## 3 Experimental Data  
A series of experiments was carried out at the \"_Laboratorio Grandi Modelli Idraulici_\" of the Department of Civil Engineering, University of Calabria, Italy. We used a hydraulic flume (11.13 m long), with the bottom made of PVC, of width \(B=0.382\) m and plexiglass walls (0.21 m high) set on a reticular beam (Figure 1). The beam was sustained by two crossbars, of which the one downstream was linked with a hinge to the beam, so that the flume could be put at the desirable slope. A small caisson sustained by the same beam, 104 cm long and with the same cross-section as the flume, upstream of this one and fed by the laboratory constant-level tanks, was equipped with calm-grids and allowed its entrance into the water without any disturbance. A valve on the input pipe allowed the flow rate regulations, and its measurement was possible by means of a Thomson weir downstream of the flume outlet. The vegetation was modeled by means of two sets of small wooden circular cylindrical rods (\(D=0.8\) and \(1.0\) cm) placed in a central portion of the flume (starting at \(x=630\) cm from the inlet) of variable length, approximately between \(1.5\) and \(2.2\) m. The rods were perpendicular to the bottom of the flume and were secured to two wooden box-structured plates. In a previous study [63], the drag forces acting on a group of stems were measured by maintaining the stem ends at a distance of about \(1\) mm from the bottom in uniform or quasi-uniform flow conditions. In this study, 29 free surface profiles were observed, with four stem densities, achieved arranging the stems on three square meshes (D4, D5, D9) at two distances, \(\Delta x=\Delta y=s=4.24\) and \(8.48\) cm, where \(\Delta x\) and \(\Delta y\) are the spatial distances between the centers of two stems in the streamwise and spanwise directions, respectively, and one staggered mesh (D4-5). The four arrangements are sketched in Figure 2. Three different bed slopes were considered, \(i_{1}=0.48\%\), \(i_{2}=1.35\%\), \(i_{3}=2.02\%\), and the flow rate was varied between \(5.27\times 10^{-3}\) and \(16.39\times 10^{-3}\) m\({}^{3}\)/s. As for the water level reading, we adopted the following procedure. Once the flume was set on the horizontal, the cross-section downstream was closed by a small penstock and the water was entered into the flume up to a depth of 3 cm. On the wall at the right side, some metric scales were put, drawn onto transparent plastic sheets, at a distance of 1 m from each other. The metric scales were then adjusted to the free water surface. Since previously the flume bottom was carefully levelled, the metric scale reading gave the water depth. In the flume reach with the stems, the metric scales were closer to each other. The average water level in cross-sections was obtained by watching through the transparent metric scales. The flume reaches from upstream, and downstream the stems presented cross-sections with a practically horizontal water surface, even though the flow had waves of amplitude 1 to 2 mm. In the reach equipped with the stems, the flow was approximately steady, presenting regular patterns of crests and hollows, so that the measurement by means of digital instruments or more refined techniques only apparently would have given better results, without any insight. In some cases, the water profiles were checked by means of photographs with good results. The experiments showed M2 or M3 - M2 free surface profiles. At the end of the stems array, we could observe, in many cases, the critical depth \(h_{c}=\sqrt[3]{q^{2}/g}\), where \(q\) is the flow rate per unit bed width (\(q=Q/B\)). In some cases, even with a M2 profile, a depth higher than the critical one was imposed downstream by means of a plate rotating around a hinge at the channel bottom. When a M3 profile was found upstream and a M2 profile downstream, a hydraulic jump was observed between the two. Table 1 provides a summary  
Figure 1: Hydraulic flume. Figure 2: Stem arrangements: (**a**) D4; (**b**) D5; (**c**) D9; (**d**) D4-5.