Late Holocene cryptotephra and a provisional 15,000-year Bayesian age model for Cascade Lake, Alaska

. Multiple chronometers can be employed for dating Holocene palaeoenvironmental records, each with its own inherent strengths and weaknesses. 10 Radiocarbon dating is one of the most widely used techniques for producing chronologies, but its application at high-latitude sites can sometimes be problematic. Here, cryptotephra identified in a core from Cascade Lake, Arctic Alaska, highlight and help to resolve an old bias in Late Holocene radiocarbon dates in the top 1.42 m of the sediment sequence. Identifiable geochemical populations of cryptotephra are shown to be present in detectable 15 concentrations in sediment from the north flank of the Brooks Range for the first time. Major element glass geochemical correlations are demonstrated between ultra-distal cryptotephra and reference samples from the Late Holocene caldera forming eruption of Opala, Kamchatka, as well as three eruptions in North America: the White River Ash (northern lobe), Ruppert tephra and the Late Holocene caldera forming eruption of Aniakchak. The 20 correlated ages of these cryptotephra provide evidence for an old-carbon effect and support preliminary PSV ages reported for Cascade Lake. Chronological data from Cascade Lake were then combined using a Bayesian approach to generate an age-depth model that extends back through the Late Holocene, and provisionally to 15,000 cal yr BP.


Introduction
The accuracy and precision of ages and chronological models produced from sedimentary records directly impacts the utility and value of the associated proxies used for palaeoenvironmental reconstructions.In Arctic North America, the majority of Holocene to late Pleistocene palaeoenvironmental reconstructions are produced from lake and peat deposits (e.g.Kaufman et al., 2016), and often rely on radiocarbon ( 14 C) dating to develop age models.
However, there are several issues that can affect the application and interpretation of 14 C ages in Arctic regions.Firstly, there may be a lack of organic material in lake sediment cores, or the terrestrial macrofossils that are often preferred for dating (e.g.Oswald et al., 2005;Turney et al., 2000) may be absent.This can be a particular problem for sediments that accumulated during colder periods.Secondly, high-latitude regions often have an abundance of old carbon due to slow rates of decomposition in cold, typically nutrient poor soils (e.g.Gaglioti et al., 2014;Schuur et al., 2008), erosion from the surrounding sediments or bedrock, and the reworking and redeposition of older, well-preserved macrofossils (e.g.Kennedy et al., 2010).
More broadly, 14 C samples can also be affected by issues relating to sample selection, remobilisation, the hard-water effect and contamination (for a general review of these topics see Olsson, 1974;Lowe and Walker, 2000).These factors can contribute to complicated age models for Arctic sediments that require careful independent verification.For example, the use of bulk sediments for dating has been shown to incorporate organic fractions of varying ages (e.g.Brock et al., 2011;Nelson et al., 1988) and hard-water effects have long been known in North American lakes (e.g.Abbott and Stafford, 1996;Karrow and Anderson, 1975;Moore et al., 1998).It is important to recognise that not all 14 C ages are affected by these issues, but at Arctic sites their accuracy and reliability cannot be assumed.Additional validation and reassurance provided, for example, by published details of the dated material and the stratigraphic sequences they were extracted from, overlapping independent chronological data, replicate dates, etc, is therefore valuable when attributing confidence to resultant age models.
The combination of multiple chronometers has been successfully used to highlight differences between chronological methods and produce more accurate final age models for lacustrine and peat cores (Davies et al., 2018;Tylmann et al., 2016).Two additional techniques that have been applied in Arctic areas are discussed here -palaeomagnetic secular variation (PSV) and tephrochronology.

Palaeomagnetic chronologies
In recent years there have been an increasing number of studies looking to improve chronologies of late Quaternary Arctic sedimentary sequences by using palaeomagnetic data (e.g.Barletta et al., 2008;Deschamps et al., 2018;Lund et al., 2016;Ólafsdóttir et al., 2013).
Sediment records can be sensitive to palaeomagnetic secular variation (PSV) -small directional changes in the geomagnetic field (Cox, 1970) that are preserved in sediment through the alignment of magnetic mineral grains with Earth's ambient field around the time of deposition.Tie-points, identified using peaks and troughs, can then be dated and used as correlative chronostratigraphic tools.These ages can be produced from both individual site measurements and geomagnetic model predictions.PSV correlation techniques are useful as they can produce more frequent data points and be applied beyond the limits of 14 C dating, or Deleted: , e.g.

Deleted: resulting
Deleted: Sediments at high-latitude sites Deleted: calculations 85 where organic material is not preserved.Their use, however, is limited geographically as high-latitude geomagnetic field dynamics are spatially complex (e.g.Stoner et al., 2013).Steen (2016) reports preliminary PSV-correlated ages for cores from Cascade Lake, Alaska, that have substantial offsets during the Late Holocene from 14 C ages from the same sediment.In the upper sections of the core sequence 14 C ages are up to ~2000 years older than palaeomagnetic correlated ages.When using multiple chronometers from the same sediment there is not always coherence or clear agreement between the results, as seen here, and additional chronological information is required to produce a reliable age-model.In this study tephrochronology was applied to Cascade Lake sediments to investigate this chronological offset.

Cryptotephra chronologies
Cryptotephra -non-visible horizons of volcanic ash from distal sources -have been studied globally (see, e.g., Davies, 2015;Lowe et al., 2017) and are a useful chronostratigraphic tool (Pilcher et al., 1995;Plunkett, 2006;Swindles et al., 2010).Where correlations can be made with well-dated tephra (e.g.historical eruptions, or tephra preserved within annually resolved records), tightly constrained associated ages can be included in agedepth models (e.g.Schoning et al., 2005).They can also be used as an independent test of other chronological methods applied to the same record (e.g.Davies et al., 2018;Oldfield et al., 1997).
In Alaska and northern Canada the majority of tephra studies have been limited to areas where visible tephra are present and only a few studies have discussed cryptotephra (de Fontaine et al., 2007;Lakeman et al., 2008;Monteath et al., 2017;Payne et al., 2008;Zoltai, 1989).However, there is significant potential for cryptotephra to be found in Alaska as it is downwind of a large number of volcanoes known to have been active over the Holocene (Fig. 1;Alaska Volcano Observatory, 2016;Global Volcanism Program, 2013).Of Alaska's 130 volcanoes and volcanic fields, 96 have been active either historically or within the Holocene (Miller et al., 1998) and historical observations show that 54 volcanoes have been active since ~ 1700 AD alone (Cameron et al., 2020).Here, key tephra are from historical eruptions, or eruptions that produced regionally widespread tephra within Alaska and have precise age estimates (Davies et al., 2016).
While there are currently no published occurrences of Kamchatkan tephra within Alaska, the large number of Kamchatkan-Kurile volcanoes active in the Holocene can also be considered as a potential source of distal cryptotephra, given prevailing wind directions and the large number of recorded major explosive eruptions (e.g.Braitseva et al., 1997;Kyle et al., 2011;Ponomareva et al., 2017).Transcontinental distribution of tephra from non-super eruptions has been established (e.g.Cook et al., 2018;Jensen et al., 2014), and Kamchatkansourced tephra have been traced to Greenland, Svalbard and the east coast of North America (van der Bilt et al., 2017;Cook et al., 2018;Jensen et al., 2021;Mackay et al., 2016).
Here, ages from Cascade Lake for cryptotephra and radiocarbon techniques were visually compared and then modelled using Bayesian statistical methods to produce a composite age-depth model.Bayesian techniques have been utilised in a wide range of fields to produce detailed age-depth models based on a relatively small number of dates (e.g.Christen et al., 1995;Litton and Buck, 1995) and, through their inclusion of additional (prior) information, they provide more precise interpolations than using raw dates alone (e.g.Blaauw and Christen, 2005;Bronk Ramsey, 2008).

