An exhaustive inventory of beachrocks was carried out by means of an extensive photogeological survey of the coast, encompassing the analysis of the available vertical aerial orthoimage series from different years (1946, 1956, 1986, 1991, 1994, 1996, 2000, 2001, 2002, 2004, 2006 and 2008 to 2018) at different resolutions (100 to 25 cm/px) and different spatial coverages (data from the Catalan Cartographic and Geological Institute (ICGC) (www.icc.cat/vissir3/) and Google Earth Pro servers). Regarding the identification of seabed morphological features, the image resolution is limited by (1) the absolute resolution of the image, (2) the sea condition at the collecting time, (3) the angle of light-incidence, and (4) the shadows cast by the coastal cliffs. In optimal conditions, beachrocks are clearly identified down to -10 m MSL.

Georeferenced images and the ICGC viewer were used to measure the length (L) and the width (W) of the exposed deposits and their minimum distance from the shoreline (the coastal distance) (Fig. 2). The coastal distance was measured according to the criteria of Pagán et al. (2016), which take as a reference the run-up limit or boundary of the wet beach in the orthoimages.

The inventoried beachrocks were studied in situ during diving surveys from 2009 to 2020; the observations performed during the dives carried out in 1995 and 1996 were also revised and updated. The visible thickness (T) was measured in exposed sections by means of a 1-metre scale (10 cm divisions). The minimum (mH) and maximum (MH) depth of shallow deposits were measured with the 1-metre scale. A plumb bob was used to measure the deepest ones. The sea level at the time of diving was taken as a reference. A ±0.25 m systematic error was assumed because of the maximum sea level variation over the year. The slope of the beachrock surface (S) was estimated as the gradient between the variation of depth and the distance along a transect perpendicular to the maximum slope (Fig. 2). The dimensions (L and W) were verified by positioning the limits using GPS integrated in Olympus TG5 and TG6 underwater cameras. The attitude of plains (joints, layers, etc.) was measured by means of the digital compass fitted in these cameras. The erosional landforms, internal layers and the features of the underlying substrate were also measured, described and photographed.

During the diving surveys, 30-cm-long rock block samples were extracted for petrological and textural characterization of the deposits by means of mace and chisel. Beachrocks are usually colonized on their surface by calcareous fouling organisms (e.g. Rhodophyta, Bryozoa and molluscs), so the external part of the block samples was removed by a diamond disc grinder. The resulting fresh blocks were conditioned to extract petrographic thin sections for microscope analysis. The study of the sediments was complemented with direct observation of the blocks with a binocular magnifying glass (×10 to ×100). The percent weight content of carbonates was roughly determined by dissolving 250 g of dry sample in HCl and comparing the initial and final weights.

Mineralogical analysis of 12 selected samples was performed by X-ray powder diffraction (XRD) (Bruker AXS D8 Advance Powder RX Diffractometer from the University of Girona Technical Research Services (STRUdG)) to determine the composition of the carbonate cement. A ZEISS DSM-960A scanning electron microscope (SEM) equipped with an Oxford Link Isis L200B energy separation RX (EDX) detector from the STRUdG was used to photograph and determine the elemental composition of the 12 samples.

Sediments of the beaches adjacent to the beachrocks were also sampled for textural and compositional analysis. A total of 1 kg of sediment was collected in three separate sampling stations at ca. +1.0 m and -1.5 m MSL (foreshore and upper shoreface, respectively, e.g. Longhitano (2015)). Particle size distribution was obtained with a standard nested column of sieves and a mechanical shaker. The petrological composition of the sediment was determined from the identification of a minimum of 250 grains using a binocular magnifying glass (×10 to ×100).

A total of 12 carbonate shells of marine molluscs (7 gastropods and 5 bivalves) included in 7 of the beachrocks (CA1, 3, 6, 7, 11, 14 and 17) were dated by the ¹⁴C method. A 30-cm-thick sample of a red algae crust embedded in CA14 and a charcoal fragment included in CA17 were also dated.

¹⁴C ages were measured in the laboratories of the Tritium and ¹⁴C Dating Service of the Universitat Autònoma de Barcelona, the Poznan Radiocarbon Laboratory and Beta Analytic.

