OSL rock surface exposure dating as a novel approach for reconstructing transport histories of coastal boulders over decadal to centennial timescales

. Wave-transported boulders represent important records of storm and tsunami impact over geological timescales. Their use for hazard assessment requires chronological information that in many cases cannot be achieved by established dating approaches. To fill this gap, this study investigated, for the first time, the potential 15 of optically stimulated luminescence rock surface exposure dating (OSL-RSED) for estimating transport ages of wave-emplaced coastal boulders. The approach was applied to calcarenite clasts at the Rabat coast, Morocco. Calibration of the OSL-RSED model was based on samples with rock surfaces exposed to sunlight for ~2 years, and OSL exposure ages were evaluated against age control deduced from satellite images. Our results show that the dating precision is limited for all boulders due to the local source rock lithology which has low amounts of 20 quartz and feldspar. The dating accuracy may be affected by erosion rates on boulder surfaces of 0.06-0.2 mm/year. Nevertheless, we propose a robust relative chronology for boulders that are not affected by significant post-depositional erosion and that share surface angles of inclination with the calibration samples. The relative chronology indicates that (i) most boulders were moved by storm waves; (ii) these storms lifted boulders with masses of up to ~40 t; and (iii) the role of storms for the formation of boulder deposits along the Rabat coast is 25 much more significant than previously assumed. Although OSL-RSED cannot provide reliable absolute exposure ages for the coastal boulders in this study, the approach has large potential for boulder deposits composed of rocks with larger amounts of quartz or feldspar, older formation histories and less susceptibility to erosion.


Introduction
Coastal boulders with masses of up to tens or hundreds of tons, located well above high tide level or far inland 30 from the shoreline, are impressive evidence for the occurrence and impact of tsunamis and extreme storms (e.g. Engel and May, 2012;May et al., 2015;Cox et al., 2019). Such geological imprints may be preserved over periods that significantly exceed instrumental and historical records (Yu et al., 2009;Ramalho et al., 2015), making them valuable archives for long-term hazard assessment. Compared to sandy tsunami and storm deposits, which are used more commonly for this purpose, wave-transported boulders are abundant along rocky coastlines and can be 35 preserved over geological time scales even in settings dominated by erosion . Furthermore, boulder transport may provide information on the magnitude of prehistoric tsunamis and storms that cannot be deduced from sandy sediments (Nandasena et al., 2011). https://doi.org/10.5194/esurf-2020-46 Preprint. Discussion started: 21 July 2020 c Author(s) 2020. CC BY 4.0 License.
For coastal boulders to be valuable for hazard assessment, they have to provide information on the frequency of the associated flooding events, which in turn requires chronological information on boulder displacement. Since 40 boulders unlike sandy storm and tsunami deposits typically lack a stratigraphic context, dating approaches rely on chronometers related to the boulder rock itself or on constructive features attached to the boulder, such as marine organisms or flow stones. Established dating approaches are based on radiocarbon ( 14 C) and U-series ( 230 Th/ 234 U) dating of organic carbonates (e.g. Zhao et al., 2009;Araoka et al., 2013), and thus require coral boulders or the presence of attached marine organisms, as well as coincidence between the death of these organisms and the 45 transportation event. Direct ages for the transport of coastal boulders were achieved by using terrestrial cosmogenic nuclide surface exposure dating (Ramalho et al., 2015;Rixhon et al., 2017) and palaeomagnetic dating (Sato et al., 2014), but due to intrinsic methodological limitations these approaches are restricted to certain boulder lithologies and time scales.
The recently developed optically stimulated luminescence (OSL) rock surface dating technique (see review by 50 King et al., 2019) offers completely new opportunities for directly dating the transport of coastal boulders. While the application of the more routinely used OSL rock surface burial dating technique (e.g. Simms et al., 2011;Sohbati et al., 2015;Jenkins et al., 2018;Rades et al., 2018) is typically impeded for coastal boulders due to logistical problems with sampling the (inaccessible) light-shielded bottom surfaces of clasts weighing several tons, the OSL rock surface exposure dating (OSL-RSED) technique introduced by Sohbati et al. (2011) can be applied 55 to the light-exposed top surfaces of such clasts. For boulders that were overturned during wave transport and that experienced negligible erosion and shielding of their top surfaces after deposition, post-transport exposure periods may be estimated based on the time-dependent progression of OSL signal resetting, the so-called bleaching front, into the uppermost millimetres to centimetres of the rock (Sohbati et al., 2012;Freiesleben et al., 2015;Lehmann et al., 2018;Gliganic et al., 2019). OSL-RSED could therefore provide ages for coastal boulders that are not datable 60 by any other technique. OSL-RSED is applicable to a wide spectrum of lithologies, as long as they contain quartz and/or feldspar, and to timescales of decades, centuries up to a few millennia.
Here, we present the first application of OSL-RSED to reconstruct storm and/or tsunami frequency patterns from wave-emplaced boulders. All analyses were conducted on carbonatic sandstone boulders from the Atlantic coast of Morocco, south of Rabat, that were previously documented by Mhammdi et al. (2008) and Medina et al. (2011). grains during stimulation with laboratory light. In natural settings, resetting of OSL signals takes place by sunlight exposure during sediment transport, so that sediment grains can provide information about the time that passed since the last sunlight exposure (burial age).

