**Research article**
17 Apr 2020

**Research article** | 17 Apr 2020

# Miniature radiocarbon measurements ( < 150 µg C) from sediments of Lake Żabińskie, Poland: effect of precision and dating density on age–depth models

Paul D. Zander Sönke Szidat Darrell S. Kaufman Maurycy Żarczyński Anna I. Poraj-Górska Petra Boltshauser-Kaltenrieder and Martin Grosjean

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**Paul D. Zander et al.**Paul D. Zander Sönke Szidat Darrell S. Kaufman Maurycy Żarczyński Anna I. Poraj-Górska Petra Boltshauser-Kaltenrieder and Martin Grosjean

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^{1}Institute of Geography & Oeschger Centre for Climate Change Research, University of Bern, Bern, 3012, Switzerland^{2}Department of Chemistry and Biochemistry & Oeschger Centre for Climate Change Research, University of Bern, Bern, 3012, Switzerland^{3}School of Earth and Sustainability, Northern Arizona University, Flagstaff, AZ 86011, USA^{4}Faculty of Oceanography and Geography, University of Gdańsk, Gdańsk, 80-309, Poland^{5}Institute of Plant Sciences & Oeschger Centre for Climate Change Research, University of Bern, Bern, 3013, Switzerland

^{1}Institute of Geography & Oeschger Centre for Climate Change Research, University of Bern, Bern, 3012, Switzerland^{2}Department of Chemistry and Biochemistry & Oeschger Centre for Climate Change Research, University of Bern, Bern, 3012, Switzerland^{3}School of Earth and Sustainability, Northern Arizona University, Flagstaff, AZ 86011, USA^{4}Faculty of Oceanography and Geography, University of Gdańsk, Gdańsk, 80-309, Poland^{5}Institute of Plant Sciences & Oeschger Centre for Climate Change Research, University of Bern, Bern, 3013, Switzerland

**Correspondence**: Paul D. Zander (paul.zander@giub.unibe.ch)

**Correspondence**: Paul D. Zander (paul.zander@giub.unibe.ch)

Received: 29 Nov 2019 – Discussion started: 17 Dec 2019 – Revised: 03 Apr 2020 – Accepted: 06 Apr 2020 – Published: 17 Apr 2020

The recent development of the MIni CArbon DAting System (MICADAS) allows
researchers to obtain radiocarbon (^{14}C) ages from a variety of samples
with miniature amounts of carbon (<150 µg C) by using a gas
ion source input that bypasses the graphitization step used for conventional
^{14}C dating with accelerator mass spectrometry (AMS). The ability to
measure smaller samples, at reduced cost compared with graphitized samples,
allows for greater dating density of sediments with low macrofossil
concentrations. In this study, we use a section of varved sediments from
Lake Żabińskie, NE Poland, as a case study to assess the usefulness
of miniature samples from terrestrial plant macrofossils for dating lake
sediments. Radiocarbon samples analyzed using gas-source techniques were
measured from the same depths as larger graphitized samples to compare the
reliability and precision of the two techniques directly. We find that the
analytical precision of gas-source measurements decreases as sample mass
decreases but is comparable with graphitized samples of a similar size
(approximately 150 µg C). For samples larger than 40 µg C and
younger than 6000 BP, the uncalibrated 1*σ* age uncertainty is
consistently less than 150 years (±0.010 F^{14}C). The reliability
of ^{14}C ages from both techniques is assessed via comparison with a
best-age estimate for the sediment sequence, which is the result of an OxCal
V sequence that integrates varve counts with ^{14}C ages. No bias is
evident in the ages produced by either gas-source input or graphitization.
None of the ^{14}C ages in our dataset are clear outliers; the 95 %
confidence intervals of all 48 calibrated ^{14}C ages overlap with the
median best-age estimate. The effects of sample mass (which defines the
expected analytical age uncertainty) and dating density on age–depth models
are evaluated via simulated sets of ^{14}C ages that are used as inputs
for OxCal P-sequence age–depth models. Nine different sampling scenarios
were simulated in which the mass of ^{14}C samples and the number of
samples were manipulated. The simulated age–depth models suggest that the
lower analytical precision associated with miniature samples can be
compensated for by increased dating density. The data presented in this
paper can improve sampling strategies and can inform expectations of age
uncertainty from miniature radiocarbon samples as well as age–depth model
outcomes for lacustrine sediments.

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Radiocarbon (^{14}C) dating is the most widely used technique to date
sedimentary sequences that are less than 50 000 years old. The robustness of
age–depth models can be limited by the availability of suitable material for
dating; this is particularly a problem for studies on sediments from alpine,
polar, or arid regions where terrestrial biomass is scarce. Most accelerator
mass spectrometry (AMS) labs recommend that samples contain 1 mg or more of
carbon for reliable ^{14}C age estimations. It is well established that
terrestrial plant macrofossils are the preferred material type for dating
lake sediments because bulk sediments or aquatic macrofossils may have an
aquatic source of carbon, which can bias ^{14}C ages (Groot et al., 2014;
MacDonald et al., 1991; Tornqvist et al., 1992; Barnekow et al., 1998; Grimm
et al., 2009). Furthermore, a high density of ^{14}C ages (i.e., one age
per 500 years) is recommended to reduce the overall chronologic uncertainty
of age–depth models (Blaauw et al., 2018).
Researchers working on sediments with low abundances of terrestrial plant
macrofossils face difficult choices about whether to date suboptimal
materials (e.g., bulk sediment or aquatic macrofossils), pool material from
wide sample intervals, or rely on few ages for their chronologies. The
problem of insufficient material can affect age estimates at all scales from
an entire sedimentary sequence to a specific event layer which a researcher
wishes to determine the age of as precisely as possible.

Recent advances have reduced the required sample mass for AMS ^{14}C
analysis, opening new opportunities for researchers (Delqué-Količ
et al., 2013; Freeman et al., 2016; Santos et al., 2007; Shah Walter et al.,
2015). The recently developed MIni CArbon DAting System (MICADAS) has the
capability to analyze samples with miniature masses via the input of samples
in a gaseous form, thus omitting sample graphitization (Ruff
et al., 2007, 2010a, 2010b; Synal et al., 2007; Szidat et al., 2014; Wacker
et al., 2010a, b, 2013). Samples containing as little as a few micrograms of C can be dated using the gas-source input of the MICADAS. The analysis of such
small samples provides several potential benefits for dating lake sediments:
(1) the possibility to date sediments that were previously not dateable using
^{14}C due to insufficient material, (2) the ability to date sedimentary
profiles with a greater sampling density and lower costs per sample, and (3) the ability to be more selective when selecting material to be analyzed for
^{14}C. The disadvantage of miniature samples is increased analytical
uncertainty, which is a consequence of lower counts of carbon isotopes and
the greater impact of contamination on the measurement results. The goal of
this study is to assess the potential benefits and limits of applying
miniature ^{14}C measurements to dating lake sediments. We aim to answer
the following questions in this study: (1) How reliable and how precise are
gas-source ^{14}C ages compared with graphitized ages? (2) What is the
variability of ^{14}C ages obtained from a single stratigraphic level? (3) How do analytical precision and dating density affect the accuracy and
precision of age–depth models for lake sediments?

In this study, we use the sediments of Lake Żabińskie, Poland, as a
case study to investigate the application of gas-source ^{14}C
measurements to lake sediments. We focus on a continuously varved segment of
the core, which spans roughly 2.1 to 6.8 ka. We report the results of
48 radiocarbon measurements (17 using graphitization and 31 using the
gas-source input) in order to compare the precision and reliability of
gas-source ^{14}C ages with graphitized samples. The core was sampled such
that up to five ages were obtained from 14 distinct stratigraphic depths. A
floating varve chronology was integrated with the ^{14}C ages to produce a
best-age estimate using the OxCal V-sequence routine (Bronk Ramsey, 2008). This best-age estimate is
used as a benchmark for the ^{14}C results. The results of our ^{14}C
measurements were used to constrain a statistical model designed to simulate
sets of ^{14}C ages in order to test nine different hypothetical sampling
scenarios in which we manipulate the number of ages and the mass of C per
sample, which determines the analytical uncertainty of the simulated ages.
By comparing the results of the simulated age–depth model outputs from these
simulated ^{14}C ages with the best-age estimate from which the simulated
ages were derived, we can improve our understanding of how the number of
ages and their analytical precision influence the accuracy and precision of
radiocarbon-based age–depth models.

