Volume 46, Issue 10 p. 5436-5444
Research Letter
Free Access

Methane Sources in the Waters of Lake Michigan and Lake Superior as Revealed by Natural Radiocarbon Measurements

DongJoo Joung

Corresponding Author

DongJoo Joung

Department of Earth and Environmental Sciences, University of Rochester, Rochester, NY, USA

Correspondence to: D. J. Joung,

[email protected]

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Mihai Leonte

Mihai Leonte

Department of Earth and Environmental Sciences, University of Rochester, Rochester, NY, USA

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John D. Kessler

John D. Kessler

Department of Earth and Environmental Sciences, University of Rochester, Rochester, NY, USA

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First published: 30 April 2019
Citations: 8


The methane dynamics in the waters of Lakes Michigan and Superior, components of the North American Great Lake system, were investigated using measurements of methane concentration and natural radiocarbon (14C-CH4) dissolved in these lake waters. All 14C-CH4 measurements were above modern levels regardless of location and depth with a range of 117-145% modern carbon (pMC). Methane concentrations in the deep basin of both lakes were low, ranging from 3.3 to 4.3 nM, with minimal vertical variation. However, the concentrations of CH4 increased toward coastal areas in both lakes, possibly due to higher groundwater inputs and aerobic methanogenesis associated with primary productivity. Except for one site, 14C-CH4 dissolved in the waters of Lake Michigan was greater than in Lake Superior by ~12 pMC, a difference that was likely due to inputs of excess 14CH4 from nuclear power plants along the coast of Lake Michigan.

Key Points

  • The sources of methane dissolved in the waters of Lakes Michigan and Superior, components of the Great Lake system, were investigated
  • Natural radiocarbon measurements of methane indicate that the methane source in both lakes was largely from the atmosphere
  • In situ aerobic methanogenesis, groundwater inputs, and nuclear power plants also appear to contribute to the methane source

Plain Language Summary

Methane is a greenhouse gas whose concentration is increasing rapidly in the modern atmosphere, and freshwater lakes globally provide a significant source to the atmosphere. Here we investigate the dynamics of methane dissolved in waters of the North American Great Lakes, one of the largest liquid freshwater environments on Earth. We found that methane dynamics in both Lakes Michigan and Superior are impacted by atmospheric input, in situ aerobic methanogenesis, groundwater, and nuclear power plants, as well as rapid vertical mixing in the water column.

1 Introduction

Freshwater lakes are known to be a source of methane (CH4) to the atmosphere, accounting for 6-16% of natural CH4 emissions (Bastviken et al., 2004; Borrel et al., 2011). This contribution is substantially higher than oceanic emissions (Rhee et al., 2009), an interesting conclusion given the much smaller surface area of lakes globally (Downing et al., 2006). Lakes are also projected to provide a positive feedback to warming climate with projected increases in stratification (McCormick, 1990), as well as CH4 production, accumulation, and emission to the atmosphere (Tranvik et al., 2009; Walter et al., 2006).

The North American Great Lake system is globally the largest liquid freshwater environment by area, yet to date CH4 and associated carbon dynamics across this system have received disproportionately minimal attention compared to other freshwater lake environments (Alin & Johnson, 2007). Townsend-Small et al. (2016) reported that Lake Erie is a net source of CH4 to the atmosphere in late summer with both natural and anthropogenic sources combining to release 1.3×108 g CH4-C per day; assuming these emissions are constant over the entire year, this extrapolates to 0.09% of the global CH4 emissions from lakes (54×1012 g C/year; Bastviken et al., 2011). Including other Laurentian Great Lakes in this emission estimate may further increase the known annual CH4 emissions from this system.

A variety of different CH4 sources and sinks are known to influence emissions from freshwater lake environments. Conventional CH4 production in lakes is viewed to occur in anoxic sediments through the anaerobic degradation of organic matter (Bartlett et al., 1988; Rudd & Hamilton, 1978), and diffusion from these sediments increases the CH4 concentration dissolved in bottom waters (Wik et al., 2016). An additional source of CH4 has more recently been documented where CH4 is produced within the oxygenated water column as a by-product of phosphorus regeneration in phosphorus-limited oligotrophic lakes (Bogard et al., 2014; Grossart et al., 2011; Yao et al., 2016). Both inputs from sediments and in situ production processes are likely responsible for CH4 supersaturation in lake water columns (Blees et al., 2015; Tang et al., 2014), leading to net CH4 emissions to the atmosphere. However, not all CH4 produced in freshwater lakes is emitted to the atmosphere since biological oxidation is substantial in both anaerobic and aerobic environments, removing 30-99% of CH4 produced in freshwater lakes (Bastviken et al., 2008). Despite these known sources and sinks, the additional processes of ebullition, diffusion, and storage in sediments and the water column, and flux through aquatic vegetation, can influence precise regional and global estimates of atmospheric CH4 emissions from freshwater lakes (Dean et al., 2018; Wik et al., 2016).