80
The uppermost millimetres to centimetres of rock surfaces exposed to sunlight experience bleaching and accumulation of OSL signals at the same time. However, OSL signal resetting or bleaching is by far the dominant process in rocks with low environmental dose rates and Holocene exposure histories (Sohbati et al., 2012). For coastal boulders with dose rates of less than 1 Gy/ka and ages post-dating the stabilization of Holocene eustatic sea level around its present position about six millennia ago (e.g. Khan et al., 2015), as investigated in this study, 85 OSL signal accumulation can be neglected. The time-dependent evolution of OSL signals in the upper layer of exposed boulder surfaces can therefore be reduced to the term for OSL signal resetting, which following Sohbati et al. (2012) is expressed by where L0 is the initial OSL signal intensity prior to exposure, L the remaining OSL signal at depth x (mm) after 90 exposure, te (s) the exposure time, 0 (s -1 ) the effective bleaching rate of the OSL signal at the rock surface (i.e. the product of the photo-ionisation cross section σ, and the light flux at the rock surface 0 ), and μ (mm -1 ) the light attenuation coefficient of the rock.  (1) can be used to estimate the transport age of boulders overturned by waves.
When attached to the cliff, only the (usually bio-eroded) upper surface of a typical boulder in the pre-transport 95 position is exposed to sunlight and experiences OSL signal resetting (Fig. 1a). Its shielded bottom side is only exposed to ionising radiation from radioactive elements in the surrounding rock and cosmic rays that, after a prolonged time, cause OSL signals to be in or close to field saturation (Fig. 1a). When overturned during transport, the new upper surface of the boulder in the post-transport position is suddenly exposed to sunlight and the bleaching front starts to move into the rock (Fig. 1b); the same is true for the surfaces of quarrying niches that are 100 formed by boulder detachment (Fig. 1b). In both cases, the exposure time can be estimated by fitting Equation (1) to the depth-dependent OSL signals measured in rock samples collected from these surfaces. The shielded bottom side of the boulder in the post-transport position is generally suitable for rock surface burial dating, by making use of the time-dependent dose accumulation in the previously bleached surface; due to inaccessibility of shielded surfaces for sample collection this was not tried in this study.

Marine flooding hazard along the Atlantic coast of Morocco
The approximately 3000 km-long Moroccan Atlantic coast is exposed to swell waves, north Atlantic winter storms and rare tsunamis that cause erosion and/or flooding of low-lying areas. The energy of swell waves is strongest along the central section of the Moroccan coast, between Agadir and Rabat, since it is not sheltered by the Canary 110 Islands or the Iberian Peninsula; waves approach from the northwest to west and are significantly stronger during winter (Medina et al., 2011). The influence of Atlantic hurricanes is comparatively small (Fig. A1a) with only two former tropical storms recorded to have made landfall as tropical depressions (core pressure 988-1000 hPa) at the coast of Morocco and the southern Iberian Peninsula between 1851 and 2016 (Fig. 2a). Instead, maximum wave heights are associated with winter storms that typically cross France or the UK (Fig. A1b), but may have tracks as 115 https://doi.org/10.5194/esurf-2020-46 Preprint. Discussion started: 21 July 2020 c Author(s) 2020. CC BY 4.0 License. far south as Morocco (Fig. 2a). During recent winter storms within the last century, wave heights of up to 7 m (compared to regular swell heights of 0.5-1.5 m) have been observed at the Rabat coast (Mhammdi et al., 2020), associated with flooding of back-beach areas and waves overtopping the coastal cliff (Fig. A2).
An additional flooding hazard emanates from tsunamis triggered by earthquakes offshore of Portugal, between the Azores triple junction and the Strait of Gibraltar, where the African and Eurasian plates converge at a rate of ~4 120 mm per year (Zitellini et al., 1999). After earthquakes in 1941After earthquakes in , 1969After earthquakes in and 1975 (Kaabouben et al., 2009). Triggered by a Mw 8.5 earthquake, probably due to the rare event of a combined rupture of different seismic structures (Baptista et al., 2003), the 125 associated tsunami is the only known destructive flooding event at the Moroccan coast. Historical sources from Rabat describe the inundation of streets as far as 2 km inland, wreckage of ships in the harbour, and drowned people and camels (Blanc, 2009). Although numerical models indicate that the wave heights of 15 m mentioned in historical reports from Tanger and Safi are most likely exaggerated and that values of 2.5-5.0 m are more realistic (Fig. 2a;Blanc, 2009;Renou et al., 2011), the effects of the 1755 tsunami on the coastal landscape of Morocco 130 were nevertheless significant (e.g. Ramalho et al., 2018).

