*4.6. Variation in Transect Profile Elevations*

Data recovered from the seven transects in this study (Figure 2) also include the requisite information for construction of individual elevation profiles. The highest elevation determined at the crest of any single transect amounts to no more than 3 m above mean sea level. Transects 1 to 3 were found to conform to profiles that rise evenly to peak elevation at or near the center of the transect from opposite ends and are not illustrated. In contrast, transects 4 to 6 (Figure 9) exhibit profiles with a marked depression at variable positions along the line. Transect 4 (Figure 9a) registers a modest decline in elevation of 50 cm across the central 5 m of the line. Transect 5 (Figure 9b) shows a similar dip but is skewed much closer to the NW end of the transect. Transect 6 (Figure 9c) exhibits the deepest depression midway through the line with a drop of about a meter. Transect 7 also features a bifurcated elevation profile, but it is not shown at the same scale because it represents a much lower overall value in maximum elevation at only 1.2 m. Among the seven transects, transect 3 (see Figure 7) registered the lowest elevation rising to only a half meter above sea level.

**Figure 8.** Set of bar graphs used to appraise variations in maximum boulder length from the three transects with similar orientations most distal from the source of coastal erosion; (**a**) Bar graphs from transect 5; (**b**) Bar graphs from transect 6; (**c**) Bar graphs from transect 7.

**Figure 9.** Comparison of selected transverse profiles in the distal part of the spit showing separation of different phases in the overall deposit. Transects 1–3 and 7 lack such distinct features; (**a**) Elevation profile through transect 4; (**b**) Elevation profile through transect 5; (**c**) Elevation profile through transect 6. See Section 3 for source of the elevation data.

The long view over the spit's axis to the NE from a location on transect 4 (Figure 10) captures the nature of the depression cutting diagonally through the more proximal part of the structure. Thus, the transverse depression in transect 4 is defined by a pair of longitudinal bars that distinctly separate one side of the spit from the other with an intermediate trough. From this vantage, it may be realized that the spit underwent a growth history in sequential phases. Following from this insight, the ramification is that the Sneed–Folk plots in Figure 4c,e,f, as well as the bar graphs in Figures 6c and 7 represent consecutive phases of development that occurred over time. In contrast, the elevation profiles for transects 1–3 that conform to a simple arc in relief, imply that the Sneed–Folk plots and bar graphs relevant to those transect samples reflect more unitary slices temporal development.

#### *4.7. Biological Data from Encrusted Boulders*

From place to place, disarticulated bivalve shells (including *Anadara grandis* and *Megapitaria squalida*) appear sporadically among the mixed cobbles and boulders forming the spit. The degree of breakage in some of the larger shells indicates a higher level of energy was entailed in their delivery to the spit, more than from normal conditions related to tidal flux. More significant are examples of large boulders encrusted by the common oyster (*Ostrea palmula*) that thrives in intertidal waters throughout the Gulf of California [22]. A block with a long axis of 70 cm found near transect 7 hosted more than two dozen oysters on its upper surface (Figure 11a) before it was transported onto the spit and left upside down. In contrast to the inarticulate shells found elsewhere separately as disarticulated shells, the oysters are encrusted in growth position and many remain articulated (Figure 11b). The biological inference is that the boulder originally sat submerged in the shallow water off to the side of the spit and was subsequently carried onto the spit by a storm of sufficient strength to lift an andesite block weighting as much as 80 to 100 kg (see range of weights in Table A7). The pristine condition of the oyster shells suggests that the storm was a relatively recent event. Weaker storms are capable of transporting cobles and smaller boulders during earlier events and may have shifted the offshore position of the block until the next major storm moved it onto the spit.

**Figure 10.** View across transect 4 northeast toward the connection with Isla San Luis Gonzaga, showing a distinct swale between two different phases of the cobble-boulder deposit. Note the raised Pleistocene marine terrace in the far distance (white arrows). The inner wall of the marine terrace is oriented NS.

**Figure 11.** Contemporary oysters (*Ostrea palmula*) encrusted on a boulder near transect 7; (**a**) Boulder as first encountered on the spit (meter stick for scale); (**b**) Same boulder overturned for better view of encrusting oysters, approximately 7 cm in shell length. Note: many of the oysters remain articulated.