The content of carbonate seashells of size greater than 2 mm in the collected samples ranged only from 0.004 g kg^-1 to 0.4 g kg^-1, which posed a severe constraint for ¹⁴C dating. However, in the beachrocks located at depths of less than -2 m MSL, some relatively large shells were recovered directly during the diving observations. Only samples lying on eroded clean surfaces and lacking coating of living organisms were collected (i.e. CA1, 2, 3, 11, 14 and 18). Where large shells were not available, it was attempted to extract large bioclasts from rock block samples according to the following procedure: (1) the external portion of the blocks was removed by a diamond disc grinder; (2) the clean block was crushed by means of a hammer to obtain fragments of ca. 1 to 5 mm in diameter; (3) finally, the bioclasts were selected using a binocular magnifying glass. This allowed us to obtain additional dateable material from CA6, 7 and 17. However, as explained below, not all recovered bioclasts were considered appropriate for dating.

The seashells provide a terminus post quem age for the beach cementation. To minimize the age difference between the death of seashell animals and the time of cementation of the beach, the bioclasts for dating were selected according to the following criteria: (1) skeletons of perforating organisms were discarded because, although they are located inside the block, they may postdate the deposit; and (2) because the post mortem residence time of the seashells on the beaches is a priori uncertain, shells were selected preferably without fragmentation and little erosion or bioerosion in order to avoid dating bioclasts that could have been sedimented on the beach long time before the cementation. Due to these criteria, several broken, eroded and burrowed seashells (mostly of Spondylus gaederopus) recovered from CA1, 2, 3, 11, 14 and 18 were dismissed for dating.

Conventional ¹⁴C ages were converted to calendar ages using the CALIB 8.2 programme (Stuiver et al. 2021) and were adjusted to two standard deviations (2σ). The Marine 20 dataset was used to calibrate the samples that corresponded to sea-living organisms. In these cases, calibration must also consider the marine reservoir effect, which makes the radiometric ages older than the contemporary ones under atmospheric conditions. However, there is significant bias due to the local marine conditions (ΔR). Here, a ΔR value of -140±74 yr was used, according to the mean values of the eight nearest (<400 km) points from the study area in which the ΔR value was reported (Siani et al. 2000). This ΔR value was contrasted by comparing the calibrated ages obtained for a seashell and for charcoals included in the same rock block sample of CA17. Both the charcoal and the shell were expected to be the same age.

Absolute ¹⁴C dating was complemented with two OSL dates of quartz grains included in the CA3 and 14 beachrocks. OSL dates were measured in the Luminescence Dating Laboratory of the University of A Coruña. One of the blocks dated by OSL corresponded to the same rock block sample from which a seashell was dated by ¹⁴C (i.e. CA3). The OSL age corresponded to the time of burial of the quartz grains, so it cannot be earlier than the age of the seashell. Both ages (OSL and ¹⁴C) obtained for the same rock block sample also allowed us to establish the extent to which the ΔR value used in the ¹⁴C calibration was correct.

The absolute dating was complemented by the age analysis of pottery remains embedded in CA3, 4, 7, 14 and 18. This allowed us to establish a relative terminus post quem age for the cementation of the deposits. These materials were recovered directly by diving visual reconnaissance of surfaces free of algae and encrusting organisms. The Archaeology Laboratory of the University of Girona and the Terracotta Museum (La Bisbal d’Empordà) supported us in classifying and establishing their chronological rank.

Up to 19 beachrocks were documented along the 215 km of the studied coastline, all of them submerged (Fig. 1). Six of them form sequences of two or more partially overlapped ledges. Their spatial distribution is highly irregular, because all the beachrocks are concentrated in the south sector of the Costa Brava. Neither the aerial photography analysis nor the diving surveys revealed any beachrock in the central and northern sectors. Fifteen kilometres north of the Costa Brava’s northernmost boundary, we found the only beachrock that we identified and explored, on Paulilles on the Côte Vermeille beach (Fig. 1).

The analysis of the temporal series of orthoimages from consecutive years revealed that some beachrocks had been exhumed by the intense wave erosion during the rough storms events of December 2008 and January 2017 and had subsequently been partially or totally buried. This analysis was not possible for the previous severe and extreme storms catalogued by Mendoza et al. (2011) and Sanuy et al. (2020) (i.e. November 1982, February 1996, December 1997, December 2000, November 2001, December 2001 and October 2003), because the orthoimages older than 2008 are not consecutive or do not cover the entire study area. During the storm in December 2008, one of the most severe recorded on this coast since 1984 (Mendoza et al. 2011, Sanchez-Vidal et al. 2012), CA13 and 19 were exposed for the first time. Furthermore, CA2, 4, 7, 9 and 14 increased in length and/or width. The effects of the January 2017 storm were especially noticeable on CA13 and 14, which were once again much more exposed. The Gloria Storm of January 2020 (which is younger than the time period analysed by orthoimages) exhumed CA5, of which there was no documentary or oral record to date. Therefore, our inventory could not be considered exhaustive, because there must be additional buried beachrocks in the study area that have not emerged but remain hidden under a sediment cover.