## 2.1 Core material and radiocarbon samples

Cores were obtained from Lake Żabińskie (coring site:
54.1318^{∘} N, 21.9836^{∘} E, 44 m water depth) in 2012 using
an UWITEC piston corer (90 mm diameter). Lake Żabińskie is a small
(41.6 ha), relatively deep (44.4 m) kettle-hole lake located at an altitude
of 120 m a.s.l. The catchment is 24.8 km^{2} and includes two other
smaller lakes: Lake Purwin and Lake Łękuk. Average temperatures range
from 17 ^{∘}C in summer to −2 ^{∘}C in winter. Annual
precipitation is 610 mm, with the annual peak in summer (JJA). The geology
of the catchment is primarily glacial till, sandy moraines, and glacial
fluvial sands and gravels (Szumański, 2000). Modern land
cover in the catchment is a mixture of cultivated fields and primarily
oak–lime–hornbeam and pine forests (Wacnik
et al., 2016). The high relative depth (6.1 %; calculated according to
Wetzel et al., 1991) of Lake Żabińskie leads to
strong seasonal stratification, bottom-water anoxia, and the preservation of
varves in the sediments (Bonk
et al., 2015a, b; Tylmann et al., 2016; Żarczyński et al.,
2018). Varve-based chronologies and ^{14}C measurements have been
published for the most recent 2000 years of the Lake Żabińskie
sedimentary sequence (Bonk et al.,
2015a; Żarczyński et al., 2018). These studies show major changes to
varve structure and a 3-fold increase in sedimentation rates in response
to increased cultivation and deforestation, beginning around 1610 CE. Prior
to this time, land cover in the region was relatively stable, with
forest or woodland cover dominating the landscape from the early Holocene until
the 17th century CE (Wacnik, 2009;
Żarczyński et al., 2019).

A composite sediment profile was constructed from overlapping, 2 m long
cores by correlating distinctive stratigraphic features. The composite
sequence spans 19.4 m. Published downcore varve counts stop above a
∼90 cm thick slump or deformed unit. This slump event is dated
to 1962–2071 cal BP (present: 1950 CE) based on an extension of the
varve count published in Żarczyński et al. (2018). This study focuses
on a section of core (7.3–13.1 m depth in our composite sequence) directly
below this slump unit; this section was selected because it features
continuous well-preserved varves throughout the section. Samples of 1 to
2 cm thick slices of sediment were taken from the core (sample locations and
core images are found in Supplement – File S1), then sieved with a 100 µm sieve. Macrofossil remains were identified and photographed
(File S2), and only identifiable terrestrial plant material was
selected for ^{14}C measurements. Suitable macrofossils from a single
stratigraphic level were divided into subsamples for analysis, with the goal
of producing one graphitized ^{14}C age and 2–4 gas-source ages from each
depth. When convenient, we grouped samples by the type of material (leaves,
periderm, needles, seeds, or woody scales), though 11 samples are a mixture
of material types. In most cases, subsamples within a stratigraphic level
are assumed to be independent, meaning they may have different true ages.
However, there are some subsamples that were taken from single macrofossil
fragments (six subsamples taken from two fragments sampled from two
different depths); thus these samples have the same true age. It is also
possible that subsamples from a single depth may be from the same original
material without our knowledge (i.e., a macrofossil could break into several
pieces while sieving, and these pieces could be analyzed as separate
subsamples).

Sample material was treated with an acid–base–acid (ABA) method at
40 ^{∘}C, using 0.5 mol L^{−1} HCl, 0.1 mol L^{−1} NaOH, and 0.5 mol L^{−1} HCl for 3, 2, and 3 h, respectively. After drying at room temperature, samples were
weighed, and those less than 300 µg were input to the gas ion source
via combustion in an Elementar Vario EL Cube elemental analyzer (Salazar et al., 2015). Larger
samples were graphitized following combustion using automated graphitization
equipment (AGE) (Szidat et al., 2014). Radiocarbon
data was processed using the software BATS (Wacker et al., 2010a). Additional corrections
were applied to the data to account for cross contamination (carryover), and
constant contamination (blanks) (Gottschalk
et al., 2018; Salazar et al., 2015). The parameters for these corrections
were calculated based on standard materials (the primary NIST standard
oxalic acid II (SRM 4990C) and sodium acetate (Sigma-Aldrich, no. 71180) as
^{14}C-free material) run with the sample batches. We applied a constant
contamination correction of 1.5±0.2 µg C with 0.72±0.11 F^{14}C and a cross contamination correction of (1.2 *%*±0.3 *%*) from the previously run sample. Measurement uncertainties were fully
propagated for each correction. In total, 48 ages were obtained from 14
distinct stratigraphic levels (17 graphitized and 31 gas-source
measurements).

## 2.2 Varve count

Varves in Lake Żabińskie are biogenic, with calcite-rich pale laminae deposited in spring and summer and darker laminae containing organic detritus and fine clastic material deposited in winter (Żarczyński et al., 2018). We defined the boundary of each varve year by the onset of calcite precipitation (i.e., the upper boundary of dark laminae and lower boundary of light-colored laminae). Varves were counted using CooRecorder software (Larsson, 2003) on core images obtained from a Specim PFD-CL-65-V10E linescan camera (Butz et al., 2015). Three people performed independent varve counts, and these three counts were synthesized and uncertainties calculated according to the methodology recommended by Żarczyński et al. (2018) yielding a master varve count with asymmetric uncertainties.

Because of the slump deposit above our section of interest, the varve
chronology is “floating” and must be constrained by the ^{14}C ages.
Several different approaches were used to compare the varve count with the
^{14}C ages, all of which rely on some assumptions. One method is to tie
the varve count to the radiocarbon-based age at a chosen depth in the core.
We tested this method using the median calibrated age of the uppermost dated
level as the tie point. Such an approach assumes that the radiocarbon-based
age at the tie point is correct. An additional drawback is that the choice
of tie point is arbitrary and can change the resulting varve count ages.
Alternatively, we used least-squares minimization to fit the varve count to
all radiocarbon ages (Hajdas et al., 1995) by
minimizing the offset between the varve count and the combined calibrated
radiocarbon age at each dated level. However, we focus on a third, more
sophisticated method, which is the OxCal 4.3 V sequence (Bronk Ramsey, 2008,
2009; Bronk Ramsey and Lee, 2013). This technique integrates all available
chronological information including varve counting and ^{14}C ages into a
single model to determine a best-age estimate for the sequence (see section
below for more details). The advantages of this approach are that all ages
are considered equally likely to be correct (or incorrect), and the error
estimate of the V sequence is relatively consistent along the profile,
whereas the error associated with the varve count is small at the top of the
section but increases downcore. Additionally, this technique allows for the
possibility that the master varve count is incorrect (within the expected
uncertainty of the count).

