# Comparison of De values from Late Pleistocene alluvial deposits on the coast of Galicia (NW Spain) using BayLum or Analyst-based procedures

Carlos Arce Chamorro, Guillaume Guérin

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Carlos Arce Chamorro, Guillaume Guérin. Comparison of De values from Late Pleistocene alluvial deposits on the coast of Galicia (NW Spain) using BayLum or Analyst-based procedures. Quaternary Geochronology, 2024, 82, pp.101540. 10.1016/j.quageo.2024.101540. insu-04575539

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# Comparison of De values from Late Pleistocene alluvial deposits on the coast of Galicia (NW Spain) using BayLum or Analyst-based procedures

Carlos Arce Chamorro, Guillaume Guérin

► To cite this version:

Carlos Arce Chamorro, Guillaume Guérin. Comparison of De values from Late Pleistocene alluvial deposits on the coast of Galicia (NW Spain) using BayLum or Analyst-based procedures. Quaternary Geochronology, 2024, 82, pp.101540. 10.1016/j.quageo.2024.101540. insu-04575539

HAL Id: insu-04575539

https://insu.hal.science/insu-04575539v1

Submitted on 15 May 2024

HAL is a multi-disciplinary open access
archive for the deposit and dissemination of sci-
entific research documents, whether they are pub-
lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.

L'archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d'enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.

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Distributed under a Creative Commons Attribution 4.0 International License
Journal Pre-proof

Des comparisons of Late Pleistocene alluvial deposits on the Coast of Galicia (NW Spain) using BayLum or Analyst-based procedures.

Carlos Arce Chamorro, Guillaume Guérin

PII: S1871-1014(24)00044-X

DOI: https://doi.org/10.1016/j.quageo.2024.101540

Reference: QUAGEO 101540

To appear in: *Quaternary Geochronology*

Received Date: 9 November 2023

Revised Date: 27 March 2024

Accepted Date: 7 May 2024

<figure><img src="image_2.png" /></figure>

Please cite this article as: Chamorro, C.A., Guérin, G., Des comparisons of Late Pleistocene alluvial deposits on the Coast of Galicia (NW Spain) using BayLum or Analyst-based procedures., *Quaternary Geochronology*, https://doi.org/10.1016/j.quageo.2024.101540.

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2024 Published by Elsevier B.V.
Journal Pre-proof

Des comparisons of Late Pleistocene alluvial deposits on the Coast of Galicia (NW Spain) using BayLum or Analyst-based procedures.

Carlos Arce Chamorro, Guillaume Guérin

PII: S1871-1014(24)00044-X

DOI: https://doi.org/10.1016/j.quageo.2024.101540

Reference: QUAGEO 101540

To appear in: *Quaternary Geochronology*

Received Date: 9 November 2023

Revised Date: 27 March 2024

Accepted Date: 7 May 2024

<figure><img src="image_2.png" /></figure>

Please cite this article as: Chamorro, C.A., Guérin, G., Des comparisons of Late Pleistocene alluvial deposits on the Coast of Galicia (NW Spain) using BayLum or Analyst-based procedures., *Quaternary Geochronology*, https://doi.org/10.1016/j.quageo.2024.101540.

This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2024 Published by Elsevier B.V.
1 Des comparisons of Late Pleistocene alluvial deposits on the Coast of Galicia (NW Spain)

2 using BayLum or Analyst-based procedures.

3

4 Carlos Arce Chamorro¹* and Guillaume Guérin²

5

6 1 Institute of Geology, University of Coruña, ESCI-Campus de Elviña, 15071, A Coruña, Spain

7

8 2 Univ Rennes1, CNRS, Géosciences, UMR 6118, Rennes, France

9

10 *Corresponding author: carlos.arce@udc.es

11

12

13 Abstract

14 The coastal sedimentary record of Galicia (NW Spain) is important to study sea-level oscillations during the Late Quaternary. The alluvial deposits preserved in the Ria de Coruña and Ria de Arousa are remnants of fluvial valleys flooded by the sea during the successive Pleistocene and Holocene transgressions. A first chronological study by Optical Stimulated Luminescence (OSL)-revealed a fast-component dominated, but dim OSL signal emitted by quartz from this area.

19 Equivalent dose distributions, as obtained with the Analyst software, yielded large overdispersion values, which were negatively correlated to the potassium concentration in the sediment, thus suggesting the influence of beta dose rate heterogeneities. Nevertheless, for most samples many aliquots were considered in saturation, leading to a palaeodose and age underestimation – regardless of the model choice for age calculation. In this paper, we present new analyses using the open-source R package BayLum, as the so-called saturated aliquots may be incorporated in age calculation. Thus, we test this model performance and more commonly used models in retrieving large doses. Then, we discuss the implications for age calculation for these continental sediments formed during the Late Pleistocene.

28

29 Keywords: Coastal alluvial deposits, overdispersion, beta dose rate heterogeneities, saturated
30 OSL signal, BayLum, Late-Pleistocene, sea-level changes, North-West Spain.

31
1 Des comparisons of Late Pleistocene alluvial deposits on the Coast of Galicia (NW Spain)

2 using BayLum or Analyst-based procedures.

3

4 Carlos Arce Chamorro¹* and Guillaume Guérin²

5

6 1 Institute of Geology, University of Coruña, ESCI-Campus de Elviña, 15071, A Coruña, Spain

7

8 2 Univ Rennes1, CNRS, Géosciences, UMR 6118, Rennes, France

9

10 *Corresponding author: carlos.arce@udc.es

11

12

13 Abstract

14 The coastal sedimentary record of Galicia (NW Spain) is important to study sea-level oscillations during the Late Quaternary. The alluvial deposits preserved in the Ria de Coruña and Ria de Arousa are remnants of fluvial valleys flooded by the sea during the successive Pleistocene and Holocene transgressions. A first chronological study by Optical Stimulated Luminescence (OSL)-revealed a fast-component dominated, but dim OSL signal emitted by quartz from this area.

19 Equivalent dose distributions, as obtained with the Analyst software, yielded large overdispersion values, which were negatively correlated to the potassium concentration in the sediment, thus suggesting the influence of beta dose rate heterogeneities. Nevertheless, for most samples many aliquots were considered in saturation, leading to a palaeodose and age underestimation – regardless of the model choice for age calculation. In this paper, we present new analyses using the open-source R package BayLum, as the so-called saturated aliquots may be incorporated in age calculation. Thus, we test this model performance and more commonly used models in retrieving large doses. Then, we discuss the implications for age calculation for these continental sediments formed during the Late Pleistocene.

28

29 Keywords: Coastal alluvial deposits, overdispersion, beta dose rate heterogeneities, saturated
30 OSL signal, BayLum, Late-Pleistocene, sea-level changes, North-West Spain.

31
## 1. Introduction

The coastal alluvial deposits in NW Spain (Figs. 1; Figs. A1 and A2 in appendix) indicate the existence of long continental processes (Escuer-Sole and Vidal-Romaní, 1987), where today a marine environment is developing (see the coastal evolution map in figure 1). Therefore, they are geological evidences of the variations in sea level that occurred as a consequence of the glacial and interglacial cycles during the Late Quaternary. The first attempt to date some of these coastal alluvial deposits by optically stimulated luminescence (OSL; Murray et al., 2021) placed the formation of most of them during the Upper Pleistocene (Arce-Chamorro et al., 2022). However, the statistical treatment of data and the estimation of the palaeodose for some of the samples (MPK and ABC) using the Analyst software (Duller, 2015) could lead to an underestimation of the age by omitting much of the information due to saturation effects (see e.g., Heydari and Guérin, 2018).

FIGURE 1

Using multigrain quartz aliquots from these deposits, a fast-component dominated but dim OSL signal was observed (Fig.2), with values from 200 to 4,000 counts (per 0.08 seconds) at high doses (>80 Gy) and a few aliquots (<20%) whose OSL signal was more intense (up to 20,000 counts/0.08s) (Arce-Chamorro, 2017). Various analyses (as interpolation, different curve fitting options such as single exponential or exponential+linear, early or late background estimation and models such as the Central Age Model (CAM), the Minimum Age Model (MAM; Galbraith et al., 1999) or the Internal External Consistency criteria (Thomsen et al., 2007)) were conducted to investigate the sensitivity of absorbed dose estimation ($D_e$) to analytical choices. In all cases, $D_{es}$ distributions are highly scattered (individual $D_{es}$ range from 20 to >200 Gy; Fig. 2c), showing large overdispersion values (up to 63%). Part of this overdispersion may be linked with the concentration in potassium within the finest fraction (<63 µm) (Fig. A3), suggesting micro-beta dose-rate heterogeneities (Arce-Chamorro and Sanjurjo-Sánchez., 2020). Nevertheless, for most samples the number of aliquots in saturation is a significant issue (Fig.2b).

FIGURE 2

A single saturating exponential function passing through the origin ($L/T=A[1-\exp(-D/D_0)]$) was used for fitting the normalized OSL signals ($L/T$; natural and regenerated at increasing doses) (Fig. 2a) to describe a single trap dominated luminescence signal and signal saturation, resulting in a highly scattered Equivalent Dose ($D_e$) distributions (Fig. 2b). This also results in a large proportion of aliquots in saturation, as aliquots for which the sum of $L_N/T_N$ and its uncertainty as calculated with Analyst does not intersect the dose response curve (DRC) (Fig. 2b and A4, A5;
## 1. Introduction

The coastal alluvial deposits in NW Spain (Figs. 1; Figs. A1 and A2 in appendix) indicate the existence of long continental processes (Escuer-Sole and Vidal-Romaní, 1987), where today a marine environment is developing (see the coastal evolution map in figure 1). Therefore, they are geological evidences of the variations in sea level that occurred as a consequence of the glacial and interglacial cycles during the Late Quaternary. The first attempt to date some of these coastal alluvial deposits by optically stimulated luminescence (OSL; Murray et al., 2021) placed the formation of most of them during the Upper Pleistocene (Arce-Chamorro et al., 2022). However, the statistical treatment of data and the estimation of the palaeodose for some of the samples (MPK and ABC) using the Analyst software (Duller, 2015) could lead to an underestimation of the age by omitting much of the information due to saturation effects (see e.g., Heydari and Guérin, 2018).

FIGURE 1

Using multigrain quartz aliquots from these deposits, a fast-component dominated but dim OSL signal was observed (Fig.2), with values from 200 to 4,000 counts (per 0.08 seconds) at high doses (>80 Gy) and a few aliquots (<20%) whose OSL signal was more intense (up to 20,000 counts/0.08s) (Arce-Chamorro, 2017). Various analyses (as interpolation, different curve fitting options such as single exponential or exponential+linear, early or late background estimation and models such as the Central Age Model (CAM), the Minimum Age Model (MAM; Galbraith et al., 1999) or the Internal External Consistency criteria (Thomsen et al., 2007)) were conducted to investigate the sensitivity of absorbed dose estimation ($D_e$) to analytical choices. In all cases, $D_{es}$ distributions are highly scattered (individual $D_{es}$ range from 20 to >200 Gy; Fig. 2c), showing large overdispersion values (up to 63%). Part of this overdispersion may be linked with the concentration in potassium within the finest fraction (<63 µm) (Fig. A3), suggesting micro-beta dose-rate heterogeneities (Arce-Chamorro and Sanjurjo-Sánchez., 2020). Nevertheless, for most samples the number of aliquots in saturation is a significant issue (Fig.2b).

FIGURE 2

A single saturating exponential function passing through the origin ($L/T=A[1-\exp(-D/D_0)]$) was used for fitting the normalized OSL signals ($L/T$; natural and regenerated at increasing doses) (Fig. 2a) to describe a single trap dominated luminescence signal and signal saturation, resulting in a highly scattered Equivalent Dose ($D_e$) distributions (Fig. 2b). This also results in a large proportion of aliquots in saturation, as aliquots for which the sum of $L_N/T_N$ and its uncertainty as calculated with Analyst does not intersect the dose response curve (DRC) (Fig. 2b and A4, A5;
Table 1), leading to notorious difficulties for dating (Duller et al., 2012; Thomsen et al., 2016; Colarossi et al., 2020). For most of the samples, there exists a proportion of aliquots (up to 30%) for which the Analyst (Duller, 2015) does not provide a known uncertainty (in the following, we call the number of such aliquots $N_{De/INF}$) (Table 1). This excludes them from calculations using frequentist statistics such as the CAM, leading to an underestimation of the burial age (Heydari and Guérin., 2018; Guérin et al., 2021; Chapot et al., 2022). The same applies to those aliquots (up to 55%) for which the Analyst provides neither equivalent dose ($D_e$) nor uncertainty (we denote the number of such aliquots by $N_{INF/INF}$) (Table A1; Fig.2). Alternatively, the Bayesian models of Combès et al. (2015) and Combès and Philippe (2017) implemented in the BayLum package (Philippe et al., 2019; Guérin et al., 2021) are able to use these saturated aliquots by estimating the individual $D_e$s and Palaeodose simultaneously from single hierarchical iteration of all $L_N/T_N$ and $L_X/T_X$ signal distributions of the DRCs (see Heydari and Guérin, 2018), without parameterizing individual $D_e$ probability densities. The comparison of the results obtained with the CAM (after $D_e$ estimation with the Analyst software) and with BayLum, according to various selections of aliquots included in the calculations ($N_{De/SIGMA}$, i.e., the aliquots not affected by saturation issues, $N_{De/INF}$ and $N_{INF/INF}$), as well as the estimation of a more accurate age are the main objectives of this work.

## 2. Material and methods.

Samples MPK and ABC were collected using steel cores. For OSL signal analysis from quartz grains, the raw sample from the central part of the core was dehydrated at room temperature and the 180-250 µm grain-size fraction was separated by dry sieving (Arce-Chamorro, 2017). Quartz purification was carried out using $H_2O_2$ and HCl (20%), as well as HF-etching (40%) during 40 minutes to remove the alpha-irradiated outer layer of the grains. Ultra-dense liquid centrifugation was carried out to isolate quartz grains and silicon spray was used to prepare ≈100-grain aliquots on steel discs (Ø=1 mm, except for samples ABC1 and ABC4 for which 10-grain aliquots were manually prepared using a binocular and a small paintbrush). A Risø reader TL/OSL DA-15 reader with a Beta $^{90}$Sr/$^{90}$Y source delivering 0.120+0.003 Gys$^{-1}$(calibrated with a sample given a 5 Gy gamma dose using a $^{137}$Cs source (40 s)) was used to build the DRCs using the SAR protocol (Murray and Wintle, 2000) (Table A2), but also to test each aliquot for feldspar contamination by measuring regenerated OSL signals after an infra-red stimulation. The OSL signal was stimulated with blue LEDs at 90% of maximum power during 40 s. The fast-OSL signal was integrated from the first 0.5 s of luminescence stimulus and the background signal from the last 4 s. For this work, dose recovery (Wallinga et al., 2000) experiments have been carried out again (see Arce-Chamorro et al., 2017, for the first set of dose recovery experiments), but at given doses of 83-84 Gy for MPK samples and 180 Gy for MPK8. To maximize the number of accepted aliquots and the information provided by Analyst, the acceptance criteria were a natural test dose error <20%
Table 1), leading to notorious difficulties for dating (Duller et al., 2012; Thomsen et al., 2016; Colarossi et al., 2020). For most of the samples, there exists a proportion of aliquots (up to 30%) for which the Analyst (Duller, 2015) does not provide a known uncertainty (in the following, we call the number of such aliquots $N_{De/INF}$) (Table 1). This excludes them from calculations using frequentist statistics such as the CAM, leading to an underestimation of the burial age (Heydari and Guérin., 2018; Guérin et al., 2021; Chapot et al., 2022). The same applies to those aliquots (up to 55%) for which the Analyst provides neither equivalent dose ($D_e$) nor uncertainty (we denote the number of such aliquots by $N_{INF/INF}$) (Table A1; Fig.2). Alternatively, the Bayesian models of Combès et al. (2015) and Combès and Philippe (2017) implemented in the BayLum package (Philippe et al., 2019; Guérin et al., 2021) are able to use these saturated aliquots by estimating the individual $D_e$s and Palaeodose simultaneously from single hierarchical iteration of all $L_N/T_N$ and $L_X/T_X$ signal distributions of the DRCs (see Heydari and Guérin, 2018), without parameterizing individual $D_e$ probability densities. The comparison of the results obtained with the CAM (after $D_e$ estimation with the Analyst software) and with BayLum, according to various selections of aliquots included in the calculations ($N_{De/SIGMA}$, i.e., the aliquots not affected by saturation issues, $N_{De/INF}$ and $N_{INF/INF}$), as well as the estimation of a more accurate age are the main objectives of this work.

