Using ice core measurements from Taylor Glacier, Antarctica to calibrate in situ cosmogenic C production rates by muons

Cosmic rays entering the Earth’s atmosphere produce showers of secondary particles such as neutrons and muons. The interaction of these neutrons and muons with oxygen-16 (O) in minerals such as ice and quartz can produce carbon-14 (C). Analyses of in situ produced cosmogenic C in quartz are commonly used to investigate the Earth’s landscape evolution. In glacial ice, C is also incorporated through trapping of C-containing atmospheric gases (CO2, CO, and CH4). Understanding the 35 production rates of in situ cosmogenic C is important to deconvolve the in situ cosmogenic and atmospheric C signals in ice, both of which contain valuable paleoenvironmental information. Unfortunately, the in situ C production rates by muons (which are the dominant production mechanism at depths of >6 m solid ice equivalent) are uncertain. In this study, we use measurements of in situ C in ancient ice (>50 kilo-annum before present, ka BP) from the Taylor Glacier ablation site, Antarctica in 40 https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c © Author(s) 2022. CC BY 4.0 License.


Potential applications of 14 C measurements in ice and in situ cosmogenic 14 C production from 16 O in Earth's surface minerals
As snow accumulates on ice sheets, it gradually densifies into firn and ice (Herron and Langway, 50 1980). During the firn to ice transition, the air in the interstitial space between the ice grains becomes trapped into bubbles within the ice matrix (Buizert, 2013). Included in the paleoatmospheric air trapped in the bubbles are 14 C-containing atmospheric gases ( 14 CO2, 14 CO, and 14 CH4) (Fireman and Norris, 1982). 14 C in ice is also produced through interactions of secondary cosmic rays with 16 O directly in the lattice of the ice grains (i.e., "in situ") . Following the cosmogenic nuclear reactions, the "hot" 14 C 55 atom interacts with atoms in the surrounding ice lattice to produce 14 CO2, 14 CO, and 14 CH4 Petrenko et al., 2013).
Both the trapped atmospheric and in situ cosmogenic 14 C signals in ice have unique applications. For example, the paleoatmospheric component of 14 CH4 in ice cores has been used to constrain past CH4 emissions from old carbon reservoirs such as methane hydrates, permafrost, and geologic seeps (Dyonisius 60 et al., 2020;Hmiel et al., 2020;Petrenko et al., 2009Petrenko et al., , 2017. Paleoatmospheric 14 CO2 can be potentially used for absolute dating of ice core gases (Andree et al., 1984;Van De Wal et al., 1994) and to improve the radiocarbon calibration curve (Reimer et al., 2020;Hogg et al., 2020) in periods where tree-ring data are not available. Measurements of 14 CO in the modern atmosphere have been used to constrain the oxidative capacity of the atmosphere (Brenninkmeijer et al., 1992;Petrenko et al., 2021) and thus, paleoatmospheric 65 14 CO in ice cores can be used for a similar application. The in situ cosmogenic component of 14 CO at ice core sites can be potentially be used to reconstruct the past cosmic ray flux (BenZvi et al., 2019). Finally, measurements of the in situ cosmogenic component of 14 CO2 and 14 CO can be used to constrain the accumulation/ablation rate of the ice core site (e.g., . Unfortunately, the paleoatmospheric and in situ cosmogenic components of 14 C in ice exist in a combined form and cannot be 70 separated analytically (Petrenko et al., 2016). To separate these signals, it is important to have accurate estimates of the cosmogenic 14 C production rates and the partitioning among the in situ produced 14 C species ( 14 CO2, 14 CO, and 14 CH4) in ice. https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License.
Measurements of in situ cosmogenic nuclides ( 3 He, 10 Be, 14 C, 21 Ne, 26 Al, and 36 Cl) in near-surface rocks are commonly used as tools to constrain various Earth surface processes such as the timing of glacial 75 retreat and erosion rates (Gosse and Phillips, 2001;Balco, 2020). Due to its short half-life of 5700 ± 30 yr (Kutschera, 2019), 14 C in quartz is uniquely suited to characterize surface processes on millennial timescales (e.g., Spector et al., 2019;Pendleton et al., 2019). In situ cosmogenic 14 C measurements are also often paired with measurements of longer-lived nuclides such as 10 Be and 26 Al (e.g., Hippe, 2017;Skov et al., 2019) to study complex surface processes such as subglacial erosion and millennial-scale glacier 80 retreats/re-advances.
In situ cosmogenic 14 C in Earth's surface minerals is produced from 16 O by 3 nuclear reactions: (1) neutron-induced spallation (Lal and Peters, 1967), (2) negative muon capture (Heisinger et al., 2002b), and (3) interactions with fast muons (Heisinger et al., 2002a). The depth-dependence of the 14 C production rate for each mechanism in ice is shown in Fig. 1. Neutron-induced spallation dominates the 14 C production at 85 the surface but is quickly attenuated with depth, while the production rates from the two muon mechanisms are lower near the surface but dominate at larger depths. Characterizing the in situ cosmogenic 14 C production rates from muons is especially important for applications of cosmogenic surface exposure dating where the samples might be exposed to subsurface cosmic-ray flux for an extended period. One example of this would be bedrock that is covered by a relatively thin (e.g., tens of meters) glacier. 90 Understanding the muogenic 14 C component is also important for 14 C studies in ice. Prior studies have shown that at snow accumulation sites, most of the in situ 14 C produced in the firn (including the majority of neutron-produced 14 C) is lost to the atmosphere via gas movement in the firn open porosity (Petrenko et al., 2013;van der Kemp et al., 2000;Wilson and Donahue, 1992). In situ cosmogenic 14 C mainly starts to accumulate in deeper ice where gas exchange with the atmosphere no longer happens and at these depths 95 the 14 C production is entirely from the muon mechanisms. Thus, the in situ cosmogenic 14 C signal in traditional deep ice cores is dominated by production from muons and constraining the muogenic 14 C production rates is critical to disentangle the in situ cosmogenic and atmospheric 14 C signals in ice cores.
Unfortunately, the in situ 14 C production rates by muons in both ice and quartz are still highly uncertain (Hippe, 2017). 100 The production rates of cosmogenic nuclides are usually determined from calibration sites where independent controls on exposure history are available such as 14 C dating from organic materials (e.g., Lifton et al., 2015) or argon ( 40 Ar/ 39 Ar) dating from lava flows (e.g., Balbas and Farley, 2020;Fenton et al., 2019). However, the commonly used estimates of muogenic 14 C production rates (for both negative muon capture and fast muon reactions) were derived through laboratory irradiation of artificial target compounds 105 (Heisinger et al., 2002a(Heisinger et al., , 2002b. To our knowledge, there is only one prior study (Lupker et al., 2015) that provided estimates of total muogenic in situ 14 C production rates based on measurements in a natural setting. Using 14 C measurements from a 15.5m deep quartzite core from Leymon High, Spain, Lupker et al. https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License.
(2015) estimated a sea level high latitude (SLHL) surface production rate of 3.34 (+0.43/-1.07) 14 C atoms g -1 quartz yr -1 for negative muon capture and 0 (+0.42/-0.00) 14 C atoms g -1 quartz yr -1 for fast muon 110 interactions (1σ uncertainties). The large uncertainties on the 14 C production rates (especially the production rate from fast muons) estimated by Lupker et al. (2015) were due to relatively large measurement uncertainty for their deepest samples and small contribution to the 14 C signal from fast muons. Petrenko et al. (2016) also used 14 C measurements ( 14 CO, 14 CO2, and 14 CH4) in >50 ka BP ice for the 2 -20 m depth range from Taylor Glacier, Antarctica to constrain the 14 C production rates in ice. The 115 old age of the ice ensured that all in-situ cosmogenic and paleoatmospheric 14 C inherited from the ice accumulation site had decayed away. Unfortunately, Petrenko et al. (2016) were unable to accurately constrain the total 14 C production rates because of the high uncertainty resulting from the melt-extraction technique used to obtain their 14 CO2 measurements (see Section 1.3).

