One of the most current and urgent challenges is making cities sustainable and resilient to climate change. From this perspective, Nature-Based Solutions (NBSs) are well-recognized strategies for stormwater control and water cycle restoration. Urban trees are an example of NBS. However, the high degree of soil sealing typically found in urban environments limits natural processes such as infiltration and hinders the water and nutrient supply for proper root development, which weakens tree stability. Permeable pavements at the base of urban trees, on the one hand, facilitate infiltration, which helps runoff control, and on the other hand, improve stormwater retention and soil humidity, which enhance root feeding. This paper proposes an analytical-probabilistic approach to estimate the contribution of permeable pavements to stormwater management. The equations developed in this study relate the runoff probability to the storage volume, the infiltration rate into the underlying soil, and the average values of the hydrological variables in the input. The model allows us to select different runoff thresholds and considers the possibility that residual volume from previous rainfall events prefills the storage capacity. An application to a case study in Sao Paulo (Brazil) has been presented. It investigates the influence of the different parameters used in the model on the results. The comparison of the outcomes obtained using the developed equations with those obtained from the continuous simulation of measured data confirmed the effectiveness of the proposed analytical-probabilistic approach and the suitability of using permeable pavements at the base of urban trees for improving stormwater retention.

Sustainable Urban Drainage Systems (SUDS) include strategies and solutions for distributed stormwater management and control. They are strongly encouraged, especially in highly urbanized areas that suffer the combined effect of impervious surfaces and the increase in extreme rainfall events due to urbanization growth and climate change. Their integration into traditional urban drainage systems can mitigate flood risk and pollution of receiving water bodies. The main goal of SUDS is to restore the natural water balance by increasing infiltration and evapotranspiration processes and promoting rainwater harvesting and reuse. This paper proposes an analytical-probabilistic approach for SUDS modeling applicable to different systems. Developed equations allow estimating the runoff and residual storage probability for evaluating the efficiency of the storage volume both in terms of flood control and, depending on SUDS type, in terms of emptying time or water needs supply. The modeling considers the possibility of consecutive chained rainfalls; this feature is relevant for SUDS, often characterized by low outflow rates. Relating characteristic parameters to a probabilistic level (the Average Return Interval, ARI) makes the formulas interesting to be used in the design practice. An application to two case studies confirmed the goodness of the proposed method.

Storage tanks from rainwater harvesting systems (RWHs) are designed to provide flow equalization between rainfall and water demand. The minimum storage capacity required to take into account the maximum variations of stored water volumes, i.e., the active storage, depends basically on the magnitude and the variability of rainfall profiles and the size of the demand. Given the random nature of the variables involved in the hydrological process, probability theory is a suitable technique for active storage estimation. This research proposes a probabilistic approach to determine an analytical expression for the cumulative distribution function (CDF) of the active storage as a function of rainfall moments, water demand and the mean number of consecutive storm events in a deficit sub-period. The equation can be used by developers to decide on the storage capacity required at a desired non-exceedance probability and under a preset water demand. The model is validated through a continuous simulation of the tank behavior using rainfall time series from Milan (Northern Italy).