## 2. Material and methods.

Samples MPK and ABC were collected using steel cores. For OSL signal analysis from quartz grains, the raw sample from the central part of the core was dehydrated at room temperature and the 180-250 µm grain-size fraction was separated by dry sieving (Arce-Chamorro, 2017). Quartz purification was carried out using $H_2O_2$ and HCl (20%), as well as HF-etching (40%) during 40 minutes to remove the alpha-irradiated outer layer of the grains. Ultra-dense liquid centrifugation was carried out to isolate quartz grains and silicon spray was used to prepare ≈100-grain aliquots on steel discs (Ø=1 mm, except for samples ABC1 and ABC4 for which 10-grain aliquots were manually prepared using a binocular and a small paintbrush). A Risø reader TL/OSL DA-15 reader with a Beta $^{90}$Sr/$^{90}$Y source delivering 0.120+0.003 Gys$^{-1}$(calibrated with a sample given a 5 Gy gamma dose using a $^{137}$Cs source (40 s)) was used to build the DRCs using the SAR protocol (Murray and Wintle, 2000) (Table A2), but also to test each aliquot for feldspar contamination by measuring regenerated OSL signals after an infra-red stimulation. The OSL signal was stimulated with blue LEDs at 90% of maximum power during 40 s. The fast-OSL signal was integrated from the first 0.5 s of luminescence stimulus and the background signal from the last 4 s. For this work, dose recovery (Wallinga et al., 2000) experiments have been carried out again (see Arce-Chamorro et al., 2017, for the first set of dose recovery experiments), but at given doses of 83-84 Gy for MPK samples and 180 Gy for MPK8. To maximize the number of accepted aliquots and the information provided by Analyst, the acceptance criteria were a natural test dose error <20%
and a $T_N$ signal >3σ above background, following Geach et al. (2015), Thomsen et al. (2016), Heydari and Guérin (2018), Chapot et al., (2022), etc. Frequentist statistical models such as the CAM or the Average Dose Model (ADM; Guérin et al., 2017) were implemented with the Luminescence R package (Kreutzer et al., 2017). Bayesian statistical analysis was carried out with the BayLum R Package, following the recommendations of Philippe et al. (2019) to check the validity of the estimates obtained with the Markov Chain Monte Carlo (MCMC) algorithms. For BayLum calculations (see in figure A6 the MCMC plots performed by BayLum iterations for samples ABC3 and MPK8), the number of iterations (from $5 \times 10^3$ to $5 \times 10^6$) and prior-age intervals were tested and compared using R Studio (R Core Team, 2020).

Dose rate estimates have been carried out throughout activity estimates of $^{238}$U, $^{235}$U and $^{232}$Th decay chains, as well as $^{40}$K, by high resolution gamma spectrometry (HRGe) using a Camberra XTRA Ge-Intrinsic detector. Conversion factors of Guérin et al., (2011) for changing Bq/kg to Gy/ky units were used. Beta attenuation from HF etching was corrected following Brennan (2003). $D_R$ attenuation due to water content was estimated from saturated and moisture values of the raw sample following Guérin and Mercier (2012). Auto-irradiation of quartz from alpha component was taken into account following Vandenberghe et al. (2008). Sampling depth within the sediment, altitude and latitude were considered to estimate cosmic dose rates following Prescott and Hutton (1994), as well as the density of sampled materials (1.8-1.9 g/cm$^3$).

## 3. Results

### 3.1 Dose rate estimates

The estimated activity of the main radioisotopes is shown in table A3 for the subsequent estimation of the $D_R$ (Gy/ka), as an indispensable parameter for the calculation of an age (section 4.3) once the palaeodoses ($D_e$=Gy) of each sample has been estimated (age=$D_e/D_R$; Aitken, 1998). No disequilibrium was observed within the $^{238}$U, $^{235}$U and $^{228}$Th decay chains. The water saturation percentage (W%) for MPK and ABC samples varies between 20 to 40%, as a parameter included in $D_R$ estimates following Aitken (1998). Moisture percentage (H%) varies between 4 and 20%, thus obtaining a H/W ratio from 25 to 55% (Arce-Chamorro, 2017). This ratio is needed to estimate the water content in the sediment along burial time, since all these alluvial sediments were fully saturated when they were deposited (W=100%). Subsequent incision of the fluvial network led to the abandonment of the alluvial deposits at higher altitudes, remaining perched and even giving rise to an inverted relief (Escuer-Sole and Vidal-Romaní, 1987). Thus, we assumed a sedimentary water content close to the average of H/W ratio for the analysed samples (W=40±10%) (Table A3).

### 3.2 Dose estimates.

#### 3.2.1 Dose recovery experiments.
and a $T_N$ signal >3σ above background, following Geach et al. (2015), Thomsen et al. (2016), Heydari and Guérin (2018), Chapot et al., (2022), etc. Frequentist statistical models such as the CAM or the Average Dose Model (ADM; Guérin et al., 2017) were implemented with the Luminescence R package (Kreutzer et al., 2017). Bayesian statistical analysis was carried out with the BayLum R Package, following the recommendations of Philippe et al. (2019) to check the validity of the estimates obtained with the Markov Chain Monte Carlo (MCMC) algorithms.
For BayLum calculations (see in figure A6 the MCMC plots performed by BayLum iterations for samples ABC3 and MPK8), the number of iterations (from $5 \times 10^3$ to $5 \times 10^6$) and prior-age intervals were tested and compared using R Studio (R Core Team, 2020).

Dose rate estimates have been carried out throughout activity estimates of $^{238}$U, $^{235}$U and $^{232}$Th decay chains, as well as $^{40}$K, by high resolution gamma spectrometry (HRGe) using a Camberra XTRA Ge-Intrinsic detector. Conversion factors of Guérin et al., (2011) for changing Bq/kg to Gy/ky units were used. Beta attenuation from HF etching was corrected following Brennan (2003). $D_R$ attenuation due to water content was estimated from saturated and moisture values of the raw sample following Guérin and Mercier (2012). Auto-irradiation of quartz from alpha component was taken into account following Vandenberghe et al. (2008). Sampling depth within the sediment, altitude and latitude were considered to estimate cosmic dose rates following Prescott and Hutton (1994), as well as the density of sampled materials (1.8-1.9 g/cm$^3$).

## 3. Results

### 3.1 Dose rate estimates

The estimated activity of the main radioisotopes is shown in table A3 for the subsequent estimation of the $D_R$ (Gy/ka), as an indispensable parameter for the calculation of an age (section 4.3) once the palaeodoses ($D_e$=Gy) of each sample has been estimated (age=$D_e/D_R$; Aitken, 1998).
No disequilibrium was observed within the $^{238}$U, $^{235}$U and $^{228}$Th decay chains. The water saturation percentage (W%) for MPK and ABC samples varies between 20 to 40%, as a parameter included in $D_R$ estimates following Aitken (1998). Moisture percentage (H%) varies between 4 and 20%, thus obtaining a H/W ratio from 25 to 55% (Arce-Chamorro, 2017). This ratio is needed to estimate the water content in the sediment along burial time, since all these alluvial sediments were fully saturated when they were deposited (W=100%). Subsequent incision of the fluvial network led to the abandonment of the alluvial deposits at higher altitudes, remaining perched and even giving rise to an inverted relief (Escuer-Sole and Vidal-Romaní, 1987). Thus, we assumed a sedimentary water content close to the average of H/W ratio for the analysed samples (W=40±10%) (Table A3).

### 3.2 Dose estimates.

#### 3.2.1 Dose recovery experiments.
Dose recovery experiments are meant to assess the performance of the SAR protocol and subsequent statistical analyses in retrieving a known artificial dose administered to a population of grains. It is generally suggested that measured to given dose ratios should lie within 10% of unity (Wallinga et al., 2000). In our case, the dose recovery ratios have been calculated using the CAM and BayLum (gaussian) ($D_{e-SIGMA}$, $D_{e-UNCERT.SAT}$ and $D_{e-TOTAL}$) with a known dose of 84 Gy (Table 1; Fig. 3). The choice of 84 Gy was made after observing that aliquots in saturation (i.e., belonging to the $N_{De/INF}$ or $N_{INF/INF}$ populations) begin to be observed at this level of dose when using a single exponential fit with the Analyst software (Table 2; Fig. A7). A known given dose of 180 Gy was also used for MPK8 sample, as $N_{De/INF}$ or $N_{INF/INF}$ aliquots only appear at higher doses for this sample (see MPK8 sample in table 1).

TABLE 1

As in previous works (Duller et al., 2012; Chapot et al., 2022), a higher dose recovery inaccuracy of CAM is observed when there is a higher proportion of saturated aliquots, in this case $N_{De/INF}$ and $N_{INF/INF}$ (>30%). Thus, BayLum results are strongly conditioned by the proportion of $N_{De/INF}$ and $N_{INF/INF}$ aliquots (Fig. 3a) providing more accurate results, like palaeodose analyses do (see next section 3.2.2). First, by looking at Table 1 we note that the average dose recovery ratio is equal to 0.90±0.03 when using the CAM, 0.94±0.02 when using BayLum with a Gaussian distribution to model equivalent doses with the same number of aliquots ($N_{De/SIGMA}$) and 1.01±0.03 with BayLum when including all aliquots and notably the so-called saturated ones. Second, to highlight the effect of saturated grains on the dose recovery estimates (Fig. 3a), we plotted the relative difference between the values obtained with the CAM and those calculated with BayLum when including all aliquots, as a function of the proportion of saturated aliquots (Fig. 3b). The clear positive trend suggests to us that indeed the CAM underestimates the given dose all the more than the frequency of ‘saturated’ aliquots is large. Our results are similar to those of Duller et al. (2012), Heydari and Guérin (2018) and Chapot et al. (2022), who all – among others – reported problems of dose recovery underestimation with large doses.

FIGURE 3

### 3.2.2 Palaeodose estimates.

We estimated the palaeodose for each sample using different statistical models and grain selections, to make our comparisons as thorough as possible (Fig.4). First, since the CAM and the ADM can only work with pairs of $D_e$ and associated uncertainty values, we are limited to $N_{De/SIGMA}$ aliquots per sample. BayLum was ran on this population of grains, using both the Gaussian and lognormal models for equivalent dose distribution. For the sake of comparison, we
Dose recovery experiments are meant to assess the performance of the SAR protocol and subsequent statistical analyses in retrieving a known artificial dose administered to a population of grains. It is generally suggested that measured to given dose ratios should lie within 10% of unity (Wallinga et al., 2000). In our case, the dose recovery ratios have been calculated using the CAM and BayLum (gaussian) ($D_{e-SIGMA}$, $D_{e-UNCERT.SAT}$ and $D_{e-TOTAL}$) with a known dose of 84 Gy (Table 1; Fig. 3). The choice of 84 Gy was made after observing that aliquots in saturation (i.e., belonging to the $N_{De/INF}$ or $N_{INF/INF}$ populations) begin to be observed at this level of dose when using a single exponential fit with the Analyst software (Table 2; Fig. A7). A known given dose of 180 Gy was also used for MPK8 sample, as $N_{De/INF}$ or $N_{INF/INF}$ aliquots only appear at higher doses for this sample (see MPK8 sample in table 1).

153

154 TABLE 1

155

As in previous works (Duller et al., 2012; Chapot et al., 2022), a higher dose recovery inaccuracy of CAM is observed when there is a higher proportion of saturated aliquots, in this case $N_{De/INF}$ and $N_{INF/INF}$ (>30%). Thus, BayLum results are strongly conditioned by the proportion of $N_{De/INF}$ and $N_{INF/INF}$ aliquots (Fig. 3a) providing more accurate results, like palaeodose analyses do (see next section 3.2.2). First, by looking at Table 1 we note that the average dose recovery ratio is equal to 0.90±0.03 when using the CAM, 0.94±0.02 when using BayLum with a Gaussian distribution to model equivalent doses with the same number of aliquots ($N_{De/SIGMA}$) and 1.01±0.03 with BayLum when including all aliquots and notably the so-called saturated ones. Second, to highlight the effect of saturated grains on the dose recovery estimates (Fig. 3a), we plotted the relative difference between the values obtained with the CAM and those calculated with BayLum when including all aliquots, as a function of the proportion of saturated aliquots (Fig. 3b). The clear positive trend suggests to us that indeed the CAM underestimates the given dose all the more than the frequency of ‘saturated’ aliquots is large. Our results are similar to those of Duller et al. (2012), Heydari and Guérin (2018) and Chapot et al. (2022), who all – among others – reported problems of dose recovery underestimation with large doses.

171

172 FIGURE 3

173

174 3.2.2 Palaeodose estimates.

We estimated the palaeodose for each sample using different statistical models and grain selections, to make our comparisons as thorough as possible (Fig.4). First, since the CAM and the ADM can only work with pairs of $D_e$ and associated uncertainty values, we are limited to $N_{De/SIGMA}$ aliquots per sample. BayLum was ran on this population of grains, using both the Gaussian and lognormal models for equivalent dose distribution. For the sake of comparison, we
used the lognormal_M model of BayLum (Fig. 4a), i.e. the model which estimates the median of the lognormal distribution. For purely mathematical reasons, this latter model – like the CAM – should underestimate the average absorbed dose in the studied population of grains (Guérin et al., 2017). In a second step of analysis, we included for each sample the number of aliquots for which Analyst provides a $D_e$ estimate but no bounded estimate of its uncertainty ($N_{De/INF}$), so that we work with a total number of aliquots $N_{De-UNCERT.SAT} = N_{De/SIGMA} + N_{De/INF}$. Finally, we also included the aliquots for which Analyst provides no finite $D_e$ value and thus, no uncertainty either ($N_{TOTAL} = N_{De/SIGMA} + N_{De/INF} + N_{INF/INF}$).