1.2.
Overview of 14 C production from muons 120 In situ cosmogenic 14 C production in ice is analogous to production in quartz because both minerals share the same target atom ( 16 O). Following Heisinger et al. (2002b), the production rate of 14 C (atoms g -1 yr -1 ) by negative muon capture (Pneg) as a function of lithospheric depth (h, typically in g cm -2 ) is given by where Rμ-(z) is the stopping rate of negative muons (muons g -1 yr -1 ) at lithospheric depth h and ftot is the overall probability of 14 C production in ice from a stopped negative muon (unitless). The stopping rate of 125 negative muons at the given depth Rμ-(h) has been empirically determined from measurements at deep underground laboratories (Heisinger et al., 2002b). The lithospheric depth (h) is a product of actual depth (z) and density (ρ) of the target mineral (ρice = 0.92 g cm -3 ).
The total probability (ftot) of 14 C production from negative muon capture is expressed by the product of the chemical compound factor (fC) representing the probability that the stopped muon is captured by one 130 of the target atoms ( 16 O in case of 14 C production), the probability that the negative muon does not decay in the K-shell before nuclear capture (fD), and the effective probability for production of cosmogenic nuclide after μcapture by the target atom (f*) (Eq.2; Heisinger et al., 2002b;Lupker et al., 2015). All probability (f) terms in Eq.2 are unitless. From experiments involving laboratory irradiation of artificial targets, the overall probability (ftot) for 14 C production in ice from negative muon was estimated to be 0.025 ± 0.002 135 (Heisinger et al., 2002b).
An expression for the production rate of nuclides by fast muon interactions (Pfast) as a function of lithospheric depth (h) is given by Heisinger et al. (2002a): where ϕ(h) is the total muon flux at depth z (muons cm -2 yr -1 sr -1 ), σ0 is the reference nuclear reaction cross section at muon energy of 1 GeV (millibarn, mb), β(h) is the unitless parameterized depth dependence 140 factor (Eq. 4), Ē(h) is the mean muon energy at depth h (GeV), α is a power factor that describes the energy dependence of the cross section (unitless), and N is the number of target nuclei per gram target mineral.
The overall production rate of 14 C from fast muons provided by Heisinger et al. (2002a) has a high uncertainty because of the uncertainty of the reference nuclear reaction cross section σ0 (σ0 = 0.0088 ± 0.0049 mb). Following Lupker et al. (2015), in this study we used ftot and σ0 as tuning parameters for the 145 two muogenic production mechanisms in a cosmogenic nuclide production model (Section 3.2) to fit our 14 C measurements.

