accepted the limitations. As an example, we are aware that some activities do not need any facility or the existence of some population-absorbing POIs will not guarantee the security of the space. Also, we selected to evaluate our method based on social data and not with other common methods such as observation, questionnaires, or interviews with people. Accordingly, we settled on what we could get from social data. Our goal has been to show the importance of social data and a way to use it in making decisions. Our study uses a different set of data sources, diverging from platforms like GBIF, which, although not being classified as VGI, serves as a pivotal global repository for biodiversity data. Despite the inherent challenges and limitations associated with using resources such as GBIF-such as variations in data quality and spatial bias-we suggest that other scientists explore similar biodiversity data sources and other sources to also include vegetation diversity. Integrating such data is critical because biodiversity indeed influences the recreational capacity of PGSs and promotes improved management and use strategies. The weightings applied in this study were derived from a rigorous process of extensive discussion and contemplation to arrive at the most accurate and reliable estimate possible of the real capacities. However, we acknowledge that the weightings used in this study may not be universally applicable and may need to be adapted to the specific conditions of other study areas. We hope that our innovative model can provide a base for other scholars who wish to adapt and apply it to their contexts.

One more limitation of this study is the reliance on user-generated VGI data from OSM and Flickr, which are by nature highly dependent on voluntary contributors and may reflect some biases. This gap could be filled if the official green space data on a small scale were available. However, future work could address this by incorporating or validating some official datasets. Additionally, data collected from Google Maps is subject to certain limitations. For example, some UPGSs exhibited a low number of users. To mitigate potential bias, we leveraged two distinct metrics provided by Google Maps: the average rating and the number of ratings. This helps ensure fairer comparisons across UPGSs. Our study relies on quantitative methods using available VGI data. Future research should consider incorporating text data from social media to enhance understanding of public perceptions of UPGS. Qualitative methods and innovative text assignment techniques could provide valuable insights. We suggest incorporating more data types for future work, e.g., reviews or photos from social media platforms. We assume such data might reveal more information about the users’ perception of green spaces.