Materials and Methods
Cascade Lake (68°22'48" N, 154°38'00" W; 990 m asl) lies on the north-central slope of the Brooks Range, the northernmost mountain range in Alaska (Fig. 1).Overall, the Brooks Range is located almost entirely above the Arctic Circle and represents a significant topographic barrier that divides the climatic influences of the Arctic and Pacific Oceans.The lake has an area of ~ 1 km 2 and a maximum depth of ~ 40 m in the main northwestern basin (Fig. 1b) with a total catchment size of ~10 km 2 .It presently has no significant inflow and one small outflow, west to Kurupa Lake (~ 920 m asl).In 2013 sediment cores were collected from two sites at Cascade Lake using a percussion-piston coring system (long cores) and Aquatic Instruments universal corer (surface cores).Cores were split and described at the National Lacustrine Core Facility (LacCore) repository at the University of Minnesota, Twin Cities, and archive halves are housed there.The top 1.42 m of a 5.2-m-long composite sedimentary sequence, CASC-4A/2D, is the focus of this study.Analyses were limited to the upper section of the core because a) it covers the range of depths where a potential offset in ages has been reported (Steen, 2016), and b) because most well-defined distal tephra deposits in Alaska are limited to the last ~4 ka (e.g.Davies et al., 2016).
The CASC-4A/2D sediment cores were undeformed by the coring procedure and the full sequence was separated into three distinct lithologic units based on visual stratigraphy, wet bulk density, organic-matter content, and variations in magnetic parameters (Fig. S1).
The new analyses reported here were made from the top 1.42 m of unit 3 (3.55-0m), which consists of irregular millimeter-to centimeter-scale bands of silt and clay.More detailed sediment descriptions are provided by Steen (2016).

Radiometric data
Radiometric data from Cascade Lake (Steen, 2016) are summarised in Table 1.
Eleven AMS 14 C samples analysed at the University of California-Irvine AMS Facility are reported.Samples consisted of terrestrial plant macrofossils, insect parts, resting eggs, and aquatic vegetation as available.The oldest sample analysed was from 348.5-351 cm and dates to ~15 cal ka BP.Six 210 Pb measurements were made from the uppermost sediment at Cascade Lake and equilibrium (~142 yr BP) is reached within the top 4 cm of the sequence.

Cryptotephra detection and analysis
The sampling and analysis of tephra for this study followed best practice guidelines (e.g.Abbott et al., 2021;Wallace et al., n.d.) to facilitate comparability with other research.210 No visible tephra were located in cores from Cascade Lake; in fact, no visible tephra are known north of the Brooks Range.Targeted cryptotephra analyses were undertaken using contiguous 1-cm-thick subsamples from 1.42 m composite depth to the surface.Standard methods (e.g.Blockley et al., 2005) were used to produce glass shard concentration profiles throughout the two core sections.Samples were sieved using 20 micron nylon mesh and the 215 heavy liquid, lithium heteropolytungstate (LST), was used for density separations.
Glass shard morphologies and grain sizes were recorded using optical microscopy and images of the processed samples (i.e.grains that are >20 µm and <2.45 g cm -3 , mounted in Canada Balsam).Shard depths were estimated by recording the number of 3µm fine-focus increments required to focus through individual grains.Other grain size measurements (e.g.220 axis lengths, perimeter, maximum projected area) were calculated using ImageJ software.
Values for maximum axis length are reported, as well as geometric size (dv) and sphericity (ψ) (calculated following the methods reported in Saxby et al., 2020).As only a small number of measurements were made due to low concentrations of glass present in the sample slides (7-15 shards/sample; Table S1), these measurements are not fully representative of 225 their source eruptions.For example, Saxby et al. (2020) recommend that 50-500+ measurements are used to characterise mean and maximum shard sizes, respectively.However, these quantitative characterisations are reported here as preliminary data for distal deposits of these tephra.Deleted: The ages of tie-points from the geometric field models are based on a database of 75 selected sedimentary palaeomagnetic records from the SED12k data compilation (Donadini et al., 2010; 245 used by CALS10k.1b,Korte et al., 2011).The database was further parsed to exclude bulk 14 C samples, archaeomagnetic data with large temporal uncertainties, and palaeomagnetic behaviour incompatible with the majority of records during the Holocene (pfm9k.1b,Nilsson et al., 2014).Both models have reported estimated temporal 250 resolutions of ± 500 a.Burial Lake tie-point ages and errors are derived from the 14 C age model of the sediment cores (Dorfman, 2013), which is based on terrestrial macrofossils and shows remarkably linear sediment accumulation over ~ 17 ka cal BP. ¶ 2.3

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Deleted: Cryptotephra analyses are reported here from the past 4 ka, as a large number of the most well-known, dated, and widely distributed tephra in Alaska were erupted during this time period (Davies et al., 2016).This is also the interval when the 14 C ages in Cascade Lake cores appear to be too old relative to the expected ages

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Glass shards for geochemical analysis were re-extracted from peaks in shard concentration using heavy liquid separation.After rinsing, the remaining sample material was pipetted into a pre-drilled hole in an acrylic puck (fixed onto a flat glass plate with double sided tape) and covered with epoxy resin.Once cured, the flat puck surface was then lightly polished to expose glass surfaces and carbon coated prior to electron probe microanalysis (EPMA).Individual glass shards were analysed on a JEOL 8900 Superprobe at the University of Alberta by wavelength dispersive X-ray spectroscopy (WDS) following established protocols (e.g.Jensen et al., 2008Jensen et al., , 2019)).
A standard suite of ten elements (Si, Ti, Al, Fe, Mn, Mg, Ca, Na, K, Cl; 30 second peak count times; ZAF correction method) was measured using a 5 μm beam with 15 keV accelerating voltage and 6 nA beam current.This focussed beam (usually 10 µm is utilised) can result in Na loss in more sensitive glasses.However, where intensity data loss does occur, it has been shown that empirical corrections can be applied if the data demonstrate linear variance over time (Nielsen and Sigurdsson, 1981).Here Na, and if necessary, Si, were corrected for Time Dependent Intensity (TDI) loss (or gain) using a self-calibrated correction with Probe for EPMA software (Donovan et al., 2015).This method at these settings has been successfully applied in several studies on tephra of different compositions and grainsizes (Foo et al., 2020;Jensen et al., 2019Jensen et al., , 2021)).
Two secondary standards of known composition were run concurrently with all tephra samples: ID 3506, a Lipari rhyolite obsidian, and a reference sample of Old Crow tephra, a well-characterised, secondarily hydrated tephra bed (Kuehn et al., 2011).All results were normalised to 100% and are presented as weight percent (wt%) oxides.New major-element geochemical data and associated standard measurements, as well as data points for relevant reference material (analysed concurrently, where possible), are reported in the Supplementary Information (Tables S2, S3).Non-glass analyses (e.g.minerals, biogenic silica) and analyses with analytical totals <94% were rejected but are available in Table S2.
Correlations to known tephra or volcanic sources were based on major-element geochemistry (including concurrent re-analyses with reference materials where possible), stratigraphic position and consistent glass morphological characteristics.

Bayesian age modelling
Three steps are detailed here for identifying and resolving problematic chronometer offsets using the radiometric data from Steen (2016) and new cryptotephra correlated ages.Deleted: (e.g.Jensen et al., 2019;Foo et al., 2020).

