## 2 Materials and Methods
### Distributed Hydrological-Hydraulic Modelling
#### 2.2.3 Surface Roughness  
[PERSON]'s equation has been used intensively in riverine hydraulics since its formulation in 1889. Extensive tables of the roughness coefficient \(n\) are available for different channel characteristics [63; 64], natural channels, and flood plains [65]. More recently, distributed hydrological simulations have shown that [PERSON]'s resistance law is also plausible to predict the runoff dynamics in roads, urban floods and agriculture areas [32; 66; 67; 68]. We classified the catchment area into six types of soils, as shown in Figure 4a, and assigned the Manning coefficient described below. Urban areas (dark green), roads (orange), and existing irrigation ponds (brown) were delimited from the most recent orthophoto. They occupy about 7% of the drainage area. The analysis of the water distribution for paved roads [69] and the urban regions [70] showed that the coefficient \(n=0.015\) s\(\cdot\)m\({}^{-1/3}\) is appropriate in both of them. For irrigation ponds finished in plastic materials, the accepted values is \(n=0.012\) s\(\cdot\)m\({}^{-1/3}\)[64]. Figure 4: (**a**) Regions defined in Section 2.2.3 to assign the Manning roughness. (**b**) Orthophoto in the dashed rectangular area of panel a showing sandy clay loam on the surface outside the olive tree canopy projection and inside streams because of the herbicide uses. The blue and red polygons are possible retention basins based on an artificial wetland or a large irrigation pond. (**c**–**e**) Possible NbS using ground branches, gravels and natural full-cover crop. The largest region occupied by olive grove (81%), see the blue area in Figure 4a, has a density of 70 trees-hectare\({}^{-1}\) and the soil management is nearly homogeneous. The traditional use implies that the vegetation surrounding the crops was removed, as observed in the orthophoto of Figure 4b. To simulate hydrological processes in the present day, we set the value \(n=0.02\) s\(\cdot\)m\({}^{-1/3}\) corresponding to fine sand (colloidal) as calibrated in our previous work [6]. We will see that the ensuing runoff velocities are high, so we would consider a possible NbS for soil erosion mitigation that seeks rising resistance to the flow. Some examples are: integrating the ground branches back into the soil after the pruning process (Figure 4c), redistributing gravels to form coarse surface structures (Figure 4d), and temporary spontaneous cover crops (Figure 4e). Following [PERSON] and [PERSON] [71], we set \(n\approx 0.2\) s\(\cdot\)m\({}^{-1/3}\) to imitate an NbS that provokes macro-roughness effects in possible future scenarios. The absence of natural cover has exposed sediment to erosion and caused a high incision of gullies and streams (green area in Figure 4a). Such regions were unknown a priori. To delimit them, we run a preliminary simulation with a constant Manning value of \(n=0.02\) s\(\cdot\)m\({}^{-1/3}\). Subsequently, we selected the regions with flood depths of \(h>0.01\) m to extract the water mask depicted in green in Figure 4a. It occupies 12% of the basin area and lacks riparian vegetation; note the sandy colour in the streams of Figure 4b. To simulate hydrological processes in the present day, we set \(n=0.025\) s\(\cdot\)m\({}^{-1/3}\) as calibrated in a catchment with similar geographical characteristics and precipitation regime [1]. Further, we would consider possible NbSs for increasing the floodplains retention area, delaying the concentration time and attenuating the peak water discharge for short rainfalls [37]. Plausible NbSs for increasing the in-channel roughness are riparian buffer installation, rock armour, willow in-ditch barriers, and timbers in a cross formation, among others. So, we simulated scenarios with the large (and realistic as well) value of \(n=0.2\) s\(\cdot\)m\({}^{-1/3}\)[65]. Lastly, the red region in Figure 4a represents a possible flood retention basin that (does not exist in present days but) would store overland waters, preventing the inundation of downstream urban areas.