**Field and Numerical Study of Resistance and Resilience on a Sea Breeze Dominated Beach in Yucatan (Mexico)**

**Gabriela Medellín 1,2,\*, Alec Torres-Freyermuth 1,2, Giuseppe Roberto Tomasicchio 3, Antonio Francone 4, Peter A. Tereszkiewicz 5, Letizia Lusito 3, Leonardo Palemón-Arcos <sup>6</sup> and José López 1,2**


Received: 3 November 2018; Accepted: 1 December 2018; Published: 8 December 2018

**Abstract:** The understanding of the beach capability to resist and recover from a disturbance is of paramount importance in coastal engineering. However, few efforts have been devoted to quantifying beach resilience. The present work aims to investigate the shoreline resistance and resilience, associated to a transient disturbance, on a sandy beach. A temporary groin was deployed for 24 h on a micro-tidal sea-breeze dominated beach to induce a shoreline perturbation. Morphological changes were measured by means of beach surveys to estimate the beach perturbation and the further beach recovery after structure removal. An Empirical Orthogonal Function (EOF) analysis of the shoreline position suggests that the first EOF mode describes the spatial-temporal evolution of the shoreline owing to the groin deployment/removal. A new one-line numerical model of beach evolution is calibrated with the field surveys, reproducing both the sediment impoundment and subsequent beach recovery after the structure removal. Thus, a parametric numerical study is conducted to quantify resistance and resilience. Numerical results suggest that beach resistance associated to the presence of a structure decreases with increasing alongshore sediment transport potential, whereas resilience after structure removal is positively correlated with the alongshore diffusivity.

**Keywords:** beach resilience; beach resistance; temporary groin; sea breezes; resilience index; GSb model; Yucatan peninsula

#### **1. Introduction**

The stability of an ecosystem depends on both resistance and resilience capability to withstand a given perturbation associated to either natural or anthropogenic disturbances [1–3]. The resilience concept has been widely employed in ecological [4] and social [5] sciences and disaster risk reduction [6,7]. However, studies incorporating resilience for coastal engineering applications are scarce [8–10] and hence further research is needed [11].

The beach resistance in the coastal vulnerability context can be associated to the amount of change produced by wave events and/or due to the presence of coastal infrastructure which alter the mean pattern of sediment transport in the coastal environment; thus, it is a measure of the beach capability to resist deviations with respect to an equilibrium morphological condition. On the contrary, the beach resilience determines the speed with which the beach morphology features (e.g., dune elevation and shoreline position) return to the pre-disturbed condition [2]. Thus, the knowledge of the beach stability (i.e., resistance and resilience) is fundamental for decision-making regarding mitigation measures against beach erosion. Beach erosion in the northern Yucatan coast is critical at many locations owing to the presence of coastal structures [12,13]. Meyer-Arendt [14] reported that construction of traditional groins, made of timber and rocks, began in the 1950s and increased significantly in the late 1960s with the construction of the port infrastructure. Furthermore, beach erosion has been exacerbated during the past decade owing to the use of impermeable groins and breakwaters. Therefore, structure removal has been considered as a mitigation measure against beach erosion in this region [13]. However, no information regarding the mechanisms controlling the recovery of the shoreline position after structure removal is available.

Temporary groins have been applied in previous studies [15–17] to measure alongshore sediment transport and to calibrate sediment transport formulations. More specifically, the beach morphology changes measured in such studies have been considered for the estimation of the *K* parameter in the CERC equation [18]. However, less efforts have been devoted to investigating beach evolution after coastal structures removal. Recent studies have focused on investigating the morphodynamic responses to seafloor artificial perturbations (e.g., excavated holes and channels) in the nearshore [19–21]. Moulton et al. [20] investigated the mechanisms controlling the infill of large excavated holes in the surf zone, finding that downslope gravity-driven bedload transport was important in morphological evolution for bathymetric features with large slopes.

The present work aims to investigate the shoreline resistance and resilience on a sea-breeze dominated beach by means of field observations and numerical modelling. The main findings are that, on sea breeze dominated environments, the: (i) beach resistance to the presence of a groin is negatively correlated with the alongshore sediment transport potential; and (ii) beach resilience after the structure removal is positively correlated with alongshore diffusivity.

The outline of the paper is as follows. Firstly, the study area is presented in Section 2. The experimental setup, numerical model and data analysis are described in the Materials and Methods section (Section 3). Section 4 presents the field observations during the experiment and the numerical model calibration and verification. Then, a discussion on the mechanisms controlling the shoreline resistance and resilience is presented (Section 5). Finally, concluding remarks are given in Section 6.