The morphometric parameters of the beachrocks are shown in Table 1. Length and width data correspond to the maximum values measured in the analysed orthoimages (from 1946 to 2018) and diving surveys (from 2009 to 2020). A single deposit unit was considered if more than one isolated deposit was in the same cove. It should be noted that the current CA3 and CA7 beaches have been subject to nourishment and sand transfer works in the last four decades, so length and weight values of these submerged deposits are influenced by the presence of artificially driven sediments.

Length varies between a 8 and of 1039 m. CA7 (1039 m), CA14 (619 m) and CA13 (524 m) were the longest and CA2 (8 m), CA4 (8 m) and CA8 (21.5 m) were the shortest. The ratio between beachrock length and the length of the beaches on which they are located was variable and usually less than 1. This is in accordance with the fact that the degree of cementation was variable, causing the beachrocks to be only partially formed or preserved (e.g. Kelletat 2006). However, CA15 exceeded the current beach length by 3.26 times, which indicates a greater deposit development at the time of its cementation (Fig. 3A). Beachrock width also showed a pronounced variability, ranging between 1.5 m (CA2 and 4) and 86.6 m (CA15). This variation was partly caused by the sequence overlapping of two to six contacting ledges, which increased the total width of the deposits. As an example, CA6 (W=73.0 m) was composed of a sequence of six ledges; CA15 (W=86.5 m) was composed of 5 (Fig. 3A); and CA16 (W=34.0 m) and CA1 (W=32.0 m) was composed of 2 (Fig. 3B). The width of those beachrocks formed by a single ledge averaged 10.4 m. Similarly, the mean width of the single ledges that form the wider beachrocks was 11.6 m.

The beachrocks’ internal architecture was built up of 5- to 20-cm-thick layers tilted 10° to 12° towards the open sea (Fig. 3C). Their tops were also tilted towards the open sea, averaging values of 4° to 8°, which are lower than those of the lamination. Minimum beachrock top depths (mH) were close to the current sea level; only CA11 (Fig. 3D) and CA6 were partially emerged (+0.5 m and +0.25 m MSL, respectively). Maximum beachrock top depths (MH) ranged between -1 m (CA2 and 4) and -5.25 m MSL (CA17). The deepest levels corresponded to the distal outcrops of the overlapping sequences, as in the case of CA1 (Fig. 3B), CA6, CA15 (Fig. 3A) and CA17. CA7, formed by a single ledge, reaches up to -4.0 m MSL. This is due to the partial deposit collapse caused by the erosion of the subjacent unconsolidated marine sediments. However, the eastern sector of this beachrock lies on a bedrock formed by weathered granite, which is Palaeozoic in age. CA2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 17 and 18 were also placed directly on this same bedrock type. CA1 lay on Palaeozoic granite and schist. No data are available on materials just below CA13, 14 and 19.

Cemented deposit thickness (T) varied between 0.4 m (CA2) and 3.25 m (CA17), averaging 1.5 m. The greater thickness of the beachrock in CA17 is related to the fact that it is built of two partially overlapping ledges. Similarly, in CA14 an upper level of 1.25 m thickness overlaps a lower one, of which a thickness of 0.5 m thick is visible. Both are divided by a 0.3-m-thick bioconstructed calcareous layer of coralline algae embedded above the lower level (Fig. 4).

The minimum distance between the beachrocks and the current beach was generally less than 5 m. Larger distances were recorded on beaches that showed a marked erosive trend in recent decades due to (1) sporadic rough storm effects, as in CA9 (9.5 m), CA13 (10.5 m) and CA19 (12.0 m); (2) generalized sand beach loss, as in CA7 (12.5 m), which led to the installation of rock groynes to counteract the erosion of the sandy coast in the 1970s; and (3) focused erosion caused by the local effect of a small pier that has limited the natural contributions of sediment in CA3 (5.5 m) since 1970.

