# Hydrodynamic Modelling in a Mediterranean Coastal Lagoon--The Case of the Stagnone Lagoon, Marsala
## 2 Materials and Methods
### Numerical Model  
As already mentioned, coastal basins such as the Stagnone are mainly characterized by tidal and wind forces. A state-of-the-art 2 DH model has been used, simulating the water depth changes and the horizontal velocity components. The model used is the MIKE 21 Flow Model (MIKE21 HD). This is a hydrodynamic model that is a general numerical modelling system for the simulation of water depths and velocities in coastal areas. The Reynolds-Averaged Navier-Stokes (RANS) and continuity equations are solved, and the model simulates unsteady two-dimensional flow in one-layer (vertically homogeneous) fluids. This module has been applied in a large number of studies related to coastal Lagoons [18; 19; 20]. For further information, refer to the official documentation (DHI suite [[https://www.mikepoweredbydhi.com](https://www.mikepoweredbydhi.com)]([https://www.mikepoweredbydhi.com](https://www.mikepoweredbydhi.com)), accessed on 5 September 2023). An unstructured mesh, composed of 15,172 nodes and 25,812 triangular elements, has been created, imposing a finer extent of mesh elements in peculiar lagoon areas such as the inner islands and the northern dredged channel. The element dimensions span from 3000 m\({}^{2}\) to 0.1834 m\({}^{2}\), representing, respectively, the flatter and more homogeneous zones and the more morphologically complex shallow shudow s. To avoid numerical inaccuracy, the mesh size has been drastically reduced where local singularity was present. Two boundary conditions were placed in the north mouth (NM) and in the south mouth (SM), imposing the recorded water depth (Figure 2a). To reach the best set-up, different conditions have been tested. A calibration related to the bed roughness has been conducted to represent the friction induced by the presence of vegetation; for this purpose, the Chezy coefficient has been expressed in terms of the Gauckler-Strickler coefficient \(K_{s}\). It was possible to attribute a friction coefficient value to represent the presence of _Posidonia oceanica_, _Caulerpa prolifera_, and _Cymodcea nodosa_. One other calibration parameter was the wind friction factor value \(f\), used to linearize the drag effect of the wind blowing over the water surface. This coefficient is difficult to calculate and depends on the geometry of the water body, the fetch available, and the intensity of the wind itself. In this case, the wind friction factor was considered independent of wind velocity intensity. Finally, the last parameter used to calibrate the model is the horizontal eddy viscosity factor, calculated using a constant eddy formulation or the Smagorinsky formulation [21]. The effective shear stresses in the momentum equations contain momentum fluxes due to turbulence and enter the equation through the \(\tau_{xx}\) and \(\tau_{yy}\) variables. This parameter takes into account the damping factors of short-wavelength oscillations and is responsible for representing sub-grid-scale effects. This horizontal viscosity is a function of the partial derivative of flux variation along the x and y directions, like the \(\frac{\partial}{\partial x}(h\tau_{xx})\) term of the following equation, thus being more relevant in those areas where velocity divergence between mesh elements is higher. For deeper information about the numerical solution, it is suggested to consult the MIKE 21 scientific documentation. In the MIKE21 numerical model, the previous parameters enter in the momentum equilibrium equation, reported below for the x direction.