*4.4. Trends: Shoreline, Volume, and Seabed Elevation*

The trends of the shoreline position, emerged beach volume, and seabed elevation were estimated for the three sites during the study period. The rates of shoreline change were calculated using the shoreline (*z* = 0) extracted from the UAV flight data (San Miguel and El Teresiano) and DGPS surveys (El Faro). The rate of volume change and seabed elevation were calculated for the emerged section of each DGPS surveyed beach profile, considering *z* = −0.5 m to be the depth of the end of the emerged beach. The three beaches showed similar behavior with respect to trends in the shoreline position and in the emerged beach volume, with positive values in the eastern sections of the beach and less positive or negative values in the western sections. However, the magnitude and extension of the region with positive trends varied widely between sites.

San Miguel beach (Figure 11) showed the highest positive and negative shoreline trends of the three beaches. In the shadow area of the eastern section of the structure, the change rate was as high as 30 m/year. On the other hand, in the western section, the shoreline trends were negative—even in the shadow area of the structure—with values as low as −20 m/year in the down-drift section (Figure 11b). Although the original flight path considered approximately 350 m on the western side of the structure, there was clear evidence that the negative trend extended as far as 500 m in the down-drift side. The change in the emerged beach volume showed similar trends with values ranging between +39.1 and −8.3 m3/m/year (Figure 11c). The beach presented a large accumulation of sediment in the eastern section of the study area. Figure 11d presents the rate of change in the elevation between 27 April 2017 (before the deployment of the structure) and 7 March 2018. In certain regions, the increase in beach elevation over the course of one year was larger than +1.5 m near the salient, whereas the decrease in the down-drift (western) locations reached values larger than −1.0 m.

**Figure 11.** San Miguel beach (**a**) mosaic of the section of beach covered by the UAV flights with the location of the impermeable structure highlighted in black and parallel lines marking the high-resolution differential global positioning system (DGPS) profiles; (**b**) rate of change of the shoreline position during the study period obtained from UAV surveys; (**c**) rate of change of the emerged beach volume during the study period obtained from DGPS surveys; and (**d**) change in elevation between the last (7 March 2018) and first (27 April 2017, no structure) DGPS surveys.

El Teresiano (Figure 12) displayed a similar pattern, although (i) positive trends showing an advance in the shoreline position were below 20 m/year, (ii) the region where the shoreline trends were positive covered a wider section along the beach, and (iii) the negative trends also showed smaller values (>−5 m/year, Figure 12b). Regarding the volume, the trends varied between +10.8 and −3.5 m3/m/year (Figure 12c). As presented in Figure 12d, the increase in elevation between 27 April and 18 April 2018 reached values similar to that in San Miguel (Figure 11d). However, the maximum decrease in elevation near the shoreline and in the emerged beach was found to be −0.4 m, less than half that in San Miguel.

**Figure 12.** El Teresiano beach (**a**) mosaic of the section of beach covered by the UAV flights with the location of the impermeable structure highlighted in gray and parallel lines marking the high-resolution DGPS profiles; (**b**) rate of change of the shoreline position during the study period obtained from UAV surveys; (**c**) rate of change of the emerged beach volume during the study period obtained from DGPS surveys; and (**d**) change in elevation between the last (18 April 2018) and first (27 April 2017, no structure) DGPS surveys.

As for El Faro (Figure 13), the shoreline advance trends were positive on the lee side of the structure, with values below 6 m/year (Figure 13b). The trends in the emerged beach volume between 4 May 2017 and 25 April 2018 varied between +8.0 and −4.3 m3/m/year. Changes in elevation after the deployment of the structure were less important at this site, with maximum increases of +0.6 m and decreases of −0.2 m.

**Figure 13.** El Faro beach (**a**) aerial picture taken by the UAV flights with the location of the permeable structure highlighted in gray and parallel lines marking the high-resolution DGPS profiles; (**b**) rate of change of the shoreline position during the study period obtained from DGPS surveys; (**c**) rate of change of the emerged beach volume during the study period obtained from DGPS surveys; and (**d**) change in elevation between the last (25 April 2018) and the first survey (4 May 2017, no structure) DGPS surveys.

#### **5. Discussion**

A major problem with LCDB design is the difficulty of predicting the morphodynamic response on the lee side of the structure [7]. Empirical formulations, relating the distance to the tip of the salient *Xoff*, the length of the structure *B*, and the distance to the undisturbed shoreline position *S*, predict a power curve relationship given by the following:

$$X\_{off} = aB\left(\frac{B}{S}\right)^b$$

where the size of the salient *Ys* = *S* − *Xoff* and the parameters *a* and *b* are those proposed by [18] and [17] for a single emergent breakwater (*a* = 0.68 and *b* = −1.22), reefs (*a* = 0.50 and *b* = −1.27), and islands (*a* = 0.40 and *b* = −1.52), respectively.

A distinct morphological response of the beach salient was observed in the three sites. The maximum shoreline salient size was measured in San Miguel, followed by El Teresiano and El Faro, respectively (Table 3 and Figures 11b, 12b and 13b). Empirical formulations (e.g., [17,18]) were employed, finding a satisfactory agreement for San Miguel (Table 3). This suggests that the beach response associated with a sand-filled geosystem can be predicted by the formulation developed by [17] for reefs. However, large differences between the observations and model predictions for El

Teresiano were found (Table 3). The latter can be ascribed to the continuous loss of sand in the middle sections of the geosystem (Figure 7b), which transformed a 140-m long breakwater into two 40-m long breakwaters separated by a 60 m gap. Applying the model developed by [17] to the case of El Teresiano for a 40-m breakwater predicted the size of the salient accurately (i.e., *Ys* = 20 m). On the other hand, the shoreline salient on the lee side of the breakwater at El Faro was not predicted by any model, owing to the high transmissivity through the modules and the gaps between the sections. The formulations by [18] consistently underpredicted the salient size for impermeable LCDBs.


**Table 3.** Measurements and predictions of shoreline salient size *Ys* at the three sites.

Sand-filled geosystems are highly vulnerable to vandalism in this area, and hence, the useful life of the structure can be drastically reduced. Furthermore, the tearing apart of the geotube sections plays an important role in beach evolution, leaving behind emptied geotextiles that are difficult to remove; moreover, the degradation of such geotextiles might have a negative ecological impact. It is not clear how the effect LCDBs with sand-filled geosystems can be correctly predicted if they are so prone to tearing and subsequent deflation.
