## 3 Data and Methods
### Beach Profiles  
Positioning data along three cross-shore transects were acquired in the northern, central and southern areas of the subaerial domain of each beach (Figure 2a-c) from September 2010 to May 2011. The beach profiles were surveyed 9 times in the Mari Ermi and Is Arutas beaches and 10 times in Maimoi beach. In Table 1, a summary of the beach profile survey operations were reported. Differential global positioning system (DGPS) technology was used to collect position data (X, Y, Z), with an accuracy of 7 cm on both the horizontal and vertical axes. The data were referred to the mean sea level of the IGM 95 Italian Geodetic National net (Rete Geodetica dell'Istituto Geografico Militare). The measured beach profiles started from the landward boundary of the beach, marked by the presence of vegetation or other features (man-made structures or physical limits), down to a depth of about 1 m below sea level. The position point (X, Y, Z) was collected every 2.5 m with the DGPS. Figure 3: (**a**) The scheme of the sampling design along a beach profile; (**b**) a scatterplot of the mean grain size vs sorting of the collected sediment; (**c**) the content of siliciclastic gravel and carbonate in the sediment collected on each beach. The labeling of each sample is characterized by the name of the beach (two letters MEMari Ermi, IA—Is Arutas, MA—Maimoi); the location of profile (N—northern, C—central, S—southern). \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \multicolumn{6}{c}{**Mari Emni**} & \multicolumn{6}{c}{**Is Arts**} & \multicolumn{6}{c}{**Mainoi**} \\ \hline Beach length (m) & 1200 & & & & 500 & & & 1000 & \\ Profiles spacing (m) & 450 & & & 150 & & & 300 & & \\  & & Profile location & & & Profile location & & & Profile location & \\  & North & Center & South & North & Center & South & North & Center & South \\ Repetition & 9 & 9 & 9 & 9 & 9 & 9 & 10 & 10 & 10 \\ Profile Length (m) & 80 & 75 & 60 & 55 & 52 & 50 & 45 & 37 & 40 \\ Min depth(m) & \(-\)1 & \(-\)1 & \(-\)1 & \(-\)1 & \(-\)1 & \(-\)1 & \(-\)1 & \(-\)1 & \(-\)1 & \(-\)1 \\ d50 (mm) & 2.74 & 1.92 & 1.96 & 1.82 & 1.78 & 1.94 & 1.98 & 1.85 & 1.68 \\ \(\alpha_{\rm b}\) (m/s) & 0.33 & 0.25 & 0.26 & 0.24 & 0.23 & 0.25 & 0.26 & 0.24 & 0.23 \\ Averaged \(\alpha_{\rm v}\) (m/s) & & 0.28 & & & 0.24 & & & & & & & & & \\ Averaged \(\delta_{\rm d}\) & 1.03 & 0.94 & 0.94 & 1 & 0.97 & 0.88 & 0.96 & 0.92 & 0.78 & \\ Survey months & S, O, D, J, J, Z, F & O, N, D, J, J, Z, & S, O, N, D, J, J, Z, F & S, O, D, J, J, Z, F & S, O, N, D, J, J, Z, F & S, O, N, D, J, J, & S, O, N, D, J, & J, \\  & Ma, A, M\({}_{\rm v}\) & F, Ma, A, M\({}_{\rm v}\) & J, Z, F, Ma, A, M\({}_{\rm v}\) & Ma, A, M\({}_{\rm v}\) & Ma, A, M\({}_{\rm v}\) & J, Z, F, Ma, A, M\({}_{\rm v}\) & J, Z, F, Ma, A, M\({}_{\rm v}\) & J, Z, F, Ma, A, M\({}_{\rm v}\) \\ \hline \end{tabular}
\end{table} 
Table 1: A summary of the relevant characteristics of the studied beaches. The letters indicate the date of the topographic survey, as follows: S = 23 September 2010, O = 22 October 2010, N = 5 November 2010, D = 14 December 2010, J = 14 January 2011, J = 17 January 2011, F = 7 February 2011, M = 4 March 2011, A = 14 April 2011, M = 13 May 2011. The vertical variation for each transect, was calculated as a standard deviation of the elevation for each point acquired along each repeated profile; the accretion/erosion volumes for each transect were also calculated considering all the profiles acquired along each transect. The variation along the beach profile section (expressed in m\({}^{3}\) m\({}^{-1}\)) was calculated between two consecutive surveys along the north and central south transect, and reported in Table 2. These values were standardized and a cross-correlation analysis was performed for the external transects (northern and southern) for each employment in order to highlight the beach rotation process [47; 48; 49]. The variation in volume from 22 October 2010 to 5 November 2010 was not considered in the analyses, because the survey of 5 November 2010 was not performed on every profile.