Gas extraction methods for ice core 14 C analysis
Common methods to liberate gas trapped in ice core bubbles include melting (wet extraction; e.g., Sowers et al., 1992;Mitchell et al., 2011) and mechanical destruction of the ice lattice (dry extraction; e.g., 150 Bereiter et al., 2013;Ahn et al., 2009;Zumbrunn et al., 1982). Dry extraction is generally preferable for CO2 analysis because the presence of liquid water in a wet extraction introduces extraneous CO2 from the carbonate-acid reaction between the meltwater and impurities in the ice (e.g., Delmas et al., 1980;Raynaud et al., 1982). Multiple studies of 14 CO2 in ice have used dry extraction methods (e.g., Van De Wal et al., 1994;Smith et al., 2000;Van der Kemp et al., 2000;Van De Wal et al., 2007). However, dry extraction 155 systems (e.g., Lüthi et al., 2008) can potentially introduce biases in CO2 mole fraction [CO2] due to incomplete gas extraction (Bereiter et al., 2015). Considering that the in situ cosmogenic production of 14 C occurs directly in the ice lattice , it has been argued that dry extraction may also not liberate all of the 14 C from the ice (e.g., van Roijen et al., 1994).
Other studies of 14 C in ice (e.g., Jull et al., 1994;Lal et al., 1997Lal et al., , 2001 have used wet 160 extraction methods. These wet-extraction studies involved an addition of acid to drive off all dissolved CO2 from the meltwater Jull et al., 1994;Lal et al., 1997Lal et al., , 2001. The acidification process may have resulted in an additional CO2 release from impurities in the ice (e.g., carbonate dust). In dust-rich Greenland ice, the presence of liquid water in a wet extraction produced "in-extractu" excess CH4 (Lee et al., 2020). It is thus possible that a wet extraction approach for 14 C analysis may also result in additional C 165 release from organics in the ice, which are not 14 C-free.
A third method to liberate gases trapped in ice cores is sublimation under vacuum (e.g., Wilson and Donahue, 1989;Wilson and Long, 1997;Wilson and Donahue, 1990;Siegenthaler et al., 2005;Schmitt et al., 2011). Sublimation can occur when the pressure and temperature on the surface of the ice are below the triple point of the water phase change diagram. In addition to being free of problems associated with wet 170 extraction methods, sublimation guarantees 100% gas extraction efficiency (Schmitt et al., 2011; al., 2013, 2015) which includes any 14 C trapped in the ice lattice. Therefore, sublimation is likely an optimal method for 14 CO2 measurements in ice.
This study presents new 14 C measurements in 3 gas species ( 14 CO, 14 CO2, and 14 CH4) in ancient (>50 ka BP) ice from the ablation zone of Taylor Glacier, Antarctica to constrain the total 14 C production rates in 175 ice by muons. Ice at this location does not contain a significant amount of 14 C inherited from the accumulation site (Petrenko et al., 2016), and the 14 C content is due almost entirely to production by muons during transport within the glacier. We improved on the earlier work by Petrenko et al. (2016) by (1) using a newly developed ice sublimation extraction device for 14 CO2 measurements (see Section 2.3.2), (2) collecting deeper samples to ~72 m to better characterize the 14 C production rate from the fast muon 180 mechanism, and (3) using a more realistic 2D ice-flow model from Buizert et al. (2012) to account for the flow trajectory and exposure history of the samples (see Section 3.1).

Site Description
The blue ice area of Taylor Glacier (Fig. 2) provides access to near-unlimited amounts of well-dated 185 ancient ice Bauska et al., 2016;Menking et al., 2019;Schilt et al., 2014;Shackleton et al., 2020). This allows Taylor Glacier ice to be measured for ultra-trace gas species that require a very large amount of ice Petrenko et al., 2016Petrenko et al., , 2017Buizert et al., 2014).
In this study, we used the same site as Petrenko et al. (2016) (77°43.699′S, 161°43.179′), where ice >50 ka in age at the surface has been previously identified. 190

Field sampling
Approximately 1000 kg of ice is needed to obtain both the necessary CH4-derived and CO-derived C mass for 14 C analyses. Because of this large sample requirement, and to avoid post-coring in situ 14 C production at the surface, the melt extraction for 14 CH4 and 14 CO samples was performed on-site using the large volume melter apparatus and technique described in Petrenko et al. (2016). The liberated air was 195 transferred to 34.9 L electropolished stainless steel canisters and shipped to our laboratories for processing and analyses. Similar to other studies using this large volume ice melter (e.g., Petrenko et al., 2016Petrenko et al., , 2017, four procedural blanks (two with 'modern' 14 CH4 standard gas and two with ' 14 C-dead' 14 CH4 standard gas) were collected in the field. These field procedural blanks allow us to characterize the addition of extraneous 14 C to the samples. The standard gases used in the field procedural 200 blanks were passed through a Sofnocat 423 reagent which removes CO (and thus 14 CO) but leaves CH4 (and 14 CH4) intact. https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License.
The overall sampling scheme for this study is shown in Fig. S1. We used the 9.5-inch diameter Blue Ice Drill (BID)  to collect 7 large-volume samples during the 2015/2016 austral summer field season for 14 CO and 14 CH4 analyses. The "surface" sample was collected from 21 x 1.5m deep shallow 205 cores, each with an average mid-depth of ~ 0.75m. Six additional deep samples with mid-depths of 19.5m, 30m, 40.5m, 51m, 61.5m, and 72m were also collected by combining ice from three ~78m deep boreholes.
Each of the deep large-volume samples spanned approximately 10.5m depth. Continuous "sticks" of ice subsamples (3x3 cm, spanning the whole length of the core) were taken from one of the three ice core boreholes ("TGDeep3") for age control (see Supplementary Material Section 3). The continuous sample 210 sticks were measured for CH4 mole fraction [CH4] using the continuous flow analysis (CFA) system described in Rhodes et al. (2013) at Oregon State University (OSU).
In addition to the large volume samples, we collected 26 smaller subsamples (~1.5-2 kg) from 13 depth levels and 2 boreholes for 14 CO2 measurements. Each depth level contained a pair of replicates; however, only 9 out of the 13 replicate pairs were "true" replicates (i.e., collected from the same borehole 215 and cut from the same depth interval). Collecting same depth-adjacent samples below 50 m depth from a single borehole was challenging because of reduced core quality (i.e., more fractures in the ice), and thus the "replicates" had to be collected from a different borehole. Immediately after removal from the borehole, ice samples become exposed to a more intense cosmic ray bombardment (post-coring in situ cosmogenic 14 C production). Five artificial "bubble-free-ice" (BFI) samples were manufactured in the field following 220 methods from Mitchell et al. (2011) but upscaled to produce 1.5-2 kg samples. The field-produced BFI samples were shipped together with the collected glacial ice samples to characterize the effects of the postcoring in situ cosmogenic 14 CO2 production in the samples.