Exploiting geological evidence for hazard assessment -The Rabat boulder fields
While instrumental and historical records demonstrate the flooding hazard at the Moroccan coast due to both storms and tsunamis, all documented events except the 1755 Lisbon Tsunami were restricted to the last decades.
This does not allow for robust estimates of long-term tsunami and storm occurrence or of all possible magnitudes 135 of storm surges and tsunami inundation. Most published regional geological tsunami and storm evidence for the pre-instrumental era is restricted to Spain and Portugal (e.g. Dawson et al., 1995;Hindson and Andrade, 1999;Lario et al., 2011;Costa et al., 2011;Feist et al., 2019), but fields of wave-emplaced boulders offer records of past storms and/or tsunamis for Morocco (Mhammdi et al., 2008;Medina et al., 2011) that could inform about the regional long-term hazard if robust chronological data were available.

140
The most prominent boulder fields are reported from a 30 km long NE-SW oriented coastal section between Rabat and Skhirat (Fig. 2a,b), consisting of hundreds of boulders with estimated masses between a few and more than 100 t (Mhammdi et al., 2008;Medina et al., 2011). The geomorphology and geology of this area is characterised by a succession of coast-parallel, Pleistocene calcarenite ridges that are related to sea-level highstands and rest on a Palaeozoic basement . A typical cross section (Fig. 2c,d) is composed of: (i) the intertidal 145 platform with an active coastal cliff; (ii) the youngest lithified calcarenite ridge, formed during MIS 5; (iii) an inter-ridge depression, called Oulja, which may be flooded at high tide (the spring tide range is 2-3 m), and which is covered by recent and/or Holocene beach deposits; and (iv) an older calcarenite ridge, probably formed during MIS 7, including an inactive cliff (Medina et al., 2011;Chakroun et al., 2017;Chahid et al., 2017). Towards Rabat, the younger calcarenite ridge is replaced by a simple sandstone platform (Fig. 2e).

150
As described by Mhammdi et al. (2008) and Medina et al. (2011), most of the calcarenite boulders were sourced from the active cliff (Fig. 2c). Since detachment is guided by lithological boundaries between the calcarenite and interbedded clay units, most of the boulders have platy shapes; only occasionally were boulders derived from subtidal positions and lifted up to 5 m vertically to the top of the first calcarenite ridge, as indicated by vermetids, or sourced from younger sandstones covering the Oulja. The boulders are deposited as single clasts, clusters, or 155 https://doi.org/10.5194/esurf-2020-46 Preprint. Discussion started: 21 July 2020 c Author(s) 2020. CC BY 4.0 License. imbricated stacks that rest on top or at the backward slope of the first calcarenite ridge, in the Oulja, or rarely at the seaward slope of the older calcarenite ridge up to 300 m inland (Fig. 2c). The position and orientation of bioerosive rock pools formed on the surface of the youngest ridge (i.e. the pre-transport surface of most boulders) offers insights into transport modes. While some boulders moved by sliding only, others were overturned during transport as indicated by down-facing rock pools on the pre-transport surface (Mhammdi et al., 2008;Medina et 160 al., 2011). For some of the larger boulders, sliding movement by storm waves after their initial detachment from the cliff is documented on satellite images (Fig. A3). Movement of smaller boulders with up to 1 m³ (~2.5 t) was frequently observed after recent winter storms such as Hercules/Christina in January 2014 (Mhammdi et al., 2020).
At some places along the coast between Rabat and Casablanca even boulders exceeding 10 t have been pushed landward during recent winter storms (Mhammdi et al., 2020).

Methods
Boulders sampled for dating were characterized in the field with regard to their position, orientation, dimension and surface taphonomy. Distance from the active cliff and elevation above mean high tide level were measured using a laser range finder. Boulder volume estimates (V) are based on tape measurements of a-(length), b-(width) and c-axes (height) and an empirical correction factor of 0.5 (Engel and May, 2012) using 170 = ( * * ) * 0.5, To calculate boulder weights, volumes are multiplied with boulder densities (ρB) determined individually for each sample using the Archimedean principle of buoyancy in water following with wa = weight of the sample in air, ww = weight of the sample in water and ρW = density of sea water (1.02 175 g/cm³). Surface orientation and inclination of sampled boulders were measured with a compass.
For OSL-RSED, samples of approximately 10 cm³ were collected from selected boulder surfaces using a combination of a battery-driven rock drill, hammer and chisel. Rock samples were wrapped in black plastic bags and brought to the Cologne Luminescence Laboratory (CLL) for further processing under dimmed red-light conditions. First, a circular rock saw was used to cut ~5 cm thick surface slabs, from which cores of ~1 cm diameter 180 and ~4 cm length were extracted using a bench drill (Proxxon Professional) with water cooled diamond core bits.
After immersion in resin (Crystalbond 509, the resin was tested to have no OSL emission) and subsequent oven drying to stabilize fragile parts of the sandstone cores, they were cut into ~0.7 mm thick slices using a water-cooled low speed diamond saw (Bühler Isomet 1000) with 0.3 mm blade thickness. Slices were gently crushed with a mortar to obtain polymineralic sand grains that were fixed on aluminium cups using silicon grease in monolayer.

