Luminescence dating of buried cobble surfaces from sandy beach ridges: a case study from Denmark

Here we investigate the use of optically stimulated luminescence (OSL) for dating cobbles from the body of successive beach ridges and compare cobble surface‐derived ages to standard quartz OSL ages from sand. Between four and eight cobbles and sand samples (age control) were dated with the luminescence method, taken from the modern beach and from beach ridges on the south and north extremes of a prograding spit on the westernmost coast of Lolland, Denmark. Luminescence‐depth profiles perpendicular to the surfaces of the cobbles show that the feldspar infrared signals stimulated at 50 °C were fully reset to various depths into the cobbles prior to final deposition; as a result, the equivalent doses determined from close to the surface of such cobbles can be used to calculate burial ages. Beach‐ridge burial ages given by the average of ages of individual cobbles taken from the same site are consistent, within errors, with the ages derived from the sand samples. Cobble‐ and sand‐derived ages show that the southernmost beach ridge at Albuen was formed around 2 ka ago, indicating that this sandy spit is younger than other coastal systems in Denmark. The agreement between ages derived from clasts and from standard quartz OSL in this study confirms that, even in the absence of sandy sediments, we can reliably date sites using OSL by targeting larger clasts. In addition, the record of prior light exposure contained in the shape of the cobbles’ luminescence‐depth profile removes one of the major uncertainties (i.e. the degree of signal reset prior to burial) in the luminescence dating of high latitude sites.

Optically stimulated luminescence (OSL) ages are based on the measurement of trapped charge in the defects in mineral crystals such as quartz and feldspars. When these minerals are exposed to daylight, the trapped charge is released in the form of luminescence, with an intensity proportional to the time that has elapsed since the last exposure to daylight (Aitken 1998). OSL dating of sandsized material is awell-established technique and has been successfully applied in many archaeological and geological studies (e.g. Fuchs & Owen 2008;Rittenour 2008;Wintle 2008;Thrasher et al. 2009;Clemmensen et al. 2012Clemmensen et al. , 2018Lampe & Lampe 2018). However, using sandsized material may be challenging in some environments. For example, the latent luminescence signal in dating glacial and related sediments may, in some cases, not be completely reset by daylight during the last transport prior to deposition (e.g. Fuchs & Owen 2008;Rittenour 2008). The completeness of signal bleaching prior to burial of sand grains is difficult to assess directly, and partial bleaching remains a significant source of uncertainty in OSL dating of sand-sized grains (e.g. Olley et al. 1999). In addition, if the sedimentary unit of interest does not contain any sand-or silt-sized material, it cannot be dated using conventional luminescence dating tech-niques. As a result, it has been difficult to apply conventional OSL dating to, for instance, scree slopes, block fields and gravelly beach ridges.
Recently, several studies have demonstrated the potential of using large clasts in OSL dating (e.g. Simms et al. 2011Simms et al. , 2018Sohbati et al. 2011Sohbati et al. , 2015Simkins et al. 2013). These studies relied on the exposure of the clast surface to daylight, and the resulting resetting of the latent luminescence to some depth into the clast interior. Because the mineral grains in the cobble matrix are fixed (in contrast to sands, which is usually transported as individual grains), this resetting profile is preserved after burial, at least in part. Thus, larger clasts preserve a record of their bleaching prior to burial, and this information is contained in the shape of the luminescencedepth profile into the rock surface (e.g. Freiesleben et al. 2015;Sohbati et al. 2015;Jenkins et al. 2018). This is a major advantage compared to sediment dating using sand-sized grains, which do not record such information.
Here we test the application of luminescence rock surface dating to the surface of buried cobbles in sandy beach ridges to determine the time of deposition. We first assess the degree of bleaching, and then compare the cobble burial ageswith those based on the OSL from sandsized quartz extracted from the material surrounding the cobbles.

