Assessing spatial scales in hydrological effectiveness and economic costs of nature-based solutions within a scale-invariance framework

This study proposed a scale-invariance framework within the fractal and Universal Multifractal (UM) framework to assess hydrological performances and economic dimensions of nature-based solutions (NBS) across various spatial scales. Firstly, a series of NBS scenarios are created by implementing NBS heterogeneously over Guyancourt city (a peri-urban catchment located in the Southwest of Paris). Then, the spatial heterogeneity and the implementation levels of NBS in the NBS scenarios are quantified by a scale-invariance indicator (fractal dimension; D_F) across various spatial scales. The X-band radar rainfall data with high space-time resolution was obtained from École des Ponts ParisTech, which is used as the rainfall forcing for numerical modelling experiments. Then, the hydrological responses of the NBS scenarios are simulated by using the fully distributed and physically-based hydrological model (Multi-Hydro) under the selected spatially variable rainfall event. The renormalised maximum probable singularity indicator (RI) is developed based on the UM framework, and it is employed to quantify the hydrological effectiveness in terms of efficiency in runoff reduction of the NBS scenarios. The economic indicator is represented by the life cycle costs (LCC), which are used to estimate the economic costs of NBS scenarios. Finally, the economic dimensions of NBS across various spatial scales are quantified by integrating D_F and the LCC of NBS scenarios. The results show that the permeable pavement scenarios 3 and 4 perform better than the other NBS scenarios in mitigating overland flow. The assessment of the economic dimensions of NBS suggests that a higher implementation level of NBS measures in the small-scale range is necessary. The economic dimensions of NBS at the large-scale range vary between 225 m² and 600 m². Overall, this study will potentially provide valuable strategies for better managing stormwater runoff in urban catchments and support the decision-making processes of implementing NBS on multiple spatial scales.