Measurements of the natural isotopic content of CH4 have been used to help constrain CH4 sources and sinks. The stable carbon and hydrogen isotopic contents of CH4 are the most widely used measurements; however, the interpretation of this stable isotopic data can be complicated due to multiple sources containing similar isotopic values and isotopic fractionations caused by both anaerobic and aerobic CH4 oxidation (Whiticar, 1999). The combination of these isotopic effects can lead to variations in measured CH4 stable isotopic values both regionally and temporally. Thus, the application and interpretation of stable isotopes to determine CH4 dynamics is most informative when the end-members of different sources and the associated isotopic fractionation processes are known (e.g., Kessler & Reeburgh, 2005; Leonte et al., 2017, 2018; Valentine et al., 2001). While measured less frequently, natural radiocarbon measurements of CH4 (14C-CH4) are uninfluenced by fractionation processes, such as oxidation, since measured 14C isotopic values are conventionally normalized to 13C (Stuiver & Polach, 1977). This measurement is particularly useful when trying to determine the source of CH4 in an environment with both fossil (e.g., hydrocarbon seeps) and modern (e.g., aerobic methanogenesis) end-members (e.g., Kessler & Reeburgh, 2005; Kessler et al., 2005; Sparrow et al., 2018). Fossil CH4 generally refers to a source of carbon that is older than approximately 10 14C half-lives, leaving analytically undetectable quantities of 14C, and is equivalent to 0% modern carbon (pMC; Stuiver & Polach, 1977). In addition, atmospheric 14C-CH4 levels are currently supersaturated relative to natural 14C production with values of ~135 pMC due to the addition of 14CH4 from nuclear reactors (Eisma et al., 1995; Lassey et al., 2007; Sparrow et al., 2018; Townsend-Small et al., 2012). Thus, radiocarbon isotopic values, together with conventional stable isotopes of CH4, can precisely constrain the age of CH4 in aquatic environments and help determine the source (e.g., Kessler et al., 2005, 2008; Kessler & Reeburgh, 2005; Sparrow et al., 2018; Sparrow & Kessler, 2017).

In this study, we investigated the radio- and stable-carbon isotopic signatures, together with the concentrations of CH4 dissolved in the waters of Lakes Michigan and Superior to constrain the dominant sources of CH4 into the waters of these two Great Lakes. This study provides critical information on CH4 sources in these environments, which can be used to help extrapolate CH4 emissions across this massive freshwater system.

2 Materials and Methods

2.1 Study Site

The North American Great Lake system is one of the largest freshwater bodies by total area and volume, containing about 21% of Earth's surface liquid freshwater (https://www.epa.gov/greatlakes). Due to their massive size, the Great Lakes have sea-like characteristics with waves, strong currents, and distant horizons, and as such, they have long been referred to as inland seas. Geologically, the Great Lakes were formed at the end of the last glacial period approximately 14,000 years ago as ice retreated and the basins filled with meltwater (Larson & Schaetzl, 2001). Lake Superior is the largest by volume among the Great Lakes with a water residence time of ~193 years (Quinn, 1992); it is an oligotrophic lake with relatively low anthropogenic impact since most of the watersheds are forested with little agriculture activities due to cool climate and poor soils (Dove & Chapra, 2015). Lake Michigan is the second largest of the Great Lakes by volume and is connected to Lake Huron to the northeast. The flushing time of water in Lake Michigan is about 60 years (Quinn, 1992). Although Lake Michigan hosts highly populated cities along the coast including Chicago, Milwaukee, Green Bay, Gary, and Muskegon, the lake is classified as oligotrophic (Dove & Chapra, 2015). Recently, the waters of Lake Michigan have been experiencing significant changes in carbon dynamics as an invasive species, quagga mussels, consume primary producers, leading to higher water clarity and increasing pCO2 in the water column (Lin & Guo, 2016). Groundwater inputs associated with Paleozoic bedrock are known to influence the hydrology of Lake Michigan as areas of saline water bodies near the land surface of the Lower Peninsula of Michigan (Lampe, 2009; Wahrer et al., 1996).