185
Separation of pure quartz and/or potassium feldspar for the grains of each slice, standard practice in conventional OSL dating, was not feasible due to the large number of slices and the small amount of polymineralic grains per slice.
To optimize the information extracted from the polymineralic samples, all luminescence measurements followed a post-IRSL-BSL protocol (e.g. Banerjee et al., 2001) that records an infrared stimulated luminescence (IRSL) 190 signal at 50 °C for 160 s, followed by a blue stimulated luminescence (BSL) signal at 125 °C for 40 s (Tab. A2).
Measurements were performed on a Risø TL/OSL DA20 reader equipped with an U340 filter for signal detection.
All thermal treatments were performed with heating rates of 2 °C/s. In the post-IRSL-BSL protocol, stimulation with infrared LEDs specifically bleached luminescence signals originating from feldspar (feldspar IRSL). This reduced the contribution of feldspar signals to the BSL signal of quartz (quartz BSL), which unlike feldspar is 195 insensitive to infrared stimulation (cf. Bailey, 2010).
For validation of the post-IRSL-BSL protocol, pure quartz and potassium feldspar extracts in the 150-200 µm grain-size fraction were prepared for the light-shielded parts (i.e. >5 cm below surface) of the 10 cm³ sample blocks of HAR 1-1 and TEM 3-1. Sample preparation followed standard coarse grain procedures including dry sieving, treatment with 10% HCl and 10% H2O2, density separation (potassium feldspar<2.58 g/cm³<2.62 For OSL-RSED, the natural OSL signals (Ln) and the OSL signals in response to a ~12 Gy test dose (Tn) of the post-IRSL-BSL protocol were measured for the polymineralic grains of all crushed slices to generate plots of OSL 210 signal versus depth below the boulder surface. The depth-dependent Ln/Tn data of each core (mean of two aliquots) were normalized to the core's individual background level calculated from the average of the deepest 5-10 slices.
The normalized data of all cores of a sample were then averaged (arithmetic mean and standard error) to receive a mean signal-depth curve for each rock sample; only apparent outliers, i.e. cores with signal-depth trends completely different from all other cores of the sample, were excluded from averaging. The mean signal-depth 215 curves were fitted with Equation (1) using the unweighted rock surface exposure dating function in the R package "Luminescence"  and the software OriginPro (version 8.5). Shared µ values for each site and shared 0 values for flat calibration surfaces were determined using the "global fit" function that allows the fitting of multiple signal-depth curves at the same time. Post-depositional erosion has recently been shown to exercise a strong effect on the depth of the bleaching front, and thus the apparent age, of exposed rock surfaces (Sohbati et 220 al., 2018;Lehmann et al., 2019a,b;Brown and Moon, 2019). Their potential effects were therefore modelled using the approach of Lehmann et al. (2019a).

Boulders selected for OSL surface exposure dating
Samples for OSL-RSED were collected from nine boulders at four different sites along the Rabat coast in July 225 2016, including Rabat (RAB), Haroura (HAR), Temara (TEM) and Val d'Or (VAL) (Fig. 2b). Boulders selected for dating were composed of carbonate-cemented sandstone (calcarenite) with clear signs of overturning during transport, indicated by down-facing rock pools and/or fresh-looking post-transport surfaces (Fig. 3d). To ensure comparable preconditions for sunlight exposure, only surfaces without significant shielding by vegetation, other boulders or water, and wherever possible without significant inclination of their top surfaces were sampled. Most 230 sampled boulders, thus, rested in supratidal positions and had relatively smooth post-transport surfaces (RAB 1, https://doi.org/10.5194/esurf-2020-46 Preprint. Discussion started: 21 July 2020 c Author(s) 2020. CC BY 4.0 License. HAR 1, HAR 2, TEM 3, VAL 4, VAL 6). However, boulders from the intertidal platform with post-transport rock pools (VAL 1, Fig. 3h) or boulders with higher surface roughness probably due to increased sea spray influence (TEM 2 and RAB 5, Fig. 3g) were also sampled for assessing the effects of post-depositional erosion on dating accuracy. In addition, surfaces of niches in the active cliff, exposed after detachment of the associated boulders, 235 were sampled at Haroura (HAR 3, Fig. 3e) and Temara (TEM 4).
The characteristic features of all sampled boulders -including post-transport position, arrangement, shape, dimension, orientation of the sampled surface and taphonomy of boulder surfaces -are summarized in Table 1.