#### *4.8. Storm Intensity as Function of Estimated Wave Height*

Average boulder sizes and maximum boulder sizes from all seven transects are summarized in Table 2, whether or not the respective Sneed–Folk diagrams and bar graphs (Figure 4, Figure 6, and Figure 8) reflect solitary events or an agglomeration of phased events. These data are a prerequisite for comparison of results estimating wave heights first directed against joint-bound blocks on the andesite rocky shore as derived from the Nott formula [18] and the subsequent formula applied by Pepe et al. [20]. There exists a general trend in reduction of average boulder size from transect 1 to transect 5 more than halfway along the Gonzaga spit from the proximal source. Thereafter in transects 6 and 7, there occurs an increase in average boulder size. The estimated mean wave height necessary to transport those boulders extracted from the rocky shore amounts to 2.7 m according to the Nott formula. However, at 73 cm the mean maximum boulder length derived from all seven transects yields a value almost twice the diameter for the average of all averages (Table 2). Moreover, the estimated mean weight of the largest single boulder from each transect amounts to 200 kg, which is more than 4.5 times the average weight computed from all boulders surveyed in the seven transects. The estimated wave height needed to shift the largest boulder in transect 7 amounts to nearly 6 m according to the Nott equation, but half that compared with the Pepe equation. However, results based on the Pepe equation for the largest boulders yield a higher wave height in four out of seven transects. In general agreement with the biological inference from the oyster-encrusted block in Figure 11, the critical insight from these comparative data is that the average impact from smaller waves is sufficient to move smaller boulders, but only the largest waves are sufficient to move the largest boulders.

**Table 2.** Summary data from Appendix A (Tables A1–A7) showing maximum bolder size and estimated weight compared to the average values for sampled boulders from each of the transects together with calculated values for wave heights estimated as necessary for CBD mobility. EWH = estimated wave height.


#### **5. Discussion**

#### *5.1. Phased Development During Holocene Time*

As projected by the orthophoto mosaic in Figure 2a and supplemented by transect elevation profiles derived from seven transects, the overall layout of the unconsolidated cobble-boulder spit at Isla San Luis Gonzaga suggests an interpretation of growth through multiple phases during Holocene time. A starting point in post-Pleistocene time is supported by the physical connection of the spit to the island adjacent to an uplifted marine terrace (see photo in Figure 5). The terrace truncates the northwest corner of the island and its outer lip rises 8.5 m above the base level of the spit. Marine erosion on the terrace ceased prior to initiation of the spit around the present sea level. The recessed terrace flat is relatively clean, showing that the Pleistocene sea cliff at the rear of the terrace was not the parent source of eroded clasts contributing to the spit. Instead, the yet active source appears along the modern sea cliffs that stretch across the northern part of the island. At the proximal end of the spit, sea cliffs on the north exposure rise steeply up to 60 m in height (Figure 1c). Headward erosion of a modern wave-cut platform cuts into the base of adjoining sea cliffs that provide the copious raw materials derived from joint-bound blocks (Figure 3). Large blocks are first smoothed by wear in the surf and subsequently transferred by storm currents in a SW direction to the spit. Undermining of the sea cliff by storm action also contributes to rock falls from higher in the exposure.

Creation of the 450-m long spit is interpreted as having evolved over the last 10,000 years during a succession of episodic storm events outlined in Figure 11. Progradation of the spit at the outset between transects 1 and 2 follows a linear pattern that left a consistent profile tracing a single, central rise in elevation roughly midway between side margins (Figure 2b). The next phase of construction entailed a curvature to the south that terminated beyond the position of transect 3 (Figure 12a). The profile across transect 3 reflects a low median rise in elevation (see Figure 7). A dense thicket of vegetation north of transect 3 (Figure 2a) signals this phase of development terminated as a side spur that ceased to receive fresh material and became isolated from the rest of the structure. Resumption of deposition with a linear extension to the SW pushed a narrow lobe of the spit beyond transect 4 (Figure 12c), presumably due to a change in storm dynamics. The pair of topographic bars that form parallel swales in transects 4 and 5 (Figure 9a,b) mark the further expansion of the spit to the SW with the more easterly bar deposited during an earlier storm event and the adjoining bar amalgamated alongside during a later event. Physical compression of the two storm events resulted in expansion of the spit's width across transects 4 and 5.

**Figure 12.** Interpretation of temporal development through Holocene time with study transects marked as reference points: (**a**) phase one; (**b**) phase two; (**c**) phase three; (**d**) phase four; (**e**) phase five. Dashed lines mark boundaries between successive additions to the structure through time.