2.2 Determination of Concentration and Isotopic Signature of Methane

Sample collections were conducted in Lakes Michigan and Superior during 14-20 June 2017 using the research vessel R/V Blue Heron (Figure 1). In this sampling campaign, water samples were collected for CH4 concentration and natural isotopic values (δ13C-CH4 and 14C-CH4) together with ancillary sensor measurements of temperature, specific conductivity, dissolved oxygen (DO), and chlorophyll a. In addition to the surface water collections, water column profiles were also collected in two deep water sites (i.e., S13 in Lake Michigan and S30 in Lake Superior) to investigate CH4 distributions in the water column. Detailed methods and procedures for the determination of CH4 concentrations and isotopic values can be found in Leonte et al. (2017) and Sparrow and Kessler (2017), respectively. Briefly, discrete bottle samples were collected for dissolved CH4 concentration analysis in both the surface waters and the vertical water column.

Details are in the caption following the image
Map of sampling locations in Lakes Michigan and Superior. The green rectangles represent sites where dissolved methane samples were collected for natural radiocarbon and stable isotope analyses. The red dots indicate where discrete dissolved methane concentration samples were collected in surface waters.

The vessel's scientific surface water supply system was used to sample surface waters, while Niskin bottles connected to the rosette sampler were used for the water column collections. A comparison of surface water samples collected using both the scientific surface water supply system and the Niskin bottles showed insignificant differences. Immediately after the water samples were collected, a 10-ml headspace of ultrahigh-purity air was injected via displacement and 100 μl of saturated HgCl2 solutions were added as a preservative. The samples were stored isothermally in an incubator at 4°C for at least 12 hr, while dissolved gases came into equilibrium with the headspace. Concentration of CH4 in the headspace was then determined on the ship with an Agilent 6850 gas chromatograph with a flame ionization detector and was used along with the solubility of CH4 and the volumes of the headspace and water to determine the initial dissolved concentration.

Samples for natural 14C-CH4 dissolved in lake waters were also collected. Due to the low concentration of CH4 dissolved in these waters (3.3-4.3 nM) and the typical sample size for an analysis via accelerator mass spectrometry (AMS) (approximately 20 μmoles of C), CH4 needed to be extracted from several thousand liters of lake water per sample. A previously published procedure was employed to perform this task in an efficient manner (Sparrow & Kessler, 2017). In brief, a high-performance discharge pump was used to pump water onto the vessel at a rate of approximately 200 liters per minute and the water was sequentially filtered to remove particles (100, 50, and 10 μm) prior to flowing through two gas-permeable membranes (Liqui-Cel, 3M). A vacuum was applied to the outside of the gas-permeable membrane, extracting the dissolved gases, and the degassed water was continuously returned overboard. The extracted gas was then compressed into a small 1.6-L gas cylinder and returned to the land-based laboratory for further sample processing and analysis. To adequately flush all water and gas handling equipment and collect sufficient quantities of CH4, up to 35,000 L of water was processed per sample. Deeper waters, up to almost 300 m, were sampled for this analysis by connecting multiple hoses together (each 10 m in length and 7.62 cm in diameter) and attaching them to the winch wire to reach the desired depth. In the Kessler laboratory at the University of Rochester, the CH4 in the gas sample was purified and combusted into CO2 and H2O. This CO2 was then stored in acid-cleaned and precombusted Pyrex tubes prior to analysis for 14C-CH4 and δ13C-CH4 via AMS and isotope ratio mass spectrometry, respectively, at the Keck Carbon Cycle AMS facility at UC Irvine. Lastly, multiple radiocarbon blank and standard analyses were also conducted showing minimal sample contamination and were used in the interpretation of the results (Figure S1 in the supporting information). Full details of the procedures, including experimental validations, can be found in Sparrow and Kessler (2017).

