## 3 Results and Discussion
### Historical Storm Surge Event, January 2019
#### 3.1.4 Numerical Simulation  
In order to validate the results of modeling the storm surge using the two-dimensional HEC-RAS model, a numerical simulation of the historical episode described above was performed. To achieve this, the flow area was represented using a rectangular numerical grid with a mesh size of 100 \(\times\) 100 m (Figure 5).  
The hydrostatic state was used as the initial condition, assuming a water level of \(-\)0.11 m asl. In the computational options of the HEC-RAS program, the dynamic wave model, described in the manual [24] as shallow water equations with a Eulerian-Lagrangian approach to solving for advection (SWE-ELM), was selected as the mathematical model of the hydrodynamics. The wind shear stress was modeled using the Hsu concept [45], lagoon's bottom friction was given as a constant value of Manning's roughness coefficient  
Figure 4: Wind parameters measured by IMGW-PIB.  
Figure 5: HEC-RAS 2D numerical mesh (gray grid) against the background of DEM (color scale).  
0.025 m\({}^{-1/3}\cdot\)s and turbulent viscosity was neglected. In the present study, turbulent viscosity was neglected due to the large spatial and temporal scales considered, where the dynamics of the shallow coastal lagoon are primarily governed by gravitational and inertial forces [46]. The conditions forcing the water movement in the lagoon were the evolution of the sea state in the Gulf of Gdansk according to IMGW-PIB observations (Figure 3) and the measured changes in wind parameters according to the graph in Figure 4. The same wind action was assumed at each point of the Vistula Lagoon water surface, although the measurement came from a single station (Nowa Pasleka), which is a significant simplification of the meteorological situation. The total simulation time was 6 days, and the calculations were performed with a time step of 5 min.  
Figure 6 shows the longitudinal profiles of the water surface, along the SW-NE axis of the lagoon, calculated with the HEC-RAS model at selected time moments (at 12 a.m. each day).  
These illustrate the evolution of the spatial distribution of the surge from the Polish to the Russian end of the lagoon. During the storm surge event, significant water level fluctuations occurred due to strong wind-driven water displacement. Initially, on 1 January, the water table was horizontal (\(-0.11\) m asl). Then, on 2 January, the first water accumulation was observed in the northeastern (Russian) part of the lagoon, where the maximum water level exceeded 0.2 m. This indicates that strong winds initially pushed water towards the northeast. However, on 3 January, a sudden reversal occurred, with the highest water level recorded at over 1.3 m asl in the Polish section, while the lowest water level was observed in the northeastern part. This suggests a strong storm-driven backflow, pushing water back towards the southwest. From 4 January onward, the water levels gradually decreased, with the highest level still observed in the Polish end (0.55 m), but significantly lower than the peak on 3 January. By 5 January, water levels continued stabilizing, with water re-accumulation at the Polish side. This sequence of water level changes clearly illustrates the two-phase storm surge dynamics, where the first phase involved water accumulation in the northeastern part, followed by a strong backflow and peak water level in the Polish section, before finally subsiding. These calculated variations highlight the dominant influence of wind-driven water movement and are consistent with observations.  
Figure 6: Calculated longitudinal profiles of the water surface in the Vistula Lagoon.