**1. Introduction**

The Gulf of California is a narrow, semi-enclosed sea that extends from its opening with the Pacific Ocean for more than 1100 km to the northwest between the Baja California peninsula and the mainland of western Mexico. As many as eight hurricanes form each year between May and October over ocean waters that attain a temperature of 27 ◦C or higher off the Mexican mainland near a latitude of N 15◦ [1]. Based on several decades of such data, 50% of such storms turn harmlessly westward into the open Pacific Ocean as they shift northward. Only a few track northeast into the Gulf of California but those that do, such as the September 2014 Hurricane Odile, are capable of causing extensive damage to infrastructure on the peninsula [2]. Odile struck the southern tip of the peninsula as a Category 4 hurricane with sustained winds reaching 215 km/h but diminished to a Category 3 event 24 h later as it tracked into the lower Gulf of California. By the time it reached the upper part of the gulf and crossed into mainland Mexico, the disturbance was reduced to a tropical storm. A detailed analysis of that storm by Gross and Mager (2020) applied mathematical models to reconstruct the impact of known meteorological conditions based on wind speed and wind direction to changes in wave height and the degree to which the water column was agitated as the storm progressed through the gulf's entire length [3]. The study's stated objective was to present a worst-case scenario on the impact of damage to tidal-energy devices that might be employed in the upper Gulf of California. Installations of this kind have yet to be built in the region, which registers tidal ranges on the order of 12 m [4]. In theory, the mechanisms engineered to harness energy from tidal exchange are not as susceptible to wind damage as they are to extreme waves. Beyond its stated purpose [3], the contribution by Gross and Mager (2020) provides the most thorough longitudinal treatment of changing physical parameters related to a major storm event in the Gulf of California.

Infrequent as they may appear on a human time frame, extreme storm events wield a measurable and persistent impact on coastal geomorphology over the long term as registered in deposits of various kinds around the world. Studies on Holocene storm chronology are focused mostly on accumulations preserved in coastal marshes, lagoons, and beach ridges [5]. Less attention has been devoted to deposits that result from the erosional retreat of sea cliffs by recurrent storm events [6–8]. On a regional basis limited to the lower Gulf of California, rocky-shore studies have focused on the Holocene development of such features where the erosion of limestone shores and volcanic sea cliffs composed of rhyolite and andesite resulted in extensive coastal boulder deposits (CBDs) and related coastal barriers [9–11]. Andesite is the most widespread rock type exposed in sea cliffs along the western Gulf of California, accounting for nearly 25% of all shoreline features including beaches and mud flats [12]. Andesite rocky coasts are under-represented compared to granite shores in the upper Gulf of California, but still common.

The goal of this study is to expand on the relationship between coastal erosion of andesite sea cliffs and the development of a massive coastal barrier deposit formed by andesite cobbles and boulders on Isla San Luis Gonzaga in the upper Gulf of California. The methods for analysis of eroded clast shapes and sizes together with estimates on the wave heights necessary for their primary generation follow those in previous contributions [9–11]. The choice of the Gonzaga study site was influenced by the prospect of superior control over the scale of sequential changes in topographic layout. It is expected that Holocene CBDs with a time range through thousands of year duration will offer better insight regarding the intensity of episodic storm events in regions like the Gulf of California otherwise perceived to suffer rare events. Civil engineers involved with planning for infrastructure ranging from artificial harbor facilities and breakwaters to potential power linkages with tidal-energy mechanisms need to be aware of such physical settings with a deep background in coastal geomorphology.

#### **2. Geographical and Geological Setting**

Located in the upper Gulf of California, the study site within Bahía San Luis Gonzaga is midway between the towns of San Felipe and Bahía de Los Angeles (Figure 1a). San Luis Gonzaga constitutes the area's largest bay (Figure 1b), covering an area of about 36 km2. Isla San Luis Gonzaga sits at the northwest side of the bay, approximately 1.5 km<sup>2</sup> in area and rising 140 m above sea level (Figure 1c). Detailed geological mapping of the island and the surrounding region confirms that the local bedrock is formed entirely of andesite flows [13]. The focus of this study is a 450-m long spit formed exclusively of andesite cobbles and boulders that extends westward from the northwest corner of the island. Tracing the phased temporal development of the spit ranks as the project's primary goal, which entails advantages in scale and layout compared to earlier studies of CBDs in the lower Gulf of California [9–11].