3 Results and Discussion

3.1 Natural Radiocarbon of CH4 Dissolved in the Water Column

Natural radiocarbon values of CH4 dissolved in both lake waters ranged from 117 to 145 pMC (Figure 2 and Table S1 in the supporting information). The average 14C-CH4 values in Lake Michigan were significantly greater than Lake Superior (approximately 142 ± 1.5 pMC, n= 5 vs. 132 ± 0.5 pMC, n=5), except at site S14 in Lake Michigan (see below). Atmospheric values of 14C-CH4 range from 135 to 136 pMC, values that are above the modern radiocarbon values for CO2 in the atmosphere (approximately 103 pMC) due to thermonuclear weapons and nuclear power generation (Figure 3; Eisma et al., 1995; Kessler et al., 2008; Lassey et al., 2007; Sparrow et al., 2018; Townsend-Small et al., 2012; Wahlen et al., 1989). Thus, 14C-CH4 in the surface waters of Lake Michigan are considerably higher than the atmosphere, whereas values in Lake Superior appear closer to equilibrium with the modern atmosphere. Along the Lake Michigan coast are five active nuclear power plants and an additional four are within 120 km from the coast (Figure S2). Thus, the higher 14C-CH4 in Lake Michigan water is likely the influence of these nuclear power plants and the subsequent introduction of power plant-derived CH4 into the lake waters.

Details are in the caption following the image
Vertical profiles of methane (a) radiocarbon (14C-CH4) and (b) stable (δ13C-CH4) isotope values in Lake Michigan and Superior. S13, S13.5, and S14 are in Lake Michigan, and S30 is in Lake Superior. The horizontal bars represent the depth of the water column.
Details are in the caption following the image
Schematic diagrams representing 14C-CH4 end-members of nuclear power plants, atmosphere, in situ production, and groundwater. The 14C-CH4 values of Lake Michigan and Superior are also shown. (a) Eisma et al. (1995); (b) Townsend-Small et al. (2012), Lassey et al. (2007), and Sparrow et al. (2018); (c) Sparrow et al. (2018); (d) Zigah et al. (2011); (e) Aravena and Wassenaar (1993); and (f) Zigah et al. (2011).

Unlike Lake Michigan, Lake Superior does not have active nuclear power plants along the coast or in the watershed (Figure S2), likely explaining the lower values of 14C-CH4 in this environment compared to Lake Michigan. Nonetheless, the water column 14C-CH4 values are greater than the 14C contents of any other C pool in the water column (particulate organic carbon (POC), dissolved organic carbon, and dissolved inorganic carbon; avg. ~104.3±3.5 pMC, n=63; Figure 3; Zigah et al., 2011), suggesting that in situ production via aerobic methanogenesis has minimal influence on the dissolved CH4 isotopic signatures. The similarity of the 14C-CH4 values between the contemporary atmosphere and dissolved in the waters of Lake Superior instead suggests that the atmosphere is the dominant source of CH4 to this environment.

While modern CH4 in the surface waters of both lakes is less surprising due to direct interaction with the atmosphere, elevated values of 14C-CH4 at the bottom of the water column in both lakes were somewhat unexpected (Figure 2). These results suggest that emissions of CH4 from the lake floor into the water column, be those emissions of fossil or modern CH4, are negligible. More specifically, Silliman et al. (1996) and Meyers (2003) reported that the age of organic matter in Great Lake sediments was widely distributed (e.g., sediment 14C ages equal ~400 years at surficial 40-cm sediment in Lake Huron and about 5,700 years at 113-119 cm and >20,000 years at 763-769 cm in Lake Ontario's sediments). In addition, Zigah et al. (2011) reported that water column POC in Lake Superior has modern 14C contents (102.5±2.0 pMC, n=21), meaning that CH4 generated after this POC is deposited on the lake floor is not a significant source to the water column. One additional argument against the sediments being significant sources of CH4 to the bottom waters follows the study by Remsen et al. (1989), which found a rapid depletion of CH4 in the surface (~2 cm) sediments of Lake Superior; this study concluded that the CH4 depletion was due to oxidation under the oxic conditions near the sediment-water interface. Similarly, since the DO concentration we measured in bottom waters from both lakes is >90% saturation (Figure S3), the sediment-water interface is likely oxic, diminishing the diffusive sedimentary fluxes. However, we note that our measurements of 14C-CH4 and DO investigated waters approximately 5 m above the actual sediment-water interface, and thus, waters closer to the lake floor may display older 14C-CH4 reflecting sedimentary diffusive fluxes. Overall, the observed 14C-CH4 throughout the water column suggests that the source of CH4 in these lake waters is largely the atmosphere, with influences from nuclear power plants in Lake Michigan, which is then mixed vertically in the water column, and any influence from sediments into the deeper waters is likely restricted to only a few meters above the lake floor.