## 2.3 Age–depth modeling

Age–depth modeling was performed using OxCal 4.3 (Bronk
Ramsey, 2008, 2009; Bronk Ramsey and Lee, 2013), which integrates the
IntCal13 calibration curve (Reimer et al.,
2013) for ^{14}C ages with statistical models that can be used to
construct age–depth sequences. As an initial test to compare the reliability
of gas-source ages and graphitized ages, and their effect on age–depth
models, we produced three P-sequence models: one using all obtained ^{14}C
ages, one using only graphitized ages, and one using only gas-source ages.
For all OxCal models in this study, ages measured from the same depth were
combined (using the function *R_combine*) into a single ^{14}C age with uncertainty
before calibration and integration into the age–depth sequence. This choice
was verified by the chi-squared statistic calculated by OxCal to test the
agreement of ages sampled from a single depth. For every combination of ages
except one, we find that the chi-squared test is passed at the 0.05 significance
level. We justify the use of the combine function even for the grouping that
failed to pass the chi-squared test (samples from 811 cm depth) because all
ages in this group overlap, and there is no significant difference when
models are run with the ages separated at this depth (less than 5 years
difference for median age and confidence interval, CI). The OxCal P sequence uses a Bayesian
approach in which sediment deposition is modeled as a Poisson (random)
process. A parameter (*k*) determines the extent to which sedimentation rates
are allowed to vary. For all P-sequence models in this study, we used a
uniformly distributed prior for k such that *k*_{0}=1, and
log_{10}(*k*∕*k*_{0}) $\sim U(-\mathrm{2}$, 2); this allows *k* to vary
between 0.01 and 100. Sediment deposition sequences are constrained by
likelihood functions produced by the calibration of radiocarbon ages.
Thousands of iterations of sediment deposition sequences are produced using
Markov Chain Monte Carlo (MCMC) sampling (Bronk
Ramsey, 2008). These iterations can then be summarized into median age
estimates, with confidence intervals.

The varve counts and all ^{14}C ages were incorporated into an OxCal
V sequence in an approach similar to that used by Rey et al. (2019). The V sequence differs from
the P sequence in that it does not model sediment deposition. Instead, the
V sequence uses “Gaps” (the amount of time between two points in a sequence)
to constrain the uncertainty of radiocarbon ages. The gap can be determined
from independent chronological information such as varve counts or tree ring
counts. We input the number of varves in 10 cm intervals to the V sequence
as an age gap with associated uncertainty. The OxCal V sequence assumes
normally distributed uncertainties for each gap, whereas our varve count
method produces asymmetric uncertainty estimates. We used the mean of the
positive and negative uncertainties as inputs to the V sequence. However,
OxCal sets the minimum uncertainty of each gap equal to 5 years, which in
most cases is larger than the mean uncertainty in our varve count over a 10 cm interval. By including the varve counts as an additional constraint, the
V sequence produces a more precise age–depth relation than the P sequence,
which only considers the radiocarbon ages.

## 2.4 Age–depth model simulation

In order to test the effects of analytical uncertainty and dating density
(number of ages per time interval) on age–depth models, we designed an
experiment in which nine different sampling scenarios were simulated for the
Lake Żabińskie sedimentary sequence to determine the expected
precision and accuracy of resulting age–depth models. Three different
sampling densities were simulated for the 5.8 m long section: 5, 10, and 20 ages (equivalent to approximately 1, 2, and 4 ages per
millennium, respectively). For each of these sampling densities three
different sample-size scenarios were simulated: 35, 90, and 500 µg C. These scenarios were designed to represent different sampling
circumstances such as high or low abundances of suitable material for
^{14}C analysis and different budgets for ^{14}C analysis. Radiocarbon
ages were simulated using a technique similar to Trachsel and Telford (2017). In brief, we
distributed the simulated samples evenly by depth across the 5.8 m long
section and then used the median output of the OxCal V sequence as the
assumed true age for a given depth. This calibrated assumed true age was
back-converted to ^{14}C years using IntCal13 (Reimer et al., 2013). A random error term was
added to the ^{14}C age to simulate the analytical uncertainty. The error
term was drawn from a normal distribution with mean zero and standard
deviation equivalent to the age uncertainty determined from the relationship
between sample mass and age uncertainty found in the results of our ^{14}C
measurements (Fig. 1a). The same expected analytical uncertainty was used
for the age uncertainty for each simulated age. For a sample with 35 µg C, we expect a measurement uncertainty of ±148 years (or ±0.0114 F^{14}C), which is representative of the average age of all
samples in this study (approximately 4000 ^{14}C BP). In reality, older
samples would have greater age uncertainty, while younger samples would have
less uncertainty. However, the effect of these differences on the
performance of simulated age–depth models would be minimal as roughly half
the ages would be more precise and half would be less precise. These
simulated ^{14}C ages were input into an OxCal P sequence using the same
uniform distribution for the *k* parameter as described in the previous
section. This experiment was repeated 30 times for each scenario to assess
the variability of possible age–model outcomes. We quantify the accuracy of
the age–depth models as the deviation of the median modeled age from the
best-age estimate at a given depth. We define precision as the width of the
age–depth model CI.

## 3.1 Radiocarbon measurements

In total, 48 radiocarbon measurements on terrestrial plant macrofossils were
obtained from the section of interest yielding values from 0.475 to 0.777 F^{14}C (2030 to 5990 ^{14}C BP; Table 1).
Thirty-one ages were measured using the gas-source input; these samples
contained between 11 and 168 µg C. Seventeen samples containing between
115 and 691 µg C were measured using graphitization. Analytical
uncertainties for the ^{14}C measurements range from ±0.0027 to
±0.0306 F^{14}C (±41 to ±328 years) with higher
values associated with the smallest sample masses. The uncertainties for
gas-source measurements and graphitized measurements are comparable for
samples that contain a similar amount of carbon (Fig. 1). Samples containing
less than 40 µg C (roughly equivalent to 80 µg of dry plant
material) produce uncertainties greater than ±150 years (1*σ*).
We use a power-model fit with least-squares regression, to estimate the
typical age uncertainty for a given sample mass (*r*^{2}=0.90, *p*<0.001, Fig. 1). The resulting power model is nearly identical to
what would be expected based on the assumed Poisson distribution of the
counting statistics where the uncertainty follows the relationship
*N*^{−0.5} (*N*: the number of measured ^{14}C atoms).

When comparing measurements taken from within a single sediment slice we
find good agreement for all ^{14}C ages, regardless of whether the samples
were analyzed with the gas-source input or via a graphitized target (Fig. 2), and no clear bias based on the type of macrofossil that was dated (Fig. 3). One method to test whether the scatter of ages is consistent with the
expectations of the analytical uncertainty is a reduced chi-squared
statistical test, also known as mean square weighted deviation (MSWD) in
geochronological studies (Reiners et al., 2017).
If the spread of ages is exactly what would be expected from the analytical
uncertainty, the value of this statistic is 1. Lower values represent less
scatter than expected, and larger values represent more scatter than
expected. Of the 11 sampled depths with three or more ages, only one (811 cm, MSWD = 3.07) returned an MSWD that exceeds a 95 % significance
threshold for acceptable MSWD values that are consistent with the assumption
that the age scatter is purely the result of analytical uncertainty.

^{1} Ages calibrated using OxCal 4.3 with the IntCal13 calibration curve (Bronk Ramsey, 2009; Reimer et
al., 2013). The range reported here represents the 95 % confidence
interval.
^{2} Range represents 95 % confidence interval.

^{3} These samples were subsampled from a single fragment prior to
analysis; thus samples within the same depth with this symbol have the same
true age.

## 3.2 Varve count and age–depth modeling

In total, 4644 (+155/−176) varves were counted in the section of
interest, with a mean varve thickness of 1.26±0.58 mm (Fig. 4). Full
varve count results are available at
https://doi.org/10.7892/boris.134606. Sedimentation rates averaged over
10 cm intervals range from 0.91 to 2.78 mm yr^{−1}. All chronological data
(^{14}C ages and varve counts) were integrated to generate a best-age
estimate for the section of interest using an OxCal V sequence (output of
the Oxcal V sequence is available at
https://doi.org/10.7892/boris.134606). This produced a well-constrained
age–depth model with a 95 % CI width that ranges
from 69 to 114 years (mean 86 years). OxCal uses an agreement index to
assess how well the posterior distributions produced by the model (modeled
ages at the depth of ^{14}C ages) agree with the prior distributions
(calibrated ^{14}C ages). The overall agreement index for our OxCal
V sequence is 66.8 %, which is greater than the acceptable index of
60 %. Three of the fourteen dated levels in the V sequence had agreement
indices less than the acceptable value of 60 % (*A*=22.8 %, 48.5 %, and 52.6 %
for sample depths of 1283.0, 1176.1, and 732.5 cm, respectively); nonetheless
we find the model fit acceptable as all 48 ^{14}C ages overlap with the
median output of the V sequence. We use the V sequence as a best-age
estimate for subsequent data comparisons and analyses. Alternative methods
of linking the floating varve count with ^{14}C ages confirm that the
^{14}C ages are consistent with the varve count results (Fig. 4). When the varve
count is tied to the combined radiocarbon ages at the uppermost dated level
(732.5 cm), we find that all other radiocarbon ages overlap with the varve
count when considering the uncertainty of the varve count. If least-squares
minimization is used to minimize the offset between all radiocarbon ages and
the varve count, we again find that all radiocarbon ages overlap with the
master varve count (without considering varve count uncertainty). The result
from the least-squares minimization technique is highly similar to the OxCal
V-sequence output.

