## 5 Sea Conditions Analysis of the Sea Storm Event of 28 December 2020
#### Tidal Analysis  
The wind waves are superimposed on the sea surface level, which oscillates because of astronomical and barometric forcing. Therefore, it is necessary to evaluate the altimetric oscillations of the sea surface to establish the level of the crests and correctly relate them with the coastal infrastructures. The sea level data collected by two tide gauges located in the Port of Naples and Gulf of Pozzuoli were used to evaluate the altimetric oscillations of the sea level during and before the sea storm (Figure 16). The maximum uplift of the sea surface level is equal to 0.308 m, including the astronomical and barometric contribution. The maximum astronomical tidal amplitude occurs in the sigitial phase, with the following values for the study area [43]:  
* maximum rise in sea level: \(S_{\text{m}}(+)=+0.21\) m,
* maximum lowering of sea level: \(S_{\text{m}}(-)=-0.21\) m.  
The atmospheric pressure contribution \(S_{\text{AP}(+)}\), the storm wind surge S and the uplift due to breaking wave motion contributions are considered for the definition of the meteorological tide. The sea surface undergoes a change in level of 0.0101329 m for each hPa of variation in the barometric pressure, in reference to the normal atmospheric pressure equal to 1013.2 hPa. In our case, we have:  
\[S_{\text{AP}(+)}=0.0101329\text{ m}\cdot hPa^{-1}\cdot(1013-996)\text{ hPa}=0. 17\text{ m}. \tag{8}\]  
For the calculation of wind-induced surge, the following relation [48] to be solved by successive attempts was adopted:  
\[S=\frac{K_{\text{p}}\,L_{\text{p}}\,U^{2}}{g\left(D-d-S\right)}\ln\frac{D}{d+S }\,, \tag{9}\]  
Figure 16: Sea surface oscillation in the Gulf of Naples on 27–29 December 2020 (Time: UTC). The diagram shows the stormy phase. where:  
- \(\rm K_{p}=3\times 10^{-6}\),  
- \(\rm G=9.8065\ m\ s^{-2}\),  
- \(\rm d=depth\) of the seabed at the point where the surge is calculated, assumed to be 0 m,
- \(\rm D=limit\) depth assumed for the continental shelf, assumed to be \(-200\ m\),  
- \(\rm U=constant\) storm wind speed (set equal to 14.4 m s\({}^{-1}\) for the event under consideration), and  
- \(\rm L_{p}=extension\) of the continental shelf (distance between d and D) equal to 15,000 m.  
The relation has converged by successive attempts to the solution of \(\rm S\approx 0.03\ m\). In the absence of wind shear effects, offshore waves break in sections characterized by a well-defined depth, thus inducing a rise of sea surface level. Along the coastal zone confined between the breakers line and the shoreline, the sea level undergoes a lowering in the wave breaking area (wave set-down) and a subsequent raising towards the shore (wave set-up). The calculation of the two terms (set-down and set-up) can be performed through the following formula:  
\[\rm S_{up}=\Delta S-S_{dw}, \tag{10}\]  
with:  
\[\Delta S=0.15\ h_{b}, \tag{11}\]  
\[\rm S_{dw}=(0.536\cdot H_{b}(^{3/2}))/(g^{1/2}\cdot T), \tag{12}\]  
where:  
- \(\rm H_{b}=H_{c,tot}\) = reference wave height at breaking = 4.5 m,  
- \(\rm T=period\) related to reference wave at breaking = 7.8 s,  
- \(\rm h_{b}=depth\) of sea bottom at breaking = 1.3 Hb = 5.85 m,  
- \(\Delta S=0.15\ hb=0.88\ m\),  
- \(\rm S_{dw}=0.536\ H_{b}(^{5/2})/g^{1/2}\ T=0.21\ m\), and  
- \(\rm S_{up}=0.88\)-\(0.21=0.67\ m\).