Study area and sampling sites
Albuen is located at the westernmost end of the island of Lolland, Denmark (Fig. 1A, B). It is a complex S-N orientated prograding spit (Fig. 1C) mainly formed by longshore currents in a microtidal environment (mean tidal range <10 cm; Danish Meteorological Institute 2018). The spit is~5 km long with a hook-shaped recursive tip on the north and made up of a succession of beach ridges built from a mixture of cobbles and sand (Fig. 1C). Such beach ridges are relict berms, typical coastal features deposited mainly by wave-related processes (e.g. Tanner 1995;Otvos 2000;Clemmensen & Nielsen 2010;Tamura 2012;Bendixen et al. 2013;Hede et al. 2015), and have been extensively studied for reconstructing coastal environments as well as for estimating relative sea-level variations using luminescence dating (e.g. Murray-Wallace et al. 2002;Nielsen et al. 2006Nielsen et al. , 2017Bjørnsen et al. 2008;Clemmensen et al. 2012;Bendixen et al. 2013;Lampe & Lampe 2018). Albuen is located in the vicinityof the hinge line where the vertical land movement in response to isostatic adjustment since the last glaciation changes from positive to negative (Lambeck et al. 1998;Hansen et al. 2012;Nielsen et al. 2014). Although the exact location of this hinge line may have changed over time, Albuen is considered to be an important study area to constrain sea-level variation as well as for geodynamic models of southwest Scandinavia.
The beach ridges at Albuen have a low relief (<2 m, Fig. 1C). Seven successive beach ridges were selected for sampling (all for sand sampling and two for both cobbles and sand sampling, Fig. 1C). From 0 to~70 cm below the surface, they are composed of sand with some dispersed rounded cobbles ( Fig. 2A, B). No systematic grain-size analysis was carried out on the bulk matrix material, but it is estimated that cobbles constitute between 10 and 30% of the total volume. Beach ridges' sediment composition and morphology (width and height) depend on both sediment availability and waveenergy level at the time of (berm) deposition (Bendixen et al. 2013). Sand and cobbles can both be deposited under swash and backwash processes on the seaward side of the berm during elevated water levels. Sand is likely to have been deposited under moderate wave conditions, whereas cobbles are likely to have been transported and deposited under more high-energy wave conditions. The present-day beach is mainly sand, with dispersed rounded cobbles (Fig. 2C). Each ridge is presumably subject to deposition by wave action during several events of elevated water, before it is abandoned as a result of spit growth.

Sampling and sample preparation
Pits with dimensions of~50950970 cm were dug into the crests of seven successive beach ridges (Fig. 1). From two beach ridges, A1 and A8 (black-filled pins in Fig. 1), both cobble and sand samples were collected. Cobbles were sampled by first digging a pit to a depth of about 60 cm, and then scraping into the base of the pit by hand, extracting a cobble surrounded by sand and placing it directly in a black plastic bag. This process tookonly a few seconds, and the cobble remained covered by sand during any possible light exposure. We do not believe there was any opportunity for significant surface bleaching during this process. At least 15 cobbles were randomly collected from 60 to 70 cm below the surface of the ridges A1 and A8. Sand samples were collected by hammering lightproof PVC tubes into the pit wall~60 cm below the surface. Additionally, sand samples were collected, in the same manner as above, from other beach ridges between A1 and A8 (hollow pins in Fig. 1) to provide a chronological framework for the growth with time of the beachridge plain. Cobbles and sand were also taken from just below the surface (~10 cm) of the backshore of the modern beach (Fig. 2C) to investigate the degree of the resetting of the luminescence signal in samples that had been exposed to light immediately before the time of sampling (i.e. modern analogues). All the cobble surfaces are expected to have been frequently exposed to daylight as they were washed up and down on the beach by swash processes before final deposition at higher levels during high-energy events. Hereafter, we use the abbreviations 'AMsed' and 'AMc', where c is a number of identification for each cobble, to refer to sand and individual cobbles collected from the modern beach, respectively. Similarly, we use the abbreviations 'Absed' and 'Abc', where b is the number of identification for each ridge (see Fig. 1C) and c is again a number of identification for each cobble, to refer to sand and individual cobbles collected from the beach ridges, respectively. For example, the code for the sand sample from the beach ridge A8 is 'A8sed', and the code for a cobble from the same site will be 'A810' ('10' being the cobble identification number).
The environmental dose rate and the water content of sand samples were estimated using the material from the light-exposed ends of the PVC tubes used for sample collection. In the case of cobble samples, external dose rateswere derived from measurements on the material that was collected with the cobbles, and it includes sand and other adjacent cobbles within the matrix.
Samples for luminescence measurements were prepared in the laboratory under low-level orange light (Sohbati et al. 2017). For sand samples, the fraction from the central part of the PVC tubes was used for equivalent dose (D e ) measurements. Quartz fractions were prepared following the standard procedure: wet sieving (180 to 250 lm), acid treatment (10% HCl for 60 min, 10% H 2 O 2 for 60 min, 10% HF for 40 min and 10% HCl for 20 min). Quartz and feldspar grainswere separated using heavy liquid (q = 2.62 g cm À3 ), and the quartz grains were additionally etched using concentrated (~40%) HF for 40 min, followed by 10% HCl for 40 min. Only the quartz fraction of the sand material was used for luminescence measurements. No heavy mineral separation was performed because, in our experience, OSL signals from heavy minerals are invariably weak, and the mass fraction is very small.
Small chips were taken from the surface of each cobble for a preliminary sensitivity test, to select those with infrared signals >10 3 cts 0.2 s À1 (in response to a test dose of~2 Gy. Cores of~10 mm in diameter and up to~25 mm long were then drilled from the selected cobbles using a diamond-tipped, water-cooled core drill. Cores were sliced into~1.2-mm-thick slices at intervals of 1.5 mm using a low-speed water-cooled saw equipped with a diamond-tipped blade with a thickness of 0.3 mm. No chemical treatment was performed on the cobble slices. Variations in slice thickness are estimated to be <100 lm; laboratory beta dose rate uncertainties introduced by such variation are likely to be <AE1.5% (based on Hansen et al. 2018: fig. 2).
After drilling, remaining cobble pieces and the material from around each cobble (~200 g per site) were prepared separately for high-resolution gamma spectrometry following the standard procedures: pulverizing, heating to 450°C for 24 h to remove organic material (only for associated material) and casting with wax to provide a reproducible counting geometry and to prevent radon loss ).