Luminescence properties of the dated sandstone
Comparative measurements on polymineralic grains and potassium feldspar extracts on sample HAR 1-1 show that post-IRSL-BSL signals from the polymineralic aliquots of all four sites are (i) the dominant emission compared to IRSL signals, and (ii) relatively unaffected by a feldspar signal contribution (Fig. A12). Therefore, 255 OSL-RSED in this study was based on the mainly quartz derived post-IRSL-BSL signal of polymineralic aliquots.
Experiments on pure quartz extracts of sample HAR 1-1 revealed adequate OSL properties in terms of rapidly decaying signals dominated by the fast component (Fig. A12a,b), independence of thermal treatment for the selected preheat temperature (Fig. A13), and good reproducibility of laboratory doses (dose recovery ratios of 1.02-1.08). Similarly, suitable OSL properties, i.e. signals dominated by the quartz fast component (Fig. A12c) 260 and successful dose recovery experiments, are also documented for post-IRSL-BSL signals of polymineralic aliquots.
When plotted against their depth below the boulder surface, test dose corrected and normalized mean post-IRSL-BSL signals from the uppermost 15 mm of each sample (note that signal-depth curves of each sample are based on 2 to 5 cores with 2 aliquots per slice) showed a general increase from completely reset signals at the rock surface 265 towards a constant background level deeper in the rock (Fig. 4, Fig. A14, A15). The background levels reflected a quartz palaeodose of ~40-50 Gy or an age of ~80-100 ka (measured on HAR 1-1 and TEM 3-1, Tab. A4), which is below the sample-specific saturation level of 50-120 Gy. The robustness of the average post-IRSL-BSL-depth trends used for dating is supported by good reproducibility of signals derived from different aliquots of the same slice (Fig. 4a), and reasonable correlation of different cores from the same sample (Fig. 4b, Fig. A14, S15). Where 270 https://doi.org/10.5194/esurf-2020-46 Preprint. Discussion started: 21 July 2020 c Author(s) 2020. CC BY 4.0 License. signal-to-noise ratios also allowed feldspar IRSL signals to be analysed (i.e. at TEM and RAB), these showed bleaching fronts that intruded deeper into the rock compared to the post-IRSL-BSL signal (Fig. 4c, Fig. A11).

Calibration of the OSL rock surface exposure dating model using artificially exposed surfaces
To estimate boulder ages with OSL-RSED, measured post-IRSL-BSL signal-depth data were fitted with the bleaching model described in Equation (1). Besides the exposure time (te), the bleaching model contains two 275 further a priori unknown parameters: the effective OSL signal bleaching rate at the rock surface ( 0 ), and the light attenuation in the rock (µ). These vary with geographical location and rock type, respectively, and have to be determined individually for each location and lithology prior to dating. Since determination on the basis of first order principles was not successful in earlier studies (Sohbati et al., 2012), for the Rabat site these parameters were obtained empirically by fitting Equation (1)  For this, fresh rock surfaces were exposed during the first field survey in July 2016 and sampled during the second survey in September 2018, equivalent to an exposure time of ~2.15 years. A total of five calibration samples, at least one rock sample from each site, were collected to account for potential site-to-site variability (CAL samples in Tab. 1). Exposures were created directly on the top surfaces of boulders RAB 5, TEM 3 and VAL 4 (Fig. 285 A17b,d), as well as by placing previously unexposed rock samples collected from boulders HAR 1 and VAL 4 on the roof top of a nearby house (Fig. A17a,c). Since the effective luminescence decay rate ( 0 ) is sensitive to the inclination and orientation of the dated rock surfaces (Gliganic et al., 2019), all exposure surfaces except from TEM 3 CAL, which had the same inclination as the associated dating sample, were orientated approximately horizontally.

290
In a first step, local values for 0 were determined. Since all samples in this study were collected within a radius of less than 20 km, the local light flux should be similar for all surfaces with comparable inclination and orientation. This was supported by fitting each calibration sample individually (Fig. 5,Tab. 2), reflecting systematic differences of 0 only between the inclined calibration surface of TEM 3-1 CAL (1.23x10 -5 s -1 ) and the horizontal calibration surfaces of all other calibration samples (2.7x10 -7 to 4.7x10 -8 s -1 ). We therefore determined 295 a shared 0 value for all horizontal surfaces by simultaneously fitting the respective calibration samples, using 0 (shared) and µ (individual best-fit value for each sample) as free variables and an exposure age of 2.15 years as a fixed parameter (Tab. 2). This resulted in shared 0 values of 1.2(±2.3)x10 -5 s -1 for the inclined surface and 9.2(±2.0)x10 -8 s -1 for the horizontal surfaces.  (1) to all samples from a site at the same time, using µ (shared) and exposure time (individual for each sample) as free variables, and the shared 0 value for horizontal surfaces determined in the previous step as a fixed parameter (only for TEM 3-1, TEM 4-1 and TEM 3-1 CAL the 0 value for inclined surfaces was used). Site-averaged µ values vary between 1.04±0.26 mm -1 at RAB and 1.54±0.31 mm -1 at TEM (Tab. 2), which seem 315 to be much more realistic when compared to the literature values for BSL signal attenuation in quartz sandstone and quartzite of 0.9-1.3 mm -1 (cf. Sohbati et al., 2012, Gliganic et al., 2019.

Model validation and dating of boulders with unknown transport history
OSL exposure ages for all non-calibration boulder and niche samples were derived by fitting their post-IRSL-BSL signal-depth profiles with Equation (1) using the site-averaged µ values and the shared 0 value for horizontal 320 surfaces (the value for inclined surfaces was only used for TEM 3-1 and TEM 4-1) as fixed parameters (Tab. 2).
Complete incorporation of both µ and 0 uncertainties resulted in relatively large fitting uncertainties (Fig. 6a) that were finally reflected in the error margins of the OSL surface exposure ages. The fitted post-IRSL-BSL signaldepth curves of all dating samples and the associated exposure ages are summarized in Figure 6b and Table 2, respectively. To evaluate the accuracy of model-derived exposure ages, they were compared with minimum 325 transport ages deduced from satellite images, eyewitness observations and the depth of bio-erosive rock pools (Fig.   6c). The OSL surface exposure ages of most samples agree with the control ages, i.e. ages either post-dated the minimum age or showed overlap within their dating uncertainties. However, the exposure ages of samples RAB 1-2, VAL 1-1, VAL 1-2, HAR 1-1 and HAR 2-1 were too young, i.e. they pre-dated the minimum control ages.