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Both manual approaches and statistical outlier analysis techniques included in OxCal v4.4 (Bronk Ramsey, 2009a, 2009b) are applied in the following order.
Firstly, ages that were obviously out of stratigraphic sequence (previously highlighted by Steen, 2016)  Finally, the remaining chronological data were combined in one composite P_Sequence model (OxCal v4.4;Bronk Ramsey, 2009a).This set-up allows variable accumulation rates; here the k parameter (deposition events defined as increments per unit length, controlling model rigidity and resolution) was set as variable rather than fixed to increase model flexibility (Bronk Ramsey and Lee, 2013).Outliers were judged statistically using OxCal's agreement indices (AI), which show the extent to which the modelled posterior distributions overlap with the original distributions, and general (Student's t) outlier analysis to identify any remaining anomalous ages in the parsed dataset (Bronk Ramsey, 2009b).All ages were given the prior probability of 5% of ages being incorrect; if an age needs to be shifted substantially (by more than two standard deviations) to fit the resulting age-depth model it was identified as an outlier and downweighed in the process (Blockley et al., 2007).

Cryptotephra abundance and geochemical data
Deleted: Steen et al. (this volume) and new cryptotephra correlated 335 ages.Firstly, ages that were obviously out of stratigraphic sequence were rejected previously by Steen et al. (this volume).…Deleted: These were then visually compared to detect offsets between the dating methods.This is more effective than using statistical techniques as a first approach as they can be biased by 340 datasets with high numbers of dates and tight distributions.Here, cryptotephra isochrons were used as independent checks for the other chronological methods, e.g. to identify 14 C outliers.…

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Deleted: (Bronk Ramsey, 2013).General (Student's t) outlier analysis was used to identify any remaining anomalous ages in the parsed dataset.All Glass shards were present in ~75% of the samples analysed in this study (108/143 total samples).The composite shard concentration profile for the 1.42 m of core samples analysed here is shown in Fig. 2. Twenty-eight peaks were chosen for geochemical analysis based on the relative abundances of shards counted at those depths.This generally was around 4-42 shards/gram, except for the top 0-1 cm, which had 88 shards/gram.For each sample, geochemical analyses were performed on single grains, but 15 of the peaks chosen resulted in fewer than five shards exposed on the EPMA puck surface.This is likely due to the relatively low concentrations of glass present overall.
Figure 2: Cascade Lake core CASC-4A/2D ensemble chronological controls.(a) The composite depths of radiometric ages ( 14 C and 210 Pb; Table 1) and correlated cryptotephra ages (Table 4).The shaded grey area shows the depth interval of core sampled for cryptotephra analysis (expanded in panel b).(b) Glass shard concentration counts produced down to 1.42 m, and the composite depths of analysed glass peaks.Twenty-eight out of one hundred and forty-two samples were geochemically analysed: circles = <5 points analysed; triangles = >5 points analysed; filled red triangles have correlated ages that are used in the age-depth model.
Of the remaining 13 samples, five have dominant unique geochemical populations (i.e.primary deposits, likely relating to a single eruption, are strongly represented), six have multiple identifiable trends/populations (representing an amalgamation of shards from multiple eruptions), and two have sparse shards with no discernible geochemical trends.
Table 3 and Figure 3 show the samples analysed, the average major-element data for identified geochemical populations, and any geochemical correlations to known eruptions with associated chronological data or similarities to known volcanic sources.Normalised Deleted: here.S2 and S3.
The shard profile shows multiple closely spaced peaks and tails (Fig. 2) that translates into several samples containing multimodal geochemical populations, especially in the top 30 cm of the core profile.This could be evidence for taphonomic problems (e.g.reworking, bioturbation), but a lack of evidence for sediment reworking and an abundance of eruptions in the late Holocene suggest this is not a substantial problem at Cascade Lake (see section 5.1.1 below for detailed discussion).

Unique glass populations
Five of the analysed samples contained glass shards that show dominant unimodal rhyolitic geochemical populations based on between 10 and 36 individual point analyses.
These are interpreted as primary tephra-fall events relating to contemporaneous eruptions.
Grain size data were measured for 7 to 15 shards per sample and show that average maximum axis length and sphericity values are very similar for all five samples (23-27 microns and 0.56-0.63respectively).Four of these five samples can be used as isochrons as they correlate to reference material from known and dated eruptions (University of Alberta reference collection samples, Fig. 3; details provided in Tables 3 and S2).Key information regarding these eruptions and the tephra deposits are summarised in Table 4. Grain size data and shard images are presented in the supplementary files (Table S1, Fig. S2).Samples are discussed here individually from oldest to youngest and previously published age estimates are given as two sigma 14 C calibrated age ranges unless otherwise stated.3 for sample details and Table S2 for individual point data.

CL-105 (Aniakchak Caldera Forming Eruption II)
CL-105, a peak concentration of 12 shards/gram, is characterised by platy and cuspate shards.It is a geochemical match for the dominant rhyodacite population of the widespread Late Holocene caldera forming eruption of Aniakchak (CFE II) (Fig. 3; see Bacon et al., 2014;Neal et al., 2001;Riehle et al., 1987 for details).Tephra from this eruption have been found visibly across southern and western Alaska, and as cryptotephra in the Bering Sea, Yukon, Newfoundland and Greenland (Davies, 2018;Denton and Pearce, 2008;Pearce et al., 2017Pearce et al., , 2004;;Ponomareva et al., 2018;Pyne-O'Donnell et al., 2012).A small second population of four points was also identified in this sample (CL-105b, The identification of an eruption event in NGRIP is supported using geochemically correlated glass shards and sulphate peaks (Coulter et al., 2012;Pearce et al., 2004).
Additional evidence for the eruption is also provided by tree ring perturbations during in this  S4 for details).The Tau_Boundary function is used here for both the upper and lower boundaries around a single-phase eruptive event.
All dates associated with the tephra are included in the model, with an exponential rise and fall before and after the eruption event (i.e.assuming that dates cluster closely around the event).For Aniakchak CFE II, the ice-core modelled age discussed above is only compatible with published 14 C ages if two of the three 14 C ages that underlie the tephra in an exposed peat section in northwest Alaska (Blackford et al., 2014) are removed as outliers.This is unexpected because the peat section is one of the most precisely dated terrestrial sequences for Aniakchak CFE II, with six samples analysed at 0.5 cm increments over 3 cm Deleted: A second population of four points was also identified in this sample (CL-105b,  S5).

CL-96 (unknown)
CL-96 represents a small peak of only four shards/gram but analytical points were obtained from 10 individual shards.These data show relatively high values for wt% TiO2, FeO and CaO (Table 3a) and are similar to CL-74 for many major elements but have substantially higher wt.%K2O (2.81 wt.% average vs. 1.91 wt.%, respectively).The shards are likely from a source in Alaska and the Aleutian Arc and are similar to published average analyses for glass from the Katmai volcanic cluster (Fierstein, 2007) but cannot be directly correlated here to a particular vent or eruption.Therefore, there are no associated age estimates that can be used here to compare with other Cascade Lake chronometers.For future comparisons, the few observed shards from CL-96 were typically chunky with a small number of vesicles or cuspate edges and the final age-model estimate for this depth is 3550-2920 cal yr BP (2 sigma; Table S6).

CL-74 (Ruppert tephra)
CL Augustine volcano, no proximal correlative is currently known.The tephra was later found in, and subsequently named after, Ruppert Lake, directly south of Cascade Lake on the southern slope of the Brooks Range (Monteath et al., 2017) and has also been identified in peatlands in the Yukon (Davies, 2018) and eastern USA (Jensen et al., 2021).
It is an unusual situation to have a distal tephra deposit correlated between multiple sites that are located up to 5000 km apart but with no identified visible deposits.Such a correlation relies heavily on the geochemical characterisation and coincident timing.While there was some uncertainty about the validity of the geochemical correlation between sites from previously published data that were analysed at different times, this has recently been addressed with concurrently analysed samples from Alaska and the eastern USA and Canada by Jensen et al., (2021).Regardless of where Ruppert tephra is sourced from, we are confident in this correlation to Cascade Lake, as Ruppert tephra has been reported (and named) in this region and its presence in Alaska is firmly established.