Large volume samples for 14 CO and 14 CH4 measurements 225
The detailed approach for sample processing, measurements and associated procedural corrections for the large volume samples have been previously described in detail (Petrenko et al., 2016). In this section, we only provide a brief overview and highlight the differences between our methods and those of . First, the δ 13 CH4 measurements were conducted at the Institute of Arctic and Alpine Research (INSTAAR) following methods described by Miller et al. (2002) (Table S1). The δ 13 CH4 230 measurements were not corrected for gravitational (Sowers et al., 1992) and diffusive isotopic fractionation  because these corrections are only necessary to reconstruct the paleoatmospheric δ 13 CH4 signal. In this study, the δ 13 CH4 values are only used to normalize and calculate the absolute 14 CH4 abundance (in molecules/g ice).
The large volume samples and field procedural blanks were measured for [CH4] using a gas 235 chromatographmultidetector (GC-MD) system (Prinn et al., 2008) (Table S2). Pressure in the sample canisters was measured using a Paroscientific Inc. Digiquartz Series 740 absolute pressure transducer at Scripps Institution of Oceanography (SIO) for total air content (TAC) determination (Table S3). Two of the field procedural blanks were also measured for Kr/N2, Xe/N2, and Xe/Kr ratio (Table S4)

at Scripps
Institution of Oceanography (SIO) following procedures described in Bereiter et al. (2018). The noble gas 240 ratios were used to constrain the gas solubility during the melt extraction. The large volume samples were measured for CO mole fraction [CO] using a Picarro G2401 analyzer (Table S5) and again for pressure at the University of Rochester (UR, Table S4).
The CH4 in the large volume samples and blanks was combusted to CO2, cryogenically separated, and flame-sealed in glass ampules using the air processing line at the University of Rochester (Dyonisius et al., 245 2020). We also processed 3 x 100 μg of CH4-derived C samples each from the "modern" 14 CH4 standard gas and " 14 C-dead" standard gas used for the field procedural blanks. Because of the larger sample size, the effect of extraneous C introduced by graphitization on these 100 μg samples is assumed to be negligible.
The CO-and CH4-derived CO2 was graphitized using the Australian Nuclear Science and Technology Organization (ANSTO) "micro" furnaces following Yang and Smith (2017). We used the 14 C activity measured on the 100 μg samples as the "true" 14 C activity of the standard gases (Table S6). Using a mass 255 balance approach described in Petrenko et al. (2017), the total extraneous C mass for the 14 CH4 samples was determined to be 0.63 ± 0.28 μgC, and the corresponding 14 C activity for the extraneous C was 16.7 ± 10.2 pMC (95% CI).
In prior studies (e.g., Petrenko et al., 2017), 14 CO measurements from the field procedural blanks were used to characterize the effects of extraneous 14 C addition from sample extraction, 260 handling, storage, transport, and processing (including the graphitization step). For this study, the field procedural blanks were still used to characterize the effects from in situ production of 14 CO in the sample air canisters by cosmic rays during storage and transport. However, to better characterize the effects from the addition of extraneous C during the graphitization process, we used a linear empirical correction from 10 commensurately-sized 14 C standards and blanks at ANSTO (see Supplementary Materials, Fig. S2A, 265 Table S7) following Petrenko et al. (2021). This approach has the benefit of bracketing the effects of extraneous C from graphitization at ANSTO with low and high 14 C standards, similar to the approach for the 14 CH4 samples. The 14 CO blank for this sample set is 22.45 ± 3.24 molecules 14 CO/cc STP (95% CI), which is higher than the 14 CO blanks reported in . This is mainly because there was https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License.
an extra year between the retrieval and processing of the samples (thus there was more in situ 14 CO 270 production in sample canisters during storage). 14 CH4 and 14 CO measurements in our samples after all associated corrections, as well as earlier Taylor Glacier results from Petrenko et al. (2016) are shown in Table 1 and Fig. 3.

2.3.2.
Sublimation and processing of samples for 14 CO2 measurements CO2 was liberated from ice samples using a new ice sublimation device at the University of Rochester 275 (Hmiel, 2020), following the design of Schmitt et al. (2011). To briefly summarize the procedure, 1.5-2 kg ice samples were loaded into a vacuum glass vessel, the vessel was then evacuated, and the ice was sublimated at vacuum with six 1500W infrared emitters (Emitted Energy, USA) for 8-10 hours. We did not sublimate 100% of the samples because as the ice sublimates away, impurities such as dust and organics start to accumulate on the surface. The aggregation of impurities on the ice sublimation front might 280 enhance unwanted chemical reactions that produce extraneous carbon (Schmitt et al., 2011). Furthermore, towards the end of the extraction, the sublimation became less efficient as less surface area was available to absorb radiation. Approximately 1 kg of ice was sublimated in 8-10 hours. However, the incomplete sublimation does not compromise the 100% extraction efficiency as all the gases trapped in the ice that is sublimated away is still released (Schmitt et al., 2011). 285 The liberated CO2 was cryogenically trapped with liquid nitrogen and the air was also cryogenically trapped with 5Å molecular sieve (Sigma Aldrich USA) under liquid nitrogen. After the sublimation was completed, the trapped CO2 and air were expanded into separate volume-calibrated manometers where pressure measurements were taken to calculate the [CO2]. Finally, the isolated CO2 was cryogenically transferred to and flame-sealed into a Pyrex glass ampule. The CO2 was graphitized at ANSTO using 290 "micro" furnaces (Yang and Smith, 2017) and the graphitized samples were measured for 14 C activity at the ANTARES AMS facility (Smith et al., 2010). One 14 CO2 sample (replicate for 30m depth sample) was unfortunately lost during sublimation because the ice fractured under vacuum during the evacuation step.  (Table S8). Five field-produced bubble-free ice (BFI) samples and 9-laboratory produced BFI samples were also sublimated along with the glacial ice samples. During the sublimation of the BFI samples, a standard gas with known 14 CO2 activity and [CO2] was introduced into the bottom of the glass vessel at 0.15 scc/min flow rate for 8-10 hours. The set flow rate mimicked the rate of air liberation from glacial ice samples and the processing time also mimicked the amount of time needed to sublimate glacial ice samples. 300 We used a standard gas with "dead" 14 CO2 activity for 4 laboratory-produced BFI samples and a standard gas with "modern" 14 CO2 activity for the other 5 laboratory-produced BFI samples. The CO2 was cryogenically trapped downstream, processed, and measured for 14 C activity following the same methods as  Table S9). Finally, 11 commensurately-sized 14 C standards and blanks (14-16 μgC) with known 14 C activities (in 0-135 pMC range) were prepared, graphitized and measured at ANSTO concurrently with all the samples (Table S7) Table S10). The 14 CO2 measurements in our samples after all associated corrections with their error-propagated uncertainties are shown in Table 1 and Fig. 3.
An in-depth discussion about the analytical uncertainty of the 14 CO2 measurements obtained from the 320 sublimation method (which is important to the interpretation of the data because it is the largest source of uncertainty for total 14 C) are provided in Section 1.4 of the Supplementary Materials. In brief, we used the pooled standard deviation of replicate pairs (±7.8 14 CO2 molecules/g ice, 2σ) as the uncertainty for all 14 CO2 measurements except the 2.25 m sample pair (where we used the error-propagated uncertainties instead, Table 1). The 14 CH4/ 14 CO ratio, 14 CO/total 14 C fraction and 14 CO2/total 14 C fraction of the samples 325 are shown in Fig. 4.