The petrological characteristics of the studied beachrocks are summarized in Table 2. Overall, the beachrocks are conglomerates of well-rounded gravels with a very coarse sand matrix. Their granulometry ranges between very fine gravel and medium gravel (2 mm to 16 mm) (Figs 5, 6A). The deposits are somewhat graded, with the coarser particles tending to be concentrated towards their base and in the distal part. In CA1, 6 and 15, the ledges furthest from the coastline (and deepest) are composed of larger particles, between medium gravel and cobble, including boulders (>256 mm) at the base of the distal part (Fig. 6B).

The grain size of the sediment from the beaches differs from that of the beachrocks (Table 3, Fig. 5). The particle size of the beachrocks is greater than that of the samples collected on the beaches at -1.5 m MSL (upper shoreface), in which sand with a variable proportion (up to 60%) of fine to medium gravel predominates. In most cases, it is greater than or practically equal to the samples collected at +1.0 m MSL (foreshore) (Fig. 5).

Regarding the mineralogy, the beachrocks are almost exclusively composed of siliciclasts derived from granitoids (quartz, feldspar and biotite) (Table 4, Fig. 5). Excluding CA1, quartz is the dominant component (mean 71.8%), followed by felsic plutonic rock fragments (mean 14.7%) and feldspar (mean 11.0%). The lithology and granulometry (very fine to medium gravel) of the sediments result from the fact that they originated from the erosion of arenaceous mantles (grus) formed by the weathering of magmatic plutonic rocks. Those rock particles with a coarse or larger gravel size correspond to fragments of unaltered granitoids (granites and granodiorites) and hypabyssal rocks (mainly, granite porphyry, aplite and lamprophyre). CA2, 3, 4, 13 and 17 include fragments of rocks from thermal metamorphism (i.e. biotite and cordierite hornfels) in a maximum proportion of 1%. The petrological composition of the CA1 clasts is different from the rest: 55.2% schist, 8.1% quartz and 2.3% granite siliciclasts, but up to 34.2% of fragments of calcite and dolomite marble (Fig. 5). The lithological composition of the current beaches matches the composition of the adjacent beachrocks, reflecting that the sediments had the same origin (Table 4, Fig 5).

The bioclasts content in the studied beachrock samples was less than 1% of the total volume (mean 0.23%), except in one sample from CA6 (8.5%) (Table 2). Most of these bioclasts were medium sand size (0.25 to 0.5 mm) and corresponded to Rhodophyta (algae) and Foraminifera (Fig. 6C), and to a lesser extent fragments of marine invertebrates (mainly bivalves, gastropods, echinoderms and Bryozoa). Exceptionally (up to 0.04% of the total volume), size seashells of bivalves larger than 2 mm (Spondylus gaederopus, Pseudochama gryphina, Glycymeris sp., Barbatia barbata, Lima lima, Acanthocardia aculeata) and gastropods (Cerithium vulgatum, Patella ulyssiponensis, Hexaplex trunculus, Vermetus triquetrus, Conus ventricosus mediterraneus, Columbella rustica, Phorcus turbinatus and Stramonita haemastoma) were observed, with variable attrition rates. All the reported species corresponded to fauna that currently inhabits the area.

The bioclast content of the current sediment collected in the foreshore was in all cases less than 5% of the total volume (mean 0.75%), and the presence of seashells larger than 2 mm was rare (up to 0.1%). Sediment samples from the upper shoreface contained a higher bioclast content (mean 2.72%), with a predominance of medium and coarse sand, but seashells larger than 2 mm were not uncommon (up to 0.5%).

The total carbonate content of the beachrock samples (i.e. percentage by weight of cement and bioclasts with respect to the total rock) ranged between 9.1% (CA14) and 18.2% (CA8), with a maximum of 22.7% corresponding to the sample richest in bioclasts from CA6 (Table 2). CA1 reached 47.3% due to its content in marble fragments.

The compositional analysis of the carbonates by XRD shows the generalized presence of high magnesium calcite (HMC), and also aragonite (ARG) only for the CA11 and CA16 samples (Table 2). Observation of samples by SEM showed that HMC formed an isopachous cement partially filling the pores, formed by steep or acute rhombohedral crystals 5 to 15 microns in size, arranged directly on the surface of the sediment particles (Fig. 7A, B). Occasionally they were partially covered by micrite, consisting of aggregates of acute rhombohedral crystals or anhedral grains (Fig. 7C). Low magnesium calcite (LMC) was also detected in the most proximal and emerged part of CA6 (0.85wt% Mg), formed by steep rhombohedral crystals ranging from 75 to 100 microns (Fig. 7D). ARG crystals were not observed in the cement samples under SEM.