FIGURE 4

Table 2 lists all palaeodose estimates. Unsurprisingly, the CAM doses always are the lowest values for each sample. Conversely, the largest values are systematically obtained with BayLum when all aliquots are used (Fig.4b), including those for which the natural OSL signal (or the sum of this signal and its uncertainty) is greater than the asymptotic limit of the DRC in Analyst. To interpret the comparisons in more detail, one needs to disentangle two different sources of differences, namely dose rate variability and saturation issues. It is worth mentioning that for sample MPK8 (Table 2) a new SAR protocol was used to investigate larger regenerative doses (120, 240, 480 and 960 Gy; Table A2), as we did not obtain convergence of the MCMC chains using BayLum when using all aliquots (De TOTAL in Fig.4). (In our previous study (Arce-Chamorro, 2017), the largest regenerative dose was 216 Gy.). For the samples MPK3 and ABC2, whose palaeodoses are higher than the larger regenerative dose of the SAR, the results obtained ($D_{e-TOTAL}$ in table 2) should be interpreted with caution, although the Late Pleistocene age calculated for these samples is consistent and reliable (see section 4.3).

TABLE 2

4. Discussion

4.1 Dose rate effects on $D_e$s estimates.

The first question that needs to be addressed when calculating an OSL age is that of the variability in equivalent doses measured on numerous aliquots. It is well-known that dose rates to quartz grains are, as a general rule, variable; this variability has been observed by beta autoradiography (e.g., Rufer and Preusser, 2009; Guérin et al., 2012b; Martin et al., 2015; Smedley et al., 2020) and modelled (Nathan et al., 2003; Mayya et al., 2006; Cunnigham et al., 2011; Guérin et al., 2015; Jankowski and Jacobs, 2018). The question then becomes to determine which quantity should be estimated from the population of $D_e$ values. Again, as a general rule, $D_e$ values may adequately be described by a lognormal distribution, both from purely luminescence
used the lognormal_M model of BayLum (Fig. 4a), i.e. the model which estimates the median of the lognormal distribution. For purely mathematical reasons, this latter model – like the CAM – should underestimate the average absorbed dose in the studied population of grains (Guérin et al., 2017). In a second step of analysis, we included for each sample the number of aliquots for which Analyst provides a $D_e$ estimate but no bounded estimate of its uncertainty ($N_{De/INF}$), so that we work with a total number of aliquots $N_{De-UNCERT.SAT} = N_{De/SIGMA} + N_{De/INF}$. Finally, we also included the aliquots for which Analyst provides no finite $D_e$ value and thus, no uncertainty either ($N_{TOTAL} = N_{De/SIGMA} + N_{De/INF} + N_{INF/INF}$).

FIGURE 4

Table 2 lists all palaeodose estimates. Unsurprisingly, the CAM doses always are the lowest values for each sample. Conversely, the largest values are systematically obtained with BayLum when all aliquots are used (Fig.4b), including those for which the natural OSL signal (or the sum of this signal and its uncertainty) is greater than the asymptotic limit of the DRC in Analyst. To interpret the comparisons in more detail, one needs to disentangle two different sources of differences, namely dose rate variability and saturation issues. It is worth mentioning that for sample MPK8 (Table 2) a new SAR protocol was used to investigate larger regenerative doses (120, 240, 480 and 960 Gy; Table A2), as we did not obtain convergence of the MCMC chains using BayLum when using all aliquots (De TOTAL in Fig.4). (In our previous study (Arce-Chamorro, 2017), the largest regenerative dose was 216 Gy.). For the samples MPK3 and ABC2, whose palaeodoses are higher than the larger regenerative dose of the SAR, the results obtained ($D_{e-TOTAL}$ in table 2) should be interpreted with caution, although the Late Pleistocene age calculated for these samples is consistent and reliable (see section 4.3).

TABLE 2

4. Discussion

4.1 Dose rate effects on $D_e$s estimates.

The first question that needs to be addressed when calculating an OSL age is that of the variability in equivalent doses measured on numerous aliquots. It is well-known that dose rates to quartz grains are, as a general rule, variable; this variability has been observed by beta autoradiography (e.g., Rufer and Preusser, 2009; Guérin et al., 2012b; Martin et al., 2015; Smedley et al., 2020) and modelled (Nathan et al., 2003; Mayya et al., 2006; Cunnigham et al., 2011; Guérin et al., 2015; Jankowski and Jacobs, 2018). The question then becomes to determine which quantity should be estimated from the population of $D_e$ values. Again, as a general rule, $D_e$ values may adequately be described by a lognormal distribution, both from purely luminescence
measurement reasons (Galbraith and Roberts, 2012) and because radioactive hotspots such as potassium feldspar grains are ubiquitous (Guérin et al., 2015). Both the CAM and the ADM assume a lognormal distribution, but the CAM calculates the median while the ADM estimates the average of this distribution – simply to match the average dose rate determined experimentally using the infinite matrix assumption. This fundamental difference explains the discrepancy between CAM and ADM doses, the former being 4-17% smaller than the latter (Table 2; Fig. 5a). It also explains, at least in part, the difference between CAM doses and estimates obtained with BayLum using a Gaussian distribution – between 5 and 30% (Table 2; Fig. 5b), with the key-difference being the estimated parameter rather than the shape of the distribution fitted to $D_e$ estimates.

The first attempts to analyze the high OD values for MPK samples (20-50%) were related with beta dose rate variability (Arce-Chamorro et al., 2020) (Fig. A3), since partial bleaching could not be demonstrated (Arce-Chamorro, 2017) and because intrinsic overdispersion (<5%) was determined from dose recovery tests (Thomsen et al., 2005). In that work, it should be noted that all $N_{De/σ}$ aliquots interpolating close to the linear part of the DRC (i.e., below the 86.5% of the maximum asymptote for the DRC or $D_e>2D_0$; Wintle and Murray, 2006) were excluded for palaeodose estimates with the CAM, as individual $D_e$s estimates from them were generally considered as unreliable. The rejection of these aliquots led to biased $D_e$s distributions and underestimation of the OD from CAM. Conversely, as observed in this work, when all aliquots with $D_e/σ$ values ($N_{De/σ}$, following the nomenclature of this manuscript for aliquots which are not affected by saturation) are included in the calculations, the OD from the CAM grows up from 26 to 69% (see Table 2).

FIGURE 5

## 4.2. Saturation effects on $D_e$s estimates.

When using $N_{De/SIGMA}$ aliquots, comparison of palaeodose estimates between CAM and BayLum (Lognormal_M) aliquots show similar values at low doses, as they both estimate the median of a lognormal distribution. However, an underestimation of $D_e$s with the CAM is observed at higher doses (Fig. 5d), which would indicate that BayLum (Log_M) provides better data handling in the non-linear part of the DRC than the CAM. In addition, $D_e$ estimates from Gaussian are higher than Lognormal_M procedures with BayLum (Fig. 5d) and, as commented, the differences with CAM estimates increases with the OD (Fig. 5c). This suggests that in case of samples with widely dispersed individual $D_e$s, BayLum (gaussian) procedures would provide more accurate results than the CAM (see also Heydari and Guérin, 2018).

For its part, when using saturated aliquots, the increase of $D_{e-TOTAL}$ ($N_{De/SIGMA}+N_{De/INF}+N_{INF/INF}$) with respect to $D_{e-SIGMA}$ ($N_{De/SIGMA}$) estimated by the CAM and BayLum (gaussian) is analysed as
measurement reasons (Galbraith and Roberts, 2012) and because radioactive hotspots such as potassium feldspar grains are ubiquitous (Guérin et al., 2015). Both the CAM and the ADM assume a lognormal distribution, but the CAM calculates the median while the ADM estimates the average of this distribution – simply to match the average dose rate determined experimentally using the infinite matrix assumption. This fundamental difference explains the discrepancy between CAM and ADM doses, the former being 4-17% smaller than the latter (Table 2; Fig. 5a). It also explains, at least in part, the difference between CAM doses and estimates obtained with BayLum using a Gaussian distribution – between 5 and 30% (Table 2; Fig. 5b), with the key-difference being the estimated parameter rather than the shape of the distribution fitted to $D_e$ estimates.

The first attempts to analyze the high OD values for MPK samples (20-50%) were related with beta dose rate variability (Arce-Chamorro et al., 2020) (Fig. A3), since partial bleaching could not be demonstrated (Arce-Chamorro, 2017) and because intrinsic overdispersion (<5%) was determined from dose recovery tests (Thomsen et al., 2005). In that work, it should be noted that all $N_{De/σ}$ aliquots interpolating close to the linear part of the DRC (i.e., below the 86.5% of the maximum asymptote for the DRC or $D_e>2D_0$; Wintle and Murray, 2006) were excluded for palaeodose estimates with the CAM, as individual $D_e$s estimates from them were generally considered as unreliable. The rejection of these aliquots led to biased $D_e$s distributions and underestimation of the OD from CAM. Conversely, as observed in this work, when all aliquots with $D_e/σ$ values ($N_{De/σ}$, following the nomenclature of this manuscript for aliquots which are not affected by saturation) are included in the calculations, the OD from the CAM grows up from 26 to 69% (see Table 2).

FIGURE 5

## 4.2. Saturation effects on $D_e$s estimates.

When using $N_{De/SIGMA}$ aliquots, comparison of palaeodose estimates between CAM and BayLum (Lognormal_M) aliquots show similar values at low doses, as they both estimate the median of a lognormal distribution. However, an underestimation of $D_e$s with the CAM is observed at higher doses (Fig. 5d), which would indicate that BayLum (Log_M) provides better data handling in the non-linear part of the DRC than the CAM. In addition, $D_e$ estimates from Gaussian are higher than Lognormal_M procedures with BayLum (Fig. 5d) and, as commented, the differences with CAM estimates increases with the OD (Fig. 5c). This suggests that in case of samples with widely dispersed individual $D_e$s, BayLum (gaussian) procedures would provide more accurate results than the CAM (see also Heydari and Guérin, 2018).

For its part, when using saturated aliquots, the increase of $D_{e-TOTAL}$ ($N_{De/SIGMA}+N_{De/INF}+N_{INF/INF}$) with respect to $D_{e-SIGMA}$ ($N_{De/SIGMA}$) estimated by the CAM and BayLum (gaussian) is analysed as
a function of the number of saturated aliquots ($N_{TOTAL} = N_{De/SIGMA} + N_{De/INF} + N_{INF/INF}$) included in the calculations with the Bayesian models (Figs. 5e and 5f). For this purpose, the ratio of aliquots was normalised as $[(N_{TOTAL} - N_{SIGMA}) / N_{TOTAL}]$ (X axis in Figs. 5e and 5f). When this ratio tends to zero, i.e.: when the proportion of aliquots ‘in saturation’ becomes negligible, $D_{e-SIGMA}$ is similar to $D_{e-TOTAL}$. However, when this ratio is increased, $D_{e-TOTAL}$ is strongly increased. When this ratio approaches unity, i.e., when most aliquots are considered saturated, $D_{e-TOTAL}$ seems to grow exponentially. The difference between $D_{e-TOTAL}$ ($N_{De/SIGMA} + N_{De/INF} + N_{INF/INF}$) and $D_{e-UNCERT.SAT}$ ($N_{De/SIGMA} + N_{De/INF}$) also follows this trend, showing the importance of the unknown information (uncertainty) included within $N_{INF/INF}$ aliquots using BayLum (inset in Fig. 5f). This observation suggests that BayLum (gaussian) provides more accurate results when working with saturated aliquots than any model excluding such aliquots, as is suggested in the literature (Heydari and Guérin, 2018; Guérin et al., 2021; Chapot et al., 2022).

## 4.3 Burial ages of MPK and ABC samples.

It seems rather clear that dose estimates obtained after rejecting many aliquots due to saturation are unreliable; only dose underestimation can result from such biased acceptance criterion (Singh et al., 2017; Guérin et al., 2015b). Thus, in the following, we assume that BayLum dose estimates making use of all aliquots [$D_{e-TOTAL}=(N_{De/SIGMA}+N_{De/INF}+N_{INF/INF})$] are more accurate. Updated OSL ages using these dose values are shown in table 3.

## TABLE 3

Based on these results, the studied coastal alluvial sediments in NW Spain were deposited during different episodes throughout the Late Pleistocene (Fig. 6). The ages of the deposits corresponding to samples MPK1, MPK5, MPK6 and ABC4 correspond to the beginning of the regressive episode at the Upper Pleistocene (MIS5b, 5a and MIS4) (Fig. 6). BayLum (gaussian) ages for these samples are 10 ky and 30 ky greater than those calculated in previous work (Arce-Chamorro, 2017) based on frequentist statistics (CAM and Minimum Age Model (MAM); Galbraith et al., 1999) (Table 3), which excluded saturated aliquots. All the rest of the samples show much older ages (>50 ky) using BayLum. The deposit corresponding to sample MPK4 formed during the Eemian interglacial (late MIS6 and MIS5e), whereas MPK7, MPK8 and MPK2 samples are of pre-Eemian age. The deposit of the sample MPK3 was formed during MIS7, with stratigraphic coherence between this sample located at +60 m above present sea level (apsl) and sample MPK4 at +10 m (apsl), formed by the same secondary course of a fluvial network (see Arce-Chamorro et al., 2023a). As for the alluvial outcrop of Catoira from which samples ABC1 of 412±49 ky, ABC2 of 182±23 ky and ABC3 of 335±48 ky were extracted, the presence of different processes of aggradation and erosion in a strictly continental environment during the
a function of the number of saturated aliquots ($N_{TOTAL} = N_{De/SIGMA} + N_{De/INF} + N_{INF/INF}$) included in the calculations with the Bayesian models (Figs. 5e and 5f). For this purpose, the ratio of aliquots was normalised as $[(N_{TOTAL} - N_{SIGMA}) / N_{TOTAL}]$ (X axis in Figs. 5e and 5f). When this ratio tends to zero, i.e.: when the proportion of aliquots ‘in saturation’ becomes negligible, $D_{e-SIGMA}$ is similar to $D_{e-TOTAL}$. However, when this ratio is increased, $D_{e-TOTAL}$ is strongly increased. When this ratio approaches unity, i.e., when most aliquots are considered saturated, $D_{e-TOTAL}$ seems to grow exponentially. The difference between $D_{e-TOTAL}$ ($N_{De/SIGMA} + N_{De/INF} + N_{INF/INF}$) and $D_{e-UNCERT.SAT}$ ($N_{De/SIGMA} + N_{De/INF}$) also follows this trend, showing the importance of the unknown information (uncertainty) included within $N_{INF/INF}$ aliquots using BayLum (inset in Fig. 5f). This observation suggests that BayLum (gaussian) provides more accurate results when working with saturated aliquots than any model excluding such aliquots, as is suggested in the literature (Heydari and Guérin, 2018; Guérin et al., 2021; Chapot et al., 2022).

266

## 4.3 Burial ages of MPK and ABC samples.

It seems rather clear that dose estimates obtained after rejecting many aliquots due to saturation are unreliable; only dose underestimation can result from such biased acceptance criterion (Singh et al., 2017; Guérin et al., 2015b). Thus, in the following, we assume that BayLum dose estimates making use of all aliquots [$D_{e-TOTAL}=(N_{De/SIGMA}+N_{De/INF}+N_{INF/INF})$] are more accurate. Updated OSL ages using these dose values are shown in table 3.