Instrumentation and measurement protocols
All luminescence measurements were carried out using a Risø TL/OSL reader (Model TL-DA 20) equipped with a calibrated 90 Sr/ 90 Y beta source. Large aliquots ( $ 8 mm) of quartz extracted from sand samples were mounted on stainless-steel cups with silicone oil for OSL measurements. Luminescence signals were stimulated using blue diodes (k = 470 nm, 80 mW cm À2 ) and detected through a Hoya U-340 glass filter. Whole cobble slices were mounted directly on a reader carousel for discs for OSL measurements (Sohbati et al. 2011). K-feldspar signals were stimulated with IR diodes (k = 875 nm, 135 mW cm À2 ) and detected through a Schott BG39/BG3 filter combination (2 and 4 mm, respectively).
A single-aliquot regenerative (SAR) protocol (Murray & Wintle 2003) was used for quartz OSL measurements. Quartz extracts were heated to 200°C for 10 s and to 180°C for 0 s after giving the natural/regenerative and test doses, respectively, and stimulated with blue diodes at 125°C for 40 s (Table 1). High-temperature blue-light stimulation at 280°C was also performed at the end of each cycle for 40 s to remove any residual luminescence (Murray & Wintle 2003). OSL signal intensities were calculated using the initial 0.32 s of the signal minus an immediate background derived from the following 0.32 s. Cobble slices were measured using a post-IR IRSL SAR protocol (e.g. Buylaert et al. 2009). The slices were preheated to 200°C for 100 s after giving both the natural/ regenerative and test doses, stimulated using IR diodes first at 50°C (IR 50 ) and then at 180°C (pIRIR 180 ), each for 200 s (Table 1). After heating to the measurement temperature, there was a 30-s pause before stimulation to minimize problems with thermal lag (Sohbati et al. 2011). At the end of each cycle, residual luminescence was minimized using IR stimulation at 205°C for 200 s. IRSL signal intensities were derived from the initial 10 s of stimulation less a background from the last 10 s of stimulation. The suitability of our SAR protocols for the samples used here was examined using the standard tests suggested by Wintle & Murray (2006): dose recovery, recycling ratio and recuperation.
Environmental dose rates were determined by measuring the concentration of radionuclides (i.e. 238 U, 232 Th, 226 Ra and 40 K) using high-resolution gamma spectrometry (Murray et al. 1987. K-rich areas on the cobble slices were identified using a Bruker M4 Tornado micro-XRF spectrometer. The micro-XRF images of such areas were then used for assessing the grain size of K-rich feldspar grains following Rades et al. (2018).

Dose rate
Radionuclide concentrations were converted to dose rate using conversion factors after Gu erin et al. (2011). The matrix moisture content absorbs radiation and thus reduces the dose rate. We accounted for this effect by averaging the field water content and the laboratory estimate of saturation water content for each sample. The cosmic ray dose rate was calculated following Prescott & Hutton (1994), and an internal alpha dose rate contribution of 0.010AE0.002 Gy ka À1 in quartz from Vandenberghe et al. (2008). Radionuclide concentrations and calculated total dose rates are summarized in Table 2.