**Figure 1.** Locality maps showing Mexico's Baja California peninsula and Gulf of California; (**a**) Mexico and border area with the United States denoting key towns with inset box marking the study area between San Felipe and Bahía de Los Angeles; (**b**) Region around Bahía San Luis Gonzaga showing Isla San Luis Gonzaga in the northwest part of the bay; (**c**) Topographic map of Isla San Luis Gonzaga with the study site marked (box) within which the study transects are indicated.

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

#### *3.1. Data Collection*

Isla San Luis Gonzaga was visited in June 2019, when the original data for this study were collected from unconsolidated andesite clasts forming the long spit attached to the island accessible from Punta Willard (Figure 1c). Cobble- and boulder-size clasts encountered on tape lines through seven transects were measured manually in three dimensions perpendicular to one another in each clast (long, intermediate, and short). All transects were laid out to cross the spit at different locations, always at right angles to the defining shore with orientations recorded by compass. Continuous tracking of elevation with respect to sea level was monitored across each transect in order to construct topographic relief profiles (see Section 3.2 for more details). Differentiated from cobbles, the base definition for a boulder adapted in this exercise is that of Wentworth (1922) for an erosional clast equal or greater than 256 mm in diameter [14]. No upper limit for this category is defined in the geological literature. Triangular plots were employed to show variations in clast shape, following the design of Sneed and Folk (1958) for river pebbles [15]. Comparative data on maximum cobble and boulder dimensions were fitted to bar graphs to show variations in composition from one transect to the next. Multiple samples

of andesite were collected from the island's rocky-shore zone for laboratory analysis to determine specific gravity.

#### *3.2. Aerial Photography and Applications for Topography*

Use of a DJI Inspire 2 Drone™ (DJI, Nanshan District, Shenzhen, China) was employed to generate the Geographic Information System (GIS) platform, photogrammetry, and digital elevation model (DEM) in this study following standard protocols [16]. Eight tarps, each covering 1 m2, were printed with a highly visible pattern that could clearly be detected from the sky. The tarps were laid out across the rocky bar and georeferenced using a handheld Geographic Positioning System (GPS). Thereafter, a flight plan was designed and uploaded to the drone with a limited flight duration between 23 and 27 min that was ample for completion while providing a stable platform. The flight plan was designed to calculate the number of images the drone needed to take based on altitude and desired image overlay (70–80%). Each image captured by the drone was automatically georeferenced and transferred to photogrammetry software, where steps were followed to join the images into a single mosaic. The first step is image alignment, wherein the software places and aligns the images taken by the drone based on the GPS data from the flight plan, as well as the control points from the tarps and GPS data collected on sight. The next step entailed object identification so that tie points could be generated to stitch the images together. A sparse cloud was next generated from a series of points using the overlaid images, points in common, and drone flight data to calculate the elevation of each point. With these data from the dense cloud, a mesh is created as a series of triangles that joins the points from the dense cloud, and the resulting layer is a continuous surface on which the original images can be "draped over". Based on the generated data in the previous step, a DEM can be generated using the kriging interpolation method. For example, the same strategy has a successful application for high accuracy surveying of beach-sand topography [17].

Using GIS software by Agisoft Metashape, the DEM was applied to determine the slope and direction of the slope traversing the spit. To determine slope the software calculates the angle on the incline based on the elevation of each pixel and its relation to the adjoining pixels. With the slope layer generated and geographic location of the layer the software determines the downslope direction for each cell within the DEM. The resulting layer indicates the main slope directions of the feature. To obtain the elevation of the associated marine terrace, its location was georeferenced from images taken by the drone. A digital marker was placed on the edge of the marine terrace. This marker was used as a geo-reference in the DEM and the elevation data were extracted with the aid of an "Identify tool." The same methodology was used to extract the height data of the highest point of the adjoining spit.

