A scale-invariant framework for integrating nature-based solutions into dense urban areas to improve accessibility and equity of access to urban blue and green spaces

Improving accessibility and spatial equity of access to Urban Blue and Green Spaces (UB&GS) could potentially benefit biodiversity and urban sustainability. Nature-Based Solutions (NBS), serving as small-scale decentralised forms of UB&GS, can enhance both environmental quality and human well-being by fostering positive interactions between humans and the natural environment. While there is growing interest in assessing the spatial distribution of UB&GS at multiple scales, existing evaluations commonly examine each spatial scale separately. Consequently, the intrinsic scaling relationships of UB&GS and the potential of NBS integration to improve accessibility and spatial equity of access across scales remain insufficiently explored. To address this gap, this study develops a scale-invariant framework based on Universal Multifractal (UM) theory to support the integration of NBS into existing UB&GS across various spatial scales, using Paris as a case study. Then, the fractal dimension ( D F ) and Gini index are employed as indicators to assess the effectiveness of NBS in enhancing accessibility and spatial equity of access to UB&GS, respectively. The results demonstrate that the developed scale-invariant framework can effectively support the optimal integration of NBS into the current UB&GS. With NBS integration, the D F increases by up to 0.07, while the Gini index decreases by a maximum of 0.27 across the study areas, indicating improved accessibility and enhanced spatial equity of access. Overall, the scale-invariant framework developed in this study provides quantitative recommendations to support the sustainable deployment of NBS in highly urbanised areas.