Luminescence characteristics and equivalent dose
The OSL signal from sediment quartz extracts ( Fig. S1) is dominated by the fast component (e.g. Jain et al. 2003;Singarayer & Bailey 2003). The purity of the quartz was tested using the so-called IR OSL depletion ratio (Duller 2003), in which IR stimulation at room temperature is inserted before the blue OSL for a repeated regeneration dose. Pure quartz is effectively insensitive to IR stimulation at room temperature (e.g. Spooner 1994;Duller 2003) and so any loss of blue-stimulated signal detected in UV resulting from prior stimulation with IR is presumed to be associated with feldspar contamination. We checked the quartz purity of three aliquots per sample and the average ratio of the post-IR blue-stimulated signal to the bluestimulated signal without prior IR stimulation was 0.97AE0.01 (n = 20), indicating that any feldspar contamination of our blue-stimulated signal was negligible. To test the ability of our protocol to measure a known dose (dose recovery, Murray 1996), five aliquots per sample were optically bleached twice in the reader using blue diodes at room temperature for 40 s, with a pause of 10 000 s between bleaching to allow for any charge transferred to shallow traps to thermally decay; these bleached aliquots were then given a dose of~3.5 Gy. The ratio of the average measured dose to the given dose was 1.01AE0.02 (n = 31), indicating that our chosen protocol is able to accurately measure a known dose given in the laboratory before any thermal treatment.
Equivalent doses were measured for at least 30 aliquots per sample (except for the modern analogue for which 18 aliquots were measured); the arithmetic mean of the distribution was used in further calculations (Gu erin et al. 2017). Aliquots with recycling ratio >10% from a unity and/or recuperation >5% of the natural signal were dismissed and not included in the D e estimation. Figure S1 shows a typical quartz OSL dose response curve for our samples. Average D e values of accepted aliquots ranged from 0.07AE0.01 Gy (n = 16; modern beach sample) to 3.10AE0.07 Gy (n = 48; beach ridge A8). As mentioned earlier, the degree of signal bleaching prior to final deposition cannot be directly assessed in sandy samples, but a modern analogue can be used to infer it. Assuming that the sand-sized sediment on the beach ridges at Albuen had experienced the same processes that the modern sand is subject to today, the relatively low D e mean value measured from the modern sand sample suggests that beach-ridge sand was probably well bleached prior to final deposition. Average D e values are given in Table 2.

Ages
The OSL ages of quartz extracted from the beach ridges where cobbles were also collected (A8 and A1) are 2.25AE0.12 ka (n = 48) and 0.66AE0.04 ka (n = 47), respectively. Quartz OSL ages of the other assessed beach ridges are given in Table 2 and Fig. 3. Sand ages show that the beach-ridge system becomes younger towards the north (Fig. 3). The calculated age for the modern beach samples is 0.04AE0.01 ka (n = 16) indicating that the effect of any residual signal in our samples is likely to be very small.

Luminescence characteristics of cobbles
In order to test the sensitivity of the quartz grains within our cobble samples, cobble slices were (i) stimulated with blue diodes at high temperature (220°C for 100 s) in order to deplete the natural quartz and feldspar signals, (ii) given a dose (of~11 Gy), (iii) stimulated with IR diodes at room temperature (at 50°C for 100 s) to deplete the feldspar signal and then stimulated with the blue LEDs (at 125°C for 40 s) and signals detected in UV. The observed OSL signals do not contain any fast component and decay very slowly, indicating that the quartz grains in our samples are not suitable for dating (Fig. 4A, B). The pIRIR 180 signals are generally anomalous, first rising to a maximum after Table 1. Outline of the SAR OSL and post-IR IRSL measurement protocols used for quartz grains and cobble slices, respectively. All measurements above 200°C were carried out in nitrogen atmosphere.
Step Quartz Rock slices Treatment Treatment about 25 s of stimulation before decreasing slowly (Fig. 4C, D). Such behaviour is likely to arise from an underlying isothermal thermoluminescence (ITL) signal (Fig. S2). Preliminary tests showed that a pause time of >1000 s before the stimulation was necessary to minimize this problem; this was considered impractical. Although for consistency we used a pIRIR 180 protocol, with an IR 50 first stimulation, for all samples, we do not consider the pIRIR 180 signals further in our study. Slices from most of the cobbles examined here emitted strong IR 50 signals ( Fig. 4C, D), and 18 cobbles were selected in total for further investigations: four from the modern beach, six from A1 and eight from A8.