To test the reliability of gas-source ages versus graphitized ages we
created three OxCal P sequences using (1) all ^{14}C ages, (2) only
graphitized ages, and (3) only gas-source ages. The results of all three of
these age–depth models agree well with the best-age estimate of the
V sequence, although with larger 95 % CIs (Fig. 2). The agreement index
was greater than the acceptable value of 60 for all three models overall
and for each dated depth within all three models. The P sequence using all
^{14}C ages spans 4838±235 years, which is slightly greater than,
but overlapping with, the total number of varves counted (the V-sequence
estimates 4681±79 years in the section). There is no clear bias
observed in the age–depth models produced using either the gas-source or
graphitized samples. The P-sequence outputs clearly show that a very precise
age can narrowly constrain the age–model uncertainty at the depth of that
sample; however, if dating density is low, the uncertainty related to
interpolation between ages becomes large. Despite the lower precision of the
gas-source ages, the model based on only gas-source ages actually has a
lower mean CI width than the model with graphitized ages (mean 95 % CI
width: 373 years for the gas-source model, 438 years for the graphitized
model). However, a direct comparison between the gas-source-only and the
graphitized-only age models is confounded by differences in the number and
spacing of samples. Specifically, there are no graphitized ages between the
top of the section (724 cm) and 811 cm and between 1082 and 1200 cm, which
results in a wide CI in these sections. On the other hand, uncertainty is
reduced compared to the gas-source model in the depths adjacent to the
graphitized ages due to higher precision such that 40 % of the section (in
terms of depth) has lower age uncertainty in the graphitized model.

## 3.3 Age–depth model simulations

Nine different sampling scenarios (described in Sect. 2.3) were simulated to
test the effects of dating density and analytical precision on age–depth
model confidence intervals. For each of the nine scenarios, sets of ^{14}C
ages were simulated 30 times to create an ensemble of age–depth models for
each scenario. One set of these simulated age–depth models is shown in Fig. 5, and an animation of the full set of simulated models is available online
(File S3). The age–depth models were evaluated for their
precision (mean width of the 95 % CI) and accuracy (the mean absolute
deviation from the best-age estimate; summarized in Fig. 6 and
Table 2). As expected, we find that increased dating
density and increased sample masses improve both the accuracy and precision
of the age–depth models. It is notable that increasing the number of ages
can compensate for the greater uncertainty associated with smaller sample
sizes. For instance, the mean CI of age–depth models based on ten 90 µg C samples is narrower than age–depth models with five 500 µg C samples (Table 2). However, the effect of analytical precision is greater on
the mean absolute deviation from the best-age estimate. Increased dating
density does tend to reduce the deviation from the best-age estimate
(especially if the ages are imprecise), but the three scenarios that use 500 µg samples perform better than all other scenarios, in terms of
deviation from the best-age estimate, regardless of the sampling density.
Additionally, increased dating density does not improve the deviation from
the best-age estimate for the 500 µg sample scenarios. This result may
be due to the relatively constant sedimentation rates in our sedimentary
sequence, which reduces errors caused by interpolation in scenarios with low
dating density. Another prominent pattern in the simulations is the large
spread of performance for models with relatively few and imprecise ages
(Fig. 6). Increasing the number of samples and, especially, the mass of
samples has a large impact on the agreement among the different iterations
of each scenario.

^{∗} Expected age uncertainty for an approximately 4000-year-old sample
used to inform age–depth model simulations.

An additional measure of age–model quality is the Chron Score rating system (Sundqvist
et al., 2014), which does not assess age–depth model fit; rather it assesses
the quality of inputs used to generate an age–depth model. Thus the Chron
Score provides an assessment of the nine sampling scenarios that is independent
of the choice of age–depth modeling software or parameter selection during
age–depth model construction. The Chron Score is calculated from three
criteria used to assess the reliability of core chronologies: (1) delineation
of downcore trend (*D*), (2) quality of dated materials (*Q*), and (3) precision
of calibrated ages (*P*). These metrics are combined using a reproducible
formula to provide a Chron Score (*G*) in which higher values represent more
reliable chronologies:

We used the default weighting parameters (*w*_{D}, *w*_{Q}, and *w*_{P}=0.001, 1 and 200) for each component of the Chron Score formula as described
in Sundqvist et al. (2014). The quality (*Q*) parameter depends on two factors
– the proportion of ages which are not rejected or reversed (i.e., an older
age stratigraphically above a younger age) and a qualitative classification
scheme for material types. We modified the threshold for determining if an
age is considered a reversal such that if a ^{14}C age is older than a
stratigraphically higher age by more than the age uncertainty (1*σ*),
the age is considered to be stratigraphically reversed. This is different
from the default setting, which is 100 years. For the material type
classification (m), the simulated age models were assigned the value 4,
which is the value assigned to chronologies based on terrestrial
macrofossils. For more details on the Chron Score calculation, see Sundqvist
et al. (2014). The mean Chron Scores for the simulated age models
(Table 2) show that doubling dating density
substantially improves the Chron Score, but the effect is greater when
moving from 5 to 10 ages than from 10 to 20 ages. The effect of increased
precision on the Chron Score is also substantial; it is essentially defined
by the Chron Score formula, in which precision is assessed as *P*= s^{−1}, where s is the mean 95 % range of all calibrated ^{14}C ages. The
effect of precision on the Chron Score is also determined by the weighting
factors mentioned above.

## 4.1 Radiocarbon measurements

The results of our ^{14}C measurements from repeated sampling of single
stratigraphic levels provide useful information for other researchers
working with miniature ^{14}C analyses or any ^{14}C samples from lake
sediments. We show that there is an exponential relationship between sample
mass and the resulting analytical uncertainty (Fig. 1). We use the
relationship shown in Fig. 1a to define the age uncertainty of our simulated
ages; however it is important to note that this relationship is only valid
for samples with a similar age to the samples in this study (approx. 2000–7000 cal BP). Older samples will yield greater age uncertainty for
the same mass of C due to fewer ^{14}C isotopes (Gottschalk et al., 2018). The
measurement uncertainty in F^{14}C units is not affected by age (Fig. 1b).
The exact parameters of these relationships will also depend on laboratory
conditions; however, the general shape of the relationship is valid. These
data can inform researchers about the expected range of uncertainty for
^{14}C ages from samples of a given size. We find that samples larger than
40 µg C yield ages that are precise enough to be useful for dating
Holocene lake sediments in most applications, and even smaller samples can
provide useful ages if no other material is available.

It is well documented that ^{14}C ages can be susceptible to sources of
error that are not included within the analytical uncertainty of the
measurements. Such errors can be due to lab contamination, sample material
which is subject to reservoir effects (i.e., bulk sediments or aquatic
organic matter; Groot
et al., 2014; MacDonald et al., 1991; Tornqvist et al., 1992), or depositional lags (terrestrial organic material, which is older than the
sediments surrounding it; Bonk
et al., 2015a; Howarth et al., 2013; Krawiec et al., 2013). Errors related to
reservoir effects can be avoided by selecting only terrestrial plant
material for dating (Oswald et al., 2005). Floating or shoreline vegetation
should also be avoided as these plants may uptake CO_{2} released by lake
degassing (Hatté and Jull, 2015). Dating
fragile material such as leaves (as opposed to wood) may reduce the chances
of dating reworked material with a depositional lag, but generally this
source of error is challenging to predict and depends on the characteristics
of each lake's depositional system. To identify ages affected by
depositional lags, it is necessary to compare with other age information.
Consequently, the identification of outlying ages is facilitated by
increased dating density.

