The optically stimulated luminescence (OSL) signal from fluvial sediment often contains a remnant from the previous deposition cycle, leading to a partially bleached equivalent-dose distribution. Although identification of the burial dose is of primary concern, the degree of bleaching could potentially provide insights into sediment transport processes. However, comparison of bleaching between samples is complicated by sample-to-sample variation in aliquot size and luminescence sensitivity. Here we begin development of an age model to account for these effects. With measurement data from multi-grain aliquots, we use Bayesian computational statistics to estimate the burial dose and bleaching parameters of the single-grain dose distribution. We apply the model to 46 samples taken from fluvial sediment of Rhine branches in the Netherlands, and compare the results with environmental predictor variables (depositional environment, texture, sample depth, depth relative to mean water level, dose rate). Although obvious correlations with predictor variables are absent, there is some suggestion that the best-bleached samples are found close to the modern mean water level, and that the extent of bleaching has changed over the recent past. We hypothesise that sediment deposited near the transition of channel to overbank deposits receives the most sunlight exposure, due to local reworking after deposition. However, nearly all samples are inferred to have at least some well-bleached grains, suggesting that bleaching also occurs during fluvial transport.

The use of optically stimulated luminescence (OSL) for dating Holocene fluvial deposits is widespread. However, fluvial sediments are not ideal for OSL dating because the intensity of sunlight under water may not be sufficient to reset the OSL signal in some grains prior to their deposition. The remnant OSL signal can then cause the burial dose to be overestimated, leading to an overestimate of the age. This phenomenon is referred to as poor, partial or heterogeneous bleaching (e.g. Wallinga, 2002a).

While the burial age is usually the primary consideration, there are good reasons to quantify the degree of bleaching too. Firstly, it may provide information on the robustness of an OSL age. Secondly, the degree of bleaching might yield information on the sediment source or sediment-transport processes (e.g. Reimann et al., 2015). For instance, if a tsunami deposit appears well bleached, it could indicate that shallow shore-face or intertidal deposits provided the primary sediment source (Murari et al., 2007). For fluvial deposits, poor bleaching might, for instance, reflect short transport distances or an old deposit acting as the primary source.

To compare the bleaching between samples, it is first necessary to
distinguish between the part of the equivalent dose (

Nevertheless, the inherent variability from sample to sample makes definitive conclusions hard to come by. The main problem arises in distinguishing signal from noise: how much of the sample-to-sample variation in bleaching is due to physical processes, as opposed to random statistical fluctuations? Studies focusing on modern or known-age deposits seldom have enough samples for confident conclusions to be drawn, and no study has quantified the variation between adjacent samples. Moreover, the review of Jain et al. (2004) showed a discrepancy in residual doses of modern fluvial samples compared to young known-age samples, with modern samples yielding larger residual doses. They argued that modern deposits may yet be remobilised, so their transport history is not representative of deposits preserved in the stratigraphic record.

Here we focus not on modern samples but on samples of various ages that have
already been used for age estimation. This approach allows for more samples
to be included, and avoids the bad-modern-analogue issue, but presents the
additional problem of separating out the burial dose from the remnant dose.
For this purpose we have designed an age model specifically for these young,
partially bleached

Map showing the sample sites. The sites Brummen and Zwolle are along the river IJssel, whereas the other two sites (Neerijnen and OB1-3) are along the river Waal. Both are branches of the river Rhine. OB1-3 refers to two cores from the Hiensche Uiterwaarden and one core from the Gouverneursche polder.

We use a data set of OSL measurements on a suite of 46 samples from embanked floodplain deposits formed during the past 700 years. Different parts of the data set have been presented by Hobo et al. (2010, 2014) and Wallinga et al. (2010). Samples come from four different sites, all located in the Rhine Delta in the Netherlands (Fig. 1). At each of the sites, several cores (diameter 14–19 cm) were taken in a cross section perpendicular to the river course (see Hobo et al., 2010, for examples). Samples were extracted from the cores in subdued orange light and prepared using methods described by Wallinga et al. (2010). For each of the sample sites, cross sections were constructed based on the borehole database of Utrecht University (Berendsen and Stouthamer, 2002) and additional hand corings. The cross sections were interpreted to identify morphogenetic units (see also Hobo et al., 2014).

