## 3 Results
### Mitigation of Urban Flooding through Basin-Scale NbSs  
The distributed hydrological simulation also provides the inundation map in the urban area near the catchment outlet. First, we use the simulated values of flow depth to verify the accuracy of the numerical simulation regarding historical information on flood levels. Later, we describe the benefits of NbSs for flood risk mitigation by analysing the outputs of the simulated future scenarios. Figure 8a depicts a zoom of the flow depth map for the present-day hydrological simulation introduced in Section 3.1. The flooded urban area corresponds with the blue rectangle in Figure 6a. The flow depth was more profound than the 1.4 m channel height in most of the reach shown on the map. Overtopping of the right bank provoked the inundation of the olive-grove floodplains. In the 45-degree channel bend upstream of the area of Figure 8a, the water flow abandoned the channel over the left bank and inundated the road and main street of the town of Arquillos. The numerical simulation predicts the flow accumulation on a corner (highlighted with a black rectangle in Figure 8a), leading to a maximum depth of about 0.5 m. The pictures taken in 1996 and 2013 in that place corroborates the numerical simulation result. Note the brown marks left by the slurry flow on the walls (Figure 8b) or the deep water flow reaching the windows (Figure 8c). Lastly, the flood left the town through the level ground surrounding the sports hall and returned to the channel. To draw an overview of the benefits of possible future scenarios that implement an NbS for flood management, we compared the simulated hydrographs \(Q(t)\) in a cross-section of the Manillas stream at the town inlet. The hydrograph was computed from the hydraulic variables \(h(\mathbf{x},t)\) and \(\mathbf{u}(\mathbf{x},t)\) during the transient numerical simulation:  
\[Q(t)=\int_{\mathbf{x}_{i}}^{\mathbf{x}_{i}}h(\mathbf{x},t)\mathbf{u}(\mathbf{ x},t)\cdot\mathbf{n}\,dl\,, \tag{10}\]  
where \(\mathbf{x}_{i}\) and \(\mathbf{x}_{e}\) denotes the initial and end points of the cross-section, respectively, and \(\mathbf{n}\) is the unit vector pointing in the direction perpendicular to the cross-section. Figure 9 shows the hydrographs for the fifteen simulations. The water discharge grew monotonously during the rising limb and attained a steady state at the end of the rainfall, i.e., \(t=3\) h, when the water discharge was at a maximum. The key variables used to evaluate the benefits of the NbS are the values of the peak water discharge and the time to peak flow, also known as the time of concentration or the duration of the rising limb. In the simulation, we defined the time of concentration \(T_{\text{sim}}\) as the instant of time when the simulated discharge \(Q(t)\) reached the 90% of the maximum value (i.e. \(Q=0.9\times Q_{\text{max}}\) at \(t=T_{\text{sim}}\)) [60]. Table 1 gives both the peak water discharge \(Q_{\text{max}}\) and the concentration-time \(T_{\text{sim}}\) for all the simulated scenarios. Figure 8: (**a**) Map of the simulated flow depth (\(h\) in meter), for the present-day scenario CN89-A at the time of peak flow (i.e., \(t=3\) h), in the urban area inundated downstream of the overtopped artificial channel. Flow from right to left. The region in panel a occupies the blue rectangle in the flow-depth map shown in Figure 6a. The pictures on the right-hand side correspond to the inundations on (**b**) 15 August 1996 and (**c**) 8 March 2013 in the boxed area of panel a when the artificial channel was unable to protect the town from flooding. The peak streamflow in the absence of infiltration (i.e., 53.8 m\({}^{3}\).s\({}^{-1}\) for CN100-A) lies very close to the theoretical value predicted using the rational method for the whole basin, i.e., \(Q_{\rm ss}=57.4\) m\({}^{3}\).s\({}^{-1}\) (5), due to the proximity of the town of Arquillos to the basin outlet. The time of concentration \(T_{\rm sim}=44\) min is also close to the theoretical prediction \(T=33\) min (6).