## 3 Data and Methods
### Wave Climate  
The wave parameters, including the significant wave height Hs (m) and the peak period T (s), were measured by an offshore buoy located in the northwest of Sardinia (Alghero buoy) and are available online from the Rete Ondametrica Nazionale website (ISPRA-R.O.N., [[http://dati.isprambiente.it/dataset/ron-rete-ondametrica-nazionale/](http://dati.isprambiente.it/dataset/ron-rete-ondametrica-nazionale/)]([http://dati.isprambiente.it/dataset/ron-rete-ondametrica-nazionale/](http://dati.isprambiente.it/dataset/ron-rete-ondametrica-nazionale/)) accessed on 30 March 2021). These data have been used to define the wave climate on the western side of Sardinia.  
The averaged Iribarren number (\(\xi_{0}\)) was calculated for each mean beach profile and obtained as the averaged value considering the whole surveyed period (from 12 September 2010 to 13 May 2011), the obtained value was reported in Table 1. Furthermore, the dimensionless fall velocity \(\Omega\)[50] (the mean values for the period between the topographic survey, as shown in [51]) was calculated for each beach.  
\[\Omega=\mathrm{H_{b}}/w_{\mathrm{s}}\mathrm{T}, \tag{1}\]  
The breaking wave height \(\mathrm{H_{b}}\) (m) used to compute \(\Omega\) was derived from the Komar and Gaughan [52] formula, as follows:  
\[\mathrm{H_{b}}=0.39\mathrm{g}^{0.2}(\mathrm{TH_{0}}^{2})^{0.4}, \tag{2}\]  
where g is the acceleration due to gravity, T the peak period (s), H\({}_{0}\) (m) is the significantly deeper wave height and _ws_ (m s\({}^{-1}\)) is the average settling velocity (Table 1).  
The'storm power index', as defined by [PERSON] et al. [53], was calculated to define the strength of the storms that occurred during the monitored period, as follows:  
\[\mathrm{Ps}=\mathrm{Hs^{2}}_{\mathrm{max}}\mathrm{D}, \tag{3}\]  
where Hs max (m) is the maximum significant storm wave height, D is the duration of the storms in hours, and Ps is expressed in (m\({}^{2}\) h). The storms are defined as events occurring for more than 6 h consecutively, which account for wave heights higher than 2 m for all the considered intervals [54].  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Mari Erm Profiles Variations (m\({}^{3}\) m\({}^{-1}\))**} & \multicolumn{3}{c}{**Is Arutas Profiles Variations (m\({}^{3}\) m\({}^{-1}\))**} & \multicolumn{3}{c}{**[PERSON] Profiles Variations (m\({}^{3}\) m\({}^{-1}\))**} \\ \hline
**Survey Number** & **Northern** & **Central** & **Southern** & **Norther** & **Central** & **Southern** & **Northern** & **Central** & **Southern** \\ \hline O–S & \(-\)6.8 & & \(-\)0.7 & \(-\)19.8 & \(-\)3.7 & \(-\)6.3 & \(-\)6.9 & 5.0 & 1.9 \\ N–O & & \(-\)8.7 & 3.2 & & 14.5 & 1.1 & \(-\)13.3 \\ D–N & \(-\)6.5 & \(-\)0.9 & \(-\)10.8 & 41.3 & 14.1 & \(-\)36.3 & \(-\)65.3 & \(-\)32.0 & \(-\)15.6 \\ J1–D & 6.4 & 16.0 & 4.9 & \(-\)12.1 & 7.5 & 22.2 & 38.6 & 6.3 & 4.4 \\ J2–J1 & 1.3 & \(-\)3.5 & 0.5 & \(-\)5.4 & \(-\)0.7 & 2.0 & 1.0 & \(-\)4.3 & 1.9 \\ F–J2 & \(-\)10.7 & 8.0 & 15.8 & \(-\)3.0 & \(-\)14.9 & 9.4 & \(-\)9.2 & 17.8 & \(-\)11.8 \\ Ma–F & 18.9 & \(-\)13.7 & \(-\)24.7 & 1.2 & 3.7 & \(-\)15.6 & \(-\)0.1 & \(-\)6.5 & 17.6 \\ A–Ma & \(-\)1.7 & 2.6 & 5.4 & \(-\)1.4 & \(-\)2.7 & \(-\)9.1 & \(-\)1.5 & 24.6 & 4.0 \\ My–A & 3.1 & \(-\)7.2 & 7.4 & \(-\)12.1 & 0.5 & 6.0 & 10.7 & \(-\)15.0 & \(-\)13.1 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The volumetric changes along the beach profiles during the date of the topographic survey. For cross correlation analyses, the second rows were not considered. The letters indicated the date of the topographic survey (see Table 1 caption).