**3. Application of the methods**

This section aims to illustrate the application of the described methods showing their general performances by means of two applications to real cases. The forecast method is applied to the northern part of the Adriatic Sea, while the hindcast one to the southern Adriatic Italian coast.

### **3.1 Forecast method: the case of Venice**

This section shows an example of the application of the forecast method to a POI located in the northern part of the Adriatic Sea. For this basin, storm surges are mainly due to Atlantic perturbations (i.e. cyclones). Due to the presence of the continental shelf and considering thermal effects, the perturbations are amplified [45]. A famous example of these effects is Venice and the phenomenon of "acqua alta" causing the partial or total flooding of the city with damage to historical monuments, economy and private buildings. The recent flooding event of November 2019 has been supposed to damage the city for 4 billion of euros.

The physical characteristics of the weather conditions can induce resonance phenomena (e.g. [14–16]) with level oscillations persisting for several days in the whole basin [46].

The worst situation for the Adriatic Sea in terms of storm surge is when the perturbations come from south-east (i.e. "sirocco winds") and propagate along the main axis of the basin (e.g. [45]).

The Adriatic Sea has been discretized in 19 areas (*N* ¼ 19). The forecast wind and pressure data have been taken by the European Centre of Medium-Range Weather Forecast. The dimension of each area is 0.25° (see **Figure 1**).

The unit wind response functions have been estimated for each of the 19 areas using the "regional ocean modelling system" (ROMS, e.g. [42, 47]). Due to the particular geographical conditions and to the prevalent wind directions (i.e. Sirocco), only the wind stress component acting along the main axis of the Adriatic Sea (i.e. ≃ 324°N) has been used. A sensitivity analysis shows that results are the same using both *U* and *V* wind components but limiting the computational effort. This means that also the constitutive equation (3) reads as

$$\eta(t\_k) = \sum\_{i}^{N} \sum\_{j=1}^{j \le M} R\_j F\_i(t\_k - j\Delta t + \Delta t) \tag{6}$$

where *Rj* is the projection of the wind stress vector along the main axis of the basin and *Fi* is the unit response function for unit wind stress blowing along the main axis of the basin at the *i*th area.

About the simulations, the grid resolution is 3<sup>0</sup> (i.e. about 5500 m, 175 � 185 computational points) including all the Adriatic Sea and a portion of the Ionian Sea (**Figure 1**). The "Etopo1" bathymetry has been used [48]. The coasts have been modelled with wall boundary conditions, while in the southern part, a radiation condition has been imposed (e.g. [46]). Each of the 19 simulations differs from others for the area in which the wind has been imposed. The duration of the wind

### **Figure 1.**

*Illustration of the discretization of the basin. The black circles indicate the POIs, while the grey arrow indicates the direction of the main axis of the basin.*

*Simplified Methods for Storm Surge Forecast and Hindcast in Semi-Enclosed Basins: A Review DOI: http://dx.doi.org/10.5772/intechopen.92171*

impulses is 6 hours (ECMWF resolution), and the response functions were given with a time resolution equal to Δ*τ* = 900 s. **Figure 2** shows an example of the computed response functions for two areas located in two different locations in the basin.

The wind stress values have been computed on the basis of wind speed by using the relationship proposed by Drago and Iovenitti [49]

$$R\_j = \chi\_s \mathbf{W}\_l |\mathbf{W}| \tag{7}$$

where *Wl* is the wind speed component along the main direction ≃324°N and *W* is the actual wind speed. The factor *γ<sup>s</sup>* is linked to the wind speed (e.g. [50]):

$$\gamma\_s = 6.9 \cdot 10^{-4} + 7.5 \cdot 10^{-5} |W| \tag{8}$$

**Figure 3** shows the performances of the forecast method. The figure shows some typical results illustrating the forecasted storm surge level (dashed grey line), the

**Figure 2.** *Example of the computed response functions for two different areas.*

**Figure 3.**

*Comparison between the forecasted storm surge level (dashed grey line), the measured storm surge level (triangle symbols), the forecasted total tide level (dashed black line) and the measured total tide level (black circles).*

measured storm surge level (triangle symbols), the forecasted total tide level (dashed black line) and the measured total tide level (black circles). The measurements have been taken using the records in the mareographic station (45.41°N, 12.44°E) located on Lido mouth (Italian National Mareographic Network). It is also illustrated in the figure the total measured tide level (grey cross symbols) and the forecasted one (solid grey lines). The harmonic component has been evaluated by means of [17] considering seven components (M2, S2, N2, K2, K1, O1, P1) as suggested in the literature (e.g. [51]).

The statistical correction have been made training 48 ANNs, one for each increasing lead time (Δ*tn* = *n*-hours, *n* = 1, 2, ..., 48). The used ANNs are multilayer networks with an input vector, two hidden layers and one output value (the storm surge). The training has been made using a back-propagation algorithm. In this case, a Levenberg–Marquardt algorithm has been used. The learning phase of the ANNs covered 3 years (2009–2011); the testing period is referred to as the year 2012, while the validation period is the year 2013.

As it is possible to see, inspecting **Figure 3**, the training phase confirms the good performances of the algorithm, and, in the validation step, at least from a qualitative point of view, it is possible to appreciate the accuracy of the model.

Talking about quantitative performances, a series of statistical parameters have been evaluated. Mean (*μ*) and standard deviation (*σ*) of the differences between predicted and observed total tide have been computed for the years 2009–2011 (training period), year 2012 (testing period) and year 2013 (validation period, e.g. [34, 47]). **Table 1** summarizes the results of the statistical analysis. It is important to observe that the absolute value of the mean is always lower than about 0.04 m, while the standard deviation (that increases as the lead time increases) ranges between 0.05 m and 0.10 m.

The comparison between the obtained results and those available in the literature (e.g. [34]) reveals that the gained reliability is satisfactory if the simplicity and computational costs of the method are considered.


**Table 1.**

*Mean (*μ*) and standard deviation (*σ*) of the differences between foreseen and measured total tide level as a function of lead time.*

*Simplified Methods for Storm Surge Forecast and Hindcast in Semi-Enclosed Basins: A Review DOI: http://dx.doi.org/10.5772/intechopen.92171*