CL-48 (White River Ash, northern lobe)
CL-48 is the largest glass concentration peak of the pre-19 th century sequence, with 36 shards/gram.These vesicular to frothy rhyolitic glass shards typically contain large numbers or microlites inclusions.They are geochemically similar to the White River Ash, which comprises two Late Holocene eruptions from Mt. Churchill (Lerbekmo, 2008;Preece et al., 2014).Major element glass geochemical data for these eruptions are very similar (with substantial overlap) but given the geographic relationship to the main plume directions, broad range of wt.% SiO2 values and bimodal geochemistry of CL-48 shards, it likely correlates with the older northern-focused eruption (WRAn).The tephra from this eruption is more Deleted: Mt.

Field Code Changed
Deleted: submitted Deleted: Ruppert Lake's geochemically diverse than that of the younger eastern lobe (Davies et al., 2019) and is preserved as a visible bed in sediment deposits north of the vent in Alaska and the Yukon.
Reference geochemical data from three WRAn samples in the Yukon (Jensen, 2007;Preece et al., 2014) are plotted in Fig. 3 to demonstrate the observed variability; distal correlatives trend towards higher wt.%SiO2 values compared to proximal samples.While geochemical differences between sites may tend to preclude a correlation, available analyses show that distal WRAn does vary geochemically by geographic location, although the entire geochemical trend is present more proximal to the volcano.Whether this is the result of a layered magma chamber or multiple, closely spaced eruptions, is unclear (e.g.Preece et al., 2014).Regardless, this manifests with the most distal cryptotephra samples trending towards having the highest average SiO2 values, which is reflected in the Cascade Lake sample (e.g.Davies et al., 2019;Harvey, 2021).
WRAn has a recently updated modelled two-sigma 14 C age of 1689-1560 cal yr BP (Reuther et al., 2020).This is slightly younger than previous published estimates (e.g.1805-1605 cal yr BP, Davies et al., 2016) as the eruption occurred at a time when there is a fluctuation in the 14 C calibration curve.An increased number of constraining ages can therefore adjust the most likely modelled age.At Cascade Lake, this age is younger than the radiometric age-model estimate for this depth by ~1370-2170 years (Table S5).
Here we report an updated modelled eruption age for OP of 1395-1305 cal yr BP (Fig. S4).This was produced using the Tau_Boundary function in OxCal v4.4 with IntCal20 (1995) (Table S4).This is in good agreement with previous published ages for the eruption but is younger than the radiometric age-model estimate for this depth by ~1470-1950 years (Table S5).

Multimodal/mixed glass populations
Glass shards from six of the remaining analysed shard peaks have mixed or multimodal geochemical data and two have scattered results with no discernible trend.It should be noted here that there are many recorded examples of heterogenous melts with bimodal geochemical trends from Alaska volcanoes (e.g.Aniakchak CFE II, Novarupta-Katmai 1912, see Table S2).However, none of the multi-model samples reported here are interpreted in this way as the different populations do not follow any geochemical trends that would be expected if they were from the same eruption.Instead they form distinct geochemical populations that more likely represent multiple eruptions from different sources.
Higher levels of background shards are present from 35 cm to the surface, and the geochemical 'noise' is also particularly evident in the youngest samples, with all peaks analysed in the past millennium showing either multimodal (>five glass geochemical populations) or scattered data.Detailed geochemical biplots for multimodal sample populations, including those with only a few shards (e.g., CL-0, -2, -31, -61), are shown in Fig. S5.Glass shards from these samples display a mix of morphologies (including platy, cuspate, vesicular and microlitic), which are all commonly seen in tephra in this area.Their grain sizes do not show any differentiation between types (as also seen for the unimodal samples discussed above); these data cannot therefore be used to identify any differences between sub-populations of these samples.
CL-61 is the only analysed mixed sample that pre-dates the past millennium, located  S6).It contains a few shards that are similar to the rhyodacite from Aniakchak volcano and also an Augustine tephra (Fortin et al., 2019;Waitt and Begét, 2009), but while these volcanoes have known activity at this time (e.g.Bacon et al., 2014;Waitt and Begét, 2009) there are not enough analyses available for a confident correlation.
Deleted: (Braitseva et al., 1995) (Table S4).This is in good agreement with previous published ages for the eruption and with Steen et al.'s (this volume) PSV-1 age estimate for this depth (Table 4) Of the six mixed samples, only two -CL-4 (180-60 cal yr BP, 2 sigma, Table S6) and CL-7 (625-75 cal yr BP, 2 sigma, Table S6) -have populations that can be identified as dominant from the analyses presented here.Rhyodacitic and dacitic glass shards from these samples overlap geochemically with reference data for Aniakchak (Davies et al., 2016) and are interpreted as strong evidence of eruptive activity at Aniakchak, given both the number of shards and the proportion of analyses that they represent.CL-7 also has six points that are geochemically similar to an Early Holocene eruption, KO (~8410-8455 cal yr BP; Braitseva et al., 1997) from Kamchatka, but this does not correlate to any known eruptions from Kamchatka in the timeframe of this deposit.While these are the three most coherent geochemical populations observed in these mixed samples, they are not deemed useful here for chronostratigraphic applications (discussed further in Sect.5.1.1).
An alternative approach for considering these mixed data is to parse by geochemical trend that can be broadly related to a source rather than to any individual eruption.Given the high levels of background shards it is possible that the chosen shard concentration peaks do not relate directly to primary tephra-fall.This is particularly likely where multiple eruptive events are closely spaced in time and therefore overlap within the temporal resolution of 1 cm of sediment accumulation.As each sample might contain shards from multiple eruptions these data can be seen as recording eruptive activity in a broader period, instead of discrete eruptions or accurately dated events.
Using this source-based classification, it is possible to identify eight geochemical groups, illustrated in Fig. 4, for the four mixed samples from the past ~1000 years, CL-31 and CL-61.Five of these eight geochemical groups correlate with reference glass data for volcanic sources in Alaska (Aniakchak, Mt.Churchill, Redoubt Volcano, Augustine Volcano, Mt.Katmai).These volcanoes all have known eruptions or suspected eruptive activity during this time period (e.g.Cameron et al., 2020).2018).Three populations with unknown sources are also shown using the same bounding line and fill.All single point analysis data are listed in Table S2.Step one of our chronometer comparison (see Sect. 2.3) considered if the individual ages fit their expected stratigraphic order.Steen (2016) noted that two 14 C ages from the full core sequence (5.5-7.5 cm and 245-248 cm) were anomalously old compared to their surrounding ages and these were therefore excluded from further consideration.While the 210 Pb ages are not discussed here in detail (given their limited applicability to the Late Holocene record) they overlap with the youngest 14 C age (2.6-4.5 cm).They therefore help constrain the broad age range (295-60 cal yr BP) of this sample that sits on a plateau in the radiocarbon calibration curve.
For step two of our comparison, an overlay of the individually modelled chronometers shows that there are substantial offsets between three of the five 14 C ages from this portion of the core and the four available cryptotephra correlated ages (Fig. 5).We place a high level of confidence on these tephra correlated ages as the four identified tephra are well characterised, widely identified in other depositional records (both intra-and extra-regionally), and in a issue within the dataset.Hence, two further 14 C ages (30.5-32.5 cm, 85.75-87.75 cm) are also identified as anomalously old and removed here as outliers.Given the trend in the correlated tephra age-model, the lower 138-140 cm 14 C age may also be slightly old (unless, 900 for example, there is an unexpected change in sedimentation rates in this part of the core).
However, as there are no tephra correlated ages within 30 cm of this 14 C sample this could not be confirmed at this stage.S5). 2 sigma uncertainties are plotted for all samples; where bars are not visible the uncertainty is smaller than the symbol.a) All 14 C dates produced by Steen (2016) from CASC-4A/2D; b) the focused upper section with new cryptotephra analyses from this study.