#### **2. Study Area**

The study area is located on a barrier island in the northern Yucatan Peninsula (Figure 1a), at the fishing village of Sisal (see Figure 1b). This coastal region is characterized by a micro-tidal range, intense sea breeze conditions, a mild continental shelf and low energy waves [22]. The field experiment was conducted between the Port and the Sisal Pier (see Figure 1c). Winds, offshore waves and mean sea level have been measured over the past years in order to characterize the main forcing mechanisms affecting the coastal region in this area (Figure 1b,c).

Wind conditions in the study area are dominated by synoptic scale patterns (i.e., Bermuda-Azores, easterly winds, cold-fronts and tropical waves) and local sea breezes [23]. The NE sea breeze winds are present throughout the year but are more frequent and intense in May. On the other hand, Central America Cold Surge events, associated with cold-front passages, are more frequent during winter months. Cold-fronts, usually originated in the Rocky Mountains [24], are characterized by sustained winds (W > 15 m s−1) from the NNW and a high-pressure system (Figure 2a). Therefore, the mean wave climate in the study area is associated to locally generated NE waves owing to sea breeze events, with significant wave height *Hs* < 1 m (at *h* = 10 m water depth) (Figure 2b). More energetic NNW swell waves (*Hs* > 2 m and *Tp* > 7 s), associated to cold-fronts, occur during winter months (see Figure 2b). Furthermore, the presence of tropical storms is ubiquitous in the area [25,26]. Tidal regime is mixed, predominantly diurnal, with a spring and neap tidal range of 0.8 m and 0.1 m, respectively [27].

**Figure 1.** Location map showing (**a**) the Yucatan peninsula at the SE of the Gulf of Mexico, (**b**) a section of the Yucatan north coast showing the barrier island and wetlands and (**c**) the study area location, existing monitoring systems (ADCP: Acoustic Doppler Velocimeter Profile; ADV: Acoustic Doppler Velocimeter) and coastal structures.

Torres-Freyermuth et al. [22] conducted a field experiment to characterize the nearshore circulation during both intense local sea breeze events and synoptic Norte events. They found that during intense sea breeze events the alongshore currents significantly increase inside the surf and swash zones. Therefore, in the present case of a coast subjected to sea breeze conditions, the highly oblique winds (see Figure 2a) play a major role in driving longshore currents and consequently longshore transport [28–30].

The beach in the study area is composed of sand with median grain size, *D*50, equal to 0.3 mm [31]. Furthermore, it presents a shoreline orientation 14◦ south of the E-W orientation [22], which is altered near the port's jetty and the Sisal Pier. The nearshore bathymetry is characterized by the presence of a sand bar system (Figure 3), where the outer bar is relatively alongshore uniform and inner bars present a high seasonal variability. Analysis of the shoreline variability, during the intense sea breeze season (May to September, 2015), at two transects bounding the study area suggests a small (<3 m) cross-shore variation at these locations (not shown). Therefore, the temporal groin experiment was conducted between these two transects located at the middle section between the two structures (Figure 3).

**Figure 2.** (**a**) Wind and (**b**) wave roses in the study area. Wind data are taken from the Sisal weather station MeteoSisal (www.weatherunderground.com 1 January 2009–17 June 2016) and the wave data were collected from an ADCP located at 10 m water depth in front of Sisal (10 December 2013–20 April 2016). *WS* and *Hs* stand for wind speed and significant wave height, respectively.

**Figure 3.** Bathymetry measured two days before the experiment (25 May 2015), showing the study area (-), the ADV (•) and the updrift/downdrift control lines (black solid lines) locations. The study site is located between the jetty of the Sisal port entrance channel (left-hand side, gray line) and the Sisal pier (right-hand side gray feature). The color bar indicates the elevation with respect to the mean sea level.

### **3. Materials and Methods**

A description of field observations and data analysis is presented in this section. Furthermore, the numerical model employed in this work is also described.

#### *3.1. Field Experiment*

The field experiment was conducted in Spring 2015 to investigate the beach stability owing to the presence/removal of an artificial perturbation in the swash zone. Beach surveys before, during and after the structure deployment allow us to investigate shoreline resistance and resilience. We focused on a short-term sea breeze event due to: (i) the important role that sea-breeze events play in the sediment transport in the study area; (ii) the difficulties for conducting the beach surveys during more energetic wave conditions (storm conditions); and (iii) the labor-intensiveness required for obtaining high- spatial and temporal resolution morphology data for a longer period.