In Lake Michigan, surface water of S14 showed the lowest 14C-CH4 (117 pMC), while the other two sites in this lake displayed much higher values (142.2±0.8 pMC, n=2; Figure 2). The S14 station is the shallowest (~10 m) and closest (approximately 4 km) site to the coast and nuclear power plants in our Lake Michigan sampling locations (Figure S2); thus, we expected the opposite, that this site would display the highest 14C-CH4. We suspect that this site has an additional source of CH4 that does not appear in the other sites. First, this suspicion is supported by the δ13C-CH4 at the S14, which is about -6 ‰ lighter than the other sites (Figure 2). Second, the concentration of CH4 at this surface station was 20 nM, the highest among the samples collected in Lake Michigan (Figure 2). Third, we suspect that the additional CH4 source is likely a combination of aerobic methanogenesis and groundwater discharge. Typically, shallow sites in water bodies have higher CH4 concentrations due to groundwater discharge and/or higher rates of aerobic methanogenesis associated with higher rates of primary production (Dulaiova et al., 2010; Lecher et al., 2016). Zigah et al. (2011) reported that the 14C contents in carbon pools from Lake Superior's water ranged from 102 to 106 pMC; thus, CH4 produced aerobically from this carbon could potentially diminish the higher 14C-CH4 values seen elsewhere in this lake. Chlorophyll concentrations were slightly higher in the southeastern side of Lake Michigan near S14 relative to the central basin (Figure S4), suggesting that the aerobically produced CH4 from the byproducts of primary production may contribute to this 14C-CH4 signal. Aravena and Wassenaar (1993) investigated C-isotopes in groundwater collected from aquifer wells in southern Ontario, Canada, north of Lake Ontario, and reported that 14C-CH4 ranged from 0.5 to 16.7 pMC (avg. 4.9±5.0, n=16). Additional groundwater measurements in the Eastern Ontario aquifer ranged from 1.1 to 26.5 pMC, with an average of ~ 11.2±8.6 pMC, n=20 (Lemieux et al., 2019). This suggests that groundwater discharge could lead to a significant reduction in the dissolved 14C-CH4 in the lake water when mixed with ambient water containing elevated 14C-CH4. In ground waters from the southern shore of Lake Michigan, specific conductivity and pH were measured to be typically in the ranges of 165-852 μS/cm and 5.7-8.0, respectively (Shedlock et al., 1993). Our measurements show a higher specific conductivity and lower pH in the region of S14 relative to the other surface waters in the more central lake (Figures S3 and S4), in agreement with potential groundwater contributions to these areas. Finally, a report from the U.S. Geological Survey also indicated that the development of surficial aquifers is greater in the eastern side of Lake Michigan relative to the west (see, Fig 26 in Olcott, 1992). Thus, the measurements of relatively older 14C-CH4, higher specific conductivity, lower pH, and higher chlorophyll in some sites along the eastern coast of Lake Michigan are likely reflecting contributions from both active groundwater discharge and aerobic methanogenesis, displaying important components of the coastal CH4 system in the waters of Lake Michigan, and possibly Lake Superior (e.g., Heilweil et al., 2015; Hofmann et al., 2010).