When exposed, beachrocks are subject to the erosive action of waves, and consequently they are progressively degraded. Remnants of partially destroyed beachrocks, consisting of grouped disaggregated blocks of sandstone and conglomerate up to 1 m³ in size and located at depths of -3 m to -6 m MSL were identified near CA2, 4 and 10. They correspond to beachrocks that had been completely obliterated due to prolonged exposure.

Processes such as dissolution and bioerosion can also contribute to the degradation of beachrocks. Although dissolution has been reported as an important process in the development of erosional features in calcareous beachrocks (e.g. Hopley and Mackay 1978), in the deposits studied here, karstification is not a significant process because they have a siliceous composition and are submerged in the sea water. By contrast, the biological activity on the surface of all the studied beachrocks was great. Algae and other fouling organisms had degraded the surface, creating an altered coating layer, 0.5 mm to 15 mm thick, which was less competent than the fresh deposit due to its poorer cementation and higher organic matter content.

Nevertheless, the role of the biological processes in the degradation of these beachrocks is very limited when compared with the erosive effects of waves. These effects are (1) the undermining of the substrate on which they settle, (2) the differential erosion of beachrock layers, and (3) direct abrasion on the beachrock surface.

The undermining of the beachrock base was a generalized process in all studied cases, predominantly at the distal part that is more exposed to wave action. The bedrock (weathered granite and schist) is less resistant to erosion than the cemented beachrock. For this reason, the bedrock is eroded and the lower layers of the beachrock form visors. This process is more intense in CA7, where the substrate is built of unconsolidated marine sediments. In CA3, 7, 13, 14, 17 and 18, the undermining has generated subvertical fractures with rectilinear trends, spaced 0.5 to 5 m, which in plan view tend to form orthogonal systems, with one of the fracturing families parallel to the maximum length and the other to the width of the deposit (Fig. 8A). This is a common pattern in beachrocks reported in the literature (e.g. Strasser and Davaud 1986, Vousdoukas et al. 2007). Tilting and collapse of blocks dissected by the fracture system contribute to beachrock degradation. This process was reported by Caron (2012) to be enhanced during rough storms in tropical regions, but we have no data to corroborate whether it occurs analogously in the study area.

There is a stratigraphic control over the differential erosion of the layer sequence of all the studied beachrocks. Differential erosion generates metric-scale cuesta-type forms, with the steep side facing landwards (Fig. 8B). These landforms have been widely reported in the literature (e.g. Danjo and Kawasaki 2014). In the studied beachrocks, rough differences in competence of the different layers generate visors (Fig. 8C), arches and short tunnels (Fig. 8D).

One of the most widespread surface erosional forms of beachrocks are rounded erosional potholes (e.g. Hopley and Mackay 1978). In all the studied beachrocks these landforms are present, with diameters ranging from 5 to 250 cm and depths of up to 50 cm (Fig. 8E). They are often filled with gravels and cobbles. Their genesis is analogous to those formed in the rocky riverbeds. The progressive enlargement of both diameter and depth is most likely the result of cavitation and abrasion caused by gravels that are trapped inside the cavity and that violently twist and impact against the walls and bottom of the potholes during storms. The enlargement of the potholes favours interference and merging with each other, leading to more complex and irregular forms (Fig. 8F). The merging of hollows may evolve to sinuous rills, which act as flow paths for sediments during wave surges. In CA3, 4, 7, 9, 13 and 14, the bottoms of some erosional potholes are partially filled with cemented gravels. The cement is usually calcium carbonate, and occasionally metal oxides. The latter derive from the alteration of artificial iron artefacts and coins (copper and bronze), which, together with lead fishing weights, become trapped at the bottom of the cavity due to their high density.

Absolute ¹⁴C ages from seven different beachrocks were determined by dating up to 12 carbonate seashells and 1 charcoal sample. The results obtained correspond to terminus post quem ages for the sediment cementing process, because shells and charcoals included in the beachrock sediments predate this process. A calcareous coralline algae bioconstructed level, emplaced between two overlapping levels in CA14, was also dated by ¹⁴C. These algae were embedded on the lower level, which was necessarily already cemented. Later, the upper level was deposited and cemented on its top. All the obtained ages are from the Late Holocene (Table 5).