Sample integrity
Several samples were excluded from the data analysis; detailed reasoning for rejecting these samples

3.
Estimating the muogenic 14 C production rates  Morse et al. (1998), at the Taylor Glacier accumulation area, the depth of ~ 80 kyr ice (which corresponds to our 72 m sample) is ~ 575 m. We thus assumed that the depth of long-term transport (zdeep) for the 72 m sample under the best-estimate ablation rate scenario (which we define as the reference 360 sample) is 575 m. For other ice parcel trajectories (i), we scaled the depth of long-term transport (zdeep) following zdeep (i) = 575 -(zrefzhead (i)) Eq.5 where zref represents the depth of the 72 m reference sample in the model at the glacier head under the bestestimate flowline (zref is 699 m) and zhead represents the depth of the ice parcel of interest at the glacier head. We assumed that the difference in depth between the reference sample and the sample of interest (i) 365 at the glacier head and during long-term transport within the glacier is the same.

14 C production in sample ice parcel
We used the model for in situ cosmogenic nuclide production by muons from Balco et al. (2008), with all relevant parameters adjusted for ice (Fig.1) 2002b) parameterizations described above and additional altitude scaling of the muon fluxes. We then used 370 a forward model that numerically integrates the total 14 C in the ice sample along its flow path in Taylor Glacier. For initial condition, we assumed that at the depth of long-term transport (zdeep), the 14 C concentration in the ice parcel is at steady state: dC dt (at z deep ) = 0 = P neg (z deep ) + P fast (z deep ) − C 0 λ Eq.6 The steady state assumption means that at zdeep, the rate of radioactive decay (C0λ) is balanced by production from negative muon capture (Pneg) and fast muon reaction (Pfast). For each ice parcel, we 375 calculated the steady-state, initial 14 C concentration (C0) from Eq.6, then used the following differential equation dC dt = P neg (z(t) ) + P fast (z(t)) − C λ Eq.7 to numerically integrate the 14 C concentration of the ice parcel along the flow trajectory. To avoid interference from spallogenic (neutron-produced) 14 C, we only considered samples deeper than 6.85m

depth. 380
We sampled the parameter space in a "grid search" approach to obtain the best-estimate values for muogenic 14 C production parameters σ0 and ftot, as follows. Using the best-estimate flow trajectory, we calculated the expected 14 C in the samples corresponding to all combinations of σ0 and ftot, with each of the parameters ranging between 0-100% of the values from Heisinger et al. (2002aHeisinger et al. ( , 2002b. To save computational time, we first conducted the grid search at a coarse resolution of 10% increments (Fig. S4A). 385 The goodness of the fit (χ 2 ) for each simulation was calculated following: where Cobs(z) is the measured total 14 C and Cexp(z) is the total 14 C ( 14 CO2 + 14 CO + 14 CH4; Fig. 3D) calculated by the forward model at sample depth z. To find more precise best-estimate σ0 and ftot, we conducted the grid-search again at a higher resolution of 0.2% increments from Heisinger et al. (2002aHeisinger et al. ( , 2002b values near the χ 2 minimum, between 0 to 0.0352 millibarn for σ0 and 0 to 0.01 for ftot (Fig. S4B). 390 To estimate the uncertainties in σ0 and ftot, we used a Monte Carlo sampling of model parameters. We assumed that the ablation rate uncertainties (Fig. S3) represent 2σ normally distributed uncertainties. We then perturbed the ablation rates within their uncertainties and generated a pool of 10,000 possible flow trajectories for each sample depth. However, in 69 out of 10,000 flow scenarios, the ice parcel backtrajectories hit the bedrock and became unphysical afterwards. These unphysical trajectories were removed 395 from the pool of possible ice flow trajectories. Next, we started with the best-estimate σ0 and ftot and assumed a normally distributed and large 200% (1σ) error for each parameter (Fig. S5A) as prior distribution for the Monte Carlo method. We removed σ0 and ftot values that are below zero from the prior distribution because they are unphysical and conducted 100,000 Monte Carlo simulations using the forward https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. 14 C production model. For each Monte Carlo simulation, we randomly picked one of the previously 400 generated possible ice flow trajectories and a random pair of σ0 and ftot from the generated prior distributions (Fig. S5A). We then calculated the expected 14 C concentrations for each sample depth using the forward model and compared the model-data fit. We accept all pairs of σ0 and ftot values that produce model-calculated total 14 C within the 95% CI (7.8 14 C atoms g -1 ice) and 67% CI (3.9 14 C atoms g -1 ice) analytical uncertainty of the best-fit, model-calculated total 14 C (black line, Fig. 6). The ranges of accepted 405 σ0 and ftot pairs are shown in Fig. 7A as contours. The discussion about the selection of acceptance criteria for estimating σ0 and ftot uncertainties is provided in Section 1.4 of the Supplementary Material.