3.2 Concentration of CH4 Dissolved in the Water Column

Along with radiocarbon analyses, CH4 concentrations were also determined (Figure 4 and Table S2). Surface CH4 concentrations ranged from 3.5 to 60 nM (Figure 4a) in these two lakes. Concentrations in Lakes Michigan and Superior were much lower than that in the neighboring lake, Lake Erie, where the concentrations ranged from 24.2 to 107.1 nM in the surface (Townsend-Small et al., 2016). This stark difference in concentrations is likely associated with active natural gas seeps, leaking natural gas pipelines, and the relatively shallow water column in Lake Eire (Townsend-Small et al., 2016). While no acoustic investigations were conducted to identify seep bubbles in Lakes Michigan and Superior (Sheikh et al., 2008), our natural 14C-CH4 measurements do not suggest that fossil seep CH4 is a significant source to either the deep or surface waters in these lakes. However, our data do not exclude the possibility that some fossil CH4 seeps may exist and have more localized influences on the CH4 dynamics. Nonetheless, in Lakes Michigan and Superior, CH4 concentrations in surface water from the deep basin of both lakes were 3.7 (at S13) and 4.3 (at S30) nM. These concentrations were approximately in equilibrium (or slight supersaturation) relative to the current (June 2017) global average atmospheric concentrations of 1842.9 ppb (or 3.2 nmol/kg at 15°C and 4.2 nmol/kg at 4°C in Lake Michigan and Superior, respectively; https://www.esrl.noaa.gov/gmd/ccgg/trends_ch4/). Production and supersaturation of CH4 at the surface layer may be associated with regeneration of phosphate from methyl-phosphonate, which is typically observed in oligotrophic lake waters (e.g., Bogard et al., 2014; Grossart et al., 2011; Yao et al., 2016).

Details are in the caption following the image
(a) Spatial and (b) vertical distributions of methane in Lake Michigan (S13) and Superior (S30). The horizontal bars represent the depth of the water column.

While both Lakes Michigan and Superior have similarly low CH4 concentrations in the center of these lakes, we observed localized CH4 enrichment along the coast of Lake Michigan, reaching up to 60 nM (Figure 4). This distribution of increasing CH4 concentration toward the coast is common, since shallow sites would likely have more primary production and associated in situ aerobic methanogenesis along with wave actions to enhance pore water exchange with the water column (Bastviken et al., 2011; Borrel et al., 2011; Dulaiova et al., 2010; Heilweil et al., 2015; Hofmann et al., 2010; Lecher et al., 2016). In both lakes, chlorophyll distributions were generally higher toward to the coast (Figure S4), and there are many active groundwater discharge sites especially along the coast of Lake Michigan (Olcott, 1992), as is suggested in our conductivity and pH distributions.

Vertical profiles of CH4 concentration in the deep sites in both lakes displayed similarly low concentrations with a range of 3.0-4.5 nM (Figure 4). Though small, there appeared to be a slight decrease in CH4 concentration from the surface toward the bottom, similar to the observations in other lakes such as Lake Baikal, Russia (Schmid et al., 2007), and Lower Lake Constance, Germany (see, Fig 2 in Hofmann, 2013), which is likely attributed to aerobic oxidation. However, in our study, bottom water CH4 concentrations (~3.0 nM in both lakes) were slightly higher than the concentrations in bottom waters from the lakes mentioned above, but close to the surface values, suggestive of rapid vertical mixing in both lakes. Overall, CH4 concentration distributions in Lakes Michigan and Superior are consistent with 14C-CH4 distributions, indicating that atmospheric input, in situ aerobic methanogenesis, groundwater, and nuclear power plants are important sources of CH4 to the water column.

4 Conclusions

Radio- and stable-carbon isotopes and concentration of CH4 dissolved in the waters of Lakes Michigan and Superior were determined to assess CH4 sources to these environments. Key results include (1) that CH4 is not fossil and (2) that all measurements of 14C-CH4 were above modern, suggesting significant inputs from atmospheric CH4 (Lakes Michigan and Superior) and nuclear power plants (Lake Michigan). Interestingly, the site closest to a nuclear power plant displayed the lowest value of 14C-CH4, likely displaying the influence of groundwater discharge and aerobic methanogenesis. Concentrations of CH4 in the central basin of both lakes were similarly low, which is approximately in equilibrium with the atmosphere. However, CH4 concentrations in the coastal regions of both lakes were higher than the central basin, and likely associated with in situ aerobic methanogenesis and groundwater inputs. Overall, our study provides fundamental information about CH4 sources and 14C-CH4 dynamics in the Great Lakes of Lakes Michigan and Superior.


We thank to the crew of R/V Blue Heron and Eleanor Arrington for their outstanding support during this research. We also acknowledge Katy Sparrow for the advice on the sample preparations and John Southon in the Keck Carbon Cycle AMS facility at UC Irvine for conducting the radiocarbon analysis. This research is funded by NSF grant OCE-1634871. Data use in this manuscript are available in the supporting information.