In our dataset, multiple ^{14}C measurements were performed on material
taken from a single layer, which enables outlier detection. We find that the
scatter of ^{14}C ages obtained from the same depths is generally
consistent with what would be expected based on the analytical uncertainties
of the ages. There are no clear outliers in the data; every single ^{14}C
age has a calibrated 95 % CI that overlaps with the median of our best-age
estimate OxCal V sequence (and this result is confirmed by alternative
methods of linking the varve count to ^{14}C ages). This agreement between
the varve count and the ^{14}C ages is evidence that no age in this
dataset is incongruent with the other available chronological information
(other ^{14}C ages and varve counts). This notion is further demonstrated
by the fact that 10 of 11 sampled levels from which we obtained three or
more ages returned an MSWD within the 95 % confidence threshold for
testing age scatter (see Sect. 3.1; Reiners et
al., 2017). This test is typically used for repeated measurements on the
same sample material; however, in our study, many of the measurements from
within a single sediment slice are from material that has different true
ages. The MSWD test indicates that the variability in ages among samples
from within a single sediment slice can reasonably be expected given the
analytical uncertainty. However, in this study, no more than five samples
were measured per depth, and thus the range of acceptable values for the
MSWD is relatively wide due to the small number of degrees of freedom.
Additionally, the analytical uncertainties are relatively large for the
gas-source samples, allowing for wide scatter in the data without exceeding
the MSWD critical value. Despite these caveats, the consistency between the
variability among ages from one level and the analytical uncertainties
allows us to make two important conclusions. (1) The analytical precision
estimates are reasonable, even for miniature gas-source samples. (2) When
material is carefully selected and taxonomically identified for dating, the
sources of error that are not considered in the analytical uncertainty (e.g., contamination or depositional lags) are relatively minor in our case study.
However, this second conclusion is highly dependent on the sediment
transport and depositional processes, which are site specific. Depositional
lags still likely have some impact on our chronology. Six ^{14}C ages from
plant material collected from the Lake Żabińskie catchment in 2015
yielded a range of ages from 1978 to 2014 CE (Bonk et al., 2015a) suggesting
that the assumption that ^{14}C ages represent the age of the sediments
surrounding macrofossils is often invalid. The scale of these age offsets is
likely on the scale of a few decades for Lake Żabińskie sediments,
which is inconsequential for many radiocarbon-based chronologies but is the
same order of magnitude as the uncertainty of our best-age estimate from the
OxCal V sequence and should be considered when reporting or interpreting
radiocarbon-based age determinations with very high precision.

The lack of outliers in our dataset is an apparent contrast with the
findings of Bonk et al. (2015)a, who report that 17 of 32 radiocarbon samples
taken from the uppermost 1000 years of the Lake Żabińskie core were
outliers. The outlying ages were older than expected based on the varve
chronology, and this offset was attributed to reworking of terrestrial plant
material. The identification of outliers did not take into account
uncertainties of the radiocarbon calibration curve and varve counts, which
could explain some of the differences between the ^{14}C and the varve
ages. Still, 8 of 32 ages reported by Bonk et al. (2015a) have calibrated
2*σ* age ranges that do not overlap with varve count age (including
the varve count uncertainty). The higher outlier frequency in the Bonk et
al. (2015a) data might be explained by their generally more precise ages and
the fact that their varve count is truly independent of the ^{14}C ages.

Additionally, our dataset allows us to compare the results of ^{14}C ages
obtained from different types of macrofossil materials, which we grouped
into the following categories: leaves (including associated twigs), needles,
seeds, periderm, woody scales, and samples containing mixed material types
(Fig. 3). When comparing the calibrated median age of each sample to the
median of our best-age estimate, we find that the difference between the age
offsets of the different material types is not significant at the *α*=0.05 level (ANOVA, *F*=2.127, *p*=0.08). This is likely due to our
selective screening of sample material, which only includes terrestrial
plant material while avoiding aquatic insect remains or possible aquatic
plant material, as well as the relatively small number of samples within
each material type. There does appear to be a tendency for seeds to produce
younger ages, and two of the three woody scale samples yielded ages that are
approximately 300 years older than the best-age estimate. This could be due
to the superior durability of woody materials compared with other
macrofossil materials, which enables wood to be stored on the landscape
prior to being deposited in the lake sediments. A larger number of samples
would allow for more robust conclusions about the likelihood of certain
material types to produce biased ages.

## 4.2 The OxCal V-sequence best-age estimate

In this study we have tested multiple approaches to assigning absolute ages
from ^{14}C ages to a floating varve count (Fig. 4). Using a single
tie point relies on a potentially arbitrary selection of tie-point location
and yields large uncertainty intervals when considering both the varve count
uncertainty and the uncertainty of calibrated ages. Using least-squares
minimization of the offset between all radiocarbon ages and the varve count
has the advantage of using all the ^{14}C ages rather than one tie point; however this approach does not consider varve count uncertainties and does
not directly yield an estimate of uncertainty derived from the radiocarbon
age uncertainties. The OxCal V sequence is unique in that all age
information is integrated into a statistical framework including the
probability functions of ^{14}C ages and the uncertainty associated with
the varve count as well. In contrast to the other two approaches, the
V sequence can change the total number of years in the sequence compared to
the original varve count. However, the addition of 37 years in the
V sequence is well within the uncertainty of the varve count ($+\mathrm{155}/-\mathrm{176}$).
The V-sequence approach is expected to provide more precise and more
reliable age estimates than either varve counting or radiocarbon-based age
models alone. The resulting age–depth relation has a relatively narrow CI
(mean 95 % CI is 86 year). Extremely precise age estimates were also
produced using this method for Moossee, Switzerland by Rey et al. (2019). A
combination of varve counts and ^{14}C ages from the Moossee sediments
generated a V-sequence output with a mean 95 % CI of 38 years. The higher
precision in the Moossee study compared to our V-sequence output is
primarily attributed to the higher dating density in Moossee with 27
radiocarbon ages over ∼3000 years (3.9–7.1 ka) versus our
study, which used 48 ages but from only 14 unique depths, over
∼4700 years. This comparison shows that repeated measurements
from the same depth are less useful than analyses from additional depths.
This approach to integrating varve counts and ^{14}C ages could
potentially be improved by a better integration of varve count uncertainties
into the OxCal program. Currently the uncertainties on age gaps in OxCal
are assumed to be normally distributed and cannot be less than 5 years.
Nevertheless, the result of the OxCal V sequence is an age–depth model that
is much more precise than those constructed only using ^{14}C ages and
provides a useful reference to compare with the ^{14}C ages. It is
important to note that the best-age estimate is not independent of the
^{14}C ages; it is directly informed by the ^{14}C ages.

## 4.3 Age–depth model simulations

The simulated age–depth modeling experiment allows us to assess the effects of dating density and sample mass (expected precision) on the outputs of age–depth models constructed for the section of interest in the Lake Żabińskie sediment core. Models based on relatively few but very precise ages, are tightly constrained at the sample depths, but the CI widens further away from these depths (Fig. 5, File S3). In contrast, models based on a greater sampling density produce confidence intervals with relatively constant width. If models are built using a high density of imprecise ages, the CI of the model output can actually be narrower than the CI of the individual ages. Bayesian age–depth models in particular can take advantage of the stratigraphic order of samples to constrain age–depth models to be more precise than the individual ages that make up the model (Blaauw et al., 2018); however, this is only achievable when dating density is high enough. The results from this experiment suggest that, in the case of the Lake Żabińskie sequence, doubling the number of ages can approximately compensate for an increased analytical uncertainty of 50 years.