330
In order to explore whether erosion offers a plausible explanation of the age underestimations recorded for samples RAB 1-2, HAR 1-1, HAR 1-2, VAL 1-1 and VAL 1-2, the potential effect of erosion on the luminescence bleaching profiles was modelled using the analytical approach of Lehmann et al. (2019a). The modelled sample ages (texp mean) and minimum independent ages (tage control) were used as model inputs, together with the shared values of µ and 0 (Tab. 2). 50 different erosion rates from 0.001 mm/year to 1 mm/year were tested together with 50 335 different times for the onset of erosion (ts) ranging from 1 year to the independent sample age (both variables were sampled equidistantly in log space). The misfits between modelled and measured values were determined and paths with normalised misfit >0.99 were retained. The sensitivity of the calculated erosion rates to the independent age was also evaluated by contrasting the results calculated for sample VAL 1-2 for independent ages of 50 years, 450 years and 6000 years, which reflect the minimum exposure age based on satellite images, a plausible estimate 340 of the boulder turning age based on the depth of post-depositional rock pools and finally the time when Holocene sea level reached approximately its present position. The calculated erosion rates vary dependent on ts (Fig. 7

350
The OSL surface exposure ages derived for boulders and niches from the Rabat coast show two striking characteristics: (1) All exposure ages are associated with relatively large dating uncertainties compared to previous applications of OSL-RSED (e.g. Sohbati et al., 2012;Lehmann et al., 2018); and (2) five of the 13 dated boulder samples yield OSL exposure ages that underestimate minimum ages deduced from satellite imagery and rock-pool depth, even when their uncertainties are considered (Fig. 6c).

355
The low dating precision achieved in this study is mainly the result of the boulder source rock, a late Pleistocene calcarenite. All rock samples dated in this study display strongly scattered post-IRSL-BSL signal-depth data (e.g. Fig. 4 and Fig. 5) that entail large fitting uncertainties, imprecisely constrained µ and 0 parameters and, eventually, large dating uncertainties. OSL signal scatter is primarily due to dim post-IRSL-BSL signals with not more than a few hundred photon counts in the analysed signal interval. Since pure quartz extracts of the same 360 samples proved to be rather sensitive (Fig. A12), dim post-IRSL-BSL signals must be the result of low percentages of quartz on the carbonate-rich polymineralic aliquots used for dating. Additional signal scatter is introduced by spatial variations of the post-IRSL-BSL signal accumulated prior to exposure (L0). Since post-IRSL-BSL signals in the relatively young source rocks of the boulders (i.e. 40-50 Gy and 80-100 ka) are not in field saturation, they depend on mineralogy-induced dose rate differences within the rock. Thirdly, a small contamination of post-IRSL-365 BSL signals by feldspar emissions remains in all dated samples. If the amount of feldspar varies from aliquot to aliquot, varying contributions of feldspar emissions to the post-IRSL-BSL signals from polymineralic aliquots will introduce additional scatter. While OSL exposure ages of rocks with more suitable luminescence properties are also affected by fitting uncertainties due to mineralogical heterogeneities (Meyer et al, 2018) and core-to-core variations of OSL signal resetting (Sellwood et al., 2019), previous studies demonstrated that lithologies with 370 brighter quartz signals in polymineralic samples (e.g. quartzite or quartz-dominated sandstone) or stronger feldspar signals to avoid using quartz OSL for dating (e.g. granite or gneiss) can provide much higher dating precision than achieved for the Rabat boulders (Sohbati et al., 2012;Freiesleben et al., 2015;Lehmann et al., 2018;Gliganic et al., 2019).
Although large post-IRSL-BSL signal scatter may also affect dating accuracy, since it prevents using individual µ 375 values for each sample as suggested e.g. by Gliganic et al. (2019), the unambiguous disagreement between exposure ages and age control for five of the boulder samples (Fig. 6c) is interpreted to result from inadequate 0 values and post-depositional erosion. In the constrained geographical area visited in this study, 0 should be comparable for all boulder surfaces as long as they share the same aspect and inclination (e.g. Sohbati et al., 2018). However, if calibration and dating samples do not share surface inclination and aspect, the use of a shared 380 0 value is inappropriate, as observed in controlled bleaching experiments (Gliganic et al., 2019) and indicated by the systematic differences of 0 between calibration samples with inclined and flat surfaces in this study. The clearly too young OSL exposure ages of samples HAR 2-1 and RAB 1-2, i.e. 25±8 and 11±3 years, although these boulders were overturned at least 50 years ago (Fig. 6c) the coastal zone as dated here, the combination of sea-spray and rain-induced weathering and strong winds is likely to cause erosion of grains at the exposed post-transport surfaces (e.g. Mottershead, 1989). By yielding erosion rates from 0.06 to 0.20 mm/year, inversion of the rock surface-exposure data for boulder samples that clearly underestimate age control (i.e. RAB 1-2, HAR 1-1, HAR 1-2, VAL 1-1 and VAL 1-2) supports the assumption of significant erosion for some of the boulders dated in this study (Fig. 7).