14 CO production model in sample ice parcel
The in-situ cosmogenic 14 CO production rates in ice are of specific interest as discussed in Section 1.1.
To characterize the 14 CO production rates, we introduced additional scaling factors fneg and ffast for negative 410 muon and fast muon mechanisms, respectively as tuned model parameters. The differential equation of Eq.7 is modified into d( CO 14 ) dt = f neg P neg (z(t) ) + f fast P fast (z(t)) − ( CO) 14 λ Eq.9 We note that Pneg and Pfast in Eq.9 are the total 14 C production rates calculated from the Balco et al. (2008) model. The scaling factors fneg and ffast each encompasses 2 terms, one that adjusts the total 14 C production rates and another that accounts for the 14 CO fraction of total 14 C. The determination of best-estimate fneg 415 and ffast and their uncertainties were similar to the approach for σ0 and ftot described above. χ 2 "grid-search" was conducted with all combinations of fneg and ffast values ranging from 0 to 0.2 at 0.001 resolution (Fig.   S4C). Similar to the total 14 C data, we used the average analytical uncertainty of the 14 CO sample set as the acceptance criteria for the Monte Carlo simulations to estimate the uncertainties of fneg and ffast. We accepted all sets of fneg and ffast from the 100,000 Monte Carlo simulations that yielded model-predicted 420 14 CO within 1.2 14 CO molecules g -1 ice (95% CI uncertainty) and 0.6 14 CO molecules g -1 ice (68% CI uncertainty) from the best-fit model (Fig. 8). Fig. 7B shows (as contours) the accepted sets of fneg and ffast values.

3.3.
Comparison with Scharffenbergbotnen ablation site van Der Kemp et al. (2002) measured 14 CO2 and 14 CO in ice from the Scharffenbergbotnen ice 425 ablation site, Antarctica. Using a 1D ablation model, we examined how the estimates of muogenic 14 C production rates from Taylor Glacier compare to the Scharffenbergbotnen data. We assumed that the measured 14 CO2 + 14 CO from Scharffenbergbotnen are comparable to our measurements of total 14 C in Taylor Glacier ice (since our data show that less than 0.3% of total 14 C from muon production forms 14 CH4, Section 4.1). We then used the 14 C concentration from the deepest Scharffenbergbotnen sample (45m) as 430 https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. the initial condition. In the 1D ablation model, the Scharffenbergbotnen ice parcel moves upward at a rate (dz/dt) equal to the ablation rate from stake measurements (Eq.10, a = 16 ± 4 cm yr -1 ). dz dt = −a Eq.10 dC dt = P′n(z(t)) + P′ neg (z(t) ) + P′ fast (z(t)) − Cλ Eq.11 The expected 14 C concentration in the ice is given by the differential equation (Eq.11) where P'n is the 14 C spallogenic production rate from Young et al. (2014), P'neg and P'fast are the muogenic production rates inferred from Taylor Glacier data scaled to the elevation of Scharffenbergbotnen (1173m above sea level) 435 using altitude scaling factors from Balco et al. (2008). We also repeated this calculation for 14 CO only, to compare the muogenic 14 CO production rates with the 14 CO data from Scharffenbergbotnen. Table 1 and Fig.3a-c show the depth profiles of 14 CO, 14 CH4 and 14 CO2 after all corrections. For the 440 14 CO2 measurements, comparison with prior results that used a wet extraction approach (Fig. S6) confirms the caveats discussed by Petrenko et al. (2016) that their 14 CO2 measurements were uncertain and represent the upper bound. The 14 CH4/ 14 CO ratios from the new samples (0.0074 ± 0.0004, 95% CI, n=4, from all samples below 19.5m) appear to be constant within uncertainties (Fig. 4A), in agreement with earlier results (0.0076 ± 0.0004, 95% CI, n=4) from Petrenko et al. (2016). This confirms that the two muon 445 reactions produce 14 C in a constant 14 CH4/ 14 CO ratio. The 14 CO and 14 CO2 fractions of total 14 C are also relatively constant at depth (Fig. 4B)suggesting that the two muon reactions produce all three 14 C species in constant ratios. For samples deeper than 6.85m, on average 33.7% (±11.4%, 95% CI) of the produced cosmogenic 14 C becomes 14 CO and 66.1% (±11.5%, 95% CI) of the produced cosmogenic 14 C becomes 14 CO2 (Fig. 4B). The uncertainties of 14 CO and 14 CO2 fractions on the deepest samples (72m depth) are 450 relatively large because of the small 14 CO2 signal (11.8 to 13.6 14 CO2 molecules/g ice) relative to the uncertainty of our measurements (±7.8 14 CO2 molecules/g ice, 95% CI). The 14 CO2 fraction in samples that are deeper than 6.85m (0.66 ± 0.12, 95% CI) is also in agreement with prior reported 14 CO2 fraction of 0.69 from the Scharffenbergbotnen ablation site (van Der Kemp et al., 2002). Finally, the shallow samples (<6m ice equivalent) show higher 14 CH4/ 14 CO ratios (Fig. 4A) and 14 CO2/total 14 C ratios. This may indicate that 455 neutron-induced spallation produces higher amounts of 14 CH4 and 14 CO2 relative to 14 CO (Petrenko et al., 2016) or that CO (and 14 CO) is not well-preserved in near-surface ice of Taylor Glacier due to potential microbial activities.

