## 2 Methods
### UGS Density  
Unlike the other two indicators, UGS density using Kernel Density Estimation is rarely used as a tool in UGS inequality studies. The Kernel Density tool in ArcMap 10.5 allows to select polygons (the four UGS types in this case) and to calculate the density based on the selected features. This tool \"Calculates a magnitude-per-unit area from point features that fall within a neighborhood around each cell\" [41]. In other words, the Kernel Density tool calculates the amount or density of UGS, in this case, that is distributed over the study area. The tool also applies differential weights to objects based on their proximity [42], meaning that areas with a higher density of UGS, whether of a large size or higher quantity, would get a higher density score. After the Kernel Density calculation, a unique density value can be assigned to each SA2 using the Zonal Statistic tool in ArcGIS 10.5. The combination of these two tools helps to address the issue of unrealistic boundaries, like buffer zones or urban compartments. For example, if an SA2 boundary is cutting a UGS polygon into two or more parts, it cannot affect the overall density value of SA2s, which is more aligned with reality. The Kernel Density tool uses point data as the input, so the polygon UGS layer should convert to point data first. For this method, it is critical to consider the wide range of UGS sizes within the Melbourne Metropolitan area while choosing the method for converting the polygon features to points. For instance, there are very large UGSs in the northeast of the study area, like natural reserves, in comparison to the ones in the compact inner-city areas. Therefore, any direct analysis of the UGS data and neglecting the significant difference between the UGS sizes would mislead the results. To address this issue, a mesh layer with 400 * 400 cells was built using the ArcMap 10.5 fishnet tool. The fishnet layer was intersected with UGS polygons using the Feature to Point tool, and a point was drawn at the center of each output feature. A graphical sample of the procedure is represented in Figure 1.  
Figure 1: UGS features’ preparation for Kernel Density analysis. The output point layer is the input layer for the Kernel Density analysis, and the result is represented in Figure 2.  
To identify a quantitative output for UGS density in each SA2, a unique density value is assigned to each SA2 using the Zonal Statistics tool, that computes a single output value for every SA2 based on the Kernel raster, and the result for Melbourne SA2s is represented in Figure 3.  
Various accessibility and provision indicators are used in different UGS studies ([5,39,42,43]). The most common approaches are buffer zones or Euclidean distance from the point of residence, or from UGS areas [21]. Network Analysis has been used in some studies [44]; however, parameters can vary like the distance, type of destination (UGS), travel mode, etc. In this study, UGS accessibility is evaluated using road network distance in ArcGIS 10.5. The Network Analysis calculates the real travelling distance using the existing routes to a  
Figure 3: UGS density level in SA2 areas. Figure 2: UGS Kernel Density map. certain destination [42], while other mentioned methods analyze accessibility based on a direct line distance that does not represent the actual distance that a person should take towards, either on foot or drive towards, the destination. For this purpose, green space polygon features are obtained from a Melbourne open space map [37] and the road line features from the Victorian Government open data website [45]. As suggested by the VPP guideline [46], areas with 400 m, equal to 5 min walking distance, from green space areas are determined using the Network Analysis tool, in ArcGIS 10.5. In such accessibility analysis, given the relatively small distance size (400 m) and the UGS polygons, not points, as the reference, it is crucial to determine destinations correctly.