273

## TABLE 3

275

Based on these results, the studied coastal alluvial sediments in NW Spain were deposited during different episodes throughout the Late Pleistocene (Fig. 6). The ages of the deposits corresponding to samples MPK1, MPK5, MPK6 and ABC4 correspond to the beginning of the regressive episode at the Upper Pleistocene (MIS5b, 5a and MIS4) (Fig. 6). BayLum (gaussian) ages for these samples are 10 ky and 30 ky greater than those calculated in previous work (Arce-Chamorro, 2017) based on frequentist statistics (CAM and Minimum Age Model (MAM); Galbraith et al., 1999) (Table 3), which excluded saturated aliquots. All the rest of the samples show much older ages (>50 ky) using BayLum. The deposit corresponding to sample MPK4 formed during the Eemian interglacial (late MIS6 and MIS5e), whereas MPK7, MPK8 and MPK2 samples are of pre-Eemian age. The deposit of the sample MPK3 was formed during MIS7, with stratigraphic coherence between this sample located at +60 m above present sea level (apsl) and sample MPK4 at +10 m (apsl), formed by the same secondary course of a fluvial network (see Arce-Chamorro et al., 2023a). As for the alluvial outcrop of Catoira from which samples ABC1 of 412±49 ky, ABC2 of 182±23 ky and ABC3 of 335±48 ky were extracted, the presence of different processes of aggradation and erosion in a strictly continental environment during the
291 glacioeustatic oscillations along the Late Pleistocene is observed (Arce-Chamorro and Vidal-Romaní, 2021) (Fig.A2), more specifically during MIS11-MIS10 (ABC1 and ABC3) and during MIS7-MIS6 (ABC2).

294

295 FIGURE 6

296

297 Thus, this system of alluvial deposits was not formed during the so called Villafranchian unit (within the Plio-Quaternary boundary from 3.5 to 1 My), as suggested by Nonn (1966) from his geomorphological study along the Coast of Galicia (NW Spain). Neither are they sediments whose formation age was indeterminately assigned to the Miocene (up to 5 My ago) (Arps et al., 1978), nor are they Holocene materials (Galán-Arias, 1981). From the chronology estimated by BayLum, we deduce a system of braided alluvial deposits (Escuer-Sole and Vidal-Romaní, 1987), whose sedimentation would be related to glacioeustatic levels which did not culminate during the Late Pleistocene (Fig. 8). These data provide greater reliability to the model of Escuer-Sole and Vidal-Romaní (1987), based on the geomorphological study - without the possibility of applying adequate absolute dating techniques at that time. This hypothesis, supported by the ages calculated here, helps to better understand the evolution of the Ria de Coruña which is located in the northern coast of Galicia (Fig.1), as well as the Ria de Arousa in the mid-south coast (Fig.1). And this could be most probably extrapolated to the rest of the Galician Rias, as they were fluvial valleys flooded during the transgressive episodes of the Late Quaternary (Vidal-Romaní and Grandal d'Anglade, 2018), giving rise to these characteristic wide embayments on the Northwest Coast of Spain.

313

314 5. Conclusions

315 Analyst procedures for MPK and ABC samples show widely scattered D<sub>es</sub> distributions at high doses. Assuming that OD arises from dose rate variability, Bayesian procedures (or any other model estimating the average absorbed dose, such as the ADM) should provide more accurate results, as the greater the OD, the larger the Palaeodose differences between BayLum and the CAM. When working with saturated aliquots, BayLum doses calculated with ‘saturated’ aliquots keep increasing at much larger doses than CAM. Dose recovery experiments also suggest that BayLum provides more accurate results than CAM. Thus, the ages calculated by BayLum are older than those previously calculated by frequentist statistics (CAM or ADM). For samples MPK1, MPK5, MPK6 and ABC1, the underestimation of the CAM is between 10-30 ky. For the rest of the samples, the differences between the statistical models can reach between 50 ky and 200 ky, or even more. Based on these results, they are not Late Miocene, Late Pliocene or Holocene deposits. On the contrary, they were deposited in the lowermost areas of these fluvial valleys at the end of the Middle Pleistocene and during the Upper Pleistocene.
291 glacioeustatic oscillations along the Late Pleistocene is observed (Arce-Chamorro and Vidal-Romaní, 2021) (Fig.A2), more specifically during MIS11-MIS10 (ABC1 and ABC3) and during MIS7-MIS6 (ABC2).

294

295 FIGURE 6

296

297 Thus, this system of alluvial deposits was not formed during the so called Villafranchian unit (within the Plio-Quaternary boundary from 3.5 to 1 My), as suggested by Nonn (1966) from his geomorphological study along the Coast of Galicia (NW Spain). Neither are they sediments whose formation age was indeterminately assigned to the Miocene (up to 5 My ago) (Arps et al., 1978), nor are they Holocene materials (Galán-Arias, 1981). From the chronology estimated by BayLum, we deduce a system of braided alluvial deposits (Escuer-Sole and Vidal-Romaní, 1987), whose sedimentation would be related to glacioeustatic levels which did not culminate during the Late Pleistocene (Fig. 8). These data provide greater reliability to the model of Escuer-Sole and Vidal-Romaní (1987), based on the geomorphological study - without the possibility of applying adequate absolute dating techniques at that time. This hypothesis, supported by the ages calculated here, helps to better understand the evolution of the Ria de Coruña which is located in the northern coast of Galicia (Fig.1), as well as the Ria de Arousa in the mid-south coast (Fig.1). And this could be most probably extrapolated to the rest of the Galician Rias, as they were fluvial valleys flooded during the transgressive episodes of the Late Quaternary (Vidal-Romaní and Grandal d'Anglade, 2018), giving rise to these characteristic wide embayments on the Northwest Coast of Spain.

313

314 5. Conclusions

315 Analyst procedures for MPK and ABC samples show widely scattered D<sub>es</sub> distributions at high doses. Assuming that OD arises from dose rate variability, Bayesian procedures (or any other model estimating the average absorbed dose, such as the ADM) should provide more accurate results, as the greater the OD, the larger the Palaeodose differences between BayLum and the CAM. When working with saturated aliquots, BayLum doses calculated with ‘saturated’ aliquots keep increasing at much larger doses than CAM. Dose recovery experiments also suggest that BayLum provides more accurate results than CAM. Thus, the ages calculated by BayLum are older than those previously calculated by frequentist statistics (CAM or ADM). For samples MPK1, MPK5, MPK6 and ABC1, the underestimation of the CAM is between 10-30 ky. For the rest of the samples, the differences between the statistical models can reach between 50 ky and 200 ky, or even more. Based on these results, they are not Late Miocene, Late Pliocene or Holocene deposits. On the contrary, they were deposited in the lowermost areas of these fluvial valleys at the end of the Middle Pleistocene and during the Upper Pleistocene.
328

329 Acknowledgments

330 Thanks to the Full Proffesor Juan Ramón Vidal Romaní for sharing his geological knowledge on
331 the dated alluvial sediments. Thanks to Dr. Jorge Sanjurjo Sánchez for his support with the
332 Luminiscence Lab of the University of Coruña. Thanks to the LED2023 Teamwork. Also thanks
333 to the editors of Quaternary Geochronolgy and to the unknown Reviewers for their suggestions.

334

335 Funding

336 This research has been funded and supported by Consellería de Cultura, Educación e Ordenación
337 Universitaria, Xunta de Galicia (programmes ED431B 2018/47 and ED431B 2021/17) through
338 the Grupo Interdisciplinar de Patrimonio Cultural e Xeolóxico (CULXEO).

339

340 References

341 Aitken, M.J., 1998. An Introduction to Optical Dating. Oxford University Press, New York.
342 280pp.

343 Arce-Chamorro, C., 2017. Datación por luminiscencia de depósitos fluviales y eólicos en el margen occidental de Galicia. Tesis Doctoral. PhD dissertation (in Spanish). Universidade da Coruña. España. 399pp. http://hdl.handle.net/2183/19810

346 Arce-Chamorro, C., Sanjurjo-Sánchez, J., 2020. Sediment beta-microdose variability as main
347 cause of dispersion in OSL-quartz dating of Upper-Pleistocene coastal fluvial-deposits preserved
348 at Mero-River Basin (A Coruña, Galicia, Spain). Cad. Lab. Xeol. Laxe 42, 169-142.
349 https://doi.org/10.17979/cadlaxe.2020.42.0.7308

350 Arce-Chamorro, C. & Vidal-Romaní, J.R., 2021. Late-Pleistocene chronology of coastal fluvial deposits at the mouth of the Ulla River in the Ría de Arousa (Galicia, NW Spain) by OSL dating. Cad. Lab. Xeol. Laxe 2021, 43, 61-88. https://doi.org/10.17979/cadlaxe.2021.43.0.8736

353 Arce-Chamorro, C., Sanjurjo-Sánchez, J., Vidal-Romaní, J.R., 2022. Chronology of Coastal Alluvial Deposits in The Ria de Coruña (NW Spain) Linked to the Upper Pleistocene Sea Level Regression. Appl. Sci. 12, 9982. https://www.mdpi.com/2076-3417/12/19/9982#

356 Arce-Chamorro, C., Vidal-Romaní, J.R., Grandal-d'Anglade, A., Sanjurjo-Sánchez, J., 2023. Aeolization on the Atlantic coast of Galicia (NW Spain) from the end of the last glacial period to the present day: Chronology, origin and evolution of coastal dunes linked to sea-level oscillations. Earth. Surf. Process. Landf. 48, 198-214. https://doi.org/10.1002/esp.5481

360 Arps, X.E.S., Buiskool, J.M.A., van Calsteren, P.W.C., Floor, P., Hilgen, J.D., Koning, H., Kuyper, R.P., Minnigh, L.D., 1978. Geological Map or Western Galicia (1:100.000) Finisterre-Santiago. State University of Leiden. Netherlands.

363 Brennan, B.J., 2003. Beta doses to spherical grains. Radiation Measurements 37, 299-303. https://doi.org/10.1016/S1350-4487(03)00011-8

365 Chapot, M.S., Duller, G.A.T., Barham, L.S., 2022. Challenges of dating quartz OSL samples with saturated grains: Lessons from single-grain analyses of low dose-rate samples from Victoria Falls, Zambia. Quat. Geochronol. 72, 101344. https://doi.org/10.1016/j.quageo.2022.101344

368 Colarossi, D., Duller, G.A.T., Roberts, H.M., Tooth, S., Botha, G.A., 2020. A comparison of multiple luminescence chronometers at Voordrag, South Africa. Quat. Geochronol. 60, 101094. https://doi.org/10.1016/j.quageo.2020.101094
328

329 Acknowledgments

330 Thanks to the Full Proffesor Juan Ramón Vidal Romaní for sharing his geological knowledge on
331 the dated alluvial sediments. Thanks to Dr. Jorge Sanjurjo Sánchez for his support with the
332 Luminiscence Lab of the University of Coruña. Thanks to the LED2023 Teamwork. Also thanks
333 to the editors of Quaternary Geochronolgy and to the unknown Reviewers for their suggestions.

334

335 Funding

336 This research has been funded and supported by Consellería de Cultura, Educación e Ordenación
337 Universitaria, Xunta de Galicia (programmes ED431B 2018/47 and ED431B 2021/17) through
338 the Grupo Interdisciplinar de Patrimonio Cultural e Xeolóxico (CULXEO).

339

340 References

341 Aitken, M.J., 1998. An Introduction to Optical Dating. Oxford University Press, New York.
342 280pp.

343 Arce-Chamorro, C., 2017. Datación por luminiscencia de depósitos fluviales y eólicos en el margen occidental de Galicia. Tesis Doctoral. PhD dissertation (in Spanish). Universidade da Coruña. España. 399pp. http://hdl.handle.net/2183/19810

346 Arce-Chamorro, C., Sanjurjo-Sánchez, J., 2020. Sediment beta-microdose variability as main
347 cause of dispersion in OSL-quartz dating of Upper-Pleistocene coastal fluvial-deposits preserved
348 at Mero-River Basin (A Coruña, Galicia, Spain). Cad. Lab. Xeol. Laxe 42, 169-142.
349 https://doi.org/10.17979/cadlaxe.2020.42.0.7308

350 Arce-Chamorro, C. & Vidal-Romaní, J.R., 2021. Late-Pleistocene chronology of coastal fluvial deposits at the mouth of the Ulla River in the Ría de Arousa (Galicia, NW Spain) by OSL dating. Cad. Lab. Xeol. Laxe 2021, 43, 61-88. https://doi.org/10.17979/cadlaxe.2021.43.0.8736

353 Arce-Chamorro, C., Sanjurjo-Sánchez, J., Vidal-Romaní, J.R., 2022. Chronology of Coastal
354 Alluvial Deposits in The Ria de Coruña (NW Spain) Linked to the Upper Pleistocene Sea Level
355 Regression. Appl. Sci. 12, 9982. https://www.mdpi.com/2076-3417/12/19/9982#

356 Arce-Chamorro, C., Vidal-Romaní, J.R., Grandal-d'Anglade, A., Sanjurjo-Sánchez, J., 2023. Aeolization on the Atlantic coast of Galicia (NW Spain) from the end of the last glacial period to the present day: Chronology, origin and evolution of coastal dunes linked to sea-level oscillations. Earth. Surf. Process. Landf. 48, 198-214. https://doi.org/10.1002/esp.5481

360 Arps, X.E.S., Buiskool, J.M.A., van Calsteren, P.W.C., Floor, P., Hilgen, J.D., Koning, H.,
361 Kuyper, R.P., Minnigh, L.D., 1978. Geological Map or Western Galicia (1:100.000) Finisterre-
362 Santiago. State University of Leiden. Netherlands.

363 Brennan, B.J., 2003. Beta doses to spherical grains. Radiation Measurements 37, 299-303. https://doi.org/10.1016/S1350-4487(03)00011-8

365 Chapot, M.S., Duller, G.A.T., Barham, L.S., 2022. Challenges of dating quartz OSL samples with saturated grains: Lessons from single-grain analyses of low dose-rate samples from Victoria Falls, Zambia. Quat. Geochronol. 72, 101344. https://doi.org/10.1016/j.quageo.2022.101344

368 Colarossi, D., Duller, G.A.T., Roberts, H.M., Tooth, S., Botha, G.A., 2020. A comparison of multiple luminescence chronometers at Voordrag, South Africa. Quat. Geochronol. 60, 101094. https://doi.org/10.1016/j.quageo.2020.101094
371 Combès, B., Philippe, A., Lanos, P., Mercier, N., Tribolo, C., Guérin, G., Guibert, P., Lahaye, C., 2015. A Bayesian central equivalent dose model for optically stimulated luminescence dating. 28, 62–70. http://dx.doi.org/10.1016/j.quageo.2015.04.001.

374 Combès, B., Philippe, A., 2017. Bayesian analysis of individual and systematic multiplicative errors for estimating ages with stratigraphic constraints in optically stimulated luminescence dating. Quat. Geochronol. 39, 24–34. https://doi.org/10.1016/j.quageo.2017.02.003

377 Cunningham, A.C., Wallinga, J., & Minderhoud, P. S., 2011. Expectations of scatter in equivalent-dose distributions when using multi-grain aliquots for OSL dating. Geochronometria, 38, 424-431. https://doi.org/10.2478/s13386-011-0048-z

380 Duller, G.A.T., 2012. Improving the accuracy and precision of equivalent doses determined using the optically stimulated luminescence signal from single grains of quartz. Radiat. Meas. 47, 770–777. https://doi.org/10.1016/j.radmeas.2012.01.006

383 Duller, G. A. T., 2015. The Analyst software package for luminescence data: overview and recent improvements. Ancient TL, 33, 35-42.