Measured 14 C values and partitioning of 14 CO2, 14 CO and 14 CH4
At depths where production from muons dominates (>6 m ice equivalent), less than 0.3% of the produced cosmogenic 14 C in ice forms 14 CH4 (Table 1, Fig. 4). Although a 14 CH4 measurement from 10 m 460 https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. depth is not available (Petrenko et al., 2016), we still include the 10 m data point in the total 14 C dataset used to infer σ0 and ftot values and their uncertainties. The contribution from 14 CH4 (which would have been on the order of ~ 0.2 14 CH4 molecules/g ice, Fig. 3B) is insignificant compared to the uncertainty in total 14 C. We account for the lack of 14 CH4 measurement at this depth by scaling the total 14 C of the 10 m sample by a factor of 1.003 ± 0.003 (95% CI, Table 1). 465

Inferred muogenic 14 C production rates in ice
The muogenic 14 C production parameters from Heisinger et al. (2002aHeisinger et al. ( , 2002b (ftot for negative muon capture and σ0 for fast muon reaction) are well outside the confidence intervals of our measurements ( indicate that the probability of the negative muon capture reaction (ftot) and reference cross-section for fast muon mechanism (σ0) for production of 14 C from 16 O given by Heisinger et al. (2002aHeisinger et al. ( , 2002b are too high by factors of 5.7 (3.6-13.9, 95% CI) and 3.7 (2.0-11.9, 95% CI) respectively.
In their experimental determination of 14 C production rate by fast muons, Heisinger et al. (2002a) used a single muon energy of 190 GeV (σ(E)). The reference nuclear reaction cross section at 1 GeV (σ0) was 475 then scaled using the following equation where α is a power factor that describes the energy dependence of the cross section (unitless). However, the mean muon energy (Ē) of 190 GeV used by Heisinger et al. (2002a), as well as the muon flux intensity were much higher than those expected in the first few hundred meters of ice in natural settings (for the top 200m of Taylor Glacier ice, Ē = 32 GeV Fig. S8). It is thus possible that the experimental results of 480 Heisinger et al (2002 a,b) are not directly transferrable to natural settings. van Der Kemp et al. (2002) measured 14 CO2 and 14 CO in ice from Scharffenbergbotnen ice ablation site using a dry extraction technique. The total measured 14 C values were significantly lower than expected values based on the stake-measured ablation rate. van Der Kemp et al. (2002) hypothesized that the low extraction efficiency of dry mechanical extraction (which resulted in an incomplete release of the in 485 situ cosmogenically produced 14 C from the ice grains) might be responsible for this discrepancy. We used a sublimation method for our 14 CO2 measurements and melt extraction method for our 14 CO measurements; both methods guarantee that all in situ cosmogenic 14 C in the ice lattice is released. Fig.9 shows how the Scharffenbergbotnen data compare with the expected total 14 C and 14 CO from Taylor Glacier-derived production rates. The good agreement between the muogenic 14 C production rates implied by our 490 measurements and by van der Kemp et al. (2002) measurements suggests that the discrepancy between the 14 C measurements and predictions based on ablation stake readings at Scharffenbergbotnen likely stems https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. from the fact that the muogenic 14 C production rates from Heisinger et al. (2002aHeisinger et al. ( , 2002b used by van der Kemp et al. (2002) were too high.
The good agreement between Taylor Glacier and Scharffenbergbotnen data also suggests that dry 495 mechanical extraction is a valid technique for extracting 14 CO2 and 14 CO from ice cores, at least for bubbly, non-clathrated ice. One possible explanation is that that after production, in situ 14 CO2 and 14 CO quickly migrate from the ice matrix to the air bubbles. This is also consistent with previous observations that the retention of in situ cosmogenic 14 C in firn grains is very low (Petrenko et al., 2013;van der Kemp et al., 2000;Wilson and Donahue, 1992). 500 For direct comparison with other studies, we used the scaling factors from Lifton et al. (2014) to calculate the corresponding sea level high latitude (SLHL) total 14 C and 14 CO-specific production rates in ice (Tables 2 and 3). Our estimates of the 14 CO-specific production rates agree with those of Petrenko et al. (2016) within errors (Table 3). Compared with the results from Petrenko et al. (2016), we also calculated a slightly smaller uncertainty on the 14 CO-specific production rate by negative muon capture (Table 3). 505 We converted the Lupker et al. (2015) estimates of ftot in quartz into ftot for ice (Table 2), using the chemical compound factors (fC) for quartz and ice from Heisinger et al. (2002b). With regards to negative muon capture, the Lupker et al. (2015) estimate of ftot is in close agreement with Heisinger et al. (2002b) ( Table 2). However, the high ftot had to be offset by their best σ0 estimate of zero for an overall lower total muogenic production rate, which is in general agreement with our results. For a direct comparison with 510 results from Lupker et al. (2015), we fit our data while forcing σ0 (and hence 14 C production from fast muons) to be zero (Fig. 6b) and cannot find a scenario with reasonable model-data agreement.
Because of the relatively large uncertainty of the 14 CO2 measurements, the total 14 C data still allow σ0 to be close to zero given sufficiently large ftot (Fig. 7A). On the other hand, our 14 CO data (which have much lower relative uncertainties and use a more established measurement technique) unambiguously 515 shows that σ0 and 14 C production from fast muon cannot be zero (Fig. 8, Fig. 7B). As discussed in Lupker et al. (2015), the 14 C data from the 15.5m Leymon-High quartzite core might not cover the depth range where production from fast muons is significant. In contrast, when integrated over the flow history, production from fast muons represents the dominant source of 14 C in our samples.