Luminescence-depth profiles
As discussed above, one of the advantages of luminescence rock surface dating compared to conventional sediment dating using sand is that solid granular matrices retain a record of the extent towhich the latent luminescence signal was reset prior to final burial (e.g. Freiesleben et al. 2015;Sohbati et al. 2015;Jenkins et al. 2018). To investigate this, we measured the natural sensitivity-corrected signal (L n /T n ) as a function of depth into the selected cobbles.
Due to their small size, we were able to drill cores through the samples to investigate the variation of the luminescence signal from one surface of the cobble to the opposite surface. Figure 5 shows the luminescence-depth profiles from two different cobbles from each site. Note that the y-axis of the plots on the left side of Fig. 5 differs from that on the right side.
In the examples shown on the left panels, L n /T n increases with depth and reaches a plateau (the socalled field saturation level) in the middle of the cobble.
In the examples on the right panels this plateau is not reached, presumably because light exposure has been sufficiently long to at least partially bleach the latent IR 50 signal throughout the cobble. For those samples that show field saturation in the middle of the cobble, the L n /T n values of all slices of the luminescence-depth profiles are normalized to the average L n /T n of the slices in field saturation. For those samples that did not reach field saturation, the L n /T n values of all sliceswere normalized to a laboratory-induced saturation level. In the cobbles from the modern beach AM, the IR 50 signal at the surface of both sides of both cobbles is small; no significant difference is observed in the degree of resetting of these surfaces of individual cobbles (Fig. 5A, B). Also, the L n / T n does not increase significantly from the first (surface) to the second slice. These observations are consistent with the expectation that these cobbles had not been buried for a long time before sampling, and that all surfaces must have been well bleached as the cobbles had been repeatedly exposed to light by wave action in the swash zone before deposition. In the case of AM03, the IR 50 signal increases with depth and reaches field saturation level in the middle of the cobble (Fig. 5A). In contrast, the luminescencedepth profile in cobble AM12 does not reach a plateau in the middle of the cobble, suggesting that the IR 50 signal has been bleached, at least to some degree, throughout this cobble (Fig. 5B).
Profile shapes similar to those observed in the cobbles from the modern beach were observed from the cobbles collected from the beach ridges A1 (Fig. 5C, D) and A8 (Fig. 5E, F). The difference, however, is that the IR 50 signal at the surface of these cobbles is not negligible but starts at some finite value (Fig. 5C-F; see also Chapot et al. 2012;Freiesleben et al. 2015;Sohbati et al. 2015). This surface signal results from the dose that these surfaces are presumed to have absorbed since deposition.

Dose recovery and D e
In order to determine whether or not our chosen protocol is able to measure a known dose in these cobble samples, the natural luminescence signals of four inner slices from two cobbles from each site (i.e. from AM, A1, and A8) were optically bleached for 48 h (24 h each side) using a H€ onle SOL2 solar simulator. Two slices from each cobble were then given a dose of~21 Gy and measured in the usual manner; the other two slices were measured without any additional dose to give an estimate of any residual dose. The ratio of the average measured dose (less the respective average residual dose) to the given dose was then calculated to give the dose recovery ratio. The residual dose for IR 50 signal, averaged over all cobbles, was 1.10AE0.18 Gy (n = 15), and the dose recovery ratio was 0.96AE0.01 (n = 14). We conclude that we are able to measure with sufficient accuracy a known laboratory dose given to a previously unheated cobble slice using our SAR protocol.
Equivalent doses were measured from as many surface slices (depth ≤1.5 mm) as possible. For some of the cobbles, we could only get two or three surface slices (n) due to their small size: A113 (n = 2); A805, A813, A814 and A815 (n = 3). The surface D e distributions from each site are shown in Fig. 6. Average D e values from samples AM, A1 and A8 were 0.38AE0.06 Gy (n = 21), 1.61AE0.17 Gy (n = 24) and 4.11AE0.23 Gy (n = 33), respectively. Relative standard deviation (RSD) values ranged from 30 to 70% (Fig. 6). Given that the calculated uncertainty of D e from individual aliquots is of the order of a few percent, these samples are considerably overdispersed. It is implicit in our treatment that different surface slices from the same cobble are exposed to the same dose rate, and so this overdispersion is surprising. We are confident that it does not arise from incomplete bleaching (see above), but presumably at least some originates from variations in effective dose rate, including variations in effective grain size, K concentration, and possibly variability in the efficiency of luminescence sensitivity between different radiation types . It is for these reasons that we adopt the recommendations of Gu erin et al.