#### 3.1.1. Temporary Groin

The temporary groin built for this study was based on the design proposed by [16]. The groin dimensions are consistent with the typical structures found along the northern Yucatan coast. The structure was made of 0.19 m thick wood-sections of dimensions 2.40 m by 1.20 m, with holes (0.08 m diameter) drilled and covered with a 63 μm sieve cloth in order to avoid a returning offshore flow near the structure [16]. The groin consisted of seven wood sections, installed over a frame made of iron pipes and clamps; 10 m are inside the surf/swash zone within the region of active transport and the remaining 4.4 m lie on the dry beach resulting on a total length of 14.4 m. Furthermore, sandbags were spread out along the base of the structure to avoid bed scouring that could lead to sediment bypassing underneath the structure. The sand bags consisted of polypropylene woven raffia bags (60 by 100 cm) filled at approximately 2/3 of their capacity with sand.

The deployment of each section started from the land toward the sea, allowing a 0.20 m overlap between sections. Each section consisted of three vertical pipes pounded 1.5 m into the sand bed using a hammer and one horizontal pipe, holding the three pipes with scaffold clamps (Figure 4a). The original design from [16] was improved by including two horizontal members, at the down-drift side of the structure (see Figure 4a), perpendicular to the groin and attached with clamps to an additional scaffold frame. This design provided additional resistance to alongshore forces induced by wind, waves and currents. The groin deployment took approximately three hours for a team of 12 people.

**Figure 4.** (**a**) Temporary groin design made of wood-sheets, lined with sand bags and a scaffold frame of iron pipes. (**b**) Picture of the shoreline perturbation 12-h after the groin deployment.

#### 3.1.2. Data Collection

Different sensors were deployed to characterize the environmental conditions occurring during the field experiment. Wind data was measured every minute using a weather station located in a tower installed near the Sisal Port (Figure 1c). Offshore wave conditions were recorded at 10 m water depth using an RDI Acoustic Doppler Current Profiler (ADCP) located 11 km offshore (see Figure 1b for instrument location). During the experiment, three breaker lines were observed at the outer and inner bars and the inner-surf/swash zone transition. Moreover, an Acoustic Doppler Velocimeter (ADV) Nortek Vector, located onshore the inner bar (Figure 5a,b) at 0.2 m above the seabed, acquired high-frequency (16 Hz) velocity measurements during 48 h (27 May to 29 May). The instantaneous velocities were measured in the *XYZ* coordinate system, where velocities are defined such that *u*, *v* and *w* velocities correspond to the *x* (cross-shore), *y* (alongshore) and *z* (vertical) directions, respectively.

A temporary groin was deployed in the inner surf/swash zone on the morning (0800 local time) of 27 May and was removed 24-h later on the morning of 28 May 2015. Beach morphology was surveyed along 15 survey lines, covering the up- and down- drift sides of the temporary structure (Figure 5a). A Leica Differential Global Positioning System (DGPS) was employed using Real Time Kinematics (RTK) for conducting high-resolution topographic surveys. The equipment in RTK mode and Kinematic (phase) moving mode has a horizontal and vertical accuracy of 10 mm and 20 mm, respectively. The alongshore distance between transects varies from 2 to 6 m, with the highest resolution corresponding to those transects located close to the structure (Figure 5a). The DGPS beach surveys were conducted every two hours for 24-h to evaluate the beach resistance owing to the structure presence. Furthermore, measurements continued after the structure removal, with the same two-hour temporal resolution for 10 h and then were resumed with a lower temporal resolution (i.e., 29 May, 3 June), continuing until the beach was fully recovered. A total of 20 beach surveys were conducted. Control lines, located 50 m updrift and downdrift from the structure location (Figure 5a), were surveyed weekly to assess the natural beach variability in this area. It is worth to notice that the survey lines only cover the swash and inner surf zone and hence do not cover the entire surf zone which extends offshore. The field data is available via author's request following the instruction in the supplementary material section.

**Figure 5.** (**a**) Plan view of the survey lines and the structure location, showing the breaker lines and ADV location. (**b**) Beach profile of the middle transect showing the ADV location with respect to the structure.