385 Escuer-Sole, J. & Vidal-Romaní, J.R., 1987. Facies y modelo local de los depósitos aluviales de la cuenca del río Mero y península de Sada (A Coruña, Galicia, NW Spain). Cad. Lab. Xeol. Laxe 11, 69–83.

388 Galán-Arias, J., Fernández-Rodríguez Arango, R., 1981. Hoja 120: Padrón. Mapa Geológico de España 1:50.000. Servicio de Publicaciones del Ministerio de Industria y Energía. Instituto Geológico y Minero de España (IGME). Madrid. España.

391 Galbraith, R.F., Roberts, R.G., Laslett, G.M., Yoshida, H., Olley, J.M., 1999. Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: Part I, experimental design and statistical models. Archaeometry 41, 339–364. https://doi.org/10.1111/j.1475-4754.1999.tb00987.x

395 Geach, M.R., Thomsen, K.J., Buylaert, J.-P., Murray, A.S., Mather, A.E., Telfer, M.W., Stokes, M., 2015. Single-grain and multi-grain OSL dating of river terrace sediments in the Tabernas Basin. SE Spain. Quat. Geochronol. 30, 213e218. https://doi.org/10.1016/j.quageo.2015.05.021

398 Guérin, G., Mercier, N., Adamiec, G., 2011. Dose rate conversion factors: update. Ancient TL 29, 5–8.

400 Guérin, G., Mercier, N., 2012. Preliminary insight into dose deposition processes in sedimentary media on a scale of single grains: Monte Carlo modelling of the effect of water on the gamma dose rate. Radiat. Meas. 47, 541–547. https://doi.org/10.1016/j.radmeas.2012.05.004

403 Guérin, G., Discamps, E., Lahaye, C., Mercier, N., Guibert, P., Turq, A., ... & Soulier, M. C., 2012b. Multi-method (TL and OSL), multi-material (quartz and flint) dating of the Mousterian site of Roc de Marsal (Dordogne, France): correlating Neanderthal occupations with the climatic variability of MIS 5–3. Journal of Archaeological Science, 39, 3071-3084. https://doi.org/10.1016/j.jas.2012.04.047

408 Guérin, G., Jain, M., Thomsen, K. J., Murray, A. S. & Mercier, N., 2015. Modelling dose rate to single grains of quartz in well-sorted sand samples: the dispersion arising from the presence of potassium feldspars and implications for single grain OSL dating. Quat. Geochronol. 27, 52-65. https://doi.org/10.1016/j.quageo.2014.12.006

412 Guérin, G., Frouin, M., Talamo, S., Aldeias, V., Bruxelles, L., Chiotti, L., ... & Turq, A., 2015. A multi-method luminescence dating of the Palaeolithic sequence of La Ferrassie based on new excavations adjacent to the La Ferrassie 1 and 2 skeletons. Journal of Archaeological Science, 58, 147-166. https://doi.org/10.1016/j.jas.2015.01.019

416 Guérin, G., Christophe, C., Philippe, A., Murray, A.S., Thomsen, K.J., ... & Lahaye, C., 2017. Absorbed dose, equivalent dose, measured dose rates, and implications for OSL age estimates:
371 Combès, B., Philippe, A., Lanos, P., Mercier, N., Tribolo, C., Guérin, G., Guibert, P., Lahaye, C., 2015. A Bayesian central equivalent dose model for optically stimulated luminescence dating. 28, 62–70. http://dx.doi.org/10.1016/j.quageo.2015.04.001.

374 Combès, B., Philippe, A., 2017. Bayesian analysis of individual and systematic multiplicative errors for estimating ages with stratigraphic constraints in optically stimulated luminescence dating. Quat. Geochronol. 39, 24–34. https://doi.org/10.1016/j.quageo.2017.02.003

377 Cunningham, A.C., Wallinga, J., & Minderhoud, P. S., 2011. Expectations of scatter in equivalent-dose distributions when using multi-grain aliquots for OSL dating. Geochronometria, 38, 424-431. https://doi.org/10.2478/s13386-011-0048-z

380 Duller, G.A.T., 2012. Improving the accuracy and precision of equivalent doses determined using the optically stimulated luminescence signal from single grains of quartz. Radiat. Meas. 47, 770–777. https://doi.org/10.1016/j.radmeas.2012.01.006

383 Duller, G. A. T., 2015. The Analyst software package for luminescence data: overview and recent improvements. Ancient TL, 33, 35-42.

385 Escuer-Sole, J. & Vidal-Romaní, J.R., 1987. Facies y modelo local de los depósitos aluviales de la cuenca del río Mero y península de Sada (A Coruña, Galicia, NW Spain). Cad. Lab. Xeol. Laxe 11, 69–83.

388 Galán-Arias, J., Fernández-Rodríguez Arango, R., 1981. Hoja 120: Padrón. Mapa Geológico de España 1:50.000. Servicio de Publicaciones del Ministerio de Industria y Energía. Instituto Geológico y Minero de España (IGME). Madrid. España.

391 Galbraith, R.F., Roberts, R.G., Laslett, G.M., Yoshida, H., Olley, J.M., 1999. Optical dating of single and multiple grains of quartz from Jinmium rock shelter, northern Australia: Part I, experimental design and statistical models. Archaeometry 41, 339–364. https://doi.org/10.1111/j.1475-4754.1999.tb00987.x

395 Geach, M.R., Thomsen, K.J., Buylaert, J.-P., Murray, A.S., Mather, A.E., Telfer, M.W., Stokes, M., 2015. Single-grain and multi-grain OSL dating of river terrace sediments in the Tabernas Basin. SE Spain. Quat. Geochronol. 30, 213e218. https://doi.org/10.1016/j.quageo.2015.05.021

398 Guérin, G., Mercier, N., Adamiec, G., 2011. Dose rate conversion factors: update. Ancient TL 29, 5–8.

400 Guérin, G., Mercier, N., 2012. Preliminary insight into dose deposition processes in sedimentary media on a scale of single grains: Monte Carlo modelling of the effect of water on the gamma dose rate. Radiat. Meas. 47, 541–547. https://doi.org/10.1016/j.radmeas.2012.05.004

403 Guérin, G., Discamps, E., Lahaye, C., Mercier, N., Guibert, P., Turq, A., ... & Soulier, M. C., 2012b. Multi-method (TL and OSL), multi-material (quartz and flint) dating of the Mousterian site of Roc de Marsal (Dordogne, France): correlating Neanderthal occupations with the climatic variability of MIS 5–3. Journal of Archaeological Science, 39, 3071-3084. https://doi.org/10.1016/j.jas.2012.04.047

408 Guérin, G., Jain, M., Thomsen, K. J., Murray, A. S. & Mercier, N., 2015. Modelling dose rate to single grains of quartz in well-sorted sand samples: the dispersion arising from the presence of potassium feldspars and implications for single grain OSL dating. Quat. Geochronol. 27, 52-65. https://doi.org/10.1016/j.quageo.2014.12.006

412 Guérin, G., Frouin, M., Talamo, S., Aldeias, V., Bruxelles, L., Chiotti, L., ... & Turq, A., 2015. A multi-method luminescence dating of the Palaeolithic sequence of La Ferrassie based on new excavations adjacent to the La Ferrassie 1 and 2 skeletons. Journal of Archaeological Science, 58, 147-166. https://doi.org/10.1016/j.jas.2015.01.019

416 Guérin, G., Christophe, C., Philippe, A., Murray, A.S., Thomsen, K.J., ... & Lahaye, C., 2017. Absorbed dose, equivalent dose, measured dose rates, and implications for OSL age estimates:
418 introducing the Average Dose Model. Quat. Geochronol. 41, 163-173.
419 https://doi.org/10.1016/j.quageo.2017.04.002

420 Guérin, G., Lahaye, C., Heydari, M., Autzen, M., Buylaert J.P., ... & Phillippe, A., 2021. Towards an improvement of optically stimulated luminescence (OSL) age uncertainties: modelling OSL ages with systematic errors, stratigraphic constraints and radiocarbon ages using the R package BayLum. GChron. 3, 1-17. 10.5194/gchron-3-229-2021

424 Gutiérrez-Becker, L., 2008. Caracterización de los sistemas dunares costeros del NW ibérico y su evolución durante el Cuaternario. Tesis doctoral. PhD dissertation (in Spanish). Universidad de Coruña. España. 283pp. https://dialnet.unirioja.es/servlet/tesis?codigo=45245

427 Heydari, M. & Guérin, G., 2018. OSL signal saturation and dose rate variability: Investigating the behaviour of different statistical models. Radiat. Meas. 120, 96-103.
429 https://doi.org/10.1016/j.radmeas.2018.05.005

430 Jankowski, N. R. & Jacobs, Z., 2018. Beta dose variability and its spatial contextualisation in samples used for optical dating: An empirical approach to examining beta microdosimetry. Quat. Geochronol. 44, 23-37. https://doi.org/10.1016/j.quageo.2017.08.005

433 Jouzel, J., Masson-Delmotte, V., Cattanni, O., ...& Dreyfus, G., 2007. Orbital and Millennial Antarctic Climate Variability over the Past 800,000 Years. Science 317, 793-796.
435 https://doi.org/10.1126/science.1141038

436 Kreutzer, S., Burow, C., Dietze, M., Fuchs, M., Fischer, M., Schmidt, C., 2017. Software in the context of luminescence dating: status, concepts and suggestions exemplified by the Rpackage 'Luminescence'. Ancient TL 35, 1-11.

439 Martin, L., Mercier, N., Incerti, S., Lefrais, Y., Pecheyran, C., Guérin, G., et al., 2015. Dosimetric study of sediments at the beta dose rate scale: Characterization and modelization with the DosiVox software. Radiat. Meas. 81, 134-141. https://doi.org/10.1016/j.radmeas.2015.02.008

442 Mayya, Y.S., Morthekai, P., Murari, M.K., Singhvi, A.K., 2006. Towards quantifying beta microdosimetric effects in single-grain quartz dose distribution. Radiat. Meas. 41, 1032-1039

444 Murray, A.S., Wintle, A.G., 2000. Luminescence dating of quartz using an improved single aliquot regenerative-dose protocol. Radiat. Meas. 32, 57-73. https://doi.org/10.1016/S1350-4487(99)00253-X

447 Murray, A.S., Arnold, L. J., Buylaert, J. P., Guérin, G., Qin, J., Singhvi, A. K., ... & Thomsen, K. J., 2021. Optically stimulated luminescence dating using quartz. Nature Reviews Methods Primers, 1(1), 72. https://doi.org/10.1038/s43586-021-00068-5

450 Nathan, R., Thomas, P.J., Murray, A.S., Rhodes, E.J., 2003. Environmental dose rateheterogeneity of beta radiation and its implications for luminescence dating: Monte Carlo modelling and experimental validation. Radiat. Meas. 37, 305-313.
453 https://doi.org/10.1016/S1350-4487(03)00008-8

454 Nonn, H., 1966. Les régiones cotières de la Galice (Espagne). Etude géomorpholigique. Publications de la Faculté des lettres de L'Université de Strasbourg. Foundation Baulig. Tomo III. 591pp.

457 Philippe, A., Guérin, G., Kreutzer, S., 2019. BayLum - an R package for Bayesian analysis of OSL ages: an introduction. Quat. Geochronol. 49, 16-24.
459 https://doi.org/10.1016/j.quageo.2018.05.009

460 Prescott, J.R., Hutton, J.T., 1994. Cosmic ray contribution to dose rates for luminescence and ESR dating: large depths and long-term time variations. Radiat. Meas. 23, 497-500.
462 https://doi.org/10.1016/1350-4487(94)90086-8

463 Railsback, L.B., Gibbard P.L., Head, M.J., Voarintsoa N.R.G., Toucanne, S., 2015. An optimized scheme of lettered marine isotope substages for the last 1.0 million years, and the
418 introducing the Average Dose Model. Quat. Geochronol. 41, 163-173.
419 https://doi.org/10.1016/j.quageo.2017.04.002

420 Guérin, G., Lahaye, C., Heydari, M., Autzen, M., Buylaert J.P., ... & Phillippe, A., 2021. Towards an improvement of optically stimulated luminescence (OSL) age uncertainties: modelling OSL ages with systematic errors, stratigraphic constraints and radiocarbon ages using the R package BayLum. GChron. 3, 1-17. 10.5194/gchron-3-229-2021

424 Gutiérrez-Becker, L., 2008. Caracterización de los sistemas dunares costeros del NW ibérico y su evolución durante el Cuaternario. Tesis doctoral. PhD dissertation (in Spanish). Universidad de Coruña. España. 283pp. https://dialnet.unirioja.es/servlet/tesis? codigo=45245

427 Heydari, M. & Guérin, G., 2018. OSL signal saturation and dose rate variability: Investigating the behaviour of different statistical models. Radiat. Meas. 120, 96-103.
429 https://doi.org/10.1016/j.radmeas.2018.05.005

430 Jankowski, N. R. & Jacobs, Z., 2018. Beta dose variability and its spatial contextualisation in samples used for optical dating: An empirical approach to examining beta microdosimetry. Quat. Geochronol. 44, 23-37. https://doi.org/10.1016/j.quageo.2017.08.005

433 Jouzel, J., Masson-Delmotte, V., Cattanni, O., ...& Dreyfus, G., 2007. Orbital and Millennial Antarctic Climate Variability over the Past 800,000 Years. Science 317, 793-796.
435 https://doi.org/10.1126/science.1141038

436 Kreutzer, S., Burow, C., Dietze, M., Fuchs, M., Fischer, M., Schmidt, C., 2017. Software in the context of luminescence dating: status, concepts and suggestions exemplified by the Rpackage 'Luminescence'. Ancient TL 35, 1-11.

439 Martin, L., Mercier, N., Incerti, S., Lefrais, Y., Pecheyran, C., Guérin, G., et al., 2015. Dosimetric study of sediments at the beta dose rate scale: Characterization and modelization with the DosiVox software. Radiat. Meas. 81, 134-141. https://doi.org/10.1016/j.radmeas.2015.02.008

442 Mayya, Y.S., Morthekai, P., Murari, M.K., Singhvi, A.K., 2006. Towards quantifying beta microdosimetric effects in single-grain quartz dose distribution. Radiat. Meas. 41, 1032-1039

444 Murray, A.S., Wintle, A.G., 2000. Luminescence dating of quartz using an improved single aliquot regenerative-dose protocol. Radiat. Meas. 32, 57-73. https://doi.org/10.1016/S1350-4487(99)00253-X

447 Murray, A.S., Arnold, L. J., Buylaert, J. P., Guérin, G., Qin, J., Singhvi, A. K., ... & Thomsen, K. J., 2021. Optically stimulated luminescence dating using quartz. Nature Reviews Methods Primers, 1(1), 72. https://doi.org/10.1038/s43586-021-00068-5

450 Nathan, R., Thomas, P.J., Murray, A.S., Rhodes, E.J., 2003. Environmental dose rateheterogeneity of beta radiation and its implications for luminescence dating: Monte Carlo modelling and experimental validation. Radiat. Meas. 37, 305-313.
453 https://doi.org/10.1016/S1350-4487(03)00008-8

454 Nonn, H., 1966. Les régiones cotières de la Galice (Espagne). Etude géomorpholigique. Publications de la Faculté des lettres de L'Université de Strasbourg. Foundation Baulig. Tomo III. 591pp.