Dose rate
Radionuclide concentrations measured with high-resolution gamma spectrometry were converted to infinite matrix dose rate data using the conversion factors of Gu erin et al. (2011). The internal total beta dose rate to K-feldspar grains from 40 K and 87 Rb, calculated assuming an effective 40 K content of 12.5AE0.5% (Huntley & Baril 1997), a 87 Rb content of 400AE100 ppm (Huntley & Hancock 2001) and an average grain size of 400 lm, is 1.522AE0.064 Gy ka À1 . An internal alpha dose rate in Kfeldspars of 0.10AE0.05 Gy ka À1 derived from the internal contribution of 238 U and 232 Th (Mejdahl 1987) was also included in the dose rates. The cosmic ray dose rate was calculated following Prescott & Hutton (1994) assuming a rock density of 2.65 g cm À3 , which is the mode density of all types of rocks (Johnson & Olhoeft 1984) and seems to be appropriate for the type of cobbles we are dating (Fig. 7).
The total effective environmental dose rate ð _ D total Þ to the surface of the cobbles was estimated by summing the relevant contributions of the cosmic radiation and beta and gamma dose rates . Although the water content of the cobbles is negligible, the surrounding sandy material does contain water, and so the infinitematrix dose rates need to be corrected for water content. This was based on that calculated using the sandy material taken from the ends of the sand sampling PVC tubes (see Fig. 4. Typical stimulation curves observed in the sensitivity test. A and B show the typical decay of the laboratory signal during a post-IR blue stimulation (i.e. for quartz sensitivity detection), and C and D during infrared stimulations at 50°C (IR 50 ) and 180°C (pIRIR 180 ) (for feldspar sensitivity detection). [Colour figure can be viewed at www.boreas.dk] above). For each cobble, the total beta ( _ Db total ) and total gamma ( _ Dc total ) dose rates were derived by summing the contributions of the cobble itself ( _ Db cobble and _ Dc cobble ) and from its associated material ( _ Db sand and _ Dc sand ). These percentage contributions were estimated as follows. Since the matrices in which the cobbles were embedded were mainly sandy (cobbles were not touching each other, Fig. 2), we estimated the variation of the total beta dose rate at the cobble/sediment interface based on Aitken (1985: appendix H) using the attenuation factor from Sohbati et al. (2015), as: _ Db cobble (Gy ka À1 ) is the cobble (dry) infinite-matrix beta dose rate, _ Db sand (Gy ka À1 ) is the water-contentcorrected infinite-matrix beta dose rate from the material associated with each cobble, 9 (mm) is the depth into cobble from the cobble/sand interface, and b (1.9 mm À1 ) is the beta linear attenuation coefficient in the cobble . The first term in Equation 1 represents half of the _ Db cobble present at the surface of the cobble (because the cobble is much thicker than the range of betaparticles), and the second term represents the build-up of the remainder of the _ Db cobble with depth into the cobble. The third term represents the attenuation with distance into the cobble of 50% of the _ Db sand present at the surface of the cobble. Equation 1 was integrated over the depth of the surface slice (1.2 mm) and divided by this thickness to give the average beta dose rate. It is thus estimated that $ 80% of the cobble (dry) infinite-matrix b dose rate ( _ Db cobble ) contributes to the total beta dose rate to the first slice ( _ Db total ); this is supplemented by $ 20% of the surrounding material infinite-matrix b dose rate ( _ Db sand ). For cobbles <12 cm in diameter, the contribution of _ Dc cobble to _ Dc total is given with sufficient accuracy by the product of the cobble density (g cm À3 ) and diameter (cm) (Aitken 1985); the resulting value is taken as the percent contribution. Assuming an average cobble density of 2.65 g cm À3 and an average cobble diameter of 5.3 cm (given an average cobble dimension of 109492 cm), $ 14% of the (dry) _ Dc cobble and $ 86% of the watercontent-corrected infinite-matrix gamma dose rate of the associated material ( _ Dc sand ) contribute to _ Dc total . Table 3 summarizes the data on the environmental dose rate calculations.

Uncorrected ages
The IR 50 cobble surface burial ages were simply derived by dividing the cobble surface D e values (without subtracting any residuals; see above) by the effective dose rate at the surface of the cobbles (see above). It is, however, known that the IR 50 signal from feldspars is unstable; a phenomenon that is known as 'anomalous fading' (Wintle 1973). As a result, the ages prior to fading corrections are regarded as minimum ages (Table 4).

Fading correction
Anomalous fading was quantified using two different approaches: the conventional g value measurements (Huntley & Lamothe 2001) and the saturation ratio (Rades et al. 2018).
The g value expresses the fading rate as a percentage of IR signal loss with storage time after irradiation (Huntley & Lamothe 2001 ; Fig. S3). Three inner slices from each cobble were reset in the reader using an IR stimulation at 205°C for 200 s, and then L x /T x cycles were repeatedly measured, both immediately after irradiation, and after a delay time of 12 h (inserted after the preheat; Auclair et al. 2003). Average g values for all samples were >6% dec. À1 (Fig. 8), giving age corrections inexcess of 50%. Measured g values from A1 samples varied the most, ranging from 1.8AE1.4 to 13.9AE1.6% dec. À1 .
The saturation ratio is an alternative approach to fading correction that has been recently proposed by Rades et al. (2018); this is specifically suitable for rock samples because they often contain a record of field saturation level in the innermost (unbleached) part of their luminescence profile, identified by a plateau. Field saturation is where the accumulation of latent luminescence as a result of dose rate is matched by the fading rate, so that the luminescence signal ceases to change with time. In this method, a fading correction factor can be derived by dividing the L n /T n value from slices from the field saturated plateau part of the profile by the corresponding laboratory saturation level (L sat /T sat ) measured using the same slices after giving them a high saturating dose (i.e. >>1 kGy) in the laboratory (Rades et al. 2018). Because Albuen cobbles are small, many are at least partially reset even at the cobble centre. Only seven out of 18 cobbles were identified as in field saturation in the middle and were deemed suitable for this fading correction approach. We first measured the natural IR 50 signal of a saturated inner slice to determine L n /T n . The measured slice was then given a dose of~4200 Gy using a 60 Co gamma source and re-measured to give L sat / T sat . The field-to-laboratory saturation ratio was then derived by dividing the L n /T n by its respective L sat /T sat . Table 4 shows calculated field-to-laboratory saturation ratios. Three samples out of seven give ratios above 1. Since such ratios are not physically meaningful, this suggests that the measurement uncertainty is significantly larger than that based on calculations, andwe note that the mean of the five largest ratios is 1.09AE0.10, indistinguishable from unity. As a result, we only consider ratios of <0.5 to be significantly different from unity, and the only two samples meeting this criterion are A111 and A805.