The choice of OxCal to produce age–depth models from these hypothetical sampling scenarios may have some influence on the results; however we expect that the key findings are replicable for any Bayesian age–depth model routine (i.e., Bacon or Bchron; Blaauw and Christen, 2011; Haslett and Parnell, 2008). To demonstrate this, we used Bacon (Blaauw and Christen, 2011, 2018) to generate age–depth models for one iteration of the simulated sampling scenarios and compared the results to those generated by OxCal. We find that the Bacon-generated models are highly similar to the OxCal models, and the patterns observed in terms of model precision and accuracy are reasonably similar to those obtained from Oxcal models. The Bacon results can be found in File S4.

The Chron Score results provide a succinct summary of the reliability of the
chronologies produced in the different simulated sampling scenarios and is
independent of model selection. The Chron Score becomes more sensitive to
changes in precision as precision increases, so the difference in the Chron
Scores between the 500 and 90 µg scenarios (1*σ*
uncertainty of ±39 and 92 years, respectively) is greater than the
difference between the 90 and 35 µg scenarios (1*σ*
uncertainty of ±92 and 148 years, respectively). Increased dating
density consistently improves the Chron Score results, with a stronger
impact seen when shifting from 5 to 10 ages compared to shifting from 10 to
20 ages. The improvement of the Chron Score due to increased dating density
is generally consistent for each of the different sample mass scenarios.
This differs from the age–depth model statistics where increased dating
density has a greater impact on precision in the larger sample mass
scenarios (more precise ages). The opposite effect is seen in the mean
absolute deviation results, where mean absolute deviation is reduced
substantially as dating density increases for the smaller sample scenarios
and not at all for the 500 µg scenario. For all measures of chronologic
performance, we find a greater improvement when increasing the number of
ages from 5 to 10 ages compared to increasing from 10 to 20 ages, suggesting
there are some diminishing returns from increased dating density. This
result is in accordance with the results of Blaauw et al. (2018). While the
Chron Score results are dependent on the parameters chosen for the
calculation, they intuitively make sense. Because Chron Score results use
only the simulated ^{14}C ages as input and are unaffected by the age
modeling routine, the patterns exhibited in the scores may be more
applicable to a variety of sedimentary records.

In real-world applications, there are additional advantages from increasing dating density. Many lacustrine sequences have greater variability in sedimentation rates than the sequence modeled here. More fluctuations in sedimentation rate require a greater number of ages to delineate the changes in sedimentation. Additionally, outlying ages and age scatter beyond analytical uncertainty are not considered in this modeling experiment. In most cases, detecting outlying ages becomes easier as dating density increases. Because this experiment is only applied to a single sedimentary sequence, the results may not be directly applicable for other sedimentary records with different depositional conditions. In the future, this type of age model simulation could be applied to a range of sedimentary sequences with a variety of depositional conditions.

## 4.4 Recommendations for radiocarbon sampling strategy

Radiocarbon sampling strategies will always be highly dependent on
project-specific considerations such as how the chronology will affect the
scientific goals of the project, budget and labor constraints, the nature of
the sedimentary record in question, and the availability of suitable
materials. A goal of this study is to provide data that can inform sampling
strategies for building robust chronologies, particularly in cases where
suitable material may be limited. Firstly, an iterative approach to ^{14}C
measurements is preferred. An initial batch of measurements should target a
low dating density of perhaps one date per 2000 years. Subsequent samples
should aim to fill in gaps where age uncertainty remains highest (Blaauw et al., 2018) or where preliminary
age–depth trends appear to be non-linear. In accordance with many previous
studies (e.g.,
Howarth et al., 2013; Oswald et al., 2005), we advocate for careful
selection of material identified as terrestrial in origin. If the mass of
such material is limited, the MICADAS gas source is useful for dating
miniature samples, and we are convinced that miniature samples of
terrestrial material are preferable to dating questionable material or bulk
sediments. Samples as small as a few micrograms of C can be measured using the
MICADAS, though samples larger than 40 µg C are recommended for more
precise results (mid to late Holocene samples containing 40 µg C are
expected to have an analytical uncertainty of ∼138 years).
Dating small amounts of material from single depths is also preferable to
pooling material from depth segments that may represent long time intervals.
A general rule of thumb is to avoid taking samples with depth intervals
representing more time than the expected uncertainty of a ^{14}C age. To
improve the accuracy of age–depth models, a higher priority should be placed
on achieving a sufficiently high dating density (ideally greater than one age
per 500 years; Blaauw et al., 2018) using narrow sample–depth intervals. In
most cases, this goal should be prioritized over the goal of gathering
larger sample masses in order to reduce analytical uncertainties. The
results of this study and others (e.g., Blaauw et al., 2018;
Trachsel and Telford, 2017) clearly indicate that increased sampling density
improves the accuracy, precision, and reliability of age–depth models.

Multiple measurements from within a single stratigraphic depth, as we have done in this study, can be useful in sediments where age scatter (possibly from reworked material) is expected. In such cases, multiple measurements from a single depth could allow for the identification of certain types of material that should be avoided. If age scatter is not expected, single measures of pooled macrofossils are more cost-effective than repeat measurements from a single depth.

Although increased dating density does incur greater cost, gas-source ages
have lower costs compared to graphitized ages allowing for greater dating
density at a similar cost. Injecting CO_{2} into the AMS rather than
generating graphite and packing a target substantially reduces the effort to
analyze a sample following pre-treatment and additionally reduces some
chance of contamination during graphitization. These advantages are partly
offset by additional operator attention required during gas-source
measurements. How these differences translate to per-sample costs depends on
the pricing structures implemented in each lab. Cost estimates from two
MICADAS labs at the University of Bern and Northern Arizona University range
between approximately 15 % and 33 % lower costs for gas-source measurements
compared to graphitized samples. The use of smaller samples can also reduce the
labor time required to isolate suitable material from the sediment; however,
handling and cleaning miniature samples can add additional challenges, which
increases labor time.

AMS ^{14}C analysis of Holocene terrestrial plant macrofossils using the
MICADAS gas-ion source produces unbiased ages with similar precision
compared to graphitized samples that contain a similar mass of carbon
(approximately 120–160 µg C).

The precision of a ^{14}C age can be approximately estimated based on the
amount of carbon within a sample. Holocene samples containing greater than
40 µg C produce ^{14}C measurements with analytical uncertainty
expected to be less than ±0.01 F^{14}C (150 years for samples than
are approximately 4000 years old). Uncertainty increases exponentially as
samples get smaller, so 10 µg C samples are expected to have an uncertainty
of ±0.021 F^{14}C (277 years).

The variability among ages obtained from 1 or 2 cm thick samples in the Lake Żabińskie sediment core is compatible with the variability expected due to analytical uncertainty alone.

We find no clear evidence in our dataset for age bias based on the type of macrofossil material dated, which we limited to terrestrial plant material.

Judging from the output of age–depth models, the lower precision of
miniature gas-source ages can be compensated for by increasing sampling
density. Based on sets of simulated ^{14}C ages that mimic the ^{14}C
ages of our study core, together with age–depth models generated using
OxCal, doubling dating density roughly compensates for a decrease in
analytical precision of 50 years.

The effect of ^{14}C age precision is among several factors that influence
chronological precision. The thickness of the depth interval used to obtain
samples, the ability to select identifiable terrestrial materials or to
analyze more than one type of material, the reliability of detecting age
outliers, and the amount of variability in sedimentation rate all determine
the accuracy and precision of an age–depth model, which are both improved by
increasing the number of ages.

This study can inform sampling strategies and provide expectations about radiocarbon-based age–depth model outcomes.

The key datasets associated with this paper (varve count results and the best-age estimate OxCal V-sequence output) are available at the Bern Open Repository and Information System: https://doi.org/10.7892/boris.134606 (Zander et al., 2019).

Supplementary File S1: Core images and location of ^{14}C ages.
Supplementary File S2: Microscope images of macrofossils used for ^{14}C
dating.
Supplementary File S3: Animation of OxCal P-sequence age–depth models for all
30 iterations of simulated sampling scenarios (animated version of Fig. 4).
Supplementary File S4: Comparison of Bacon and OxCal simulated
age–depth models. The supplement related to this article is available online at: https://doi.org/10.5194/gchron-2-63-2020-supplement.

