*3.3. Coastal Vulnerability Assessment*

The vulnerability to coastal erosion and inundation was evaluated for the test areas by means of the Coastal Vulnerability Assessment (CVA), a method developed by Di Paola et al. (2014) [37], starting from the preliminary approach used for the coastal vulnerability assessment of several coastal areas [37–40]. For the vulnerability evaluation, the CVA method allowed us to consider both the beach retreat due to storm surges (using wave climate and geomorphological data such as bathymetry, beach sedimentology, and beach width) and the coastal inundation due to run-up on the beach. To this aim, morphosedimentary beach features, wave climate, and multi-temporal series of aerial photographs and topographic maps were analysed.

In detail, the CVA method evaluates the coastal vulnerability for each considered period according to the following equation:

$$\text{CVA} = \text{I}\_{\text{Ru}} + \text{I}\_{\text{R}} + \text{E} + \text{T}\_{\text{i}} \tag{1}$$

where IRu is the wave run-up height index, which is given by the run-up level divided by the beach foreshore slope [41]; IR is the short-term erosion index, which provides a measurement of the maximum beach recession due to storms, normalized with the beach width [42]; E is the beach erosion rate in m/y, and Ti measures the horizontal distance travelled by the tidal range. In this work, Ti = 0, because the Molise coast is microtidal and experiences ordinary tidal excursions of 30–40 cm [21].

The IRu index provides the measurement of the potential inundation capacity that characterizes natural beaches during wave storms. According to Stockdon et al. [41], the wave run-up height is provided by Ru2%, i.e., the wave run-up level exceeded by 2% of the number of incoming waves, which is measured vertically from the still water line. This value is projected along the beach through the calculation of XRu2%, which corresponds to the horizontal distance travelled by the wave in the run-up process. Therefore, IRu takes on values that depend on the percentage associated with the maximum horizontal run-up distance of the wave on the beach (XRu2%), which is normalized with respect to the width of the emerged beach (L). In this way, the IRu index can be customarily clustered into four discrete levels, as shown in Table 3.


**Table 3.** Coastal vulnerability assessment (CVA) classification scheme (according to [37]).

The IR index instead provides the measurement of the potential beach retreat and is used for the dynamical calculation of the shoreline retreat based on the convolution method of Kriebel and Dean (1993) [42]. IR values depend on the percentage associated with the maximum beach retreat (Rmax), normalized with the beach width L. As a result, IR values depend on the percentage associated with Rmax, normalized with respect to the width of L. In addition, the IRu and IR indexes can be customarily clustered into four discrete levels (Table 3).

Considering that the evolution of a beach is not only linked to the effects produced by coastal inundation during extreme events (Ht = 3.5 m, Table 1) but also to those caused by ordinary wave dynamics (Hs = 0.7 m, Table 1), the parameters IRu and IR were calibrated considering both conditions, using Formula (2) and (3), respectively.

$$\mathbf{I}\_{\rm Ru} = \left(\mathbf{I}\_{\rm Ru\ (\rm H}\right) + 2 \cdot \mathbf{I}\_{\rm Ru\ (\rm H}\right) / 3 \tag{2}$$

$$\mathbf{I}\_{\rm R} = \left(\mathbf{I}\_{\rm R\ (H\_s)} + \mathbf{2} \cdot \mathbf{I}\_{\rm R\ (H\_t)}\right) / 3\tag{3}$$

Regarding the E index, the evolution of the shoreline in the mid-term (periods 1954– 2004 (E1) and 2004–2016 (E2)) and the short term (periods 2016–2019 (E2019), 2016–2020 (E2020), and 2016–2021 (E2021)) were considered. To this aim, we used the indications proposed by Cromwell [43], following Equation (4).

$$\mathbf{E} = \left(\mathbf{E}\_1 + \mathbf{2} \cdot \mathbf{E}\_2 + \mathbf{3} \cdot \mathbf{E}\_{2019/2020/2021}\right) / 6\tag{4}$$

The E index can be customarily clustered into four discrete levels (Table 3).