Corrected ages
The ages for all the samples were corrected using both cobble-specific (g cobble ) and average g values (g average ). In addition, the ages of two samples (A111 and A805) were corrected using field-to-laboratory saturation ratios (see Fig. 6. Equivalent dose distributions derived from surface slices of (A) the modern beach, (B) beach ridge A1, and (C) beach ridge A8 cobbles. Errors on the mean correspond to standard error; RSD = relative standard deviation (or coefficient of variation); n = number of accepted aliquots (each aliquot corresponds to a cobble surface slice). above). All uncorrected and corrected ages are given in Table 4. In general, average corrected ages from each site have a relative standard deviation of >40%, regardless of the fading correction approach (Table 4). Ages corrected using g cobble are not statistically different from the ages corrected with g average ; only g average corrected ages will be discussed further. The final average ages from AM, A1 and A8 are 0.13AE0.03, 0.55AE0.11 and 1.76AE0.38 ka, respectively. Final ages of samples A111 and A805 given by the field-to-laboratory saturation ratios are 0.69AE0.04 and 1.29AE0.10 ka, respectively; these are consistent with the respective g average corrected ages (Table 4).

The importance of the assumed grain size
In the calculation of dose rates, we assumed an average K-feldspar grain size of 400 lm to allow us to calculate both the attenuation of the external beta dose rate, and the Table 3. Environmental dose rate information for the cobble and sand samples. Cobbles' _ D total includes the contribution of effective beta and gamma dose rates from both cobble and associated sand. Dose rates in feldspar assume a K concentration of 12.5AE0.5% for 400 lm K-feldspar grains (Huntley & Baril 1997 Table 4. Cobble IRSL D e values and uncorrected and corrected ages using the cobble-specific (g cobble ) and site-averaged (g average ) g values, and the field-to-laboratory saturation ratios. Cobble ages are corrected using the field-to-laboratory saturation ratio only in cases where the ratio is <0.5.
Sample D e (Gy) n Uncorrected age ( build-up of the internal beta dose rate from 40 K and 87 Rb (see above). However, we have very little information about this grain size, and it is important to consider the effect of this assumption. For instance, had the assumed grain size been smaller, the beta dose rate contributions from internal 40 K and 87 Rb would also be smaller; this would tend to decrease the total dose rate ( _ D total ) and increase the final cobble age.
In order to investigate the effect of the grain-size assumption, we first attempted to estimate the actual average grain size of K-feldspar grains in our cobble slices and then assessed the sensitivity of the cobble ages to changes in the grain-size assumption. Micro-XRF images of surface and second slices of each sample show that Krich areas vary considerably in size from sample to sample (see examples in Fig. S4). We selected the micro-XRF images of two extreme samples with apparent small (sample A811) and large (sample A815) constituent 40 K rich grains, in order to estimate the range of grain-size variation in our samples. Following Rades et al. (2018), we analysed these images to derive the grain-size distri-bution using Image J (Fig. S4). The resulting average 40 K rich grain diameters are 370AE10 and 740AE40 lm for samples A811 and A815, respectively. This implies that while for some samples the assumed grain size of 400 lm is valid, for others it can be underestimated by up to~50% and so might have biased our cobble age estimations.
We recalculated the ages of three cobbles from each site, assuming a range of grain diameters: 100, 200, 400, 1000 and 2000 lm. These cobbles were chosen to contain different measured bulk K concentrations (as measured by high-resolution gamma spectroscopy), and so different dose rates. As can be seen in Fig. 9, the higher the cobble dose rate, the less sensitive is the dose rate to the grain size (Fig. 9A), and thus the less dependent the cobble age is on the grain-size assumption (Fig. 9B). For example, the variation of _ D total with grain size for sample A815 with high bulk K content ( 40 K = 3878 Bq kg À1 ; Table 3) is small (Fig. 9A), while the _ D total for sample A812 with low K content ( 40 K = 54 Bq ka À1 ; Table 3) increases by a factor of~3 from the grain size of 100 lm to the grain size 2000 lm (Fig. 9A). As a result, the ages show a similar trend in dependence on grain size where the samples with low radioactivity are the most sensitive ( Fig. 9B; Table 5). The age of cobble A812, for example, ranges from 6.3AE1.2 to 1.4AE0.2 ka, for grain sizes of 100 and 2000 lm, respectively (Fig. 9B), whereas the ages of cobble A815are indistinguishable for 100 and 2000 lm grains (0.72AE0.13 and 0.83AE0.16 ka, respectively, Fig. 9B).