The complete geochronology of the sequence of two beachrocks that overlap on CA14 was established from six dates by ¹⁴C (Fig. 4). The upper level (-0.25 to -2.5 m MSL deep) was dated between the 13^th and 20^th centuries AD (SP4, 1207-1586 cal AD; SP3, 1275-1644 cal AD; SP6, 1532-1939 cal AD). A significantly older age was reported for the lower level samples (mH= -3.75 m MSL) (SP5, 343 cal BC-146 cal AD; SP2, 59 cal BC-448 cal AD). In agreement with the intermediate stratigraphic position, the age of the embedded coralline algae level (SP1, 144-618 cal AD) is between those of the upper and lower levels.

The ¹⁴C ages of two seashells from the upper level of CA1 (-1.0 to -2.5 m MSL deep, unit “a” in Fig. 3B) are similar to those of the upper level of CA14, ranging from the 11^th to the 20^th centuries AD (PF1, 1071-1454 cal AD; PF2, 1598-Post 1950 cal AD). The upper level of CA17 (-2.0 to -3.0 m MSL) also yielded a similar age (MM1, 1673-1743 AD (28%), 1798-1942 AD (66%); MM2, 1679-1950 AD).

The dating results of seashells from shallower beachrocks also falls within the same age range: CA3 (LLA1, 1042-1427 cal AD), CA7 (SAC1, 1665-post 1950 cal AD) and CA11 (BEL1, 1188-1529 cal AD), while CA6 sample is older (CP1, 693-1110 cal AD).

The upper level of CA14 was also dated by OSL (SPSW1, 1674-1718 AD), and the OSL date falls within the same time span as that obtained by ¹⁴C. CA3 was also dated by OSL (LLAW1, 1207-1297 AD). The CA3 rock block sample was dated by both OSL and ¹⁴C. The calibrated ¹⁴C age (1042-1427 cal AD) is in agreement with the OSL date, and constrains the formation of this beachrock to around the 13^th century AD, because the OSL age cannot be earlier than the age of the seashell.

Absolute ages were complemented by studying anthropic materials embedded in five of the beachrocks (Table 6). As bioclasts and charcoal, these artifacts establish a relative terminus post quem age for the cementation of the deposit. These artifacts are mostly worn fragments of tegulae, amphorae and pottery from the Roman Period (2^nd c BC-5^th c AD) (CA3, 14 and 18), although ceramic material from the Iberian period (6^th c-1^st c BC) (CA4) and from the Middle Ages to modern times (11^th-18^th c AD) was also identified with certainty (CA7 and 14). The overall results confirm the Late Holocene age of the studied beachrocks, which is consistent with the absolute ¹⁴C and OSL ages. The upper level of CA14 (Fig. 4, Table 6, samples SPS1-9) yielded eight roughly worn ceramic shards and one glass fragment. Their ages span from Roman to medieval times (2^nd c BC-15^th c AD). The medieval artefacts (7^th-15^th c AD) are the ones that would be closest to the cementing date, since they are the youngest. Four ceramic fragments from Roman times were recovered from the intermediate level of CA14 (bioconstructed level of coralline algae, samples SPI1-4), whose chronology ranges from the 1^st c BC to the 2^nd c AD. Among all the elements, an amphora rim of the Tarraconense-1 type (sample SPI4) produced from 40 BC to 5 AD stands out (Tremoleda 2000).

It is widely accepted that, with some exceptions, the cementation of the beachrocks occurs in the intertidal beach zone (Webb et al. 1999, Vousdoukas et al. 2007) and that it is a consequence of the chemical and biological processes that take place there. On the studied coast, the astronomic tidal range is ca. 15 cm, so it lacks a proper intertidal zone.

Comparing the characteristics of the beachrock sediments and those of the foreshore and upper shoreface of the current beaches with the mineralogy of the beachrock cements allows us to establish that the cementation occurs in the swash zone and adjacent foreshore. This finding is well supported: First, the proportion of bioclasts determined in the samples rules out the possibility that the upper shoreface is part of the cemented sediments, because it contains a greater quantity of bioclasts (mean 2.72%) than the beachrocks (mean 0.23%). An exceptional sample from CA6 contains 8.5% of bioclasts, but its size is that of sand and it contains no shells larger than 2 mm. In contrast, the current shoreline sediment samples from this site contain up to 0.2% of seashells larger than 2 mm. The content (mean 0.75%) and size of the bioclasts in the sediment samples from the foreshore match better those of the beachrocks, suggesting that the cementing occurred in or near the emerged sector of the beach. Second, the grain size of the beachrocks is greater than that of the upper shoreface sediments of the current beaches (Fig. 5A, Table 3). Conversely, the current foreshore shows a particle size similar to that of the cemented deposits, but generally slightly finer. It should be noted that the CA3 and CA7 beaches have been subjected to nourishment with fine sand in recent years. However, this slight difference in grain size is also observed on beaches that have not been anthropically altered (for example CA1, 4 and 11). This suggests that the cementing could also affect sediments from the swash zone, which usually has a higher average particle size than the foreshore. Third, the beachrock cement (HMC) indicates that the precipitation occurred in contact with the seawater, which restricts the beachrock formation zone to the swash zone and adjacent foreshore. The ARG detected on two samples by XRD, which was not observed by SEM, may correspond to bioclasts. The presence of LMC in a sample from the most superficial part of CA6 (above the current sea level) indicates the local influence of meteoric water on the cementing processes.