For all samples, radionuclide concentrations were determined with
high-resolution gamma-ray spectroscopy, from which dose rates were estimated
using standard conversion factors. Sand-sized quartz grains were extracted
for single-aliquot regeneration OSL measurements (Murray and Wintle, 2003) for equivalent-dose
measurements. Details of the procedure are described by Hobo et al. (2010)
and Wallinga et al. (2010). The grain-size fractions varied between samples
(180–212

We identified nine variables that could influence the bleaching of the
sample either directly or by proxy. The choice of variables is based on our
judgement of possible relevance and data availability. With regard to sample
position, we considered the average river water level at the site (recorded
in 2001), the height of the present surface at the sample location, the
depth of the sample below the present surface, and the depth of the sample
relative to the 2001 average water level. With regards to the sample nature,
we considered the depositional environment (ordinal classes of distal
overbank, overbank, proximal overbank, channel); the sediment texture (clay,
loam, silt, sand, coarse sand/gravel); the dose rate; the

We seek to define a poor-bleaching score based on the measured

Aliquot size and SG sensitivity may vary between samples, so for a statistic
to be useful, it must be independent of these factors for the range of
samples considered. A model defined directly on the

The magnitude of the OSL signal induced by a given radiation dose varies
from grain to grain. The sensitivity distribution also varies between
samples (Duller et al., 2000). Quantifying the SG sensitivity is important
for dating partially bleached samples, because it governs the extent of
averaging across multi-grain aliquots (Cunningham et al., 2011). We
therefore need to define the SG sensitivity distribution in order to
simulate an MG

Here we use computational Bayesian statistics to estimate the SG sensitivity
distribution from the MG sensitivity data. The first step is to parameterise
the SG sensitivity, for which we use the gamma distribution. The gamma
distribution can be formatted with two parameters: a shape parameter

Posterior distribution of the burial dose

The single-grain parameters are as follows:

SG sensitivity, drawn from the gamma distribution with parameters:

The burial dose, drawn from a normal distribution with parameters:

The remnant dose, drawn from the positive part of a normal distribution with
mean of 0 and:

Additional parameters:

With the

In our model, the posterior is sampled using a Markov chain Monte Carlo (MCMC) process. Single-grain parameters for four Markov chains are drawn from a starting distribution, and these parameters are then corrected to better approximate the target posterior. The approximate distributions are improved at each step using the Metropolis algorithm. When the simulation has run long enough, each step can be considered a random draw from the target distribution. The length of the sequence is determined by the convergence of the Markov chains; this is monitored by comparing the within-chain and between-chain variance, following the procedure of Gelman et al. (2004). The first half of each Markov chain is discarded to ensure that the choice of starting values does not influence the result.

Five parameters are determined in the computational processing:

Parameters with positive values (

Results of the simulation recovery: “recovered” values are defined
by the mean and standard deviation of the posterior distribution.

Example model output for three samples that are

The model is run in two phases. The first is a short run, giving an approximate range of the parameter space. The output of the first run is summarised by a multivariate normal distribution, which is used to define the starting distribution and jumping distributions for phase two. The second phase is run until convergence.

Here we perform a simulation-recovery test to check that the model is
performing as expected. Single-grain parameters are chosen, and then used to
simulate

For both aliquot sizes, the SG parameters can be reconstructed (Table 1).
Reconstruction of the 1 Gy burial dose is reasonably precise (8 %) for the
80-grain aliquots, and very close to the bootstrapped MAM3 estimate of the
burial dose on the MG aliquot data set (1.03

As a further step, it would be interesting to see how the age model applied
to multi-grain aliquot data compares to single-grain data from the same
sample. However, this comparison is not as simple as it sounds. Our model
uses multi-grain aliquot data to estimate the assumed parameters of the SG

The reconstructed SG sensitivity distribution is similar for all samples
measured here, not surprising as they are all from recent Rhine deposits.
The shape parameter

The distribution of

Three examples of the model output are shown in Fig. 4, each indicating a
different degree of bleaching. For each sample, the histograms indicate the
posterior density of the burial dose

When the burial dose is very close to zero, the posterior distribution is shaped like an exponential decay (not shown here). Such distributions are not well described by the mean and standard deviation, and thus may need to be summarised differently. We will not dwell on the issue here, but will leave it for future consideration.