A similar sequence of staggered events took place with further extension of the spit to the SW beyond transect 6 (Figure 12d). During the earlier phase of expansion in this area, the spit was narrower but doubled in width with amalgamation of the adjoining later phase. The pattern repeated itself, once again, under progradation of the spit beyond transect 7 (Figure 12e) to reach the present terminal length of 450 m. The number of discrete storm events that contributed to the phased growth of the spit is difficult to estimate, but the presence of boulders across all transects makes clear that major storms were involved.

The incremental rate of the structure's progradation from the bedrock source on Isla San Luis Gonzaga is difficult to calculate with any accuracy, but an estimate can be offered on the assumption that phased growth resulted from storms of hurricane strength that occurred as often as every 100 years. This metric is suggested in reference to the popular notion of recurrent events outside the living memory of a long human lifetime. Holocene mega-storms with a measurable recurrence between 100 and 300 years are tested on the basis of coastal storm ridges that incorporate coral heads dated by isotope chronology [5]. Recurrence of mega-storms on a centennial scale also is suggested by the isotope chronology of speleothem deposits from caves commonly impacted by landfall of tropical cyclones [23]. No such method of absolute dating is possible with regard to the storm-deposited andesite boulders from Isla San Luis Gonzaga. The rocks are dated by radiometric means, but the dates so derived represent the age when lava flows solidified during the Miocene [13] and not the time of coastal erosion.

Storms of hurricane intensity reaching Isla San Luis Gonzaga would have entailed wave heights at or exceeding 5 m based on equations from Nott [18] and Pepe et al. [20]. Such waves would impact the island's north shore following a pattern of cyclonic rotation with northward travel. Extraction of large andesite blocks from the base of the sea cliffs (Figure 3) was influenced by hydraulic wedging of joints and partings in the layered andesite during wave impact. The subsequent transport of boulders to the proximal end of the spit was driven by vigorous storm-generated currents. Successive big storms may have moved the larger boulders piece-meal for shorter distances during each event. Over the 10,000-year span of the Holocene, 100 super-storms may have reached the upper Gulf of California. Such a reckoning is reasonable, given the spit's geometry and various internal boundaries demarcated by amalgamated bars (Figure 12). An episodic growth rate between 7 and 8 m/century is informed by the total length of the various components adding up to a composite total of 750 m. Whereas each cobble and boulder in the construction is ultimately traced to the sea cliffs on the island's north shore, the residency time of large blocks resting offshore also must be considered. Thus, large andesite blocks of considerable weight may sit offshore near the distal end of the spit for some time during which biological encrustations accumulate (Figure 11), before the block is shifted from inter-tidal waters up onto the spit during a major storm.

#### *5.2. Inference from Historical Hurricanes*

Hurricane Odile entered the Gulf of California as a Category 4 storm in September 2014 and its economic impact is regarded as one of the most destructive events to affect the peninsular state of Baja California Sur, having caused more than 1654 million USD in damage to coastal infrastructure largely as a result of high winds [1]. According to a subsequent assessment by Gross and Magar (2020) [3], the same storm had the capacity to damage tidal-energy transformers due to wind-driven waves if such mechanisms were in place as part of the energy grid serving the state of Baja California at the far end of the gulf in the north. No such infrastructure presently exists in the region, but the study offers a cautionary warning about the potential for such damage even in the upper part of the gulf where hurricanes typically degrade to tropical storms. The last major storm to have crossed the upper gulf was Hurricane Kathleen in September 1976 as a Category 3 hurricane [21]. The passage of time since that event is considerable in terms of human memory and may be thought of as a once in a lifetime event by local residents living around Bahía San Luis Gonzaga.

The peninsular region of western Mexico was spared a potentially catastrophic event during the 2015 storm season, when Hurricane Patricia formed as a Category 5 storm with wind speeds up to 346 km/h off the Mexican mainland well south of the Baja California peninsula. That storm still holds the record as the most powerful hurricane to have originated in the eastern North Pacific Ocean [24]. Only the storm's outer most bands brushed across the opening to the Gulf of California, but the center of the storm made landfall on the Mexican mainland after an unexpected turn to the east. Had Hurricane Patricia tracked into the Gulf of California, it was certain to have caused more damage to coastal infrastructure than Hurricane Odile during the previous season. The occurrence of these two powerful storms, one after the other in subsequent years, raises the question of accountability for storms attributed to 100-year events. With growing conditions of global warming now experienced

around the world, the increase of such events is sure to be compressed in frequency as suggested by re-evaluations of storm data on a decadal basis [25]. Under such circumstances, the study of coastal boulder deposits and their development in recent geologic time offers a window on natural processes of interest not only to geomorphologists but also to engineers challenged to design infrastructures better suited to withstand more intense storms and any future rise in sea level.