#### *3.3. Hydraulic Model*

With determination of specific gravity based on the value of 2.3 g/cm<sup>3</sup> for andesite, a hydraulic model may be applied to predict the energy needed for the erosion of joint-bound blocks from a rocky shoreline and their subsequent transfer to an adjacent coastal boulder deposit as a function of wave impact. Andesite is a volcanic rock that forms from surface flows with variable thicknesses and a propensity to develop vertical fractures. These factors regulate the size and general shape of blocks loosened by erosion in the cliff face. Herein, two formulas are applied to estimate the magnitude of storm waves against joint-bounded boulders derived, respectively, from Equation (36) in the original work of Nott [18] (Equation (1)) and from an alternative formula that uses the velocity equations of Nandasena et al. [19] as applied by Pepe et al. (2018) [20] to estimate wave heights (Equation (2)):

$$H\_S = \left(\frac{\left(\frac{\rho\_s - \rho\_w}{\rho\_w}\right)a}{\mathbf{C}\_l}\right) \tag{1}$$

$$Hs = \frac{2\frac{\left(\frac{\rho\_b - \rho\_W}{\rho\_W}\right) \cdot c \cdot \left[\cos F + (\mu\_s \cdot \sin F)\right]}{c\_1}}{100} \tag{2}$$

where *Hs* is the maximum height of the storm wave at breaking point; ρ*<sup>s</sup>* is the density of the boulder (2.3 g/cm3); ρ*<sup>w</sup>* is the density of water at 1.02 g/cm3; *a* is the length of boulder on long axis in cm; *c* is the length of boulder on short axis in cm; θ is the angle of the bed slope at the pre-transport location (1◦ for joint-bounded boulders); μ*<sup>s</sup>* is the coefficient of static friction (= 0.7); and *C*<sup>l</sup> is the lift coefficient (= 0.178). Equation (1) is more sensitive to the length of a boulder at the long axis, whereas Equation (2) is more sensitive to the length of a boulder on the short axis. Therefore, some differences are expected in the estimates of *HS*.

#### **4. Results**

#### *4.1. Base Maps and Transect Lines*

A set of base maps constructed on the basis of aerial photography illustrate the principal attributes of the spit (Figure 2), as located on the topographic map in Figure 1c. The massive agglomeration of loose cobbles and boulders extends for a distance of 450 m westward from the source at sea cliffs on the north side of Isla San Luis Gonzaga. A mosaic image pieced together from the aerial survey and shown in natural sunlight (Figure 2a), marks the location of seven transects with the first (T1) closest to the source of eroded andesite clasts on the north face of the island and the last (T7) most distal at the end of the spit. The surface area represented by the spit amounts to 15,600 m2, of which less than 5% is obscured by plant cover dominated by the Sweet Mangrove (*Maytenus phyllanthoides*) [21]. Variations in topography (Figure 2b) reveal that the maximum elevation through the central axis of the spit rises to 3 m above mean sea level. Variations in slope direction along the divergent axes of the spit descend dominantly to the northwest (Figure 2c). Key aspects related to the layout of all transects and registered content are compiled in Table 1.


**Table 1.** Comparative data drawn from transect lines across the bar system at Bahía San Luis Gonzaga.

Average transect length amounts to 29 m and the dispositions of all but transect 3 are roughly parallel, oriented along a NW to SE trend. Transect 3 follows an orientation roughly 90◦ out of phase with the others, trending NE to SW. The average density of cobble and boulder clasts measured per transect is substantial at 94 with an average spacing of 3.3 clasts per meter. Transect 3 records the fewest boulders compared to all other transects at less than one in 10. Overall, the dominance of boulders over cobbles is greatest in transects 1 and 2 located most proximal to the source rocks at the beginning of the spit at a ratio 2:1. That ratio falls closer to parity between cobbles and boulders in transect 4 diagonal to the spit roughly midway along its length. Farther out along the spit in transects 5 and 6, the ratio of boulders to cobbles is 1:3. Near the tip of the spit (Figure 2a), transect 7 is the most distal from the source of eroded clasts and reflects a modest return in the relationship between boulders and cobbles at parity.

**Figure 2.** Base maps for the unconsolidated spit off the northeast end of Isla San Luis Gonzaga; (**a**) Orthophoto mosaic under natural light showing the position of transects 1 to 7; (**b**) Orthophoto color-coded map showing variations in elevation above mean sea level; (**c**) Color-coded map showing variations in slope direction.