4.3.
Implications for muogenic 14 C production rates in quartz 520 There are several additional uncertainties to consider when transferring the muogenic 14 C production rates in ice estimated by this study to quartz. The reference cross-section σ0 for the fast muon mechanism is independent of the target mineral, so our estimate should be directly applicable to quartz. On the other hand, the ratio of chemical compound factors (fC) between quartz and ice (Heisinger et al., 2002b;von Egidy and Hartmann, 1982) is needed to convert our estimate of ftot in ice to quartz. The chemical 525 compound factor of ice/water is known to be 1, as hydrogen cannot capture muons. However, the chemical https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. compound factor of quartz is not 1 because the stopped muon can also be captured by silicon atoms (von Egidy and Hartmann, 1982). Constraining the chemical compound factor of quartz is beyond the scope of this study. Nonetheless, it seems highly unlikely that the chemical compound factor of quartz is incorrect by a factor of ~5. 530 Although 14 CO2 and 14 CO likely constitute the large majority of in situ produced 14 C in ice (Lal et al., 1997(Lal et al., , 2000, a small amount of in situ produced 14 C can also form 14 C-bearing organic materials.
Measurements of 14 C in organic carbon from alpine ice for the purpose of radiocarbon dating have shown elevated 14 C values attributed to in situ cosmogenic production (Fang et al., 2021;Hoffmann, 2016). A laboratory irradiation experiment of glacier ice with an artificial neutron flux showed that 11-25% of 535 produced 14 C forms organic carbon (Hoffmann, 2016). Measuring 14 C in organic compounds is also unfortunately beyond the scope of this study, as it requires an entirely different analytical setup. Even if other organic species account for as much as 25% of the total 14 C, it would still not explain the large discrepancy in ftot and σ0 values observed between our results and the Heisinger et al. (2002aHeisinger et al. ( , 2002b values. 540

Conclusions
This study presents 14 CO2 measurements in ablating ice obtained via a new ice sublimation technique, combined with 14 CO and 14 CH4 measurements obtained from a well-established large-volume meltextraction method to estimate the total in situ-produced cosmogenic 14 C in ice. Our results indicate that commonly used literature values for rates of in situ production of 14 C by muons in ice are overestimated by 545 a factor of 5.7 (3.6-13.9, 95% CI) and 3.7 (2.0-11.9, 95% CI) for negative muon capture and fast muon interactions, respectively. Comparison between the data presented in this study and previous data from Scharffenbergbotnen (van der Kemp et al., 2002) strengthens this conclusion. This comparison also suggests that a dry extraction technique appears to release essentially all in situ 14 C in bubbly (nonclathrated) ice. 550 The constraints on muogenic 14 C production rates in ice and the partitioning between the in-situ produced 14 C-bearing gas species provided by this study will allow for future measurements of 14 C gases in other ice cores to be used for several applications, including using 14 CO2 measurements for absolute dating of the bubbles in ice cores (Andree et al., 1984;Van De Wal et al., 1994) and using 14 CO measurements to either constrain the oxidative capacity of the atmosphere (Brenninkmeijer et al., 1992;Petrenko et al., 555 2021) or reconstruct the past cosmic ray flux (BenZvi et al., 2019).
Finally, our results also strongly imply that the muogenic 14 C production rates in quartz (Heisinger et al., 2002a, Heisinger et al., 2002b are overestimated, although there may be additional uncertainties in transferring our results from ice to quartz. The disagreement between the muogenic 14 C production rates https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. inferred from laboratory experiments (Heisinger et al., 2002a, Heisinger et al., 2002b and measurements in 560 natural settings (this study, Lupker et al., 2015) highlights the need for more site calibration studies.

Data availability
Data from this work will be available through the USAP Data Center (https://www.usap-dc.org/data). IV made the δ 13 CO measurement for the CO dilution gas. CB developed the ice flow model. MND developed the 14 C production model with input from CB and VVP. MND, BH, and VVP analysed the results and wrote the manuscript with input from all authors.

Competing interests 580
We declare no competing interests     6. (A). Model-data comparison between total 14 C measurements with modeled best-estimate σ0 and ftot parameters from this study and Heisinger et al. (2002a,b). (B). Model-data comparison between total 14 C measurements with modeled best-estimate σ0 and ftot parameters from this study and modeled total 14 C with best-fit ftot when σ0 is forced to be zero. The colored lines on both figures represent the 95% CI envelope of the model results (corresponding to the contour plot in Fig. 7A). The error bars shown on the data are also 95% CI. We only fit to samples that are below 6.85m to avoid interference from 14 C produced by the neutron mechanism.
https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. Fig.7. (A). 68% and 95% CI contours of accepted σ0 and ftot values for total 14 C. (B) 68% and 95% CI contours of accepted fneg and ffast values for 14 CO (see Section 5.4.3). For comparison, the σ0 and ftot values from Heisinger et al. (2002aHeisinger et al. ( , 2002b are shown as a blue star. The best-fit values for σ0, ftot, fneg, and ffast are shown as a red star star in both figures. 5 https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. Fig.8. Model-data comparison between 14 CO measurements with modeled best-estimate fneg and ffast parameters from this study and modeled 14 CO with best-fit fneg when ffast is forced to be zero. The colored lines represent the 95% CI envelope of the model results (corresponding to the contour plot in Fig. 7B). The error bars shown on the data are 95% CI. 10 https://doi.org/10.5194/tc-2021-375 Preprint. Discussion started: 26 January 2022 c Author(s) 2022. CC BY 4.0 License. Fig. 9. A. Comparison between measured total 14 C from Scharffenbergbotnen, expected total 14 C using production rates inferred in this study, and expected total 14 C using Heisinger et al. (2002a,b) production rates. B. Comparison between measured 14 CO from Scharffenbergbotnen and expected 14 CO using production rates inferred from Taylor Glacier. The colored lines on both figures represent the 95% CI envelope of the model results. At the depths plotted in this 15 figure (deeper than 5m), production from neutron-induced spallation is negligible.