The bleaching statistic

The mean (and standard deviation) of the

While there are no clear relationships between

Comparison of burial-dose estimates. The modelled dose is defined by
the mean and standard deviation of the posterior, and is compared to the
original MAM3 minimum dose (using

There appear to be significant relationships between the sensitivity
parameters

The large degree of uncertainty in our model results prevents convincing
conclusions from being drawn. This uncertainty is again down to
aliquot size. Firstly, the aliquot sizes used were often too large. Second,
our post hoc estimates of the aliquot size were not sufficiently accurate (as noted
by Heer et al., 2012). These issues affected model efficiency and outcome
by amplifying the difficulty of distinguishing high

Two possible structures in the proportion of well-bleached grains

With these caveats established, it is worth considering two structures in
the modelled data that might, possibly, have geomorphic significance. These
concern the relationship between

There is also structure in Fig. 7b, which shows

There are three possible reasons for the structure. It could be an artefact
of the model through the high-

A sand bar deposited close to the river Waal during high discharge (photo by Gilbert Maas, Alterra). Due to the absence of vegetation, such deposits may be reworked through aeolian processes, which may enhance bleaching for deposits formed above the mean water level.

The requirements of this project led us to develop a specific “age model”
for partially bleached, multi-grain-aliquot data. It uses Bayesian
computational methods to estimate the parameters of the single-grain dose
distribution, without the need for any single-grain measurements. Along the
way, the parameters of the single-grain sensitivity distribution are
estimated from multi-grain aliquot sensitivity data. Our approach has
significant advantages over existing models:

The interaction of aliquot size and SG sensitivity is incorporated, meaning that prior quantification of the averaging effect is not necessary.

It includes uncertainty deriving from the number of aliquots consistent with the burial dose.

It should provide an unbiased estimate of the burial dose, even when no aliquots are “well bleached”. Poorly bleached samples give a very imprecise, but still accurate, estimate of the burial dose.

The degree of bleaching is quantified, and is potentially independent of the SG sensitivity, aliquot size and burial dose.

Different data sets from the same sample (i.e. different aliquot sizes) can be combined to produce a single estimate of the burial dose.

Of course, the validity of the outcome rests on a number of assumptions. The parameterisation of the SG dose and sensitivity distributions must be appropriate and, crucially, the estimate of aliquot size should be reasonable. This paper uses archive data, so aliquot size was estimated only roughly. When applied in future, careful grain counting should take place; this could be performed manually, or with a digital camera plus image-recognition software.

Compared to familiar and well-used age models in OSL dating (e.g. CAM and
MAM3), this model is a different beast altogether. It requires more data to
be input per sample, and careful consideration and specification of model
parameters and priors. It includes the MAM3 (Galbraith et al., 1999) and
bootstrap likelihoods (Cunningham and Wallinga, 2012) as a small part of
it, and requires

The model could be immediately improved by treating

There are a particular set of challenges in estimating the degree of
bleaching for unknown-age OSL samples, and these problems relate closely to
the burial-dose calculation. We have begun to refashion the burial-dose
calculation by using Bayesian computational statistics to reduce the

Nevertheless, the results do show some interesting features that may point to geomorphic controls on sediment bleaching. We found a concentration of well-bleached samples around the modern mean water level, indicating to us that sediment receives a “kick” of bleaching upon deposition, through local reworking, in addition to the bleaching that occurs during transport. We also speculate on whether changes in the degree of bleaching over time could relate to river management changes, especially the construction of groynes in the lower Rhine around AD 1850.

Despite the limitations of this study, it seems clear that processes of sediment provenance, transport and deposition can influence the measured OSL signal. The challenge lies in extracting meaningful information from the OSL data. The computational approach explored in this study has real potential, and we hope aspects of our model will be taken forward.

This work was partially funded through a Technology Foundation (STW) VIDI grant (DSF.7553). We would like to thank Geoff Duller (Aberystwyth University) for making the data set on single-grain sensitivity distributions available. Zhixiong Shen and an anonymous reviewer are kindly thanked for their constructive comments. Matlab code is available in the supplement files. Edited by: A. Lang