Deleted: PSV-1 tie-points (light grey shading) and
Deleted: (values in Table S3).Correlated tephra ages are overlain For step two of our comparison, an initial overlay of the individually modelled chronometers (Fig. 5) showed that there are substantial offsets between 14 C and PSV-1 models above 175 cm, as noted by Steen et al. (this volume).As outlined in Sect.3.1 and Table 4, the four available cryptotephra correlated ages agree well with PSV-1 tie-points (Fig. 5b) and three further 14 C ages (32.5-30.5 cm, 87.75-85.75cm and 140-138 cm) are therefore also removed as outliers.From 180-290 cm there is also a noticeable divergence between the PSV data model tie-points used from geomagnetic field models and the Burial Lake record (Fig. 5a).
For step three of the comparison, a P_Sequence model was produced (OxCal v4.4., Bronk Ramsey 2009a) that incorporates the remaining data.As Steen (2016) demonstrated better agreement between their chronometers below 2 m depth, 14 C ages for the rest of the sequence (down to 3.51 m; Table 1, Figure 2a) are also included here.The data initially included in the model were: six 210 Pb ages, four tephra correlated ages and seven 14 C ages.
For this step, both OxCal's agreement indices and a general student's t-test were used to statistically identify outliers.The initial combined P_Sequence model had good model agreement (Amodel = 81.5)and no further 14 C dates were identified as outliers by the student's t-test.The two oldest 14 C dates (303-304 cm, 348.5-351 cm) have posterior values that are slightly over the set threshold (9 and 6 respectively compared to the prior of 5) but are not excluded here.
A final model for CASC-4A/2D is shown in Fig. 6.Below the top 4 cm, six ages (four correlated tephra, two 14 C) are used to date down to 1.4m (~6 ka BP), providing a robust age model for this portion of the lake sediments.Four 14 C ages are used for 1.4-3.51m(~9 ka, 6-15 ka BP) of the sequence and as there are no independent tephra data for this section, these data are reported as provisional.Additional data -especially from independent chronometers -would increase confidence in the lower half of this model.

955
Deleted: PSV tie-points from Burial Lake (177 cm and 228 cm).The 284 cm composite depth tie-point from Burial Lake was also removed as it failed the chi-squared test when combined with the tiepoint from the pfm9k1b field model and was significantly older than the model results for that depth.These five… 960 Deleted: not included in the final version of the age-depth model presented here, as their removal improved the model agreement and reduced the associated uncertainties (Fig. S5).…

965
areas show the 1 sigma (68.2%) and 2 sigma (95.4%) confidence ranges.Filled symbols are included in the model and white symbols are identified as outliers.2 sigma errors are included for all ages; where they are not visible the error is smaller than the symbol used.Full details and values can be found in Table S6.

Discussion
The data reported here have implications for cryptotephra records in northwestern North America and for Arctic sedimentary sequences and age models through the successful application of multi-chronometer Bayesian age-modelling.

Cryptotephra in Arctic Alaska
This study demonstrates that identifiable concentrations of volcanic glass reach the north flank of the Brooks Range and can be used as chronostratigraphic tools where clear evidence of primary tephra-fall is preserved.In particular, this is the first report of ultra-distal glass from the Late Holocene eruption of Opala, Kamchatka (>3000 km from Cascade Lake), as well as an unknown tephra, CL-96, likely from a source in the Alaska Peninsula-Aleutian Arc.Ruppert tephra and Aniakchak CFE II are both documented on the southern slope of the Brooks Range (Monteath et al., 2017), and their distributions are expanded here across this large topographic barrier.This is also the first distal identification of WRAn this far to the northwest of Mt.Churchill.
Glass shard morphologies and preliminary grain size measurement data are reported for the unimodal tephra populations at Cascade Lake.However, these data are not used here to differentiate between samples or subpopulations -for example, the five tephra with distinct geochemical populations all have similar maximum axis length and sphericity values.This is not surprising for maximum axis length, as previous studies have shown that the grain sizes reported here (20-40 µm) are commonly found in deposits located 500-3000 km from their source (Stevenson et al., 2015).Quantitative grain size measurements provide valuable information for a range of research questions but are not commonly reported for cryptotephra (Saxby et al., 2020).Hence, these data are provided here as preliminary values for distal deposits of these correlated tephra.
While the cryptotephra profile here only covers the Late Holocene, it highlights eruptive events that are both locally important and widespread and provides possibilities for correlating proxy data within North America and across the Pacific in Kamchatka.Our focus was specifically on the past ~4 ka as there are several widespread, well-dated and geochemically characterised tephra within Alaska during this time period.From 12-4 ka, there is a paucity of well-dated regional tephra that are documented and fully characterised, but it is possible that new tephra from other regions may be identified as more tephra studies are published, as seen here with OP.
Compared to the cryptotephra stratigraphies published in Monteath et al. (2017) from Ruppert Lake and Woody Bog Pond, located ~150 km south of Cascade Lake on the southern slope of the Brooks Range, large differences can be seen in both the number of primary tephra preserved and the overall shard presence and concentrations.Reported glass abundances at the southern sites are at least an order of magnitude higher than those from Cascade Lake (100s-1000s vs 10s shards/gram or less).This likely relates in part to the topographic barrier presented by the Brooks Range, causing increased rain-out of shards being transported from the south (e.g. in north trending plumes from Aniakchak CFE II) and deposition of shards before they reach the northern slope (e.g.Watt et al., 2015).Other factors may include lake size and bathymetry, catchment size, local topography and hydrology (e.g.Pyne-O'Donnell, 2010).Cascade Lake is an order of magnitude larger and deeper than the southern sites and hence has a larger surface area (~1 km 2 vs 0.04 and 0.01 km 2 ) but its catchment area is not proportionally larger (~10 km 2 vs <4 km 2 ) and it has no current inflow.Hence, it is suggested here that topography is a primary influence on Cascade Lake shard concentrations (compared to other sites further south) and not lake characteristics.
There are common issues affecting cryptotephra research in Alaska that still apply at this distal, Arctic site.Cascade Lake is downwind of multiple active volcanic sources where records show that multiple closely spaced eruptions have occurred.This, combined with relatively low sediment accumulation rates, is likely to cause geochemical variability within individual samples where 1 cm of sediment represents decades of accumulation (25-67 years/cm calculated for Cascade Lake's 15 ka age-depth model).The presence of glass in ~75% of the samples analysed here shows a level of background deposition that must be considered when interpreting data from identified shard concentration peaks.This is particularly important here as a) the peak concentrations are relatively low compared to other cryptotephra records in the region (e.g.Davies, 2018;Monteath et al., 2017;Payne and Blackford, 2004), and b) the signal:noise ratio between peaks that have been correlated with known eruptions and the (fairly consistent) background shard concentration is relatively high.
Reworking and secondary deposition of tephra in the landscape can also be a substantial issue for records from this region, but this is not a likely problem at Cascade Lake as there is so little tephra present in the area (i.e.there is no clear source for tephra to be reworked from).
Furthermore, a broader issue that affects how much confidence can be attributed to a geochemical correlation is the available glass data for reference material from given 1040 eruptions or volcanoes.Here, this is relatively limited in scope compared to the number of Late Holocene eruptions reported in Alaska.Comparisons are often made with tephra data that relate to a small number of eruptions (or possibly only one) from a subset of the volcanoes with known activity.A degree of uncertainty will therefore affect correlations with given eruptions or sources until more characterisations are published from both proximal and 1045 distal tephra deposits.