Some limitations in the beachrocks formation ages obtained from dating seashells by ¹⁴C should be considered. The post mortem residence time of seashells in the sediments of the beaches before their cementation is one of the longest. Long residence times imply that the dates obtained can be hundreds of years older than the cementation of the deposit (Mouslopoulou et al. 2015). In general, residence in carbonate environments is shorter than in siliciclastic environments due to greater bioerosion and dissolution (Kidwell et al. 2005). The seashell post mortem residence time in the study area is likely to be of the order of a few years to a few decades at most. Thus, by selecting for dating the seashells with little evidence of mechanical and biological erosion, it can be assumed that the ages obtained are close to the cementing time. This finding is well supported: First, the grain size of the deposits is dominated by gravel and the lithology by quartz, so the competence against mechanical erosion of the seashells during events of wave surges is presumably too low. Second, some of the studied beaches are very small (beach length <100 m in CA5, 8, 11, 12 and 15) (Table 1), and their uncemented sediments are almost completely washed after intense storms (e.g. CA4, 5 and 6 after the December 2008 and January 2020 storms). Third, in the cemented deposits and in the foreshore of the current beaches, the total bioclast content is very low (mean 0.23% and 0.75%, respectively) and the presence of seashells larger than 2 mm is exceptional (maximum of 0.04% and 0.1%, respectively), whereas in the current shoreface it is much higher (up to 0.5%). This suggests that the seashells are destroyed in the surf zone in a short time. Fourth, given the fragility of charcoal within a high-energy medium such as a beach, it can be assumed that its residence time is very low. The charcoal and shell dated at CA17, coming from the same rock block sample, show the same age, supporting the hypothesis that the residence time of the seashells is also low. Fifth, the time span for the ceramics embedded in the beachrocks is prior to the ¹⁴C ages, which shows that the residence time of ceramic artefacts is longer than that of seashells. In addition, this also indicates that dating beachrocks only because of their archaeological remains may lead to overestimation of their real ages of formation.

Another limitation of ¹⁴C dating is the incorporation of old carbon in the seashells (Mouslopoulou et al. 2015). Old carbon from substrate carbonates can accumulate in carbonate skeletons of marine organisms through ingestion. The only beachrock with calcareous rocks in the area is CA1, which includes 34.2% of marble lithoclasts (Fig. 5B, Table 4). The two ages obtained from the dating of this beachrock (1071-1454 cal AD and 1598-post 1950 cal AD) are the same as those obtained from the nearest and strictly siliciclastic ones (i.e. CA3, 1042-1427 cal AD; CA11, 1188-1529 cal AD; CA7, 1665-post 1950 cal AD), suggesting that the effect of old carbon is not significant here.

The main problem with the obtained ¹⁴C ages is the calibration of the seashells due to the highly variability of the local reservoir effect of the sea (ΔR). The available values of ΔR applicable in the study area were reported by Siani et al. (2000) and are part of the Marine20 database. The eight nearest points (<400 km) have ΔR values that vary between -39±35 (Banyuls, at 6 km from the northern limit of the study area) and -255±35 (Toulon, ca. 230 km to the northeast). The weighted mean ΔR of these eight points is -140 ±74 yr.

The correspondence between the CA17’s charcoal-calibrated age-which does not require ΔR correction-and the seashell extracted from the same rock block was used to adjust the applicable ΔR values. The charcoal has a median probability date (MPD) of 1834 cal AD and, applying the weighted mean ΔR of the eight nearest points in the seashell calibration, the MPD is 1836 cal AD. Therefore, the set ΔR value was considered suitable to calibrate all the ¹⁴C ages of the seashells in the study area.