Discussion
The luminescence-depth profiles of all sensitive cobbles are evidence that the latent IR 50 luminescence signal was

BOREAS
fully bleached, at least at the cobble surfaces. In some cobbles the IR 50 signal has been bleached to some degree throughout the cobble. Other studies have reported similar observation of bleaching to depths >20 mm (e.g. Sohbati et al. 2012;Ou et al. 2018;Gliganic et al. 2019), although these were usually observed in visibly translucent samples, such as quartzite.
On average, cobble ages are within errors, in agreement with respective quartz OSL ages from the sandy material surrounding the rocks (age control; Fig. 10) despite (i) the significant scatter in D e estimates of aliquots from the same cobble surface, (ii) age estimates based on an assumed grain size (400 lm), and (iii) high fading correction factors. Simkins et al. (2015) have also reported significant overdispersion in aliquot D e of cobble quartz grains, and they also obtained ages that agreed with independent age control (Simkins et al. 2013). Here, IR 50 signals from cobbles taken from the modern beach gave ages about a hundred years older than those based on quartz OSL from the surrounding sand (Fig. 10).
Analysis of the size of 40 K rich areas using micro-XRF data suggests that the grain size assumed in the dose rate calculations was not necessarily appropriate for all samples. Nevertheless, we have shown that the importance of the grain-size assumption on the final ages is dependent on the 40 K concentration of the cobble (Fig. 9). At least from the dosimetry perspective, it may be preferable to work with high K concentration cobbles because they show less dependence on the assumed grain size. Nevertheless, the sample that was almost pure K-feldspar (according to its measured bulk K concentration, sample A815) provided an age about~35% of the expected value (based on A8sed, see Tables 2 and 4). Our results probably reflect the observations of Buylaert et al. (2018); they investigated the dose recorded by single-and multi-grain aliquots of feldspars, and showed that the relationship between K concentration, grain volume and apparent dose rate is more complex than previously understood.
Despite these difficulties, the average IR 50 cobble ages are generally consistent, within errors, with the quartz OSL ages of the surrounding sand. Both cobble and sand ages show that the oldest beach ridges on Albuen were formed in the south and that the beach-ridge system has developed towards the north over a time period of 2000 years (Fig. 3, Tables 2, 4). The number of major beach ridges formed between A8 and A1 during an average time period of~1400 years is about 10; this indicates that each major beach ridge records sedimentation of about 140 years, between the initial building of the berm and its final abandonment. The presence of minor beach ridges between the major ones indicates that the 'true' time period of formation for the major ridges is <140 years, and may be as short as a few decades. Even so this would support our earlier expectation that the major beach ridges in Albuen are the result of several episodes of elevated water level deposition. Also, the error bars on the luminescence ages of both sand and cobble samples are larger than the formation time of the investigated ridges, at least in the case of the olderones. Thus, even if cobbles and  The beach-ridge system in Albuen is noticeably younger than other beach-ridge systems in the region, most of which initiated 4500-7000 years ago (Clemmensen et al. 2012(Clemmensen et al. , 2018Hede et al. 2015). However, Lampe & Lampe (2018) have studied another beach-ridge plain in NE Germany, also close to the hinge line of isostatic adjustment, which began to form around 2000 years ago; this is when the Holocene relative sea-level rise in the region slowed down significantly, although with some minor fluctuations. The causes of the progradation of Albuen over the last 2000 years are not yet fully understood, but are probably due to changes in the intensity of the longshore transport of sediments from the south, and to sediment availability and accommodation space in the pre-existing glacial topography of the seabed.

Conclusions
In this study we have investigated the use of cobble surfaces as chronometers by examining the luminescence ages of buried cobbles taken from beach ridges and the modern beach on the westernmost coast of Lolland, Denmark. Clast-specific burial doses and dosimetry were used to derive apparent ages for those cobbles identified as well bleached, based on their luminescence profiles with depth. We conclude that, although the effective environmental dose rates are complex and not yet fully understood, the average ages of individual cobbles provide depositional ages consistent with those based on more conventional dating of the surrounding sandy material. This demonstrates that similar sites can be dated reliably using the luminescence from cobble surfaces. This is particularly important because it opens up the possibility of determining the depositional history of more challenging areas that lack materials for conventional OSL dating.     S4. Grain-size analysis based on the micro-XRF images of the first two slices from cobbles A811 (left column) and A815 (right column).