Multi-modal samples and historical activity
The issue of 'clear evidence of primary tephra-fall' being preserved is one that affects all cryptotephra records.Low numbers of shard analyses cannot be interpreted as conclusive evidence of an eruption, especially if multiple geochemical populations or trends are 1050 observed.This appears to only be a problem for certain parts of the Cascade Lake tephrostratigraphic record; there are discernible changes in shard concentrations and sample compositions from the younger portion of the core.For example, samples analysed from 0-30 cm have multiple geochemical populations, which are not frequently seen below this.This is likely related to an overall increase in the shard-concentrations and peak density that is 1055 particularly notable for the top 15 cm of the core.These differences could be the result of a myriad of regional (e.g.weather patterns) and local (e.g.reworking) factors that affect the distribution and preservation of shards (e.g. Watson et al., 2015), but at Cascade Lake we hypothesize this may largely be the result of changing sedimentation rates.
Overall, it is possible that the background shards evident in the full Cascade Lake 1060 shard concentration profile (Fig. 2b) could be the result of taphonomic problems such as reworking, bioturbation or secondary in-wash.However, this is not likely a substantial problem for the record presented here.The lake sediments are laminated and do not show signs of deformation (from either in-situ processes or the core extraction).These shards are also unlikely to represent significant reworking from the surrounding landscape, or within the 1065 lake sediment itself, as there is little ash in the area and therefore no obvious source for Deleted: The shard concentration profile reported for Cascade Lake is affected by closely spaced eruptions from multiple sources combined with relatively low sediment accumulation rates, causing geochemically variability within individual samples.The presence of 1070 glass in the majority of samples analysed shows a level of background deposition that must be considered when interpreting data from identified shard concentration peaks.This is particularly important here as the signal:noise ratio between the peaks that have been correlated with known eruptions and the (fairly consistent) .A succinct summary for these factors relating to cryptotephra in peatlands is given in Watson et al., (2015), and is … 1095 Deleted: applicable for redeposition.Furthermore, the tails and multiple peaks do not show repetition of a common geochemical signal, which would be expected if the shards were reworked or secondary inwash (e.g., as seen with Askja 1875 in Swedish lake in Davies et al., 2007, or with the eastern lobe of the White River Ash at Sydney Bog in Jensen et al., 2021).1100 Geochemical data from the top 30 cm do show some repetition between samples so it is not possible to rule out reworking for this portion of the core, but this may also be the result of multiple eruptions from single sources in this ~1000-year time period.
Sedimentation rates are relatively low at this site, particularly for this interval at 30-67 years/cm (Table S6), which would cause increased overlap for closely spaced events.Hence, 1105 the glass shard data from the last ~1000 years are interpreted as evidence for trace amounts of tephra reaching the north flank of the Brooks Range.Beyond the five clearly defined cryptotephra samples described above, we present evidence of volcanic activity from Augustine, Redoubt, Aniakchak, Mt.Churchill, Mt.Katmai (e.g., Bolton et al., 2020) and further possible sources in Kamchatka and Alaska based on geochemically similarities to 1110 available reference data for characterised eruptions (Fig. 4).This supposition is supported by records of eruptions from the past millennium (e.g., Cameron et al., 2020), which include Novarupta-Katmai 1912, six eruptions from Redoubt and 14 from Augustine.A higher sampling resolution for this period may help distinguish individual eruptive events and resolve this question, but with such low sedimentation rates it may instead highlight the limit 1115 of this record's preservation potential.
Eruptions in the past millennium from both Mt.Churchill and Aniakchak have been identified distally elsewhere in Alaska.For Mt. Churchill there is published evidence for an eruption in the last 500 years: the Lena tephra is dated to 310-285 cal yr BP (Payne et al., 2008).It is possible that shards from CL-0 and -2 relate to this tephra, but their modelled age 1120 is too young to support a correlation (AD 1930(AD -2010)).Proximal records at Aniakchak indicate multiple eruptions have occurred between 560 to 70 yr BP (Bacon et al., 2014;Neal et al., 2001), and a distal tephra in the Akhlun Mountains, southwest Alaska is dated at around 400 yr BP (Kaufman et al., 2012).The large number of analyses that geochemically correlate with Aniakchak (47, including 4 dacitic points) over four samples from Cascade 1125 Lake (CL-0, 2, 4 and 7) are interpreted here as representing at least one eruptive event in the last ~400 years.However, any correlations here are limited by both the lack of glass Deleted: .Deleted: Beyond the five clearly defined cryptotephra samples, we present evidence here of volcanic activity using glass that is 1130 geochemically similar to reference data for Mt.Augustine, Redoubt, Aniakchak, Mt.Churchill, Novarupta-Katmai (e.g.Bolton et al., 2020) and further possible sources in Kamchatka and Alaska.Focusing on the modern period, this is interpreted as evidence for trace amounts of glass reaching the north flank of the Brooks Range 1135 from known eruptions, but without the resolution to interpret individual eruptive events.These shards are unlikely to represent significant reworking from the surrounding landscape, or within the lake sediment itself, as there is little ash in the area.This supposition is supported by the record of known eruptions in the past millennium, 1140 including Novarupta-Katmai 1912, six eruptions from Redoubt and 13 from Augustine (Alaska Volcano Observatory, 2016).¶ Furthermore, sedimentation rates calculated from the age-model data using OxCal v4.4 (Table S3) show that there is a significant decrease, by ~50%, for the depth interval of 12-4 cm (~1840-1250 CE) 1145 compared to the Holocene average values (0.015 vs 0.029 cm a -1 ).This period, coinciding with the Little Ice Age, is therefore expected to show increased background shard concentrations and multi-modal data from 1-cm-resolution samples as each centimetre represents ~67 years of accumulation compared to ~25-40 years as seen here over 1150 the Holocene.A higher resolution record for this time period may help to address some of the issues detailed here.¶ For Mt.

Deleted:
-Deleted: It forms a visible bed in Yukon Territory (Preece et al., 1155(Preece et al., 2014) ) where it sits on top of ~10 cm of peat accumulation above the WRAe.It is possible that shards from CL-0 and -2 relate to these events, although their age is younger than expected.There has not been any observed modern eruptive activity at Mt. Churchill.¶ There is published evidence for proximal activity at Aniakchak 1160 Deleted: (Neal et al., 2001), but only a small proportion of the associated whole rock geochemical data have a rhyodacitic composition similar to the mid-Holocene CFE II eruption (Bacon et al., 2014).Distal tephra preserved in sediment from lakes in the Akhlun Mountains, southwest Alaska, however, have similar glass 1165 geochemistry and have been da Deleted: .As our age model places the Cascade Lake samples between 350-100 cal yr BP, this currently precludes correlation with these known events.This age range is associated with a relatively high uncertainty due to decreased sedimentation rates, so it is 1170 possible the chronology does not negate these correlations, but an alternative correlation with a younger eruption from Aniakchak (that has not yet been identified distally) cannot be ruled out.…Deleted: therefore Deleted: as 1175 Deleted: from Aniakchak geochemical data on proximal tephra and the high uncertainty in modelled ages for these samples at Cascade Lake.Our age model places these samples between 630-10 cal yr BP (2sigma) due to decreased sedimentation rates at this time, so additional correlation(s) with other younger eruption(s) from Aniakchak also cannot be ruled out.1180

Cascade Lake age models
It is not uncommon for ages produced by multiple chronometers to diverge over part or all of a sediment sequence.Individual chronometers have their own inherent strengths and weaknesses, and their different physical properties can be affected by a number of different processes, which in turn affect the preserved and eventually measured signal (e.g.Davies et 1185Davies et al., 2018)).This is somewhat disheartening as using multiple techniques should provide a check for bias and inaccurate data, but additional independent data can be used to identify and reconcile observed offsets, as shown here.
Once any obvious outliers have been addressed (i.e.step one from Sect.2.3), it is not always easy to resolve any remaining disagreements between chronometers.Here, the 1190 importance of independent chronological validation from marker horizons (Late Holocene cryptotephra, which provide additional data in a key period) and the power of Bayesian statistics for age modelling are demonstrated.The identification of periods of offset and anomalous or biased ages can allow further investigation of the potential causes, such as mechanical (e.g.mobilisation or redeposition) or chemical (e.g.alteration or degradation) 1195 processes affecting the analysed sample material.In this case, however, the resulting agedepth model for the whole core can still be strengthened by the addition of further independent chronological data, especially for the lower section (1.42-3.51m).
The commonly applied method of 14 C dating can have low reported uncertainties but is restricted at some Arctic sites by a lack of suitable material.Where macrofossils are 1200 available, they may be affected by old carbon contamination or the redeposition of older material.Cascade Lake's location in limestone terrain likely resulted in a hard-water effect, which could explain the anomalously old 14 C ages identified here: four of the Holocene 14 C ages are variably 500-5000 years too old compared to median modelled ages for their given depths.As mentioned in other studies the use of either terrestrial material or the humic 1205 fraction of sediment is recommended, especially when in limestone terrane (Lowe and Deleted: steps Deleted: and two Deleted: 4 Deleted: For example, from 303-175 cm in Cascade Lake cores 1210 there is a divergence between PSV-1 tie-points from geomagnetic field models, from Burial Lake and 14 C ages.Logically, the geomagnetic field models incorporate data from multiple regional palaeomagnetic records, which should give a valuable, albeit spatially smoothed, resulting record for the area.Their reliability at any given 1215 coordinate, however, will depend on the amount and quality of data that is in close proximity.A single, nearby well-dated PSV record (here, Burial Lake) could arguably be more relevant than a field model that incorporates multiple datasets.The use of terrestrial macrofossils for radiocarbon dating at Burial Lake and their 1220 consistency over the sedimentary sequence suggests they are not affected by, for example, old carbon effects.But, if accurate, the Burial Lake tie-point ages are up to 2000 years older than the other methods for the same composite depths.Outlier analysis performed within OxCal v4.4 was used to assess the ages and statistically 1225 identify remaining outliers here (two 14 C ages and three Burial Lake PSV tie-points) in order to resolve this divergence.¶ The combination of all three chronometers using Bayesian modelling techniques is therefore shown to result in a refined dataset that produces a reliable age model for the past ~21 ka.This 1230 Deleted: -here, Deleted: -Deleted: .Furthermore, the Deleted: Data from Cascade Lake show that PSV-1 provides reliable and accurate tie-points in the Late Holocene that are in 1235 agreement with four cryptotephra correlated ages.Comparison of these data across the whole core shows that at least six 14 C ages are too old, including two initially identified as out of sequence (likely old carbon contamination).However, while the 'best ages' produced by PSV-1 are in good agreement with the final age-depth model, the  , 2000).Nonetheless, this study adds to a growing body of literature that demonstrates that using multiple independent chronometers with Bayesian age modelling techniques can produce accurate and reliable age-depth models for Arctic lake sediments.

Conclusions
This research demonstrates the potential for dating Arctic lake sediments in Alaska using cryptotephra correlations.The advantages of tephrochronology include the relatively long period of time over which it can be applied (compared to 210 Pb and 14 C), the level of precision associated with known tephra ages (especially those from documented historical events) and the potential for independently testing and validating other chronometers with tephra correlated ages.We suggest here that the most robust age models can be produced by using a combination of chronostratigraphic techniques in a Bayesian statistical model.While cryptotephra are best defined regionally for the Late Holocene, it is possible that other welldated cryptotephra from Alaska (e.g. the Early Holocene caldera forming eruptions from Fisher, Stelling et al., 2005; the late Pleistocene Tephra D, Davies et al., 2016) and ultradistal sources (e.g.Kamchatka, Japan) could be identified in northern regions.
Figure S3: Bayesian Tau_Boundary probability density function plots derived using OxCal v4.4 and IntCal20 for the age of Aniakchak CFE II tephra with: all 14 C dates are included (grey right-hand distribution); two 14 C dates removed (green central distribution); and all but two 14 C dates and the NGRIP ice core chronology age (Pearce et al., 2017) (blue left-hand bar).See Table S4 for the ages used for this model.S4 for the ages used for this model.Table S1: Grain size measurements for unimodal tephra samples reported at Cascade Lake.Measurements were made using optical microscopy (Grain depth) and image analysis with ImageJ software.Geometric size (here, dv -diameter of a volume equivalent sphere) and sphericity (ψ) were calculated following the methods reported in Saxby et al. (2020).
Table S2: Single point major element glass geochemical data for Cascade Lake samples and reference material.
Table S3: Secondary standard data (ID 3506 and Old Crow) for EPMA glass analyses of Cascade Lake samples and reference material.
Table S4: Ages for tephras reviewed within this study, listed by associated tephra.
Table S5: OxCal age model output for the initial multi-method chronometer comparison.Age models based on a) radiometric ages and b) correlated tephra ages.

Figure 1 :
Figure 1: Location map showing Cascade Lake, coring sites, and other relevant locations and volcanoes mentioned in the text.Grey circles = active Holocene volcanoes (Global Volcanism Program, 2013); black triangles = volcanic sources mentioned in the text; grey shading = Brooks Range; star outlines = lakes mentioned in the text.
New data are reported here from single point major-element geochemical data and associated standard analyses are provided in Tables

Figure 3 :
Figure 3: Geochemical biplots showing major element data for the five unique populations of cryptotephra glass identified from Cascade Lake sediment, and data for reference material where relevant.Points for CL-105b are also plotted, for reference.See Table3for sample details and TableS2for individual point data.

Figure 4 :
Figure4: Geochemical biplots showing mixed-glass samples from Cascade Lake.Bounding shapes represent simplified geochemical fields for potential source volcanoes (to aid visualisation).For the full glass geochemical-data ranges associated with these volcanic sources seeBolton et al. (2020),Davies et al. (2016),Fortin et al. (2019), Zander et al. (2018).Three populations with unknown sources are also shown using the same bounding line and fill.All single point analysis data are listed in TableS2.
to one another.The radiometric model also had very low agreement (Amodel=10.3;individual age AI values range from 19.7-78.8),indicating a likely

Figure 5 :
Figure 5: Cascade Lake core CASC-4A/2D multi-method chronometer comparison of downcore age models based on 905 910 at their identified depths and show good agreement with the PSV-1 model.(a) Whole model down to 520 cm.Note disagreement between the geomagnetic field model and Burial Lake tie-points from 284-177 cm.PSV-1 model is extrapolated from 520-509 cm (from the base of the unit to the lowest dated sample); (b) enlarged 145 cm 915 section, highlighted with the grey shaded box in panel a, showing cryptotephra correlated ages and the substantial offsets between 14 C and PSV-1 age models.
the PSV-1 tie-point ages, Deleted: cryptotephra Deleted: the six remaining 14 C ages (details for OxCal input are given in File S1).This age-depth model was run with a Student's… Deleted: outlier 950 Deleted: , which Deleted: four ages with strong likelihoods of being outliers ( Deleted: of 68-100; Deleted: S4).These include two further 14 C Deleted: 199-197 cm and 235.5-233.5 cm) and

Figure 6 :
Figure 6: Age-depth plot showing the final Bayesian age model for Cascade Lake composite core CASC-4A/2D.Shaded Other factors may include lake size and bathymetry, 1035 catchment size, local topography and hydrology.…

1075
background shard concentration is relatively high.This is mostly due to the low concentrations of shards in the identified peaks, compared to other cryptotephra records in the area.… Deleted: samples Deleted: contains multiple geochemical populations/trends.1080 Deleted: -0 Deleted: However, this view may be biased by the relatively higher number of samples with more than five analyses in this period.Also, the overall Deleted: concentration profile over 1085 Deleted: has higher average and peak shard concentration values than the rest of the analysed sediment.…Deleted: eruption style, plume altitude, wind direction and strength, shard characteristics) and local (e.g.Deleted: fallout on snow, sediment accumulation, hydrology, 1090 bioturbation) factors that affect the Deleted: , deposition, reworking, Deleted: ultimately Deleted: 1240 associated uncertainty produced by the geomagnetic field models (± 500 years) is broad compared to other methods that can be applied to this time period.¶ analysed samples were included in the final agedepth model and the identified outliers were… 1250 Deleted: -Walker

Figure S4 :
Figure S4: Bayesian Tau_Boundary probability density function plots derived using OxCal v4.4 and IntCal20 for the age of OP tephra, Opala, Kamchatka.See TableS4for the ages used for this model.

Figure S6 :
Figure S6: OxCal age-depth output for the final Bayesian model for Cascade Lake.The students'-t outlier analysis results shown good agreement.

CASC13
OxCal age-depth plot output for the initial Bayesian 1325 model for Cascade Lake (v1).Students'-t outlier analysis results are shown.Four ages have more than 50% chance of being an outlier.BL-284 is also excluded as it has an outlier posterior value of 49 and it fails the chi 2 when combined with pfm9k1b-284.¶ FigureS51330 Deleted: (v2).Five outliers from the previous model (v1) were removed and the… Deleted: TableS1Deleted: S2 Deleted: TableS3: Final OxCal age model output for 0-520 cm of 1335

Table 1 :
Radiometric ages from Cascade Lake (fromSteen, 2016.).Ages are reported to the nearest whole year ( 210 Pb) or five years ( 14 C) * = 14 C ages rejected as outliers; † = samples from surface core CASC-4B, all other samples are from

(a) 210 Pb CRS ages
Deleted: The 5.2-m-long composite sedimentary sequence, CASC-4A/2D, described by Steen et al. (this volume) is the focus of the agedepth model reported here, which extends down to the boundary with an underlying diamicton.…195 Formatted: Heading 2 Deleted: Previous geochronological data ¶ 2.1.1Deleted: are detailed in full in Steen et al. (this volume) and Deleted: here Deleted: 350 200 Deleted: composite depth, dating Deleted: , but as Deleted: cores these ages are not discussed in the context of the Holocene age models.¶

Table 3 :
Normalised average major element geochemical glass data for identifiable populations of analysed tephra samples and suggested correlations.Popn: unimodal geochemical data are labelled as '-'; where multiple geochemical populations are identified, they are labelled separately (e.g., a, b), but if they are interpreted as being related heterogenous populations a combined average is also shown (e.g., a+b).FeOt = total iron oxide as FeO; H2Od = water by difference; numbers listed in brackets = 1 S.D.. (a) Samples used here as tie-points; (b) Reference material analysed at the University of Alberta, for full details regarding the original sample details please see listed references.(c)Sampleswith multiple populations or too few points to use as tiepoints.Only groups of 3 or more analyses are shown here -for full details see TableS2.
a) Samples used as tie-points

Table 4 :
Cascade Lake cryptotephra and their suggested correlative eruptions.Radiocarbon modelled age estimates produced in this paper for the core depth of the cryptotephra are compared 570 with published ages for the listed eruptions.Bayesian modelled ages for both Aniakchak CFE II and Opala are updated here using OxCal v4.4 (Bronk Ramsey, 2009a) and IntCal20(Reimer et  al., 2020).

Table 3c )
; they do not Deleted:

Table 4 :
Cascade Lake cryptotephra and their suggested correlative eruptions.Age estimates for the core depth of the cryptotephra from Steen et al. (this issue) are compared with published ages for the listed eruptions.Bayesian modelled ages for both Aniakchak CFE II and Opala are updated here using OxCal and

:
Davies et al., 2016Neal et al., 2001;Riehle et al., 1987).615correlatewithreferencematerialfor this eruption (e.g.Wallace et al., 2017)but it is unclear if these represent a separate event or shards from the main population with alkali loss .Chronologically, the Aniakchak CFE II tephra has disparate age estimates where modelled radiocarbon dates and ice core ages are notably offset (seeDavies et al., 2016, for a detailed summary of references).Radiocarbon age estimates have been produced from sequences with visible tephra as well as distal lakes and peat bogs with correlated cryptotephra.A precise ice-core model age estimate is associated with distal cryptotephra identified in North Greenland Ice Core Project (NGRIP) samples.
(Adolphi and Muscheler, 2016;Pearce et al., 2017)t a separate event or alkali loss from the main population…Davies et al., 2016; Fig. S1, see TableS4for details).The 665 ice-core chronology… immediately surrounding the tephra.While there are no obvious reasons for disregarding these two ages, beyond the disagreement with the ages from the ice cores, in this instance it seems pertinent to do so.Modelled Tau_Boundary estimates for the eruption age are: a) 3545-3425 cal yr BP when all 14 C dates are included, b) 3610-3450 cal yr BP with two 14 C dates removed, and c) 3590-3545 cal yr BP including all but two 14 C dates and the NGRIP ice core chronology age (Fig.S3).At Cascade Lake, using either the ice core chronology age estimate of 3572 ± 4 cal yr BP(Adolphi and Muscheler, 2016;Pearce et al., 2017)or the Tau_Boundary model age (c, above) for Aniakchak CFE II shows that this age is younger than the radiometric age-model estimate for this depth by ~1000-1800 years (Table (Pearce et al., 2017)r, 2016)y and Baillie, 2019;Pearce et al., 2004)diocarbon from sequences with visible tephra and distal lakes and peat bogs with correlated cryptotephra, as well as with a precise icecore model age estimate from distal cryptotephra identified in Greenland ice cores.The latter is supported using geochemically correlated glass shards as well as sulphate peaks and tree ring 655 perturbations recorded in this interval(Coulter et al., 2012;McAneney and Baillie, 2019;Pearce et al., 2004).Glass shards correlated to the eruption in two NGRIP intervals have overlapping associated ice-core modelled ages of 3594-3589 yr BP (1641-1639 BCE -QUB-1198, 1644-1643 BCE -… 660 Deleted: When a correction factor of -19 ± 3 a Deleted:(Adolphi and Muscheler, 2016)Deleted:(Pearce et al., 2017).Deleted: with IntCal20 ( Deleted: -74 has aPyne-O'DonnellMonteath et al., 2017)ds/gram but a disproportionately high number of analyses (38) when compared to other samples.This rhyolitic glass population of platy and cuspate shards has relatively low wt.%K2O values (~2.0%) compared to most other known tephra from Alaska and is a geochemical match for the Ruppert tephra.This tephra was first identified in Newfoundland(NDN-230;Pyne-O'Donnell et al., 2012)and tentatively correlated to Augustine G tephra, although this is now known to be incorrect(Blockley et al., 2015;Monteath et al., 2017).While it is geochemically similar to glass from Deleted: while neither estimated age for this depth from Steen et al. 700 (this volume) overlaps here, the PSV-1 age model is substantially closer than the 14 C age model (Table 4… Deleted: yielded 10 Deleted: that have Deleted: ).These analyses 705 Deleted: , Deleted: distinctly