395
Such impact of erosion agrees with expectations based on geomorphological evidence for boulders with posttransport surfaces covered by bio-erosive rock pools, such as boulder VAL 1. Since the lower part of this boulders is lying in the intertidal zone, it is regularly covered by sea spray and overtopping waves. Surfaces between bioerosive rock pools, which can form with erosion rates of up to 1 mm/year (e.g. Kelletat, 2013), were sampled in the case of VAL 1-1 and VAL 1-2. For these samples relatively large modelled erosion rates of 0.20 mm/year, 400 when assuming an age of ~450 years based on rock-pool depth and bio-erosion rates of 1 mm/year (Fig. 7a), may therefore be realistic. These data illustrate the spatial heterogeneity in erosion rates for some of the coastal boulders sampled and the importance of careful sample location selection. Erosion rates are assumed to be much lower for boulders in supratidal positions, as indicated by much smoother post-transport surfaces (see Tab. 1). This is consistent with inverse modelling on boulder HAR 1, whose OSL exposure age of 9±1 years slightly 405 underestimates the minimum age of 15 years (Fig. 6c). This indicates a comparatively low erosion rate of 0.06 mm/year, consistent with its flat and apparently smooth post-transport surface (Fig. 7b). Our data suggest that some influence of erosion cannot unambiguously be ruled out even for calcarenite boulders with apparently smooth surfaces, and all OSL-RSED ages for boulders in this study should be interpreted with caution.
Other environmental factors that might affect OSL exposure ages are assumed to be negligible for all dated 410 boulders. The post-transport surfaces of all boulders are bare of vegetation and not shielded by topography or houses. The surfaces of boulders in the intertidal zone (i.e. VAL 1) may be overtopped by waves during stronger storms (particularly contemporaneous with high-tide conditions), but periods with submersion are insignificantly short compared to the total exposure time. Likewise, the exposure duration of the calibration surfaces, i.e. another important parameter for model calibration, had no negative effect on dating accuracy. The exposure time of ~2 415 years used in this study was more than sufficient to generate pronounced bleaching fronts in all calcarenite samples.
Although model calibration generally benefits from calibration samples with long, and in the best case several different, exposure durations, even shorter exposure intervals than 2 years would have sufficed. In boulder samples with bright IRSL signals, these were even better bleached than the associated post-IRSL-BSL signals (Fig. 4c), potentially because longer wavelengths that feldspar signals are sensitive to are less attenuated by the rock than 420 the shorter wavelengths (Ou et al., 2018) that bleach quartz signals (Wallinga, 2002). While IRSL signals were not used in this study due to insufficiently bright signals for most samples, the application of IRSL instead of post-IRSL-BSL signals may reduce the time required for calibration to durations as short as a few months (Freiesleben et al., 2015;Ou et al., 2018).

425
Knowing the chronology of boulder transport can help to better assess the local flooding hazard at the Rabat coast.
Energetic waves during storms and tsunamis will generally exacerbate the effects of coastal flooding in the course of climate-induced sea-level rise (Nicholls et al., 2018). It is therefore of paramount interest whether coastal https://doi.org/10.5194/esurf-2020-46 Preprint. Discussion started: 21 July 2020 c Author(s) 2020. CC BY 4.0 License.
inundation strong enough to lift boulders at the Rabat coast only occurred during the very rare tsunami events, such as the 1755 Lisbon Tsunami, or also during much more frequent winter storms.