457 Philippe, A., Guérin, G., Kreutzer, S., 2019. BayLum - an R package for Bayesian analysis of OSL ages: an introduction. Quat. Geochronol. 49, 16-24.
459 https://doi.org/10.1016/j.quageo.2018.05.009

460 Prescott, J.R., Hutton, J.T., 1994. Cosmic ray contribution to dose rates for luminescence and ESR dating: large depths and long-term time variations. Radiat. Meas. 23, 497-500.
462 https://doi.org/10.1016/1350-4487(94)90086-8

463 Railsback, L.B., Gibbard P.L., Head, M.J., Voarintsoa N.R.G., Toucanne, S., 2015. An optimized scheme of lettered marine isotope substages for the last 1.0 million years, and the
465 climatostratigraphic nature of isotope stages and substages. Quat. Sci. Rev. 111, 94-106
466 https://doi.org/10.1016/j.quascirev.2015.01.012

467 Rohling, E.J., Foster, G.L., Grant, K.M., Marino, G., Roberts, A.P., Tamisiea, M.E., Williams, F., 2014. Sea-level and deep-sea-temperature variability over the past 5.3 million years. Nature 508, 477-482. https://doi.org/10.1038/nature13230

470 R Core Team (2020). RStudio: Integrated Development for R. RStudio, PBC, Boston, MA
471 URL http://www.rstudio.com/.

472 Rufer, D. & Preusser, F., 2009. Potential of autoradiography to detect spatially resolved radiation patterns in the context of trapped charge dating. Geochronometria, 34(1), 1-13.
473 https://doi.org/10.2478/v10003-009-0014-4

475 Singh, A., Thomsen, K.J., Sinha, R., Buylaert, J.P., Carter, A., Mark, D.F., et al., 2017. Counter-intuitive influence of Himalayan River morphodynamic on Indus Civilisation urban settlements.
476 Nature communications, 8(1), 1617. https://doi.org/10.1038/s41467-017-01643-9

478 Smedley R.K., Duller, G.A.T., Rufer, D., Utley, J.E.P., 2020. Empirical assessment of beta dose heterogeneity in sediments: Implications for luminescence dating. Quat. Geochronol. 56, 101052.
480 https://doi.org/10.1016/j.quageo.2020.101052.

481 Thomsen, K.J., Murray, A.S., Bøtter-Jensen, L., 2005. Sources of variability in OSL dose measurements using single grains of Quartz. Radiat. Meas. 39, 47-61.
482 https://doi.org/10.1016/j.radmeas.2004.01.039

484 Thomsen, K.J., Murray, A.S., Bøtter-Jensen, L., Kinahan, J., 2007. Determination of burial dose in incompletely bleached fluvial samples using single grains of quartz. Radiat. Meas. 42, 370-379.
485 https://doi.org/10.1016/j.radmeas.2007.01.041.

487 Thomsen, K.J., Murray, A.S., Buylaert, J.-P., Jain, M., Helt-Hansen, J., Aubry, T., 2016. Testing single-grain quartz OSL methods using known age samples from the Bordes-Fitte rockshelter (Roches d'Abilly site, Central France). Quat. Geochronol. 31, 77-96.
488 https://doi.org/10.1016/j.quageo.2015.11.002
489 490 https://doi.org/10.1016/j.radmeas.2008.01.016.

491 Vandenberghe, D., De Corte, F., Buylaert, J.-P., Kučera, J., Van den Haute, P., 2008. On the internal radioactivity in quartz. Radiat. Meas. 43, 771-775.
492 https://doi.org/10.1016/j.radmeas.2008.01.016.

494 Vidal-Romaní, J.R. & Grandal-d'Anglade A., 2018. Nota sobre la última transgresión marina en la costa de Galicia. Cad. Lab. Xeol. Laxe 40, 229-246.
495 https://doi.org/10.17979/cadlaxe.2018.40.0.4921

497 Wallinga, J., Murray, A.S., Wintle, A.G., 2000. The single-aliquot regenerative-dose (SAR) protocol applied to coarse-grain feldspar. Radiat. Meas. 32, 529-533.
498 https://doi.org/10.1016/S1350-4487(00)00091-3.

500 Wintle, A.G., Murray, A.S., 2006. A review of quartz optically stimulated luminescence characteristics and their relevance in single-aliquot regeneration dating protocols. Radiat. Meas. 41, 369-391.
501 https://doi.org/10.1016/j.radmeas.2005.11.001

503

504
465 climatostratigraphic nature of isotope stages and substages. Quat. Sci. Rev. 111, 94-106
466 https://doi.org/10.1016/j.quascirev.2015.01.012

467 Rohling, E.J., Foster, G.L., Grant, K.M., Marino, G., Roberts, A.P., Tamisiea, M.E., Williams, F., 2014. Sea-level and deep-sea-temperature variability over the past 5.3 million years. Nature 508, 477-482. https://doi.org/10.1038/nature13230

470 R Core Team (2020). RStudio: Integrated Development for R. RStudio, PBC, Boston, MA
471 URL http://www.rstudio.com/.

472 Rufer, D. & Preusser, F., 2009. Potential of autoradiography to detect spatially resolved radiation patterns in the context of trapped charge dating. Geochronometria, 34(1), 1-13.
473 https://doi.org/10.2478/v10003-009-0014-4

475 Singh, A., Thomsen, K.J., Sinha, R., Buylaert, J.P., Carter, A., Mark, D.F., et al., 2017. Counter-intuitive influence of Himalayan River morphodynamic on Indus Civilisation urban settlements.
476 Nature communications, 8(1), 1617. https://doi.org/10.1038/s41467-017-01643-9

478 Smedley R.K., Duller, G.A.T., Rufer, D., Utley, J.E.P., 2020. Empirical assessment of beta dose heterogeneity in sediments: Implications for luminescence dating. Quat. Geochronol. 56, 101052.
480 https://doi.org/10.1016/j.quageo.2020.101052.

481 Thomsen, K.J., Murray, A.S., Bøtter-Jensen, L., 2005. Sources of variability in OSL dose measurements using single grains of Quartz. Radiat. Meas. 39, 47-61.
482 https://doi.org/10.1016/j.radmeas.2004.01.039

484 Thomsen, K.J., Murray, A.S., Bøtter-Jensen, L., Kinahan, J., 2007. Determination of burial dose in incompletely bleached fluvial samples using single grains of quartz. Radiat. Meas. 42, 370-379. https://doi.org/10.1016/j.radmeas.2007.01.041.

487 Thomsen, K.J., Murray, A.S., Buylaert, J.-P., Jain, M., Helt-Hansen, J., Aubry, T., 2016. Testing single-grain quartz OSL methods using known age samples from the Bordes-Fitte rockshelter (Roches d'Abilly site, Central France). Quat. Geochronol. 31, 77-96.
488 https://doi.org/10.1016/j.quageo.2015.11.002
490

491 Vandenberghe, D., De Corte, F., Buylaert, J.-P., Kučera, J., Van den Haute, P., 2008. On the internal radioactivity in quartz. Radiat. Meas. 43, 771-775.
492 https://doi.org/10.1016/j.radmeas.2008.01.016.
493

494 Vidal-Romaní, J.R. & Grandal-d'Anglade A., 2018. Nota sobre la última transgresión marina en la costa de Galicia. Cad. Lab. Xeol. Laxe 40, 229-246.
495 https://doi.org/10.17979/cadlaxe.2018.40.0.4921
496

497 Wallinga, J., Murray, A.S., Wintle, A.G., 2000. The single-aliquot regenerative-dose (SAR) protocol applied to coarse-grain feldspar. Radiat. Meas. 32, 529-533.
498 https://doi.org/10.1016/S1350-4487(00)00091-3.
499

500 Wintle, A.G., Murray, A.S., 2006. A review of quartz optically stimulated luminescence characteristics and their relevance in single-aliquot regeneration dating protocols. Radiat. Meas. 41, 369-391. https://doi.org/10.1016/j.radmeas.2005.11.001

503

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505 Figures

506

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**Figure 1.** Present day and regressive coastline (-120 m; yellow area) of Galicia (NW Spain): (a) Coastal evolution map (modified from Arce-Chamorro et al., 2023) and some of the alluvial deposits previously studied (Arce-Chamorro, 2017): (b,d) MPK2 sample (43°22'21''N, 8°20'18''W); (c) ABC1,2,3 samples (42°40'25''N, 8°43'20''W); (e) MPK1 sample (43°16'33''N, 8°18'46''W); (f) MPK3 sample (43°21'26''N, 8°19'52''W). (WGS84 coordinates).

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<caption>**Figure 1.** Present day and regressive coastline (-120 m; yellow area) of Galicia (NW Spain): (a) Coastal evolution map (modified from Arce-Chamorro et al., 2023) and some of the alluvial deposits previously studied (Arce-Chamorro, 2017): (b,d) MPK2 sample (43°22'21''N, 8°20'18''W); (c) ABC1,2,3 samples (42°40'25''N, 8°43'20''W); (e) MPK1 sample (43°16'33''N, 8°18'46''W); (f) MPK3 sample (43°21'26''N, 8°19'52''W). (WGS84 coordinates).</caption>

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<figure><img src="image_5.png" /><figcaption>**Figure 2.** (a) Examples of dose response curves (DRCs) for MPK samples, by a single saturating exponential fitting of the normalized OSL signals (L/T), representing N De/sigma, N De/INF and N INF/INF aliquots using Analyst (Duller, 2015); Y axis: normalized OSL-signal (L~X~/T~X~ and L~N~/T~N~); X axis: given dose (seconds) at each cycle of single aliquot regenerative dose protocol (SAR; Murray and Wintle, 2000) from $^{90}$Sr/$^{90}$Y beta source of 0.12±0.03 Gy of Risø TL/OSL DA-15 reader; (Inset): OSL decay curve examples with natural OSL counts (per 0.08 s) (blue line) and 3rd cycle of SAR (orange line) along luminescence stimulation time (40 s; X axis). Integration of fast-OSL signal (red lines) and background (green lines). (b) Examples of characteristic dose (D~0~) for single exponential growth curves and D~e~s distribution of N De/sigma (blue squares), N De/INF (green dots) and N INF/INF (red dots) aliquots. Non-realistic D~e~s for N INF/INF aliquots.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>**Figure 2.** (a) Examples of dose response curves (DRCs) for MPK samples, by a single saturating exponential fitting of the normalized OSL signals (L/T), representing N De/sigma, N De/INF and N INF/INF aliquots using Analyst (Duller, 2015); Y axis: normalized OSL-signal (L~X~/T~X~ and L~N~/T~N~); X axis: given dose (seconds) at each cycle of single aliquot regenerative dose protocol (SAR; Murray and Wintle, 2000) from ⁹⁰Sr/ ⁹⁰Y beta source of 0.12±0.03 Gy of Risø TL/OSL DA-15 reader; (Inset): OSL decay curve examples with natural OSL counts (per 0.08 s) (blue line) and 3rd cycle of SAR (orange line) along luminescence stimulation time (40 s; X axis). Integration of fast-OSL signal (red lines) and background (green lines). (b) Examples of characteristic dose (D~0~) for single exponential growth curves and D~e~s distribution of N De/sigma (blue squares), N De/INF (green dots) and N INF/INF (red dots) aliquots. Non-realistic D~e~s for N INF/INF aliquots.</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>**Figure 3.** Dose Recovery analysis using BayLum (Gaussian) and CAM. (a) Dose recovery ratios ($D_{\text{ESTIMATE}}/D_{\text{GIVEN}}$) from CAM and BayLum (arithmetic mean; CAM using $N_{\text{De/SIGMA}}$ aliquots; BayL.$_{\text{De/SIGMA}}$ using $N_{\text{De/SIGMA}}$; BayL.$_{\text{De/INF}}$ using ($N_{\text{De/SIGMA}}+N_{\text{De/INF}}$); BayL.$_{\text{TOTAL}}$ using ($N_{\text{De/SIGMA}}+N_{\text{De/INF}}+N_{\text{INF/INF}}$). Dotted grey lines show 10% criteria (0.9-1.1) for recovery test (Wallinga et al., 2000). (b) Differences in the $D_{\text{e-TOTAL}}$ and $D_{\text{e-CAM}}$ from dose recovery according to the proportion of aliquots used. Aliquots proportion: $N_{\text{TOTAL}}$= ($N_{\text{De/SIGMA}}+N_{\text{De/INF}}+N_{\text{INF/INF}}$); $N_{\text{CAM}}$ = ($N_{\text{De/SIGMA}}$). $D_{\text{s}}$ estimates: $D_{\text{e-TOTAL}}$ using ($N_{\text{De/SIGMA}}+N_{\text{De/INF}}+N_{\text{INF/INF}}$); $D_{\text{e-CAM}}$ using ($N_{\text{De/SIGMA}}$).</figcaption></figure>

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<figure><img src="image_5.png" /><figcaption>**Figure 3.** Dose Recovery analysis using BayLum (Gaussian) and CAM. (a) Dose recovery ratios ($D_{\text{ESTIMATE}}/D_{\text{GIVEN}}$) from CAM and BayLum (arithmetic mean; CAM using $N_{\text{De/SIGMA}}$ aliquots; BayL.$_{\text{De/SIGMA}}$ using $N_{\text{De/SIGMA}}$; BayL.$_{\text{De/INF}}$ using ($N_{\text{De/SIGMA}}+N_{\text{De/INF}}$); BayL.$_{\text{TOTAL}}$ using ($N_{\text{De/SIGMA}}+N_{\text{De/INF}}+N_{\text{INF/INF}}$). Dotted grey lines show 10% criteria (0.9-1.1) for recovery test (Wallinga et al., 2000). (b) Differences in the $D_{\text{e-TOTAL}}$ and $D_{\text{e-CAM}}$ from dose recovery according to the proportion of aliquots used. Aliquots proportion: $N_{\text{TOTAL}}$= ($N_{\text{De/SIGMA}}+N_{\text{De/INF}}+N_{\text{INF/INF}}$); $N_{\text{CAM}}$ = ($N_{\text{De/SIGMA}}$). $D_{\text{s}}$ estimates: $D_{\text{e-TOTAL}}$ using ($N_{\text{De/SIGMA}}+N_{\text{De/INF}}+N_{\text{INF/INF}}$); $D_{\text{e-CAM}}$ using ($N_{\text{De/SIGMA}}$).</figcaption></figure>

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<figure><img src="image_7.png" /><figcaption>**Figure 4.** Palaeodose analysis for MPK and ABC samples. (a) D<sub>eS</sub> estimates from CAM, ADM and BayLum (lognormal_M) using N<sub>DE/SIGMA</sub> aliquots. (b) D<sub>eS</sub> estimates: De<sub>SIGMA</sub> from CAM and BayLum using N<sub>De/SIGMA</sub> aliquots; De<sub>UNCERT.SAT</sub> using N<sub>De/SIGMA</sub> + N<sub>De/INF</sub> aliquots; De<sub>TOTAL</sub> using N<sub>De/SIGMA</sub> + N<sub>De/INF</sub> + N<sub>INF/INF</sub> aliquots); the lines (black, blue and green) show the exponential fit for each palaeodose analysis.</figcaption></figure>