The OSL age of the rock block sample from CA3 beachrock further allowed us to test the consistency of the ΔR calibration value. Applying the nearest ΔR value (-39±35 yr), the MPD is 1338 cal AD. This age is younger than that obtained by OSL (1252 cal AD), which is not consistent, since the seashell must be either synchronous with or older than the burial date of the sediment in which it is included. Conversely, by applying the weighted mean ΔR of the eight nearest points (-140±74 yr), the MPD is 1243 cal AD, which in this case is consistent enough with the OSL results.

Both the absolute dates (¹⁴C, OSL) and the anthropic material dating indicate that the studied beachrocks are Late Holocene in age, corresponding to three main phases of formation (Fig. 9), from oldest to more modern:

Phase I is reported at the lower level (below -3.75 m MSL) of the beachrock CA14, with MPD ranging from 85 cal BC to 198 cal AD. These ages are consistent with that of the covering bioconstructed layer (MPD 386 cal AD), which formed after the lower level was cemented (Fig. 4). The lack of additional age data does not allow us to establish whether other beachrock levels located at similar depths (i.e. lower levels of CA1, CA16 and CA17) are contemporary, nor is possible to discern the age of the distant and deeper ledges that form the multiple-sequence beachrocks (i.e. CA6 and CA15).

Phase II is reported by the sample of the proximal and shallower level of the CA6 multiple-sequence beachrock (+0.25 m to -2.5 m MSL), with an MPD of 906 cal AD.

Phase III is reported in the upper levels (+0.5 m to -3.0 m) of CA1, 14 and 17 and in the CA3, 7 and 11. This phase comprises an MPD between 1243 and 1836 cal AD. All the shallowest and proximal beachrocks in the study area were probably formed during this phase. Specifically, the dates obtained for this phase are grouped into four sets: Phases IIIa, IIIb, IIIc and IIId. Samples PF1, LLA1 and LLAW1 belong to Phase IIIa, which chronologically comprises an MPD between 1243 and 1283 cal AD. Phase IIIb includes samples BEL1, SP3 and SP4, which have an MPD of between 1365 and 1439 cal AD. Phase IIIc includes samples PF2, SP6 and SPSW1, which have an MPD of between 1696 and 1779 cal AD. Phase IIId includes samples SAC1, MM1 and MM2, which have an MPD of between 1824 and 1836 cal AD (Fig. 9).

The SST is assumed to play a key role in the formation of beachrocks, because it controls the chemical reactions of calcium carbonate precipitation, evaporation and microbiological activity, which are favoured at higher temperatures (e.g. Morse and Mackenzie 1990, Zhao et al. 2019). Therefore, a correspondence between the phases of beachrock formation and warm climatic conditions would be expected. The SST variability during the last 2.7 kyr in the western Mediterranean was established from sediment cores recovered from the north of Minorca island (Fig. 1), from the Mg/Ca_{G. bulloides} and alkenones ratios and from δ¹⁸O measurements (i.e. Moreno et al. 2012, Cisneros et al. 2016, Margaritelli et al. 2018). This SST variability and the climate periods are represented in Figure 9. The MPD of samples corresponding to Phase I and the algal bioconstructed layer fall within the warm and humid Roman Period. It is noteworthy that Roman Period conditions are the warmest of the last 2 kyr (Margaritelli et al. 2020). Phase II corresponds to the warm and arid Medieval Climate Anomaly, which indicates that a dry climate also favours cementation by evaporation of the beach sediment porewater. Phase III covers the Little Ice Age and the Industrial Period. Specifically, Phase IIIa and Phase IIIb correspond to the early warmer Little Ice Age interval (LIAa, Cisneros et al. 2016). A fitted positive correlation between the age ranges of both phases and the SST variation is observed, illustrating that the SST rise promotes beachrock formation (Fig. 9). On the other hand, Phase IIIc does not fit the high SST condition, but the age range for Phase IIIc (MPD 1696-1779 cal AD) roughly matches the relative climate optimum recorded in Europe between 1715 and 1760 cal AD (Oliva et al. 2018). Furthermore, the arid pulse recorded at several sites of NE Spain between 1730 and 1790 cal AD (Corella et al. 2013) also matches Phase IIIc. Phase IIId (MPD 1824-1836 cal AD), dated within the Industrial Period, also does not correlate with high SST records. According to Oliva et al. (2018), the study area suffered extreme events between 1815 and 1835, including prolonged droughts. The instrumental precipitation records also reported a dry period between the 1810s and the 1840s, with more than 80% of the precipitation records below the average (Prohom et al. 2015). These data suggest that this beachrock formation phase may be related to severe porewater evaporation processes.