4.4.1. The Wave Run-Up Height Index IRU

IRU2% levels were obtained by calculating the run-up values Ru2% and the related parameters XRu2% and XRu2%/L (width of the beach affected by run-up and relative percentage) for the beach profiles P1–P7 and C1–C5 for years 2019, 2020, and 2021 (Tables 8 and 9). Both normal wave (Hs = 0.7 m) and average extreme wave conditions (Ht = 3.5 m) were considered.


**Table 8.** Estimated run-up index values IRu2% and related parameters XRu2% and XRu2%/L under normal wave (Hs = 0.7 m) and average extreme wave conditions (Ht = 3.5 m).

**Table 9.** Evaluation of short-term erosion indexes IR for profiles P1–P7 and C1–C5, based on R values calculated for normal wave (Hs = 0.7 m) and average extreme wave conditions (Ht = 3.5 m), respectively.


Regarding test area A, the results highlight the stable run-up height conditions under normal wave conditions (Hs = 0.7 m) from 2019 to 2021, with indexes **IRu2%** maintaining a minimum value of 1 for all profiles.

However, with regard to mean extreme wave conditions (Ht = 3.5 m), IRU2% levels reached values between 2 and 3 in 2019 (P5 and P7, Table 8). In 2020, several negative variations in the IRU2% levels were registered in the northern (P1–P2) and especially in the southern part (P5–P7) of the test area, where maximum values of 4 were calculated. Then, in 2021, both negative and positive variations were registered for parts of the profiles, resulting in final values between 2 and 4, and a condition substantially similar to that in 2020.

Regarding test area B, data highlight overall higher IRU2% values under normal wave conditions (Table 8) for 2019 when compared with test area A, as well as several positive and negative variations in the IRU2% values from 2019 to 2021, oscillating between 1 and 4. These variations, however, do not suggest any persisting positive or negative trend. Worthy of mention is the IRU2% value of C3, which remained equal to 1 during all the three years.

When considering the average extreme wave conditions, all profiles were characterized by a maximum IRU2% value of 4 in 2020 and 2021, except for C3 (IRU2% value of 2, Table 8). This result highlights the generally worse run-up conditions of this beach during average extreme wave conditions, which can be generally related to the scarce width of the backshore. This is not the case for C3, i.e., the central portion of test area B, where the backshore is significantly wider and undergoes only a slight restriction from 2019 to 2021 (from 24.1 m to 20.0 m, Table 4). In this case, the increase of the run-up index value to 4 can be related to the decrease of the foreshore slope (from 10% to 5.3%, Table 5). In fact, as illustrated in Section 4.2, this portion of the beach has undergone important human interventions, resulting in enlargements, levelling, and the overall topographic lowering of the beach. Therefore, in our opinion, the worsening of the run-up conditions along C3 in 2021 is most likely related to these human interventions, showing that the latter did not contribute to the maintenance of the beach but, conversely, contributed to its major vulnerability to erosion.