#### *5.3. Comparison with Other Gulf of California Deposits*

Study of coastal boulder deposits (CBDs) and related boulder barrier deposits (BBDs) in the Gulf of California is a pursuit that has gained momentum during the last few years but, heretofore, only in the lower Gulf of California [9–11]. This contribution is the first to focus on the upper Gulf of California, a region generally thought to be impacted much less from the severity of hurricanes than the more southern parts closer to the Tropic of Cancer. Earlier work looked at limestone boulders pulled by storm action from Pliocene sea cliffs on Isla del Carmen, where a line of eroded boulders sits high on a marine terrace [9]. In this regard, the Carmen example conforms to a classic CBD pealed back from the front of a sea cliff by storm-related overwash. The Isla San Luis Gonzaga example in this study corresponds to the formation of boulder bars, where large blocks of andesite are leveraged from joint-bound layers at the base of sea cliffs and transported laterally by storm-generated currents where they accumulate as spits. Compared to previous examples in the southern Gulf region also formed by volcanic boulders derived from joint-bound blocks [11,12], the Isla San Luis Gonzaga structure is larger and more complex with components that can be differentiated as having accumulated during discrete storm events. For example, the earliest phases of extension ending beyond transect 3 off Isla San Luis Gonzaga (Figure 12a) are comparable to the half-ring structure constructed from rhyolite boulders at Ensenada Almeja [10]. The Almeja structure traces a pattern of clockwise extension stretching in an arc over a distance of about 250 m from the original bedrock source with joint-bound blocks. That pattern is replicated in the same dimensions by the earliest phases of construction at Isla San Luis Gonzaga. In both examples, fewer boulders are found on top of the bar closer to its termination, suggesting that wave energy declined with distance from the proximal end of those structures at the bedrock source.

After isolation of the spur leading to transect 3 from the rest of the spit at Isla San Luis Gonzaga (Figure 12b), new growth was extended in a strictly linear fashion similar to the unidirectional extension of bars across the front of Puerto Escondido in the lower Gulf of California [11]. There, two bars follow a linear fault trace with a small island connected in between. Not including the islet, the two bars extend for a length of 250 and 140 m, respectively. By comparison, the apparent length of the Gonzaga spit amounts to 450 m. However, development of parallel bars that became progressively attached to the core from one side, the total length of component parts including duplications amounts to a distance of 750 m. As such, the Gonzaga spit is one of most complex structures of its kind formed by loose cobbles and boulders in the entire Gulf of California region. Based on shape analyses from the various localities throughout the gulf region, there is little difference in the blocks of rock that were worn by marine erosion from limestone, rhyolite, and andesite into oblong cobbles and boulders. The factor that makes results of the Isla San Luis Gonzaga study so important is the apparent correspondence between extraordinary size, complexity, and the length of time necessary for development of BBDs. Given the weight of the largest boulders distributed across much of the Isla San Luis Gonzaga spit, it is apparent that their transport occurred during episodic hurricanes of high intensity. With greater attention to examples of CBDs throughout the Gulf of California and the expectation that the frequency of future hurricanes is likely to increase, it is proposed that known sites [9–11] including the Isla San Luis Gonzaga spit be monitored for changes once a selection of the largest boulders is tagged for reference.

#### *5.4. Comparison with island deposits in the North Atlantic*

Studies on CBDs on islands in the North Atlantic Ocean show much promise for similar research applying the same kind of analyses performed in the Gulf of California. An identical program using the same techniques of analyses for boulder shapes and sizes was conducted on modern and Pleistocene CBDs on Santa Maria Island in the Azores [26]. In particular, the same equations have been applied to estimate wave heights during the Late Pleistocene (Marine Isotope Substage 5e) on basalt-dominated shores dated by fossils to approximately 125,000 years ago. Future studies that incorporate Pleistocene fossils may be expected in other Atlantic archipelagos such as the Canary and Cape Verde Islands.