430
Comparison with satellite images showed that OSL-RSED ages are definitely inaccurate for boulders affected by severe post-depositional erosion (VAL 1-1 and VAL 1-2, squares in Fig. 6c) and for boulder samples with significantly inclined surfaces (HAR 2-1 and RAB 1-2, stars in Fig. 6c); the associated OSL exposure ages cannot be considered for any further interpretation. All other boulder samples, including those with apparently smooth surfaces, were likely affected to some extent by erosion as well. Slight age underestimation, thus, cannot be 435 excluded and their exposure ages should be interpreted carefully. We nevertheless are confident that the latter provide valuable relative chronological information for boulder transport that is shown in Figure 8a and allows differentiation between boulder ages.
The reliability of this relative chronology is supported by correlation between OSL exposure ages and the surface taphonomy of the associated boulders and niches (Fig. 8a, b). Exposure ages younger than ~10 years were achieved 440 for boulders and niches with smooth surfaces and fresh fractures, i.e. taphonomy classes 4 and 5 (TEM 4, TEM 3, HAR 1; Fig. 8b1). Boulders with exposure ages between ~10 and ~100 years are characterised by smooth surfaces with very scarce lichen or algae cover, i.e. taphonomy classes 3 and 4 (HAR 3, RAB 1, VAL 6, TEM 2; Fig. 8b2).
Finally, boulders with exposure ages older than ~100 years are characterised by weathered fractures and rougher surfaces, i.e. taphonomy classes 2 and 3 (VAL 4, RAB 5; Fig. 8b3,b4). According to the chronology presented 445 here, with OSL exposure ages of 152±52 years (VAL 4) and 577±247 years (RAB 5) and rather rough/weathered rock surfaces, these boulders are the only clasts that may have been moved by the 1755 Lisbon Tsunami. However, with masses of 16-24 t and positions on the intertidal platform (RAB 5) or on top of cliffs 3-4 m above sea level, they do not systematically differ from the other dated boulders in terms of wave power required for transportation.
Although the relative chronology does not unambiguously allow for correlating individual boulders with specific 450 historical storms or tsunamis, two important conclusions with regard to the local flooding hazard can be drawn from the dataset. Firstly, the relative chronology in Figure 8a implies that most boulders at the Rabat coast were detached from the cliff and overturned by storm waves. The large spread of OSL exposure ages between a few years and several centuries indicates that numerous transport events were responsible for the formation of the dated boulders. Since the 1755 Lisbon Tsunami was the only tsunami with significant flooding at the Moroccan Atlantic 455 coast during the last 1000 years (Kaabouben et al., 2009), boulder transport dominated by tsunamis is assumed to have resulted in more significant clustering of ages around ~260 years ago.
Secondly, correlation of exposure ages and masses of the associated boulders shows that storm waves were capable of lifting much larger boulders than observed during recent winter storms. At the Rabat coast, observations from the last decade are restricted to the lifting of smaller boulders (Mhammdi et al., 2020), while boulders larger than 460 ~5 t were only observed to move by sliding (Fig. A3). However, boulders with OSL exposure ages that clearly postdate the 1755 Lisbon Tsunami and therefore must have been lifted by storms reach up to 38 t (RAB 1). These storm boulders yield comparable or even larger masses than boulders that, based on their exposure ages, might have been transported and overturned during the 1755 Lisbon Tsunami (i.e. VAL 4 and RAB 5 with masses of 16-24 t). Of course, we cannot exclude that the largest boulders at the Rabat coast, such as VAL 1 with ~65 t that 465 could not be dated with OSL-RSED due to strong erosion of their post-transport surface, can exclusively be overturned by tsunamis. Nevertheless, in agreement with hydrodynamic experiments (Cox et al., 2019) and observations after recent tropical cyclones (e.g. May et al., 2015), our results support the perception that storm waves significantly contribute to boulder quarrying along cliffs and may be considered an important driver for the https://doi.org/10.5194/esurf-2020-46 Preprint. Discussion started: 21 July 2020 c Author(s) 2020. CC BY 4.0 License. evolution of wave-emplaced coarse-clast deposits worldwide, including boulders with masses of several tens of 470 tons that have previously been associated with tsunamis. It is, therefore, likely that also other boulders documented along the Atlantic coasts of Morocco (Mhammdi et al., 2008;Medina et al., 2011), and the Iberian Peninsula (Whelan and Kelletat, 2005;Scheffers and Kelletat, 2005;Costa et al., 2011), which have tentatively been related to the 1755 Lisbon Tsunami and potential predecessors previously but mainly lack sound chronological data, in fact represent storm boulders.

Conclusions
OSL rock surface exposure dating was for the first time applied to coastal boulders overturned during wave transport. Successful calibration of the bleaching model using surfaces exposed for ~2 years and evaluation of OSL exposure ages against satellite images indicate the potential of the approach for boulders with limited postdepositional erosion and with surface inclination in agreement with that of the calibration samples. Although fitting 480 uncertainties as a consequence of low amounts of quartz and potassium feldspar in the source rock introduced relatively large dating uncertainties, and although a bias due to post-depositional erosion cannot be excluded even for boulders with smooth surfaces, OSL rock surface exposure dating provides a relative chronology for boulders that could not be dated with any other approach so far. This relative chronology indicates a large variability of boulder ages, most of them different from the only tsunami event at the Rabat coast within the last 2000 years.

485
Thus, OSL exposure ages suggest that even boulders weighing ~40 t were moved and overturned by storm waves.
This supports the conclusion of previous studies that storms rather than tsunamis can be the most important driver for the formation of coastal boulder deposits in general.
While OSL-RSED offered important relative chronological information for the Rabat coastal boulders but could not provide absolute ages, the approach offers a powerful tool for dating boulder deposits with more favourable 490 lithologies. Magmatic rocks, such as granites, are not only significantly less susceptible to erosion, typically they also allow measurement of the luminescence signal of potassium feldspar. Different from the quartz signals of the calcarenite used in this study, IRSL signals of potassium feldspar measured on polymineralic aliquots do not suffer from contamination by other minerals and are typically much brighter than those of quartz. Such lithological properties promise to reduce the uncertainties and inaccuracies related to OSL surface exposure dating of coastal 495 boulders in this study significantly.