## 2 Materials and Methods
### Numerical Modeling  
A series of numerical experiments were conducted using the Regional Ocean Model System (ROMS) to analyse the hydrodynamic wind response in small and shallow estuaries. The ROMS numerical model is a 3D, free-surface, terrain-following numerical model that solves the Reynolds-averaged Navier-Stokes equations using hydrostatic and Boussinesq assumptions [24]. ROMS uses the Arakawa-C differentiation scheme to discretize the horizontal grid in curvilinear orthogonal coordinates and finite difference approximations on vertical stretched coordinates [25]. The numerical details of ROMS are described extensively in [24]. This model has been used and validated in similar ways and estuaries, such as Alfacs Bay located south of the Ebro Delta (e.g., [13; 26; 27]). The domain used is inspired in Fangar Bay and consists in an idealized domain due to the difficulty of achieving good bathymetry. The domain consists of a regular \(37\times 27\) grid with a horizontal resolution of about 70 m (Figure 2a) and 10 sigma levels in the vertical direction (the bottom layer being the first and the surface layer the tenth, Figure 2b). The model boundary is located 10 points away of the mouth entrance to avoid boundary noise (faster than show in the Figure 2a). The 2D variables were accommodated with the Chapman and Flather algorithms [28], whereas a clamped boundary condition is imposed on the 3D variables. The same model configuration has been used and validated in the bay located south of the Delta, the Alfacs Bay [27]. Figure 2a presents the different geometries used for the numerical experiments. We modeled a simple case, regarding the water body as a channel 2.5 km long and 1.9 km wide, to simplify the response of the wind to the idealized bathymetry similar to that of the Fangar Bay. The first was of a homogeneous depth of 4 m (GEO 1). The second was variable bathymetry (v-shape channel with 1 m to the sides up to 4 m in the central part, GEO 2). The same experiment was then conducted, but reducing the mouth of the channel to simulate the narrow entrance of the Fangar Bay (GEO 3). Finally, it was simulated to include variable bathymetry (GEO 4). Experiments were conducted up-bay wind and down-bay wind according to the axis of the estuary (wind spatially homogenous). An additional simulation took into account the Coriolis effect for GEO 1 to verify the influence of the Earth's rotation. All simulations are summarized in Table 2. Constant temperature (20 \({}^{\circ}\)C) and salinity (36) conditions were applied. Freshwater inputs were deactivated in order to observe the behaviour of the currents only as a function of wind and bathymetry. The bottom boundary layer was parameterized with a logarithmic profile using a characteristic bottom roughness height of 0.002 m. The turbulence closure scheme for the vertical mixing was the generic length scale (GLS) tuned to behave as a k-\(\epsilon\)[29]. Horizontal harmonic mixing of momentum was defined with constant values of 5 m\({}^{2}\)-s\({}^{-1}\). Long-term simulations (around 2 months each) were performed in order to analyze the wind response avoiding spurious velocities. The wind is constant throughout the simulation. According to  
\begin{table}