The mean sea level was acquired every minute by a tidal gauge located inside the Sisal Port (Figure 1c). Mean sea level in the study area presents a cyclic annual variation [32], showing a minimum in July and a maximum in October. Therefore, when a short-term experiment is carried out (days to weeks), the seasonality of the mean sea level (msl) elevation should be considered. The vertical datum of the surveys corresponds to the MEX97 geoid [33] and the difference between the vertical datum and the mean water elevation during the experiment is approximately 0.2 m. Beach surveys in the present paper are referenced to the msl during the experiment period (May–June 2015). A summary of the field data collected is presented in Table 1.

**Table 1.** Measured data, sensor employed, sampling frequency and measured period.


#### 3.1.3. Field Data Analysis

The shoreline position (*z* = 0) was extracted from each of the cross-shore DGPS survey lines. An Empirical Orthogonal Function (EOF) analysis of the shoreline position [34–36], with respect to the initial shoreline, was performed in order to investigate the dominant modes of variability during the experiment. The EOF analysis allows to represent the coastline data, *x*(*y*, *t*), as a summation of *n* spatial (*en*(*y*)) and temporal functions (*cn*(*t*)), where the variance explained decreases with the mode number, as follows:

$$\mathbf{x}(y,t) = \sum\_{n=1}^{N} c\_n(t)e\_n(y)$$

The shoreline variability associated to the presence of the temporal groin can be evaluated by analyzing the resulting spatial and temporal functions.

Wind magnitude and direction, from the meteorological tower, were averaged every 5 min. Wave statistics measured by the ADCP were computed every 60 min based on pressure and velocity measured at 2 Hz. On the other hand, the ADVs velocity information was removed when the correlation value was less than 80% with the aim of identifying potentially inaccurate measurements. The measured velocities were averaged over 512-s intervals to ensure stationary conditions and further estimate the (cross- and along- shore) currents inside the surf zone.

#### *3.2. Numerical Model*

### 3.2.1. Model Description

Numerical simulations have been conducted by means of a newly proposed morphodynamic model, named General Shoreline beach 1.0 (GSb), belonging to the one-line model typology [37]. This typology assumes that the beach cross-shore profile remains unchanged [38,39], thereby allowing beach change to be described uniquely in terms of the shoreline position. The peculiarity of the GSb model consists of simulating shoreline evolution based on a longshore transport formula/procedure suitable at any coastal mound: sand, gravel, cobbles, shingle and rock beaches [40–44]. The GSb model presents one calibration coefficient solely, KGSb, which does not depend on the grain size diameter and depends on the alongshore gradient in breaking wave height [45]. The proposed general formula/procedure considers an energy flux approach combined with an empirical/statistical relationship between the wave-induced forcing and the number of moving units. GSb model allows to determine short-term (daily base) or long-term (years base) shoreline change for arbitrary combinations and configurations of structures (groins, jetties, detached breakwaters and seawalls) and beach fills that can be represented on a modelled reach of coast. A demo version of the numerical model can be downloaded by following the instructions in the supplementary material section.

#### 3.2.2. Data Analysis

The results from the numerical simulations have been adopted to investigate the shoreline beach resistance and resilience at the considered stretch of coast. The resistance index, *RS* and resilience index, *RL*, proposed by [2], to investigate ecological stability, were adapted for the present study. *RS* is then defined as,

$$RS(t\_0) = 1 - \frac{2|\Delta S\_0|}{(l + |\Delta S\_0|)}\tag{1}$$

where Δ*S*<sup>0</sup> represents the cross-shore distance, at *t*<sup>0</sup> = 720 h, between the perturbed shoreline and the unperturbed shoreline, in vicinity of the groin and *l* is the perturbation length which equals to the groin length. *RS* ranges between 0 and 1; minimal resistance (largest effect) to the beach perturbation corresponds to smaller values of *RS*. Similarly, the resilience index *RL*(*t*) is defined as,

$$RL(t) = \frac{2|\Delta S\_0|}{(|\Delta S| + |\Delta S\_0|)} - 1\tag{2}$$

where Δ*S* represents the cross-shore distance, at time *t*, between the perturbed shoreline and the unperturbed shoreline with *RL* = 1 corresponding to a fully recovered shoreline (i.e., return to the pre-disturbed condition). Shoreline beach resistance and resilience are illustrated in Figure 6.

**Figure 6.** Definition sketch of shoreline evolution between points A and B for the cases of: (**a**) beach resistance owing to the groin (original shoreline: blue line; disturbed shoreline: red dashed line) and (**b**) beach resilience after the structure removal (perturbed shoreline: red-dashed line; shoreline position at time *ti* after structure removal: yellow line).

#### **4. Results**

#### *4.1. Field Observations*