PDZ prepared samples, designed and performed the age modeling experiment,
analyzed results, and prepared the paper with contributions from all
authors. MG, DSK, SS, and PDZ designed the strategy and goals of the study.
MZ, AIP-G, and PDZ performed varve counting. PB-K identified and selected
suitable macrofossils. SS oversaw ^{14}C analyses. DSK assisted with
laboratory work.

The authors declare that they have no conflict of interest.

Core materials were supplied by Wojciech Tylmann, University of Gdańsk.
Edith Vogel and Gary Salazar assisted with ^{14}C sample measurements.

This research has been supported by the Polish National Science Centre (grant no. 2014/13/B/ST10/01311) and the Swiss National Science Foundation (grant nos. 200021_172586 and IZSEZO-180887).

This paper was edited by Christine Hatté and reviewed by one anonymous referee.

Barnekow, L., Possnert, G., and Sandgren, P.: AMS ^{14}C chronologies of Holocene lake sediments in the Abisko area, northern Sweden – a comparison between dated bulk sediment and macrofossil samples, GFF, 120, 59–67, https://doi.org/10.1080/11035899801201059, 1998.

Blaauw, M. and Christen, J. A.: Flexible paleoclimate age-depth models using an autoregressive gamma process, Bayesian Anal., 6, 457–474, https://doi.org/10.1214/11-BA618, 2011.

Blaauw, M. and Christen, J. A.: rbacon: Age-Depth Modelling using Bayesian Statistics, R package version 2.3.4, available at: https://CRAN.R-project.org/package=rbacon (last access: 23 March 2020), 1–14, 2018.

Blaauw, M., Christen, J. A., Bennett, K. D., and Reimer, P. J.: Double the dates and go for Bayes – Impacts of model choice, dating density and quality on chronologies, Quaternary Sci. Rev., 188, 58–66, https://doi.org/10.1016/j.quascirev.2018.03.032, 2018.

Bonk, A., Tylmann, W., Goslar, T., Wacnik, A., and Grosjean, M.: Comparing
varve counting and ^{14}C-Ams chronologies in the sediments of Lake
Żabińskie, Northeastern Poland: Implications for accurate ^{14}C
dating of lake sediments, Geochronometria, 42, 157–171,
https://doi.org/10.1515/geochr-2015-0019, 2015a.

Bonk, A., Tylmann, W., Amann, B., Enters, D., and Grosjean, M.: Modern limnology and varve-formation processes in lake Żabińskie, northeastern Poland: Comprehensive process studies as a key to understand the sediment record, J. Limnol., 74, 358–370, https://doi.org/10.4081/jlimnol.2014.1117, 2015b.

Bronk Ramsey, C.: Deposition models for chronological records, Quaternary Sci. Rev., 27, 42–60, https://doi.org/10.1016/j.quascirev.2007.01.019, 2008.

Bronk Ramsey, C.: Bayesian Analysis of Radiocarbon Dates, Radiocarbon, 51, 337–360, https://doi.org/10.1017/s0033822200033865, 2009.

Bronk Ramsey, C. and Lee, S.: Recent and Planned Developments of the Program OxCal, Radiocarbon, 55, 720–730, https://doi.org/10.1017/s0033822200057878, 2013.

Butz, C., Grosjean, M., Fischer, D., Wunderle, S., Tylmann, W., and Rein, B.: Hyperspectral imaging spectroscopy: a promising method for the biogeochemical analysis of lake sediments, J. Appl. Remote Sens., 9, 096031, https://doi.org/10.1117/1.jrs.9.096031, 2015.

Delqué-Količ, E., Comby-Zerbino, C., Ferkane, S., Moreau, C., Dumoulin, J. P., Caffy, I., Souprayen, C., Quilès, A., Bavay, D., Hain, S., and Setti, V.: Preparing and measuring ultra-small radiocarbon samples with the ARTEMIS AMS facility in Saclay, France, Nucl. Instruments Methods Phys. Res. Sect. B, 294, 189–193, 2013.

Freeman, E., Skinner, L. C., Reimer, R., Scrivner, A., and Fallon, S.: Graphitization of small carbonate samples for paleoceanographic research at the godwin radiocarbon laboratory, University of Cambridge, Radiocarbon, 58, 89–97, https://doi.org/10.1017/RDC.2015.8, 2016.

Gottschalk, J., Szidat, S., Michel, E., Mazaud, A., Salazar, G., Battaglia, M., Lippold, J., and Jaccard, S. L.: Radiocarbon Measurements of Small-Size Foraminiferal Samples with the Mini Carbon Dating System (MICADAS) at the University of Bern: Implications for Paleoclimate Reconstructions, Radiocarbon, 60, 469–491, https://doi.org/10.1017/RDC.2018.3, 2018.

Grimm, E. C., Maher, L. J., and Nelson, D. M.: The magnitude of error in conventional bulk-sediment radiocarbon dates from central North America, Quaternary Res., 72, 301–308, https://doi.org/10.1016/j.yqres.2009.05.006, 2009.

Groot, M. H. M., van der Plicht, J., Hooghiemstra, H., Lourens, L. J., and Rowe, H. D.: Age modelling for Pleistocene lake sediments: A comparison of methods from the Andean Fúquene Basin (Colombia) case study, Quat. Geochronol., 22, 144–154, https://doi.org/10.1016/j.quageo.2014.01.002, 2014.

Hajdas, I., Bonani, G., and Goslar, T.: Radiocarbon dating the Holocene in the Gosciaz Lake floating varve chronology, Radiocarbon, 37, 71–74, https://doi.org/10.1017/S0033822200014806, 1995.

Haslett, J. and Parnell, A.: A simple monotone process with application to radiocarbon-dated depth chronologies, J. Roy. Stat. Soc. Ser. C, 57, 399–418, https://doi.org/10.1111/j.1467-9876.2008.00623.x, 2008.

Hatté, C. and Jull, A. J. T.: ^{14}C in Plant Macrofossils, in:
Encyclopedia of Scientific Dating Methods, edited by: Rink, J. W. and
Thompson, J. W., 1–79, Springer Science and Business Media, Dordrecht, 2015.

Howarth, J. D., Fitzsimons, S. J., Jacobsen, G. E., Vandergoes, M. J., and Norris, R. J.: Identifying a reliable target fraction for radiocarbon dating sedimentary records from lakes, Quat. Geochronol., 17, 68–80, https://doi.org/10.1016/j.quageo.2013.02.001, 2013.

Krawiec, A. C. L., Kaufman, D. S., and Vaillencourt, D. A.: Age models and tephrostratigraphy from two lakes on Adak Island, Alaska, Quat. Geochronol., 18, 41–53, https://doi.org/10.1016/j.quageo.2013.07.002, 2013.

Larsson, L.: COORECORDER v2. 3.13: Image Co-ordinate Recording Program, Cybis Elektronik & Data AB, Saltsjöbaden, Sweden, 2003.

MacDonald, G. M., Beukens, R. P., and Kieser, W. E.: Radiocarbon Dating of Limnic Sediments: A Comparative Analysis and Discussion, Ecology, 72, 1150–1155, https://doi.org/10.2307/1940612, 1991.

Oswald, W. W., Anderson, P. M., Brown, T. A., Brubaker, L. B., Feng, S. H., Lozhkin, A. V., Tinner, W., and Kaltenrieder, P.: Effects of sample mass and macrofossil type on radiocarbon dating of arctic and boreal lake sediments, Holocene, 15, 758–767, https://doi.org/10.1191/0959683605hl849rr, 2005.

Reimer, P. J., Bard, E., Bayliss, A., Beck, J. W., Blackwell, P. G., Ramsey, C. B., Buck, C. E., Cheng, H., Edwards, R. L., Friedrich, M., Grootes, P. M., Guilderson, T. P., Haflidason, H., Hajdas, I., Hatté, C., Heaton, T. J., Hoffmann, D. L., Hogg, A. G., Hughen, K. A., Kaiser, K. F., Kromer, B., Manning, S. W., Niu, M., Reimer, R. W., Richards, D. A., Scott, E. M., Southon, J. R., Staff, R. A., Turney, C. S. M., and van der Plicht, J.: IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP, Radiocarbon, 55, 1869–1887, https://doi.org/10.2458/azu_js_rc.55.16947, 2013.

