# Hydrodynamic Modelling in a Mediterranean Coastal Lagoon--The Case of the Stagnone Lagoon, Marsala
## 2 Materials and Methods
### Field Data
The period of these oscillations is about one second (like the wind waves), and in this temporal frame, the velocity Vy can range from \(+0.12\) m/s to \(-0.04\) m/s (Figure 4b; Vy is positive northward). In the 2 DH numerical model, these sinusoidal velocities are not reproduced since only the averaged velocities are simulated. Then, the recorded oscillations were filtered using a digital low-pass filter (Butterworth filter) to erase the wave-induced velocity effects. In the 20 s sketch reported in Figure 4b, the filtered velocity Vy was nearly \(+0.04\) m/s. This means that in the Adv_07 station, the mean current flows northward, in accordance with the entering tide in the lagoon from the south mouth. It is also possible to observe that the component Vx is oscillating around zero during the recording time (Figure 4c) so that the mean flow in the east-west direction is almost  
Figure 4: Comparison between filtered and raw signals in vertical (**a**), northward (**b**), and eastward (**c**) velocity components of ADV_07 (20 s sketch). insignificant with respect to the Vy mean motion. In addition, the Vz vertical velocities are oscillating around zero (Figure 4a). Now, we consider the water depth h and the horizontal velocities Vy and Vx recorded for 24 h at the station Vec_07, located near the south mouth, with a frequency of 1 Hz (Figure 5). The variability in the raw data (blue line) is due to the orbital motion of wind waves. Then, a digital filtration of the wind waves is performed (magenta line). Figure 5: Water depth (**a**) and horizontal velocities northward and eastward, (**b**) and (**c**) respectively, recorded in 24 h at 1 Hz by Vec_07. Primarily, a long period of sinusoidal behaviour related to the tide oscillations is clearly recognizable. When the water depth h is decreasing, then the water velocity Vy is negative, i.e., the tide leaves the Stagnone towards the south. When the water depth h is increasing, then the water velocity Vy is positive, i.e., the tide enters the Stagnone from the north. A secondary phenomenon recorded by the instruments is the seiches, with a period lower than one hour. During a seiche oscillation of the level, the water velocity accelerates and decelerates. In fact, in less than one hour, during a seiche period on 24 July at 02:00, it is possible to appreciate that the filtered velocities Vy, recorded by Vec_07, decelerate from +0.05 m/s to 0.00 m/s, then return to +0.04 m/s (Figure 5b). Seiches are typical lagoon or semi-enclosed basin phenomena. External forces generate a local elevation of the free surface, which is reflected within the basin. Seiches characterize the whole lagoon basin; in fact, they can be observed in all field measurements. The water depth measured in the first week of July 2006 at the north and south mouths shows first the 12 h period of the tide signal and second the presence of seiches (Figure 6). These unfiltered water levels will be imposed as boundary conditions in the north mouth (NM) and in the south mouth (SM) to force each simulation to introduce a tide-induced effect. In these stations, no velocity data were collected, so only the tidal effect was imposed along the boundary conditions. In fact, these two station were placed in strategic points of the area in order to collect both diurnal and semi-diurnal tidal effects and the peculiar phenomena of the induced seiches. The two mouths are 7 km apart from each other, and the tidal signal is sometimes slightly shifted. The north mouth signal, in fact, appears to be more affected by seiches and strong winds, which induce, respectively, a higher noise along the signal and a more rapid decrease in water depth in correspondence with northward-directed wind. Both boundary conditions are set constant along the boundary as the measurement is considered representative of tide effect along the boundary.