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<figure><img src="image_6.png" /><figcaption>**Figure 4.** Palaeodose analysis for MPK and ABC samples. (a) D<sub>eS</sub> estimates from CAM, ADM and BayLum (lognormal_M) using N<sub>DE/SIGMA</sub> aliquots. (b) D<sub>eS</sub> estimates: De<sub>SIGMA</sub> from CAM and BayLum using N<sub>De/SIGMA</sub> aliquots; De<sub>UNCERT.SAT</sub> using N<sub>De/SIGMA</sub> + N<sub>De/INF</sub> aliquots; De<sub>TOTAL</sub> using N<sub>De/SIGMA</sub> + N<sub>De/INF</sub> + N<sub>INF/INF</sub> aliquots); the lines (black, blue and green) show the exponential fit for each palaeodose analysis.</figcaption></figure>

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**Figure 5.** Palaeodose comparison. (a,b,c,d): D<sub>e</sub>s estimates of MPK and ABC samples from CAM, ADM and BayLum using N<sub>De/SIGMA</sub> aliquots from Analyst. (a) CAM vs ADM. (b): CAM vs BayLum gaussian. (c) D<sub>e</sub>s differences from D<sub>e</sub>BayLum-gaussian/D<sub>e</sub>CAM vs OD-CAM (%). (d): D<sub>e</sub> CAM vs BayLum Lognormal_M. (d). (e,f) Differences in the D<sub>e</sub>s estimates according to the proportion of aliquots used for each case. Aliquots proportion: N<sub>TOTAL</sub>= (N<sub>De/SIGMA</sub>+N<sub>De/INF</sub>+N<sub>INF/INF</sub>); N<sub>CAM</sub> and N<sub>SIGMA</sub>= (N<sub>De/SIGMA</sub>); N<sub>UNCERT.INF</sub>= (N<sub>De/SIGMA</sub> +N<sub>De/INF</sub>). (e): D<sub>e</sub>-TOTAL using (N<sub>De/SIGMA</sub>+N<sub>De/INF</sub>+N<sub>INF/INF</sub>); D<sub>e</sub> CAM using (N<sub>De/SIGMA</sub>). (f): D<sub>e</sub>-SIGMA using (N<sub>De/SIGMA</sub>) with BayLum (gauss.). (Inset in f): D<sub>e</sub>-UNCERT.SAT. using (N<sub>De/INF</sub>+N<sub>INF/INF</sub>) with BayLum (gauss.).
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**Figure 5.** Palaeodose comparison. (a,b,c,d): D<sub>e</sub>s estimates of MPK and ABC samples from CAM, ADM and BayLum using N<sub>De/SIGMA</sub> aliquots from Analyst. (a) CAM vs ADM. (b): CAM vs BayLum gaussian. (c) D<sub>e</sub>s differences from D<sub>e</sub>BayLum-gaussian/D<sub>e</sub>CAM vs OD-CAM (%). (d): D<sub>e</sub> CAM vs BayLum Lognormal_M. (d). (e,f) Differences in the D<sub>e</sub>s estimates according to the proportion of aliquots used for each case. Aliquots proportion: N<sub>TOTAL</sub>= (N<sub>De/SIGMA</sub>+N<sub>De/INF</sub>+N<sub>INF/INF</sub>); N<sub>CAM</sub> and N<sub>SIGMA</sub>= (N<sub>De/SIGMA</sub>); N<sub>UNCERT.INF</sub>= (N<sub>De/SIGMA</sub> +N<sub>De/INF</sub>). (e): D<sub>e</sub>-TOTAL using (N<sub>De/SIGMA</sub>+N<sub>De/INF</sub>+N<sub>INF/INF</sub>); D<sub>e</sub> CAM using (N<sub>De/SIGMA</sub>). (f): D<sub>e</sub>-SIGMA using (N<sub>De/SIGMA</sub>) with BayLum (gauss.). (Inset in f): D<sub>e</sub>-UNCERT.SAT. using (N<sub>De/INF</sub>+N<sub>INF/INF</sub>) with BayLum (gauss.).
<figure><img src="image_14.png" /><figcaption>**Figure 6.** MPK and ABC ages with BayLum using all aliquots ($D_{e-TOTAL} = N_{De/SIGMA} + N_{De/INF} + N_{INF/INF}$) and temperature anomaly (blue line) from Deuterium Record of Antartica-Dome C ice-core (Jouzel et al., 2007). Orange line: Relative sea-level (Rohling et al., 2014). Marine Isotopic Stages (MIS) (Railback et al., 2015).</figcaption></figure>

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<figure><img src="image_13.png" /><figcaption>**Figure 6.** MPK and ABC ages with BayLum using all aliquots ($D_{e-TOTAL} = N_{De/SIGMA} + N_{De/INF} + N_{INF/INF}$) and temperature anomaly (blue line) from Deuterium Record of Antartica-Dome C ice-core (Jouzel et al., 2007). Orange line: Relative sea-level (Rohling et al., 2014). Marine Isotopic Stages (MIS) (Railback et al., 2015).</figcaption></figure>

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582 **Table 1.** Measured and accepted aliquots (Meas. aliq.; accept.) for the dose recovery analysis for MPK

583 samples, showing the dose recovery ratios from CAM and BayLum (Gaussian) using N<sub>De/SIGMA</sub> and using

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<table><thead><tr><th>Sample</th><th>Meas.<br>Aliq.</th><th>Accept.<br>N<sub>De/SIGMA</sub></th><th>Accept.<br>N<sub>De/INF</sub></th><th>Accept.<br>N<sub>INF/INF</sub></th><th>CAM<br>(N<sub>De/σ</sub>)</th><th>OD<br>CAM</th><th>BayLum<br>(N<sub>De/σ</sub>)</th><th>BayLum<br>(ALL aliquots)</th></tr></thead><tbody><tr><td>MPK1 (84 Gy)</td><td>40</td><td>34 (85%)</td><td>5 (13%)</td><td>1 (3%)</td><td>0.89 ± 0.02</td><td>10±3</td><td>0.98 ± 0.04</td><td>0.99 ± 0.04</td></tr><tr><td>MPK2 (84 Gy)</td><td>75</td><td>54 (72%)</td><td>9 (12%)</td><td>6 (8%)</td><td>1.07 ± 0.04</td><td>16±6</td><td>1.05 ± 0.05</td><td>1.11 ± 0.04</td></tr><tr><td>MPK3 (84 Gy)</td><td>48</td><td>32 (67%)</td><td>14 (29%)</td><td>2 (4%)</td><td>0.96 ± 0.04</td><td>3±1</td><td>0.99 ± 0.02</td><td>1.07 ± 0.05</td></tr><tr><td>MPK4 (84 Gy)</td><td>30</td><td>22 (73%)</td><td>5 (17%)</td><td>3 (10%)</td><td>0.81 ± 0.02</td><td>2±1</td><td>0.89 ± 0.05</td><td>0.91 ± 0.05</td></tr><tr><td>MPK5 (84 Gy)</td><td>58</td><td>19 (33%)</td><td>13 (22%)</td><td>10 (17%)</td><td>0.77 ± 0.05</td><td>15±7</td><td>0.86 ± 0.06</td><td>1.06 ± 0.08</td></tr><tr><td>MPK7 (83 Gy)</td><td>35</td><td>29 (83%)</td><td>2 (6%)</td><td>4 (11%)</td><td>0.87 ± 0.04</td><td>18±4</td><td>0.91 ± 0.04</td><td>0.94 ± 0.04</td></tr><tr><td>MPK8 (83 Gy)</td><td>38</td><td>38 (100%)</td><td>0</td><td>0</td><td>0.88 ± 0.01</td><td>4±2</td><td>0.91 ± 0.01</td><td>0.91 ± 0.01</td></tr><tr><td>MPK8 (180 Gy)</td><td>44</td><td>24 (55%)</td><td>7 (16%)</td><td>13 (30%)</td><td>0.91 ± 0.03</td><td>4±1</td><td>0.94 ± 0.05</td><td>1.07 ± 0.06</td></tr><tr><td>Average Dose-<br>recovery ratio</td><td></td><td></td><td></td><td></td><td>0.90±0.03</td><td></td><td>0.94±0.02</td><td>1.01±0.03</td></tr></tbody></table>

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<table><caption>**Table 1.** Measured and accepted aliquots (Meas. aliq.; accept.) for the dose recovery analysis for MPK samples, showing the dose recovery ratios from CAM and BayLum (Gaussian) using N<sub>De/SIGMA</sub> and using saturated aliquots (all aliquots=N<sub>De/SIGMA</sub> + N<sub>De/INF</sub> + N<sub>INF/INF</sub>).</caption><thead><tr><th>Sample</th><th>Meas.<br>Aliq.</th><th>Accept.<br>N<sub>De/SIGMA</sub></th><th>Accept.<br>N<sub>De/INF</sub></th><th>Accept.<br>N<sub>INF/INF</sub></th><th>CAM<br>(N<sub>De/σ</sub>)</th><th>OD<br>CAM</th><th>BayLum<br>(N<sub>De/σ</sub>)</th><th>BayLum<br>(ALL aliquots)</th></tr></thead><tbody><tr><td>MPK1 (84 Gy)</td><td>40</td><td>34 (85%)</td><td>5 (13%)</td><td>1 (3%)</td><td>0.89 ± 0.02</td><td>10±3</td><td>0.98 ± 0.04</td><td>0.99 ± 0.04</td></tr><tr><td>MPK2 (84 Gy)</td><td>75</td><td>54 (72%)</td><td>9 (12%)</td><td>6 (8%)</td><td>1.07 ± 0.04</td><td>16±6</td><td>1.05 ± 0.05</td><td>1.11 ± 0.04</td></tr><tr><td>MPK3 (84 Gy)</td><td>48</td><td>32 (67%)</td><td>14 (29%)</td><td>2 (4%)</td><td>0.96 ± 0.04</td><td>3±1</td><td>0.99 ± 0.02</td><td>1.07 ± 0.05</td></tr><tr><td>MPK4 (84 Gy)</td><td>30</td><td>22 (73%)</td><td>5 (17%)</td><td>3 (10%)</td><td>0.81 ± 0.02</td><td>2±1</td><td>0.89 ± 0.05</td><td>0.91 ± 0.05</td></tr><tr><td>MPK5 (84 Gy)</td><td>58</td><td>19 (33%)</td><td>13 (22%)</td><td>10 (17%)</td><td>0.77 ± 0.05</td><td>15±7</td><td>0.86 ± 0.06</td><td>1.06 ± 0.08</td></tr><tr><td>MPK7 (83 Gy)</td><td>35</td><td>29 (83%)</td><td>2 (6%)</td><td>4 (11%)</td><td>0.87 ± 0.04</td><td>18±4</td><td>0.91 ± 0.04</td><td>0.94 ± 0.04</td></tr><tr><td>MPK8 (83 Gy)</td><td>38</td><td>38 (100%)</td><td>0</td><td>0</td><td>0.88 ± 0.01</td><td>4±2</td><td>0.91 ± 0.01</td><td>0.91 ± 0.01</td></tr><tr><td>MPK8 (180 Gy)</td><td>44</td><td>24 (55%)</td><td>7 (16%)</td><td>13 (30%)</td><td>0.91 ± 0.03</td><td>4±1</td><td>0.94 ± 0.05</td><td>1.07 ± 0.06</td></tr><tr><td>Average Dose-<br>recovery ratio</td><td></td><td></td><td></td><td></td><td>0.90±0.03</td><td></td><td>0.94±0.02</td><td>1.01±0.03</td></tr></tbody></table>

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590 **Table 2.** Palaeodose estimates ($D_e$ values in Gy) for MPK and ABC samples using the central dose model (CAM; Galbraith et al., 1999), the average dose model (ADM; Guérin et al., 591 2017) and BayLum (Guérin et al., 2021) from accepted aliquots (N) for which single exponential fit of Analyst (Duller, 2015) provides (or not) $D_e$ and uncertainty ($N_{De/SIGMA}$, $N_{De/INF}$ and 592 $N_{INF/INF}$). (g.): Gaussian distribution; (Log.M): Lognormal_M distribution; Underest.: palaeodose underestimation; OD: overdispersion percentage from CAM. (*) New SAR at higher 593 doses (960 Gy) for MPK8, as no convergence of the MCMC chains using BayLum using saturated aliquots ($N_{De/SIGMA}$, $N_{De/INF}$ and $N_{INF/INF}$) from previous measurements (Arce-Chamorro, 594 2017).