Reiners, P. W., Carlson, R. W., Renne, P. R., Cooper, K. M., Granger, D. E., McLean, N. M., and Schoene, B.: Geochronology and thermochronology, Wiley Blackwell, Hoboken, NJ, USA, p. 480, 2017.

Rey, F., Gobet, E., Szidat, S., Lotter, A. F., Gilli, A., Hafner, A., and Tinner, W.: Radiocarbon wiggle matching on laminated sediments delivers high-precision chronologies, Radiocarbon, 61, 265–285, https://doi.org/10.1017/RDC.2018.47, 2019.

Ruff, M., Wacker, L., Gäggeler, H. W., Suter, M., Synal, H. A., and Szidat, S.: A gas ion source for radiocarbon measurements at 200 kv, Radiocarbon, 49, 307–314, https://doi.org/10.1017/S0033822200042235, 2007.

Ruff, M., Szidat, S., Gäggeler, H. W., Suter, M., Synal, H. A., and Wacker, L.: Gaseous radiocarbon measurements of small samples, Nucl. Instruments Methods Phys. Res. Sect. B, 268, 790–794, https://doi.org/10.1016/j.nimb.2009.10.032, 2010a.

Ruff, M., Fahrni, S., Gäggeler, H. W., Hajdas, I., Suter, M., Synal, H. A., Szidat, S., and Wacker, L.: On-line radiocarbon measurements of small samples using elemental analyzer and MICADAS gas ion source, Radiocarbon, 52, 1645–1656, https://doi.org/10.1017/S003382220005637X, 2010b.

Salazar, G., Zhang, Y. L., Agrios, K., and Szidat, S.: Development of a method for fast and automatic radiocarbon measurement of aerosol samples by online coupling of an elemental analyzer with a MICADAS AMS, Nucl. Instruments Methods Phys. Res. Sect. B, 361, 163–167, https://doi.org/10.1016/j.nimb.2015.03.051, 2015.

Santos, G. M., Southon, J. R., Griffin, S., Beaupre, S. R., and Druffel, E.
R. M.: Ultra small-mass AMS ^{14}C sample preparation and analyses at
KCCAMS/UCI Facility, Nucl. Instruments Methods Phys. Res. Sect. B, 259, 293–302, https://doi.org/10.1016/j.nimb.2007.01.172, 2007.

Shah Walter, S. R., Gagnon, A. R., Roberts, M. L., McNichol, A. P., Gaylord,
M. C. L., and Klein, E.: Ultra-Small Graphitization Reactors for
Ultra-Microscale ^{14}C Analysis at the National Ocean Sciences
Accelerator Mass Spectrometry (NOSAMS) Facility, Radiocarbon, 57,
109–122, https://doi.org/10.2458/azu_rc.57.18118, 2015.

Sundqvist, H. S., Kaufman, D. S., McKay, N. P., Balascio, N. L., Briner, J. P., Cwynar, L. C., Sejrup, H. P., Seppä, H., Subetto, D. A., Andrews, J. T., Axford, Y., Bakke, J., Birks, H. J. B., Brooks, S. J., de Vernal, A., Jennings, A. E., Ljungqvist, F. C., Rühland, K. M., Saenger, C., Smol, J. P., and Viau, A. E.: Arctic Holocene proxy climate database – new approaches to assessing geochronological accuracy and encoding climate variables, Clim. Past, 10, 1605–1631, https://doi.org/10.5194/cp-10-1605-2014, 2014.

Synal, H. A., Stocker, M., and Suter, M.: MICADAS: A new compact radiocarbon AMS system, Nucl. Instruments Methods Phys. Res. Sect. B, 259, 7–13, https://doi.org/10.1016/j.nimb.2007.01.138, 2007.

Szidat, S., Salazar, G. A., Vogel, E., Battaglia, M., Wacker, L., Synal,
H.-A., and Türler, A.: ^{14}C analysis and sample preparation at the
new Bern Laboratory for the Analysis of Radiocarbon with AMS (LARA),
Radiocarbon, 56, 561–566, https://doi.org/10.2458/56.17457, 2014.

Szumański, A.: Objaśnienia do Szczegółowej Mapy Geologicznej Polski, Arkusz Giżycko, (Explanation to the Detailed Geological Map of Poland, Sheet Gizycko (104)), Polish Geological Institute, Warsaw, Poland, 2000.

Tornqvist, T. E., De Jong, A. F. M., Oosterbaan, W. A., and Van Der Borg, K.:
Accurate dating of organic deposits by AMS ^{14}C measurement of
macrofossils, Radiocarbon, 34, 566–577, https://doi.org/10.1017/S0033822200063840,
1992.

Trachsel, M. and Telford, R. J.: All age–depth models are wrong, but are getting better, Holocene, 27, 860–869, https://doi.org/10.1177/0959683616675939, 2017.

Tylmann, W., Bonk, A., Goslar, T., Wulf, S., and Grosjean, M.: Calibrating
^{210}Pb dating results with varve chronology and independent
chronostratigraphic markers: Problems and implications, Quat. Geochronol.,
32, 1–10, https://doi.org/10.1016/j.quageo.2015.11.004, 2016.

Wacker, L., Christl, M., and Synal, H. A.: Bats: A new tool for AMS data reduction, Nucl. Instruments Methods Phys. Res. Sect. B, 268, 976–979, https://doi.org/10.1016/j.nimb.2009.10.078, 2010a.

Wacker, L., Bonani, G., Friedrich, M., Hajdas, I., Kromer, B., Němec, M., Ruff, M., Suter, M., Synal, H. A., and Vockenhuber, C.: MICADAS: Routine and high-precision radiocarbon dating, Radiocarbon, 52, 252–262, https://doi.org/10.1017/S0033822200045288, 2010b.

Wacker, L., Fahrni, S. M., Hajdas, I., Molnar, M., Synal, H. A., Szidat, S., and Zhang, Y. L.: A versatile gas interface for routine radiocarbon analysis with a gas ion source, Nucl. Instruments Methods Phys. Res. Sect. B, 294, 315–319, 2013.

Wacnik, A.: From foraging to farming in the Great Mazurian Lake District: Palynological studies on Lake Miłkowskie sediments, northeast Poland, Veg. Hist. Archaeobot., 18, 187–203, https://doi.org/10.1007/s00334-008-0196-0, 2009.

Wacnik, A., Tylmann, W., Bonk, A., Goslar, T., Enters, D., Meyer-Jacob, C., and Grosjean, M.: Determining the responses of vegetation to natural processes and human impacts in north-eastern Poland during the last millennium: combined pollen, geochemical and historical data, Veg. Hist. Archaeobot., 25, 479–498, https://doi.org/10.1007/s00334-016-0565-z, 2016.

Wetzel, R. G., Likens, G. E., Wetzel, R. G., and Likens, G. E.: Lake Basin Characteristics and Morphometry, in: Limnological Analyses, 1–14, Springer, New York, 1991.

Zander, P. D., Szidat, S., Grosjean, M., Kaufmann, D. S., Boltshauser-Kaltenrieder, P., Żarczyński, M., and Poraj-Górska, A.: Data tables – Lake Zabinskie Geochronology, BORIS, https://doi.org/10.7892/boris.134606, 2019.

Żarczyński, M., Tylmann, W., and Goslar, T.: Multiple varve chronologies for the last 2000 years from the sediments of Lake Żabińskie (northeastern Poland) – Comparison of strategies for varve counting and uncertainty estimations, Quat. Geochronol., 47, 107–119, https://doi.org/10.1016/j.quageo.2018.06.001, 2018.

Żarczyński, M., Wacnik, A., and Tylmann, W.: Tracing lake mixing and oxygenation regime using the Fe/Mn ratio in varved sediments: 2000 year-long record of human-induced changes from Lake Żabińskie (NE Poland), Sci. Total Environ., 657, 585–596, https://doi.org/10.1016/j.scitotenv.2018.12.078, 2019.