## 4 Discussion  
This study examined accessibility, density, and provision indicators to assess UGS availability in SA2s with different SES levels, from the most disadvantaged to the most advantaged quintiles. The findings suggest that in the Melbourne Metropolitan area, SA2s with higher UGS density and better access to UGS, defined as being within a five-minute walking distance, have a lower proportion of people with CVD. Furthermore, the areas with higher SES tend to have UGS privileges in terms of density and accessibility. This pattern is unlike SA2s with lower SES levels, where the UGS inequities could have aggravated the resident's physical health, in addition to all the disadvantages associated with the lower social and economic conditions. In contrast to the accessibility measure utilized in this analysis, the UGS per capita has not demonstrated a meaningful difference among areas with different SES levels. Indeed, personal characteristics are influential factors for CVD, but living environment factors play a role too [48]. Our findings show a correlation between higher UGS availability and decreased CVD rates, similar to the existing studies ([15, 17, 48, 49]). Our findings are specifically consistent with the study of [PERSON] et al. [19], which used the NDVI method and a 1600 m service area. By focusing on four specific types of UGS and excluding smaller tree canopies and bushes that may lack public use or access, this study provides a more targeted analysis of the features of UGSs that could influence CVD rates. The study found that the per capita measure is not associated with socioeconomic disparity and, therefore, might not be the most appropriate area-level measure to include in similar studies. This can also be the case for other area-related measures like the UGS percent ratio to the total study unit boundary, that is broadly used in similar studies [21]. However, the findings in other contexts might not be similar to this study, but the Melbourne case shows that a more cautious approach should be taken regarding UGS studies. Besides the statistical analysis results, a spatial viewpoint can highlight the underlying reasons. The per capita number in a particular area (e.g., SA2 boundary) does not capture sufficient attributes about UGS availability within the area. As represented in Figure 9, there might be other UGS areas next to the defined SA2 border that are unrealistically excluded from the analysis. The defined border does not limit people's exposure and access to UGS areas in the neighboring SA2s. Figure 9: (1–3) Per capita flaws. Unlike per capita, the results about UGS accessibility and density correlate with the SES in Melbourne. SA2s with higher SES (quintiles 4 and 5) have significantly better access to UGS areas and have higher UGS density. The more disadvantaged SA2s (quintiles 1, 2, and 3) have much less access to UGS areas, while the UGS density remains almost unchanged here. This finding is aligned with [PERSON] at al. 's [4] earlier study, utilizing the gravity model, which showed not only that UGS is more accessible in higher SES areas but also lower income Melbourne residents' mobility is towards areas with lower UGS access. Furthermore, a recent study showed that in addition to UGS accessibility and density, areas with higher SES benefit from better UGS quality in terms of safety and maintenance [50]. Regarding the nature of UGS Kernel Density Estimation, which includes the size, count, and distribution of UGS areas, the two latter factors have played a more significant role in achieving a higher density rank than large-scale UGSs. While SA2s with higher SES showed a higher density score, the spatial UGS patterns in different areas become noteworthy. Consequently, as Figure 10 suggests, SA2s with numerous and dispersed UGSs achieve a higher density rank, which is the case for quintiles 4 and 5. In contrast, the lower quintiles have lower UGSs and less distribution accordingly. Therefore, existing large-scale UGSs do not result in a higher UGS density.