595

<table><thead><tr><th rowspan="3">Sample</th><th colspan="8">De SIGMA</th><th colspan="3">De UNCERT.SAT</th><th colspan="3">De TOTAL</th></tr><tr><th colspan="8">(N<sub>De/SIGMA</sub>)</th><th colspan="3">(N<sub>De/SIGMA</sub> + N<sub>De/INF</sub>)</th><th colspan="3">(N<sub>De/SIGMA</sub> + N<sub>De/INF</sub> + N<sub>INF/INF</sub>)</th></tr><tr><th>N</th><th>De CAM</th><th>OD CAM (%)</th><th>De BayLum (g.)</th><th>Underest. CAM vs BayL. (g.)</th><th>De ADM</th><th>Underest. CAM vs ADM</th><th>De BayLum Log_M</th><th>Underest. CAM vs BayL(log.M)</th><th>N</th><th>BayLum (g.)</th><th>Underest. BayL. (g.) (N<sub>De/SIGMA</sub>)</th><th>N</th><th>BayLum (g.)</th><th>Underest. BayL. (g.) (N<sub>De/INF</sub>)</th></tr></thead><tbody><tr><td>MPK1</td><td>62/141</td><td>71±5</td><td>32±6</td><td>86±5</td><td>17%</td><td>79±5</td><td>10%</td><td>79±5</td><td>10%</td><td>89/141</td><td>94±5</td><td>9%</td><td>130/141</td><td>123±6</td><td>24%</td></tr><tr><td>MPK2</td><td>108/202</td><td>122±6</td><td>46±4</td><td>132±6</td><td>7%</td><td>134±6</td><td>9%</td><td>124±7</td><td>2%</td><td>158/202</td><td>145±5</td><td>9%</td><td>187/202</td><td>155±5</td><td>7%</td></tr><tr><td>MPK3</td><td>36/168</td><td>63±5</td><td>45±7</td><td>76±6</td><td>17%</td><td>69±4</td><td>9%</td><td>71±7</td><td>11%</td><td>61/168</td><td>95±6</td><td>20%</td><td>146/168</td><td>261±34</td><td>64%</td></tr><tr><td>MPK4</td><td>34/91</td><td>62±5</td><td>38±6</td><td>72±5</td><td>14%</td><td>70±5</td><td>11%</td><td>68±5</td><td>9%</td><td>61/91</td><td>89±4</td><td>19%</td><td>86/91</td><td>117±8</td><td>24%</td></tr><tr><td>MPK5</td><td>50/125</td><td>64±4</td><td>33±5</td><td>74±5</td><td>15%</td><td>67±4</td><td>4%</td><td>71±4</td><td>10%</td><td>88/125</td><td>92±5</td><td>20%</td><td>105/125</td><td>101±6</td><td>9%</td></tr><tr><td>MPK6</td><td>139/188</td><td>35±2</td><td>52±4</td><td>44±2</td><td>20%</td><td>40±2</td><td>13%</td><td>40±2</td><td>13%</td><td>142/188</td><td>45±2</td><td>2%</td><td>142/188</td><td>45±2</td><td>0%</td></tr><tr><td>MPK7</td><td>102/219</td><td>139±6</td><td>37±3</td><td>147±5</td><td>5%</td><td>153±5</td><td>9%</td><td>141±6</td><td>1%</td><td>128/219</td><td>154±5</td><td>5%</td><td>206/219</td><td>195±6</td><td>21%</td></tr><tr><td>MPK8</td><td>35/195</td><td>134±11</td><td>45±6</td><td>161±11</td><td>17%</td><td>147±9</td><td>9%</td><td>161±13</td><td>17%</td><td>85/195</td><td>217±10</td><td>26%</td><td>192/195</td><td>no data</td><td>--</td></tr><tr><td>MPK8*</td><td>24/32</td><td>167±14</td><td>35±7</td><td>191±21</td><td>12%</td><td>172±16</td><td>3%</td><td>186±22</td><td>10%</td><td>29/32</td><td>195±14</td><td>2%</td><td>30/32</td><td>252±32</td><td>24%</td></tr><tr><td>ABC1</td><td>59/133</td><td>136±9</td><td>45±4</td><td>194±8</td><td>30%</td><td>149±8</td><td>9%</td><td>186±9</td><td>27%</td><td>82/133</td><td>220±11</td><td>12%</td><td>119/133</td><td>286±18</td><td>32%</td></tr><tr><td>ABC2</td><td>56/168</td><td>181±11</td><td>41±4</td><td>229±11</td><td>21%</td><td>195±10</td><td>7%</td><td>218±12</td><td>17%</td><td>80/168</td><td>272±14</td><td>16%</td><td>138/168</td><td>355±23</td><td>35%</td></tr><tr><td>ABC3</td><td>34/83</td><td>226±14</td><td>34±5</td><td>294±17</td><td>23%</td><td>237±13</td><td>5%</td><td>286±20</td><td>21%</td><td>47/83</td><td>314±16</td><td>6%</td><td>63/83</td><td>360±25</td><td>18%</td></tr><tr><td>ABC4</td><td>81/112</td><td>109±8</td><td>63±6</td><td>150±8</td><td>17%</td><td>132±10</td><td>17%</td><td>130±8</td><td>16%</td><td>88/112</td><td>153±9</td><td>2%</td><td>102/112</td><td>175±11</td><td>14%</td></tr></tbody></table>

596

597
589

590 Table 2. Palaeodose estimates ($D_e$ values in Gy) for MPK and ABC samples using the central dose model (CAM; Galbraith et al., 1999), the average dose model (ADM; Guérin et al., 591 2017) and BayLum (Guérin et al., 2021) from accepted aliquots (N) for which single exponential fit of Analyst (Duller, 2015) provides (or not) $D_e$ and uncertainty ($N_{De/SIGMA}$, $N_{De/INF}$ and 592 $N_{INF/INF}$). (g.): Gaussian distribution; (Log.M): Lognormal_M distribution; Underest.: palaeodose underestimation; OD: overdispersion percentage from CAM. (*) New SAR at higher 593 doses (960 Gy) for MPK8, as no convergence of the MCMC chains using BayLum using saturated aliquots ($N_{De/SIGMA}$, $N_{De/INF}$ and $N_{INF/INF}$) from previous measurements (Arce-Chamorro, 594 2017).

595

<table><thead><tr><th rowspan="3">Sample</th><th colspan="8">De SIGMA</th><th colspan="3">De UNCERT.SAT</th><th colspan="3">De TOTAL</th></tr><tr><th colspan="8">(N<sub>De/SIGMA</sub>)</th><th colspan="3">(N<sub>De/SIGMA</sub> + N<sub>De/INF</sub>)</th><th colspan="3">(N<sub>De/SIGMA</sub> + N<sub>De/INF</sub> + N<sub>INF/INF</sub>)</th></tr><tr><th>N</th><th>De CAM</th><th>OD CAM</th><th>De BayLum</th><th>Underest. CAM vs BayL. (g.)</th><th>De ADM</th><th>Underest. CAM vs ADM</th><th>De BayLum Log_M</th><th>Underest. CAM vs BayL(log.M)</th><th>N</th><th>BayLum (g.)</th><th>Underest. BayL. (g.) (N<sub>De/SIGMA</sub>)</th><th>N</th><th>BayLum (g.)</th><th>Underest. BayL. (g.) (N<sub>De/INF</sub>)</th></tr></thead><tbody><tr><td>MPK1</td><td>62/141</td><td>71±5</td><td>32±6</td><td>86±5</td><td>17%</td><td>79±5</td><td>10%</td><td>79±5</td><td>10%</td><td>89/141</td><td>94±5</td><td>9%</td><td>130/141</td><td>123±6</td><td>24%</td></tr><tr><td>MPK2</td><td>108/202</td><td>122±6</td><td>46±4</td><td>132±6</td><td>7%</td><td>134±6</td><td>9%</td><td>124±7</td><td>2%</td><td>158/202</td><td>145±5</td><td>9%</td><td>187/202</td><td>155±5</td><td>7%</td></tr><tr><td>MPK3</td><td>36/168</td><td>63±5</td><td>45±7</td><td>76±6</td><td>17%</td><td>69±4</td><td>9%</td><td>71±7</td><td>11%</td><td>61/168</td><td>95±6</td><td>20%</td><td>146/168</td><td>261±34</td><td>64%</td></tr><tr><td>MPK4</td><td>34/91</td><td>62±5</td><td>38±6</td><td>72±5</td><td>14%</td><td>70±5</td><td>11%</td><td>68±5</td><td>9%</td><td>61/91</td><td>89±4</td><td>19%</td><td>86/91</td><td>117±8</td><td>24%</td></tr><tr><td>MPK5</td><td>50/125</td><td>64±4</td><td>33±5</td><td>74±5</td><td>15%</td><td>67±4</td><td>4%</td><td>71±4</td><td>10%</td><td>88/125</td><td>92±5</td><td>20%</td><td>105/125</td><td>101±6</td><td>9%</td></tr><tr><td>MPK6</td><td>139/188</td><td>35±2</td><td>52±4</td><td>44±2</td><td>20%</td><td>40±2</td><td>13%</td><td>40±2</td><td>13%</td><td>142/188</td><td>45±2</td><td>2%</td><td>142/188</td><td>45±2</td><td>0%</td></tr><tr><td>MPK7</td><td>102/219</td><td>139±6</td><td>37±3</td><td>147±5</td><td>5%</td><td>153±5</td><td>9%</td><td>141±6</td><td>1%</td><td>128/219</td><td>154±5</td><td>5%</td><td>206/219</td><td>195±6</td><td>21%</td></tr><tr><td>MPK8</td><td>35/195</td><td>134±11</td><td>45±6</td><td>161±11</td><td>17%</td><td>147±9</td><td>9%</td><td>161±13</td><td>17%</td><td>85/195</td><td>217±10</td><td>26%</td><td>192/195</td><td>no data</td><td>--</td></tr><tr><td>MPK8*</td><td>24/32</td><td>167±14</td><td>35±7</td><td>191±21</td><td>12%</td><td>172±16</td><td>3%</td><td>186±22</td><td>10%</td><td>29/32</td><td>195±14</td><td>2%</td><td>30/32</td><td>252±32</td><td>24%</td></tr><tr><td>ABC1</td><td>59/133</td><td>136±9</td><td>45±4</td><td>194±8</td><td>30%</td><td>149±8</td><td>9%</td><td>186±9</td><td>27%</td><td>82/133</td><td>220±11</td><td>12%</td><td>119/133</td><td>286±18</td><td>32%</td></tr><tr><td>ABC2</td><td>56/168</td><td>181±11</td><td>41±4</td><td>229±11</td><td>21%</td><td>195±10</td><td>7%</td><td>218±12</td><td>17%</td><td>80/168</td><td>272±14</td><td>16%</td><td>138/168</td><td>355±23</td><td>35%</td></tr><tr><td>ABC3</td><td>34/83</td><td>226±14</td><td>34±5</td><td>294±17</td><td>23%</td><td>237±13</td><td>5%</td><td>286±20</td><td>21%</td><td>47/83</td><td>314±16</td><td>6%</td><td>63/83</td><td>360±25</td><td>18%</td></tr><tr><td>ABC4</td><td>81/112</td><td>109±8</td><td>63±6</td><td>150±8</td><td>17%</td><td>132±10</td><td>17%</td><td>130±8</td><td>16%</td><td>88/112</td><td>153±9</td><td>2%</td><td>102/112</td><td>175±11</td><td>14%</td></tr></tbody></table>

596

597
598

599

600

601

602

603

604

<table><caption>**Table 3.** Ages for MPK and ABC simples, as function of the saturated aliquots included in bayesian calculations: De-SIGMA using (N<sub>De/SIGMA</sub>) aliquots, De-UNCERT.SAT using (N<sub>De/SIGMA</sub> +N<sub>De/INF</sub>) aliquots and De-TOTAL using (N<sub>De/SIGMA</sub>+N<sub>De/INF</sub>+N<sub>INF/INF</sub>) aliquots. Ages using CAM with (N<sub>De/SIGMA</sub>) aliquots from previous work (Arce-Chamorro, 2017), except MPK6 and ABC3 samples for which minimum age model (MAM; Galbraith et al., 1999) were used.</caption><thead><tr><th>Sample</th><th>DR-Total<br>(Gy/ky)</th><th>Age CAM/MAM*<br>De-SIGMA<br>(ky)</th><th>Age BayL (g.)<br>De-SIGMA<br>(ky)</th><th>Age BayL (g.)<br>De-UNCERT.SAT<br>(ky)</th><th>Age BayL (g.)<br>De-TOTAL<br>(ky)</th></tr></thead><tbody><tr><td>MPK1</td><td>1.5±0.06</td><td>65±13</td><td>58±11</td><td>64±6</td><td>84±8</td></tr><tr><td>MPK2</td><td>1.01±0.02</td><td>59±8</td><td>131±19</td><td>140±20</td><td>149±21</td></tr><tr><td>MPK3</td><td>1.21±0.04</td><td>95±19</td><td>64±17</td><td>78±14</td><td>214±44</td></tr><tr><td>MPK4</td><td>0.9±0.02</td><td>105±23</td><td>78±12</td><td>96±15</td><td>129±21</td></tr><tr><td>MPK5</td><td>1.15±0.01</td><td>77±11</td><td>63±5</td><td>80±7</td><td>89±8</td></tr><tr><td>MPK6</td><td>0.68±0.01</td><td>46±12</td><td>63±1</td><td>63±9</td><td>63±9</td></tr><tr><td>MPK7</td><td>1.37±0.07</td><td>99±22</td><td>107±22</td><td>109±21</td><td>140±26</td></tr><tr><td>MPK8</td><td>1.64±0.02</td><td>102±19</td><td>117±18</td><td>123±19</td><td>157±23</td></tr><tr><td>ABC1</td><td>0.69±0.01</td><td>180±46</td><td>243±32</td><td>272±37</td><td>412±49</td></tr><tr><td>ABC2</td><td>1.94±0.04</td><td>71±13</td><td>102±12</td><td>118±14</td><td>182±23</td></tr><tr><td>ABC3</td><td>1.07±0.02</td><td>72±20</td><td>227±32</td><td>277±39</td><td>335±48</td></tr><tr><td>ABC4</td><td>1.81±0.08</td><td>62±24</td><td>81±12</td><td>81±13</td><td>94±16</td></tr></tbody></table>

605

606

607
598

599

600

601

602

603

604

<table><caption>**Table 3.** Ages for MPK and ABC simples, as function of the saturated aliquots included in bayesian calculations: De-SIGMA using (N<sub>De/SIGMA</sub>) aliquots, De-UNCERT.SAT using (N<sub>De/SIGMA</sub> +N<sub>De/INF</sub>) aliquots and De-TOTAL using (N<sub>De/SIGMA</sub>+N<sub>De/INF</sub>+N<sub>INF/INF</sub>) aliquots. Ages using CAM with (N<sub>De/SIGMA</sub>) aliquots from previous work (Arce-Chamorro, 2017), except MPK6 and ABC3 samples for which minimum age model (MAM; Galbraith et al., 1999) were used.</caption><thead><tr><th>Sample</th><th>DR-Total<br>(Gy/ky)</th><th>Age CAM/MAM*<br>De-SIGMA<br>(ky)</th><th>Age BayL (g.)<br>De-SIGMA<br>(ky)</th><th>Age BayL (g.)<br>De-UNCERT.SAT<br>(ky)</th><th>Age BayL (g.)<br>De-TOTAL<br>(ky)</th></tr></thead><tbody><tr><td>MPK1</td><td>1.5±0.06</td><td>65±13</td><td>58±11</td><td>64±6</td><td>84±8</td></tr><tr><td>MPK2</td><td>1.01±0.02</td><td>59±8</td><td>131±19</td><td>140±20</td><td>149±21</td></tr><tr><td>MPK3</td><td>1.21±0.04</td><td>95±19</td><td>64±17</td><td>78±14</td><td>214±44</td></tr><tr><td>MPK4</td><td>0.9±0.02</td><td>105±23</td><td>78±12</td><td>96±15</td><td>129±21</td></tr><tr><td>MPK5</td><td>1.15±0.01</td><td>77±11</td><td>63±5</td><td>80±7</td><td>89±8</td></tr><tr><td>MPK6</td><td>0.68±0.01</td><td>46±12</td><td>63±1</td><td>63±9</td><td>63±9</td></tr><tr><td>MPK7</td><td>1.37±0.07</td><td>99±22</td><td>107±22</td><td>109±21</td><td>140±26</td></tr><tr><td>MPK8</td><td>1.64±0.02</td><td>102±19</td><td>117±18</td><td>123±19</td><td>157±23</td></tr><tr><td>ABC1</td><td>0.69±0.01</td><td>180±46</td><td>243±32</td><td>272±37</td><td>412±49</td></tr><tr><td>ABC2</td><td>1.94±0.04</td><td>71±13</td><td>102±12</td><td>118±14</td><td>182±23</td></tr><tr><td>ABC3</td><td>1.07±0.02</td><td>72±20</td><td>227±32</td><td>277±39</td><td>335±48</td></tr><tr><td>ABC4</td><td>1.81±0.08</td><td>62±24</td><td>81±12</td><td>81±13</td><td>94±16</td></tr></tbody></table>

605

606

607
<figure><img src="image_15.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_16.png" /></figure>

<figure><img src="image_17.png" /></figure>
<figure><img src="image_14.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_15.png" /></figure>

<figure><img src="image_16.png" /></figure>
**Declaration of interests**

[x] The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

[ ] The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

<figure><img src="image_18.png" /></figure>
**Declaration of interests**

[x] The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

[ ] The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: