Joanne Egan1, Richard Staff2 and Jeff Blackford3

A revised age estimate of the Holocene Plinian eruption of Mount Mazama,

Oregon using Bayesian statistical modelling

1 Department of Geography, School of Environment, Education and Development, The University of

Manchester, UK, email: [email protected]

2 Oxford Radiocarbon Accelerator Unit (ORAU), University of Oxford, UK

3 Department of Geography, Environment and Earth Sciences, University of Hull, UK

Abstract

The climactic eruption of Mount Mazama in Oregon, North America, resulted in the deposition of the most widespread Holocene tephra deposit in the conterminous United States and south-western Canada. The tephra forms an isochronous marker horizon for palaeoenvironmental, sedimentary and archaeological reconstructions, despite the current lack of a precise age-estimate for the source eruption. Previous radiocarbon age estimates for the eruption have varied, and Greenland ice-core ages are in disagreement. For the Mazama tephra to be fully utilised in tephrochronology and palaeoenvironmental research a refined

(precise and accurate) age for the eruption is required. Here, we apply a meta-analysis of all previously published radiocarbon age estimations (n=81), and perform Bayesian statistical modelling to this data set, to provide a refined age of 7682-7584 cal. years BP (95.4% probability range ). Although the depositional histories of the published ages vary, this estimate is consistent with that estimated from the GISP2 ice-core of 7627 ± 150 years BP

(Zdanowicz et al., 1999)

Keywords: Mazama tephra, Holocene, radiocarbon dating, tephrochronology, Bayesian statistics, geochronology.

Introduction 1 Tephrochronology is the use of uniquely characterised (ideally geochemically identified) tephra to provide relative ages for stratigraphical sequences as a means of linking one environmental archive with another using correlated tephrostratigraphies (Buck et al., 2003;

Lowe, 2011). If the age of a tephra deposit is known, this age can then be transferred to enclosing sediment sequences. Numerical ages can be provided by historical records (e.g.

Meier et al., 2007), or derived by geochronological methods including radiocarbon dating

(e.g. Smith et al., 2013), varve counting (e.g. Van Den Bogaard and Schmincke, 1985), dendrochronology (e.g. Hall et al., 1994), K-Ar and 40Ar/39Ar techniques (e.g. Lanphere,

2000), and ice core chronologies (e.g. Zdanowicz et al. 1999).

Tephra from the climactic eruption of Mount Mazama has been recognised as an important isochronous marker in North American tephrochronology. Mount Mazama (42.9436° N,

122.1067° W) was one of the major volcanoes of the Cascade Arc, reaching a maximum altitude of approximately 3700 m. The volcano has had many eruptions, but none as significant as the Plinian eruption approximately 7700 years before present (BP) (Bacon and

Lanphere, 2006), which caused the collapse and formation of the Crater Lake caldera. During this eruption nearly 50 km3 of rhyodacitic magma was ejected into the atmosphere, and ash was deposited over an area of approximately 1.7x106 km2 (Zdanowicz et al., 1999) in a predominantly north-easterly direction (Figure 1). The tephra covered most of Oregon and

Washington, all of Idaho, north-eastern California, northern Nevada, north-western Utah, western Wyoming and Montana, southern British Columbia and Alberta, and south-western

Saskatchewan (Sarna-Wojcicki et al., 1984), making it the most widespread visible

Holocenetephra layer in the conterminous United States and south-western Canada

(Zdanowicz et al., 1999). Its distribution as a cryptotephra remains unknown, but Pyne-

O’Donnell et al., (2012) have highlighted its potential as a continent-wide marker horizon, discovering the Mazama tephra at Nordens Pond Bog in Newfoundland, approximately 5000

2 km away. However, there is some debate as to the number of eruptions during the climactic phase, with a possible eruption approximately 200 years previously (Bacon, 1983), to which components of the extensive tephra layer may be attributed.

The wide distribution and significant thickness of the Mazama tephra provides a chronostratigraphic marker bed for Holocene tephrochronology in the region, and there have

3 been many radiocarbon estimates for the event, ranging from 8380 ±150 14C years BP (Dyck et al., 1965) to 5380 ±130 14C years BP (Blinman et al., 1979). Because of the widespread distribution of the tephra, a more reliable age for the eruption of Mount Mazama would be of considerable importance for tephrochronological applications. The aims of this paper are to draw together and evaluate previous radiocarbon age estimates for the Mazama ash, and to generate a high-precision age estimate for the eruption using Bayesian analytical tools.

Mazama deposits and previous age estimations

The assemblages of age estimates previously obtained are primarily based on radiocarbon dating. Over 80 previous age estimations have been obtained from fossil plant material and other organic matter (e.g. charred wood fragments, concentrates of pollen, twigs and rat dung), chiefly from peat and lake sediments taken from below, within and above the visible tephra deposit (Table 1).

Dating tephra layers

Not all of the radiocarbon estimates precisely date the Mazama eruption directly. Samples taken stratigraphically below or above the tephra deposit reflect the maximum and minimum ages of the tephra. Samples taken stratigraphically constrained within the tephra are, in theory, the most likely to reflect the actual eruption age (Hallett et al., 1997). However, it cannot be assumed that organic samples dated from within a tephra deposit precisely date the tephra. It has been shown that sedimentary tephra can have an extended vertical distribution in cores or sections, representing a longer period of accumulation than the primary deposition event itself, especially in lacustrine environments, due to post-depositional tephra influx

(Davies et al., 2007), bioturbation,vertical mixing (Thompson et al., 1986), and aeolian and fluvial processes (Boygle, 1999).

4 If the tephra deposits in any of the locations reported in Table 1 have been subject to erosion, re-deposition, re-working or re-mobilisation then the point in the sediment sequence that has been dated may not precisely relate to the time of primary tephra deposition. For example

Peterson et al., (2012) reported an age of 7240 ± 40 14C years BP at the top of the deposit, intended to give a minimum age, and a strikingly younger age of 6150 ± 50 14C years BP, taken from wood within the tephra. These reversed ages were deemed unreliable, with the older date possibly due to the incorporation of older wood. The younger date suggests the possibility of residual tephra being re-mobilised and deposited for at least several centuries after the eruption. Issues of re-deposition and large vertical ranges may be more significant when samples are taken below or above the tephra layer, and this may again help to explain the extended range of ages observed in Table 1. For example, Dyck et al., (1965) reported an age estimate of 8380 ± 150 14C years BP from plant detritus below the tephra deposit and stated that the age was ‘too old’ as an age estimate for the Mazama event, attributed to sample mixture with older material. Although issues of re-deposition and large vertical ranges are problematic, it is also important to consider that these dates reflect only the minimum and maximum ages of the eruption, and it is not necessarily known how close these dates are to the true age of the eruption.

Reports of one or multiple tephra layers attributed to Mount Mazama raise the question of whether the age estimates relate to a single, climactic eruption or multiple eruptions (e.g.

Mehringer et al., 1977a; Blinman et al., 1979; Mack et al., 1979; Sarna-Wojcicki et al., 1984;

Abella, 1988; Zdanowicz et al., 1999). Bacon (1983) showed two phases of the climactic eruption, known as the ‘single vent’ and ‘ring vent’ phases. The single vent phase ejected the widespread tephra deposit that has been used extensively as a stratigraphic marker

(Mehringer et al., 1977a; Mehringer et al., 1977b; Abella, 1988; Zdanowicz et al., 1999),

5 tending to yield a single unit with no interbedded organic lenses, and with pyroclast particle sizes that decrease up the profile, such as that seen in Lake Washington (Abella, 1988). The ring vent phase followed shortly afterwards, perhaps a maximum of three years later based on pollen influx data (Mehringer et al.1977a) and a minimum of a few days based on likely eruption rates (Wilson et al., 1978), but certainly less than a period resolvable by radiocarbon dating (Bacon, 1983), and it was this phase that ultimately caused the caldera to collapse.

Where two tephra deposits have been identified it is possible that the second, finer deposit is from the ring vent phase, whilst the thicker and more significant deposit is from the initial single vent phase (Bacon, 1983). Alternatively, it has also been acknowledged that an eruption from the Llao Rock eruptive centre of Mount Mazama approximately 200 years earlier also emitted tephra, and distal tephras attributable to this event may have been detected in lake sediment sequences in Oregon (Blinman et al. 1979) and in Washington

(Mack et al., 1979). Blinman et al. (1979) identified the first tephra layer as a 1mm thick grey ash, and the second as a 20-25-mm-thick white ash with alternating fine and coarse laminae.

Mack et al. (1979) found two tephra layers of 8 cm and 12 cm thicknesses, with different glass shard geochemistry and almost 50 cm of peat between them, indicating a clear separation of the two units. Ages ranged from 6930 to 6810 14C years BP and single standard deviations ranged from 110 to190 years. Elemental analyses of the two units was undertaken by electron microprobe and gave calcium, potassium and iron percentages of 1.23, 2.17, and

1.52, respectively, for the upper ash unit, while the lower unit gave percentages of 1.14, 2.12, and 1.54 for the same three elements. Both proportions fall within the known ranges for the

Mazama ash. Mack et al. (1979) concluded that this is evidence of two eruptions within a

200 year period. Therefore, some of the slightly older ages published may reflect this earlier eruption.

6 It is possible that some locations in the Pacific northwest did not receive tephra deposition from the climactic eruption of Mount Mazama because of meteorological factors ( Grattan and Pyatt, 1994; Boygle, 1999; Lawson et al., 2012), although they could have received tephra deposition from the lesser eruptive phase approximately 200 years earlier, or from both eruptions, or from neither.

A further issue is that only a small number of studies have identified the Mazama tephra definitively through geochemical analyses (Sanger, 1967; Westgate and Dreimanis, 1967;

Davis, 1978; Blinman et al., 1979; Mack et al., 1979; Sarna-Wojcicki et al., 1984; Hallett et al., 1997;Gilbert and Desloges, 2012; Peterson et al., 2012). The majority have assumed that the tephra is from Mount Mazama, based on the approximate age, stratigraphic position, colour and thickness. Some reports have questioned the validity of this assumption (e.g Dyck et al., 1966; Lowdon et al., 1969, 1971; Lowdon and Blake, 1970; Barnosky, 1981), and misidentification could account for some of the variability shown in Table 1 and Figures 2 and 3. Further, with the question regarding the number of eruptions it has been suggested that there will be some difference in the tephra compositions, with tephra from Llao Rock producing rhyodacite and dacite lavas while the climactic eruption produced basaltic lavas

(McBirney, 1968), but with few geochemical analyses carried out in these studies it is currently impossible to determine to which eruption(s) the published ages pertain. In this paper, all of the published ages are assumed to be from Mount Mazama, and it is not the scope of this paper to reassess the origin of the tephras at each site, but to build a Bayesian model based upon the previously published assumptions of others. All of the authors’ work included has specific site information, and their stratigraphic assumptions are not disputed here. However, the model has been constructed with an allowable margin of freedom or variation to factor in possible mis-attribution of the tephra, through the implementation of objective outlier analysis (described below).

7 Further sources of variability in the collated data set include reservoir effects (hard-water), inbuilt age, and contamination. Samples may also contain more recent carbon that can give age estimates that are up to several hundred years too young. Arnold and Libby (1951) expressed doubts about the Mazama age of 6453 ± 250 14C years BP (C-247) based on charcoal from a tree killed by the eruption, due to the possibility of post-depositional exchange of more recent carbon from groundwater. Since that time, developments in radiocarbon dating have led to improved chemical pre-treatment of samples, which should reduce such problems.

The chosen sample material can help to minimise the likelihood of contamination from old or young carbon. For example, peat that is free of aquatic mosses is not likely to suffer old carbon effects, but it may contain reworked plant detritus that is older than Mazama (Hallett et al. 1997). This is an especially prominent problem where bulk samples have been collected. It has been acknowledged that bulk sediments and gyjtta tend to give less precise ages due to sources of contamination, such as detrital carbonate (Blockley et al., 2008) and the various processes that can occur in sediment profiles such as humic acid percolation down through a sequence (Walker et al., 2003). Bulk samples can have poor chronological resolution with 1 cm thickness representing as little as 5 years or as many as 50 years or more

(Blackford, 2000)., and this adds imprecisions to the radiocarbon determination. While bulk samples of organic material are not ideal, in some cases they are the only material present.

Whilst charcoal dates can be more precise the charcoal can have an ‘inbuilt age’ where the wood may be older than the fire event (Gavin, 2001). Colman et al., (2004) published strikingly older dates for the Mazama tephra than previous studies (+400 years). They attributed this to contamination from the detrital input of old carbon. Organic material was sparse, with only a few wood fragments found and analysed, but this was discovered further

8 down the core. Instead, Total Organic Carbon (TOC) from bulk sediment was dated, which is problematic as the actual sample being dated, and thus the routing of carbon from the atmosphere, is unknown. Hallett et al., (1997) analysed previous age estimates of Mazama and considered that estimates from bulk sediment should not be considered as reliable ages due to the high potential for contamination from old and new carbon, and re-working of the sediment and tephra. Hallett et al., (1997) suggested that the best material for dating the eruption would be the outermost ring of rooted trees killed by a pyroclastic flow or tephra fall. However, such tree remains have not yet been found or dated.

Indirect vs. direct radiocarbon dating

The actual 14C measurements may be obtained by two differing means: (i) measuring a sample’s radioactivity by counting the emission rate of  particles per gram of carbon present; or (ii) directly measuring the ratio of 14C:12C atoms present in a sample through accelerator mass spectrometry (AMS) (Alloway et al., 2013). AMS allows significantly smaller samples to be 14C dated than with the ‘conventional’ -counting technique, being able to routinely process samples of < 1 mg organic C. Thus, AMS allows the dating of individual leaves or seeds, and therefore enables 14C dating at much greater stratigraphic resolution than was previously possible (Hatté and Jull, 2007). It is not uncommon to use the conventional method where perhaps only bulk sediment is available (e.g. Colman et al., 2004), but this choice of sample material inevitably compromises the quality of the 14C date (as described above).

It is evident from Table 1 that many of the age estimations for Mazama were before the introduction of advanced chemical pre-treatments, especially where bulk sediments were dated. Blockley et al., (2008) excluded measurements made pre-1980 in their study of Late

9 Quaternary tephras due to the lack of robust chemical pre-treatment, and issues surrounding dating of bulk sediment (although this is not confined to pre-1980 samples).

Taking into consideration the issues outlined above, it may be expected that the most recent

(post 1990) age estimates of Mount Mazama that have used more desirable materials (e.g. twigs, charcoal) found within the tephra layer, and were obtained using AMS techniques with appropriate pre-treatments are likely to have provided the most accurate and precise age estimates (e.g. Hallett et al., 1997; Gilbert and Desloges, 2012). These examples suggested an age of approximately 7600 cal. years BP, which is in agreement with Bacon and

Lanphere’s (2006) commonly cited age. However, analyses of ice cores, which can have a relatively high dating resolution by counting of annual ice layers and accumulation rate modelling (Walker, 2005), have provided two contrasting ages, seemingly low in precision.

Hammer et al., (1980) estimated the age to be 6350 ±110 ice-core years BP at Camp Century,

Greenland, while Zdanowicz et al., (1999) derived an age estimate of 7627 ±150 ice-core years BP from GISP2 (also Greenland). This uncertainty reflects the overall uncertainty of the age of the Mazama ash and encourages caution to be taken when accepting both radiocarbon and ice-core ages.

10 Table 1: 81 previously published radiocarbon ages of Mount Mazama

Author(s) Laboratory Convention Calibrated Location Material dated and position with Number al 14C age age BP respect to tephra layer BP ± 1σ (95.4% range)* Below Mazama Preston et al., (1955) Y-109 7610 ± 120 8691-8168 Paisley Cave, Oregon Rat dung immediately below tephra Broecker et al., (1956) L-269C 6500 ± 200 7759-6948 Covington Wash, Peat immediately below tephra Washington Rigg and Gould (1957) L-269B 6950 ± 200 8177-7461 Moss Lake, Peat below tephra Washington Rubin and Alexander (1960) W-776 6600 ± 400 8312-6659 Arrow Lake, Peat below tephra Washington Rubin and Alexander (1960) W-779 5950 ± 400 7606-5985 Bow Lake, Peat immediately below tephra Washington Dyck et al., (1965) GSC-206 7510 ± 75 8595-8011 Deep Creek, British Organic muck below tephra Columbia Dyck et al., (1965) GSC-213 8380 ± 75 9665-9006 Lower Arrow Lake, Plant detritus below tephra British Columbia Dyck et al., (1966) GSC-321 7340 ±180 9025-7552 Burnaby Lake, British Peat below the tephra Columbia Haynes et al., (1967) A-728 6990 ± 300 8411-7318 Osgood Swamp, Peat 1cm below the tephra California Sanger (1967) GSC-530 7530 ± 135 9024-7826 Drynoch Slide Bone sample buried within Cultural Archaeological Site, deposits buried beneath tephra British Columbia Buckley and Willis (1969) I-3159 7670 ± 220 9030-8016 Columbia River, Charcoal 30 cm below tephra British Columbia

11 Lowdon et al., (1969) GSC-459 7190 ± 75 8331-7722 Fraser Canyon, British Charcoal below tephra Columbia Lowdon and Blake (1970) GSC-1004 8320 ± 70 9547-8995 Lavington, British Fibrous organic matter 200 cm below Columbia tephra Lowdon and Blake (1970) GSC-963 6390 ± 80 7584-6937 Rithets Bog, Gyttja below tephra Vancouver Island, British Columbia Mathewes et al., (1972) I-5347 6930 ± 135 8012-7523 Squeah Lake, British Gyttja below tephra Columbia Lowdon and Blake (1973) GSC-1487 7190 ± 75 8331-7722 Chase, British Marl below tephra Columbia Lowdon and Blake (1973) GSC-1487- 7400 ± 80 8537-8530 Chase, British Marl below tephra 2 Columbia Mathewes (1973) I-6821 7645 ± 340 9400-9350 Marion Lake, British Gyttja below tephra Columbia Mathewes (1973) I-6966 8275 ± 135 9539-8807 Surprise Lake, British Gyttja below tephra Columbia Mehringer et al., (1977a) WSU-1553 6720 ± 120 7834-7420 Lost Trail Pass Bog, Peat immediately below the tephra Idaho layer Duford and Osborn (1978) Gx-4039 7390 ± 250 8766-7686 Dunn Peak, British Charcoal below tephra Columbia Mack et al., (1978) TX-2116 6630 ± 80 7659-7420 Hager Pond, Idaho Wood or <5 cm segment of the core (not specified) below tephra Mack et al., (1979) TX-2884 8300 ± 80 9476-9034 Bonaparte Meadows, Peat immediately below tephra Washington Barnosky (1981) QL-1435 7460 ± 120 8510-8014 Davis Lake, Gyttja below tephra Washington Leopold et al., (1982) QL-1514 6930 ± 110 7957-7588 Lake Washington, Gyttja below tephra Washington Bacon (1983) USGS-870 7015 ± 45 7945-7740 Wineglass, Oregon Twig immediately below tephra

12 Brown et al., (1989) RIDDL-648 7080 ± 60 8015- Lake Mike, British Bulk sediment below tephra Columbia Brown et al. (1989) RIDDL- 6470 ± 100 7569-7179 Lake Mike, British Pollen concentrate below tephra 1058 Columbia Peterson et al., (2012) Beta 7000 ± 50 7939-7711 Lower Colombia Wood below tephra 271646 River Valley, Washington and Oregon Peterson et al., (2012) Beta 6990 ± 40 7933-7720 Lower Colombia Wood below tephra 276969 River Valley, Washington and Oregon Reeves and Dormaar (1972) GSC-1298 6720 ± 70 7917-7330 Southern Alberta Charcoal

Freeman et al., (2006) TO-10923 6870 ± 60 7835-7595 Southern Alberta Collagen from bone found 40 cm below Freeman et al., (2006) TO-12154 6630 ± 70 7616-7424 Southern Alberta Collagen from bone found 50 cm below Syn-Mazama Arnold and Libby (1951) C-247 6453 ± 250 7826-6787 Muir Creek, Oregon Charcoal from a tree killed by eruption Crane (1956) C-247b 6500 ± 500 8380-6319 Muir Creek, Oregon Reduced carbon sample from Arnold and Libby (1951) Rubin and Alexander (1960) W-858 6640 ± 250 7669-7001 Toketee Falls, Oregon Road cut between Rosenburg and Diamond Lake (charcoal within pumice) Westgate and Dreimanis (1967) S-191 6020 ± 90 7156-6671 Banff National Park, Bulk sample of paleosol and charcoal Alberta within tephra Valastro et al., (1968) Tx-487 6940 ± 120 7978-7579 Muir Creek, Oregon Charcoal enclosed in pumice

13 Fulton, (1971) I-3809 6560 ± 115 7654-7263 Columbia River Charcoal within tephra Valley, British Columbia Kittleman (1973) GaK-1124 7010 ± 120 8045-7606 Muir Creek, Oregon Charcoal from tephra flow deposit- Replication of Tx-487 Davis (1978) TX-2597 6710 ± 110 7789-7422 Virgin Creek, Nevada Organic material within tephra

Blinman et al. (1979) WSU-1742 6750 ± 90 7785-7444 Wildcat Lake, Organic lake sediment within the Washington tephra Blinman et al. (1979) WSU-2035 6765 ± 70 7741-7496 Wildhorse Lake, Organic lake sediment within the Oregon tephra Mack et al., (1979) TX-2883 6930 ± 110 7957-7588 Bonaparte Meadows, Peat within tephra Washington Mack et al. (1979) TX-2882 6810 ± 190 8014-7327 Bonaparte Meadows, Peat within tephra Washington Mack et al. (1979) TX-2881 6870 ± 110 7938-7522 Bonaparte Meadows, Peat within tephra Washington Bacon (1983) W-4288 6780 ± 100 7835-7467 North Umpqua River Charcoal fragment in tephra Valley, Oregon Bacon (1983) W-4290 6830 ± 110 7929-7502 North Umpqua River Charcoal fragment in tephra Valley, Oregon Bacon (1983) W-4255 6880 ± 70 7916-7589 North Umpqua River Small branch in tephra Valley, Oregon Bacon (1983) W-4256 7000 ± 60 7944-7698 North Umpqua River Log in tephra Valley, Oregon Bacon (1983) W-4295 6840 ± 100 7927-7513 North Umpqua River Twigs in tephra Valley, Oregon Hallett et al., (1997) TO-5192 6720 ± 70 7685-7463 Dog Lake, Kootenay Charcoal and twig fragments within National Park, British tephra Columbia

14 Hallett et al. (1997) TO-5196 6760 ± 70 7733-7489 Cobb Lake, Kootenay Charcoal and twig fragments within National Park, British tephra Columbia Gilbert and Desloges (2012) Beta 6660 ± 40 7595-7461 Quesnel Lake, British Twig within tephra 315832 Columbia Peterson et al., (2012) Beta 7020 ± 50 7954-7734 Lower Colombia Wood within tephra 271637 River Valley, Washington and Oregon Peterson et al. (2012) Beta 6700 ± 50 7660-7484 Lower Colombia Wood within tephra 260169 River Valley, Washington and Oregon Peterson et al. (2012) Beta 7240 ± 40 8163-7978 Lower Colombia Wood within tephra 288781 River Valley, Washington and Oregon Above Mazama Rubin and Alexander (1960) W-777 6600 ± 400 8312-6659 Arrow Lake, Peat directly above tephra Washington Dyck et al., (1965) GSC-214 6270 ± 70 7438-6800 Deep Creek, British Organic muck above tephra Columbia Buckley and Willis (1969) I-3158 6190 ± 120 7413-6786 Columbia River, Charcoal above tephra British Columbia Buckley and Willis (1970) I-3647 6670 ± 120 7755-7324 Portage Inlet, Peat above tephra Vancouver Island, British Columbia Fulton, (1971) I-3807 5550 ± 120 6637-6019 Columbia River Wood above tephra Valley, British Columbia

15 Lowdon et al., (1971) GSC-1183 5500 ± 70 6652-6002 Mount Revelstoke, Peat above tephra British Columbia Mullineaux (1974) W-2422 6730 ± 250 8157-7160 Mount Rainier Peat immediately above the tephra National Park Mehringer et al. (1977a) WSU-1552 6700 ± 100 7739-7423 Lost Trail Pass Bog, Lake sediments above tephra Idaho Mack et al., (1978) TX-2121 6350 ± 230 7667-6734 Hagar Pond, Idaho Wood above tephra Blinman et al. (1979) WSU-1452 5380 ± 130 6435-5905 Wildcat Lake, Organic lake sediment above tephra Washington Barnosky (1981)Barnosky QL-1434 6420 ± 110 7568-7156 Davis Lake, Gyttja above tephra (1981) Washington Leopold et al., (1982) QL-1513 7200 ± 200 8396-7668 Lake Washington, Gyttja above tephra Washington Luckman et al., (1986) GSC-2648 6570 ± 35 7581-7328 Tonquin Pass, British Log above tephra Columbia Brown et al., (1989) RIDDL-647 6860 ± 60 7917-7575 Lake Mike, British Bulk sediment above tephra Columbia Brown et al. (1989) RIDDL- 6490 ± 80 7563-7264 Lake Mike, British Pollen concentrate above tephra 1057 Columbia White and Osborn (1992) BGS-1098 6850 ± 140 7955-7476 Copper Lake, Banff Gyttja above tephra National Park, Alberta White and Osborn (1992) BGS-1084 7980 ± 220 9421-8410 Copper Lake, Banff Gyttja above tephra National Park, Alberta Colman et al., (2004) CAMS- 7260 ± 60 7680 ± 100*** Upper Klamath Lake, Total Organic Carbon in bulk 38121 Oregon sediment above tephra layer Colman et al. (2004) CAMS- 7310 ± 50 7710 ± 110*** Upper Klamath Lake, Total Organic Carbon in bulk 38122 Oregon sediment above tephra layer Colman et al. (2004) CAMS- 7300 ± 50 7690 ± 115** Upper Klamath Lake, Total Organic Carbon in bulk 38123 Oregon sediment above tephra layer

16 Colman et al. (2004) CAMS- 7330 ± 50 7750 ± 125** Upper Klamath Lake, Total Organic Carbon in bulk 38124 Oregon sediment above tephra layer Colman et al. (2004) CAMS- 6790 ± 70 7674 ± 114** Upper Klamath Lake, Total Organic Carbon in bulk 12658 Oregon sediment above the tephra layer Peterson et al., (2012) Beta 6150 ± 50 7033 ± 137 Lower Colombia Wood above tephra 271645 River Valley Landals (1986) RL-508 6420 ± 160 7595-6955 Southern Alberta Bone

Ice-core ages Ice-core layer counted age BP Hammer et al., (1980) 6350 ± 110 Camp Century, Greenland Zdanowicz et al., 7627 ± 150 GISP2, Greenland (1999) *Unmodelled calibrated ages (95.4%highest probability density range) determined using the IntCal13 (Reimer et al. 2013) calibration curve and OxCal software (v.4.2; Bronk Ramsey 2013)

**’Corrected’ ages (-400 years) provided by Colman et al., (2004) due to contamination of old carbon.

17 Bayesian Statistical Modelling

The implementation of Bayesian statistical methodologies to radiocarbon data, developed since the 1990s (and facilitated by the advancement of computer processing power that enables the multiplicity of calculations required in such methods) has “revolutionised’ the field (Bayliss, 2009). The Bayesian approach to data analysis provides a mechanism for handling uncertainty, and formalises the relationship between assumptions and conclusions in terms of probabilities (Buck et al., 1996). There have been ongoing developments of age modelling software based on Markov Chain Monte Carlo (MCMC) simulation techniques that are implemented in packages such as OxCal (Bronk Ramsey, 1995; 2013), BCal (Buck et al.,

1999), Datelab (Jones and Nicholls, 2002), and BPeat (Blaauw et al., 2003; Blaauw and

Christen, 2005; Blaauw and Christen, 2011), which apply Bayes' theorem (1763) to radiocarbon calibration (Christen, 1994; Buck et al. 1996). They have been applied to questions in archaeology (e.g. Parker-Pearson et al., 2007; Beramendi-Orosco et al., 2009;

Alberti, 2013; Quiles et al., 2013) and Quaternary science (e.g. Blockley et al., 2004; Riede and Edinborough, 2012), including the determination of the timing of volcanic eruptions (e.g.

Buck et al., 2003; Davies et al., 2004; Plunkett et al., 2004;Wohlfarth et al., 2006; Petrie and

Torrence, 2008; Schiff et al., 2008; Lowe et al., 2013; Smith et al., 2013).

Bayes’ theorem (1763) allows for the explicit inclusion of prior information, and may include information such as depths of a stratigraphical sequence or the scale of any reservoir offsets.

The radiocarbon measurements themselves, the likelihood, are combined mathematically with the model Prior to construct a set of posterior probability distributions giving the modelled calendar age (Ramsey, 2008, 2009b).

Method

18 Possible issues associated with the sampling procedures (including sample type, and unreliable stratigraphic integrity), and radiocarbon dating (including lack of rigorous chemical pre-treatment) has produced a somewhat broad scatter of age estimates for the climactic eruption of Mount Mazama (Table 1). To derive a precise age for the eruption, an extensive literature search was first undertaken for published ages pertaining to the eruption

(Table 1). Included in Table 1 are the individually calibrated ages of each sample, applying the IntCal13 radiocarbon calibration curve (Reimer, 2013). A contiguous three Phase

Bayesian model, was constructed using OxCal v.4.2 (Bronk Ramsey, 2014), with the three phases including all of the 14C data obtained from the literature review and grouped ’below’

(i.e. chronologically before), syn- (i.e. contemporaneous with), or ‘above’ (i.e. chronologically after) the eruption . Whilst individual age estimates from samples above or below tephra deposits provide minimum or maximum ages, respectively, they can still provide useful constraining information when combined in such a model. Since samples falling into the ‘above’ and ‘below’ phases should be skewed to lie closer in time to the

Mazama eruption age (as they were initially selected by the original papers’ authors to provide ‘best’ estimates for the Mazama ash), the ‘Tau_Boundary’ function was applied in

OxCal to reflect this assumption. It is unlikely that the dates in the “below” and “above” phases are uniformly distributed (figure 4a in supplementary materials). Instead, the dates are likely to tail off at the ends (figure 4b in supplementary materials), which essentially assists the model to give a more precise age for the “syn-Mazama” phase. Such an approach has also been applied by Lowe et al. (2013) and Vandergoes et al. (2013) to constrain tephra age estimates.

All data were included in the model reported here so that no subjective bias was created by excluding certain samples. An alternative approach would be to filter the dates according to

19 certain ‘quality assurance’ criteria prior to modelling. This approach was used when refining the age of the Glacier Peak eruption by Kuehn et al., (2009) for example. They excluded all ages on bulk sediments, gyttja and aquatic macrofossils because of the potential hard water effects of these materials and the chronological ‘smoothing’ of ages on the bulk material.

Here, we ran a supplementary model for the Mazama ash, using the same model construction as for the main model, but excluding those samples that failed the criteria set out by Kuehn et al. (2009). The resultant age estimate for the Mount Mazama ash was in good agreement with the full model reported here, though offering reduced precision due to the much smaller remaining dataset. Further filtering of data from studies that did not report robust chemical pre-treatment of samples again gave an age estimate in good agreement with the full model

(the results are provided in the supplementary material). The second phase (syn-Mazama) includes a ‘Date’ function, which is a tool to specify a date with no prior assumptions. Here it is used to represent the ‘true’ age for the eruption. Included in the model are several additional features. The R_Combine function allows the user to combine dates, and was used for sample C-247, dated twice by Arnold and Libby (1951) and Crane (1956), and again for sample Tx-487/GaK-1124 dated by Valastro et al. (1968) and Kittleman (1973). There is a nested Sequence for the data of Lowdon and Blake (1973) as they reported two ages in stratigraphic order below the tephra, and a sequence for ages reported by Mack et al. (1979) as they published three ages in stratigraphic order within the tephra layer. Two outlier models were applied, Outlier_Model(“Charcoal”) and Outlier_Model(“General”), to statistically determine any outliers and down-weight any such ages so that they did not exert undue influence on the refined calculated age (Bronk Ramsey, 2009b; Bronk Ramsey et al.,

2010). The Outlier_Model(“Charcoal”) was applied to the ages whose sample material was charcoal. This model was deemed most appropriate as charcoal often provides older ages

(than the burning event in question), due to the burning of wood with an ‘inbuilt age’, giving

20 a long tail for this distribution (Bronk Ramsey, 2009a). The Outlier_Model (“General”) was chosen for the remaining ages, which allows for a Normal prior probability distribution for the outliers, with an equal probability of samples being younger, or older than the ‘true’ age.

Such a prior, is deemed the most appropriate as it draws from long-tailed distributionwhich is useful as the scale of any offsets are not known (Bronk Ramsey, 2009a). The reason for using such a long tailed distribution in this type of model is that, under the processes of outlier identification, there are sometimes a few very extreme outliers, and we do not wish the modelled outlier distribution to be too heavily dependent on these, meaning other potential outliers go unidentified (Bronk Ramsey, 2009a). The two ice-core ages are plotted for comparison only and to determine which age was closer to the radiocarbon estimate, but they do not contribute to the determination of the independent, radiocarbon-derived age estimate.

In addition, cluster analysis was performed in order to partially test the Bayesian radiocarbon model as it would be expected that similar groupings would be identified i.e. those identified by the Bayesian model as outliers. as the ages are much older, should be grouped together. In order for this to be most successful, the data were separated into three cluster analyses to reflect the ages that were from below, within or above the tephra layer. Euclidean cluster analysis was performed using Past V. 3.01 (Hammer, 2014).

Results

Figure 2 displays all of the Bayesian modelled ages and the results of outlier analysis. Several ages can be considered significant outliers (here, we list those with posterior outlier probabilities >50%): TX-2116 (posterior outlier probability= 59%) (Mack et al. 1978), GSC-

963 (74%) (Lowdon and Blake, 1970), Beta 271637(78%) (Peterson et al. 2012), S-191

21 (100%) (Westgate and Dreimanis, 1967), Beta 288781(100%) (Peterson et al. 2012), BGS-

1084 (100%) (White and Osborn, 1992), CAMS-38121 (100%), CAMS-38122 (100%),

CAMS-38123 (100%) and CAMS-38124 (100%) (Colman et al. 2004). Those with a posterior outlier probability of 100% are down-weighted completely, such that they have no influence on the final model output (Bronk Ramsey, 2009b).

22 23 24 Based on this analysis, and having taken the outliers into consideration, the climatic eruption of Mazama most likely took place between 7682 and 7584 cal. years BP at the 95.4% highest probability density (HPD) range (Figure 3).

Figures a-4c show the results of the cluster analyses, which have grouped the various ages to reflect how far away those ages are from the modelled date of Mazama, and has successfully identified some as outliers by placing them in exclusive groups, as discussed further below.

25 26 Cluster analyses (Figure 4a-c) have been performed on all the radiocarbon dates included in

Table 1, divided into 3 phases as for Bayesian analysis. For the ages before-Mazama, five zones are identified, with Zone 1 consisting of the oldest ages, with central dates ranging from 8380 to 8275 14C years BP. None of these were identified as statistically significant outliers during the Bayesian analyses, due perhaps to low precisions and long tail in their probability distributions. Zone 2 has ages ranging from 7610 to 7510 14C years BP, older than the modelled probability peak, and stratigraphically below the tephra. Zone 3 reflects ages below Mazama that are closest to the modelled age, ranging from 7190-6990 14C years

BP, and Zone 4 consists of ages ranging from 6600-6390 14C years BP, ‘too young’ for this phase despite being below the tephra. Two of these ages were identified as outliers (>60% posterior outlier probability) by the Bayesian analyses (TX-2116 and GSC-963). Lowdon and Blake (1970) (GSC-963) dated gyttja below the tephra, and Mack et al. (1978) (TX-

2116) dated either wood or a segment of bulk sediment (<5 cm); it was not specified which for this particular sample. Zone 5, a single determination, is the youngest age reported in this phase below Mazama, at 5950 ± 400 14C years BP, and the age is given a 19% probability of being an outlier by the Bayesian model. The sample was not considered to have 100% probability of being an outlier due to the low precision of this age, and resulting overlap with the modelled, calibrated age. If the measurement had been more precise, the probability of it being an outlier would have been higher.

Zones 6-10 (Figure 4b) reflect the ages syn-Mazama. Zone 6 consists of ages ranging from

7020 to 6940 14C years BP, which are approximately 200 years older than the modelled age of

Mazama. There is a possibility that these ages reflect the earlier eruption of the Llao Rock eruptive centre. The strongest case for this hypothesis comes from the ages obtained by Mack et al. (1979) who identified two distinct tephra layers separated by 50 cm of peat (as measured by extracted core length). The sample that gave an age approximately 200 years

27 older than the modelled Mazama age (TX-2883) came from the lower, older tephra unit within the stratigraphic sequence, however this implies a very rapid accumulation rate.

Bayesian analyses identified Beta-271637 (Peterson et al. 2012) as an outlier. This is the oldest age within Zone 6, on wood from within the tephra layer in lacustrine sediment from the Lower Colombia River Valley, and Peterson et al. (2012) identified possible incorporation of older wood into the suspended tephra during transport downriver. Zone 7 consists of ages ranging from 6880 to 6710 14C years BP, closest to the modelled age of

Mazama and the Zdanowicz et al. (1999) ice-core age. Within this zone is a cluster of ages that had the ‘best fit’ (± 46 years) with the modelled age of Mazama. These determinations ranged from mean values of 6780 to 6750 14C years BP (7650-7613 cal. years BP) and came from various sediment types: organic lake sediments (Blinman et al. 1979), charcoal (Bacon,

1983), and twig fragments (Hallett et al. 1997) from within the tephra layer. The tephra layers were all of substantial thicknesses, ranging from 7-10 cm. Zone 8 consisted of ages that were slightly ‘too young’ compared to the model, with ages ranging from 6640 to 6453

14C years BP. Zones 9 and 10 consisted of single ages that were too young (S-191: 6020 ±90

14C years BP) and too old (Beta-288781- 7240 ±40 14C years BP), and were both identified as outliers in the Bayesian analyses. Westgate and Dreimanis (1967) (S-191) dated charcoal retrieved from sediment. Mixing processes may have caused younger carbon to become incorporated with the Mazama tephra layer, or post-sampling contamination may have affected the conventional age. Alternatively, the younger age may reflect the problems associated with a lack of reliable chemical pre-treatments. Peterson et al. (2012) dated wood, as for Beta-271637, and suggested that the sample may have been contaminated by older carbon.

Cluster analysis for samples above Mazama tephra identified six further zones (Figure 4c).

Zone 11 consists of younger material with ages ranging from 6350 to 6270 14C years BP.

28 None of these were identified as outliers during the Bayesian analyses, as their distributions are consistent with the model prior that these samples post-date the tephra. Zone 12 consisted of ages closest to the modelled Mazama age in this phase, and show a minimum age. These ages ranged from 6790 to 6570 14C years BP. Zones 13, 14 and 15 consisted of the older ages for this phase (QL-1513, CAMS-38121, CAMS-38122, CAMS-38123, CAMS-38124), the strikingly oldest being in zone 15 (BGS-1084). These ages ranged from 7980 to7200 14C years BP. Bayesian analyses identified most as outliers with posterior values of 100%, so they had no influence on the model output. QL-1513 was given a posterior value of 38% and is the youngest age within this zone. White and Osborn (1992) (BGS-1084) recognised that an old carbon effect in gyttja was the likely cause of the older ages. Zone 16 contained the youngest ages of the phase above Mazama with ages ranging from 5380 to 5550 14C years

BP. These ages were given posterior values of 15-18%, so their influence on the Bayesian model was down-weighted.

The ages from zones 4, 5, 9, 10, 13, 14 15 and 16 contain ages that are strikingly much older or younger than other ages within that phase. There are 19 age estimations in total in these zones (excluding CAMS-38121, CAMS-38122, CAMS-38123 and CAMS-38124 from

Colman et al. 2004 due to their unreliability), and out of these 19 age estimations, 11 were measured before reliable chemical pre-treatments and 14 dated bulk sediments, illustrating the caution that is needed when analysing pre-1980 measurements and the importance of the dating material, although charcoal and lake sediment samples were also included in the cluster that most closely matches the modelled age estimate.

Discussion

29 Bayesian modelling of all reported determinations on the Mazama eruption has provided an age estimate in close agreement with 14 of the previous age estimates (zone 7 figure 4b) taken from within the Mazama tephra layer, four of which are especially close. These are

WSU-1742, a date of 6750 ± 90 14C years BP on organic lake sediment from within the tephra layer at Wildcat Lake, Washington (Blinman et al. 1979), WSU-2035 at 6765 ± 70 14C years BP, also on organic lake sediments, but from Wildhorse lake, Oregon, (Blinman et al.

1979), W-4288, a date of 6780 ± 100 14C years BP on charcoal from road cuts along Oregon

Highway 138 at the North Umpqua River Valley(Bacon, 1983), and TO-5196, a determination of 6720 ± 10014C years BP on charcoal and twigs from within the tephra from

Dog Lake, British Columbia (Hallett et al. 1997). Cluster analysis was undertaken to test the output from the Bayesian model and identified similar groupings of ages (Figure 4), with a sub-set of four determinations in particular being closest to the modelled age.

The modelled age of the climactic phase of the eruption of Mazama has been refined to an approximately 100 year age range (7682-7584 cal. years BP) at the 95.4% HPD (highest probability density) range. This range is reduced to under 50 years at the 1σ (68.2% HPD) confidence level (7652-7605 cal. years BP), and the model represents a 176 year range at the

99.7% confidence level (7743-7567 cal. years BP). These results are consistent with, but more precise than, the GISP2 ice-core age provided by Zdanowicz et al., (1999) of 7627 ±

150 years BP with 2σ error. The more precise modelled age shown here could be used to add precision to the GISP2 chronology, if the provenance of the volcanic record in the GISP2 core is assured. Blaauw (2012) suggested that caution is needed when assuming that acid peaks pertain to known eruptions, as previous ice core ages of the eruption of Hekla-3, for example, were a century younger than the age estimate provided by radiocarbon dating.

Hogg et al., (2011) also found ice-core ages to be inaccurate, as they showed an acid peak originally assumed to be from the Taupo eruption dated AD 181 ±2, different from a

30 radiocarbon wiggle-matched age estimate of AD 232 ±5. The overlap with the GISP2 ice-core age (Zdanowicz et al. 1999) suggests that the Zdanowicz et al. (1999) data do relate to the correct sulphate peak and that the age from Hammer et al. (1980) should be rejected, with implications for the core chronology used at that time from Camp Century or, more likely, suggesting that the attribution of this acidity peak to the Mazama eruption is incorrect.

Potential problems with the model produced here can be noted. There was little information about the depositional history of these samples and issues of re-working and re-deposition are still important considerations. However, the reported radiocarbon dates closest to the modelled, ‘most likely’ age range come from a variety of sediment types and materials, and include AMS and conventional determinations. Although Bayesian analysis has produced the most likely age, and cluster analyses concur with the Bayesian analyses, ideally more tightly constrained depositional histories could be used to improve this precision further. There were many reports of ages that did not give any clear indication about the stratigraphy of the core, any evidence of mixing, whether there was more than one tephra layer, or the depths that samples were taken from; specifying how far away from the tephra layer samples were taken.

However, with 81ages included, without many constraining assumptions, we believe the analysis is robust enough to have confidence in the resulting age estimate.

Conclusion

Through the Bayesian modelling of all previous radiocarbon age estimations relating to the

Plinian eruption of Mount Mazama, a refined age of 7682-7584 cal. years BP (2σ, 95.4%

HPD) (7652-7605 cal. years BP, 68.2% HPD; 7743-7567 cal. years BP, 99.7% HPD) has been produced. The age estimate agrees well with a previous ice-core derived age estimate of

7627 ±150 years BP (Zdanowicz et al., 1999), but is more precise. This age estimate can now

31 be used with confidence as an age marker as well as a correlation point in palaeoenvironmental reconstructions.

The analysis has exemplified that in order to obtain an accurate age of the eruption of a tephra layer, the material dated ideally needs to come from the points of highest tephra concentration within the tephra layer, rather than the first point of tephra deposition as boundaries may have been disturbed by mixing processes. Information can be utilised from dating material above and below tephra deposits, but such data are most useful when combined in a Bayesian framework, as performed here, otherwise they can only provide maximum or minimum age constraints. While the more reliable dating material (as confirmed by this study) is wood (ideally, twigs) and (identifiable) charcoal, in some cases the ages from these types of materials were found to be outliers (e.g. Peterson et al.,

2012:Beta 288781), which is likely to be a result of contamination or old wood offsets. The age-range reported here can be tested and further refined by radiocarbon dating short-lived plant material such as Sphagnum leaves (Barber et al., 2008) or Cyperaceous remains

(Blackford et al., 2014), with multiple dates in sequence.

Acknowledgements

We would like to thank Dr. Christine Lane (University of Manchester) for her invaluable comments on the paper.

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