## 3 Results
### Average Wave Overtopping Discharge
Table 3 reports the values of the most common metrics used to assess the prediction effectiveness: the Nash-Sutcliffe model efficiency parameter NSE, the Mean Absolute Error MAE, the Root Mean Squared Error RMSE and the Normalized Root Mean Squared Error NRMSE. They are defined as follows:  
\[\rm NSE\ =\ 1-\sum\
olimits_{i=\ 1}^{n}\left(y_{i}-x_{i}\right)^{2}/\sum \
olimits_{i=\ 1}^{n}\left(\overline{x}-x_{i}\right)^{2} \tag{7}\]  
\[\rm MAE\ =\ \sum\
olimits_{i=\ 1}^{n}\left|y_{i}-x_{i}\right|/n \tag{8}\]  
\[\rm RMSE\ =\ \left[\sum\
olimits_{i=\ 1}^{n}\left(x_{i}-y_{i}\right)^{2}/n \right]^{0.5} \tag{9}\]  
\[\rm NRMSE\ =\ n\cdot RMSE/\sum\
olimits_{i=\ 1}^{n}\left(y_{i}\right) \tag{10}\]In the previous formulae from Equation (7) to Equation (10), n is the total number of observations; \(\rm x_{i}\) and \(\rm y_{i}\) are the measured and predicted values, respectively, at the data point i; and \(\rm\overline{x}\) is the average value of the experimental data. The values of NSE of Table 3 are always smaller than 0.50, and this demonstrates that the reliability of the herein considered equations is very poor. Given the relevant inaccuracy of the standard relations to predict \(\rm q_{\rm Pear}\)*, the observed overtopping discharges are also compared with some reference formulae derived to take the reducing effect of a storm wall with a nose and of the combination of a storm wall, a nose and a promenade into account. In the first scenario, EurOtop Manual [30] suggested to calculate \(\rm q_{\rm Pear}\)* as follows:  
\[\rm q_{\rm Pear}\text{*}=0.09\cdot exp\{-[1.50\cdot(R_{c}/H_{m0})\cdot 1/(\gamma_{v }\gamma_{par}\gamma_{s0,par})]^{1.3}\} \tag{11}\]  
where \(\gamma_{v}\) is a storm wall influence factor defined, for \(\rm h_{wall}/R_{c}<1.24\), as follows [26]:  
\[q_{\rm rear}*=0.2\cdot\exp(1.57\cdot\cot\alpha-4.88) \tag{4}\]0  
Moreover, \(\rm\gamma_{par}\) considers, instead, the extra-reducing effect related to the presence of the nose on the storm wall. [PERSON] et al. [60] defined \(\rm\gamma_{par}\) as a function of \(\rm\gamma_{\epsilon}\) and \(\rm\gamma_{\lambda}\). These factors were introduced to describe the influence of \(\rm\varepsilon\) and \(\rm\lambda\), respectively, and, for \(\rm h_{w}/R_{c}\geq 0.25\) (Table 1), they give \(\rm\gamma_{par}\) as follows:  
\[q_{\rm rear}*=0.2\cdot\exp(1.57\cdot\cot\alpha-4.88) \tag{4}\]1  
\[q_{\rm rear}*=0.2\cdot\exp(1.57\cdot\cot\alpha-4.88) \tag{4}\]2 Measured and predicted dimensionless average overtopping discharge against the relative free-board of the crown wall. \begin{table}
\begin{tabular}{c c c c} \hline  & **Equation (3) [30]** & **Equation (4) [58]** & **Equations (3), (5) and (6) [59]** \\ \hline NSE & 0.46 & \(-1.81\) & 0.36 \\ MAE & \(3.35\times 10^{-4}\) & \(1.98\times 10^{-3}\) & \(3.13\times 10^{-4}\) \\ RMSE & \(1.04\times 10^{-3}\) & \(2.38\times 10^{-3}\) & \(1.13\times 10^{-3}\) \\ NRMSE & 2.61 & 0.97 & 4.51 \\ \hline \end{tabular}
\end{table} 
Table 3: Statistics of the accuracy of [30; 58; 59] in the prediction of \(\rm q_{\rm Pear}\)*. where \(\gamma_{\epsilon}=(1.53\times 10^{-4}.\epsilon^{2})-(1.63\times 10^{-2}. \epsilon)+1\), for \(15^{\circ}\leq\epsilon\leq 50^{\circ}\), and \(\gamma_{\lambda}=0.75-0.20\lambda\), for \(0.125\leq\lambda\)\(\leq\) 0.6 (Section 2.2) [60]. In the end, \(\gamma_{\text{s0,par}}\) aims to account for the wave overtopping increase due to \(\mathsf{s}_{\text{m}-1,0}\). In this regard, [PERSON] et al. [60] suggested to apply the following equation for \(\gamma_{\text{s0,par}}\):  
\[\gamma_{\text{s0,par}}=1.33-10\cdot\mathsf{s}_{\text{m}-1,0} \tag{14}\]  
When a storm wall equipped with a nose is placed at the end of a promenade, EurOtop Manual [30] provides the following equation to derive \(\mathsf{q}_{\text{rear}}\)*:  
\[\mathsf{q}_{\text{rear}}\text{*}=0.09\cdot\exp\{-[1.50\cdot(\text{R}_{\text{c} }/\text{H}_{\text{m}0})\cdot 1/(1.19\cdot\gamma_{\text{par}}\cdot\gamma_{\text{prom} })]^{1.3}\} \tag{15}\]  
in which the reducing factor, \(\gamma_{\text{prom}}\), models the effect due to the promenade.