Towards a quantitative understanding of the
late Neoproterozoic carbon cycle
Christian J. Bjerruma,1 and Donald E. Canfieldb,1
a
Nordic Center for Earth Evolution (NordCEE) and Department of Geography and Geology, University of Copenhagen, Øster Voldgade, 10,
DK-1350 København K., Denmark; and bNordic Center for Earth Evolution (NordCEE) and Institute of Biology, University of Southern Denmark,
Campusvej, 55, DK-5230 Odense M, Denmark
Contributed by Donald E. Canfield, February 1, 2011 (sent for review November 25, 2010)
The cycles of carbon and oxygen at the Earth surface are intimately
linked, where the burial of organic carbon into sediments represents a source of oxygen to the surface environment. This coupling
is typically quantified through the isotope records of organic and
inorganic carbon. Yet, the late Neoproterozoic Eon, the time when
animals first evolved, experienced wild isotope fluctuations which
do not conform to our normal understanding of the carbon cycle
and carbon-oxygen coupling. We interpret these fluctuations with
a new carbon cycle model and demonstrate that all of the main
features of the carbonate and organic carbon isotope record can
be explained by the release of methane hydrates from an anoxic
dissolved organic carbon-rich ocean into an atmosphere containing
oxygen levels considerably less than today.
carbon isotope excursion ∣ carbon monoxide ∣ Shuram-Wonoka anomaly ∣
earth evolution ∣ atmospheric chemistry
T
he Neoproterozoic Eon was one of the most dynamic, yet
enigmatic, times in Earth history. The Eon saw the breakup
of super continent Rodinia and was punctuated by several glacial
episodes, some of which were global in extent (1). The Eon saw
the evolution and expansion of the first animals on Earth (2), as
well as a rise in atmospheric oxygen and a major oxygenation of
the deep ocean (3, 4). The isotopic composition* of carbonate
(δ13 CIC ) in sedimentary rocks reveals some of the largest isotope
fluctuations in marine dissolved inorganic carbon (DIC) in Earth
history (e.g., 4–6). Such isotope fluctuations are considered to
reflect dynamics in the carbon cycle, and they have been used to
reconstruct the history of atmospheric oxygen (e.g., 7, 8).
The Neoproterozoic δ13 CIC record, however, reveals excursions to less than mantle values (< − 5‰), and the assumed
input value to the oceans (5, 9) (Fig. 1). Prolonged negative
δ13 CIC excursions such as these cannot be explained by our normal understanding of the carbon cycle (e.g., 10, 11). While a
diagenetic origin has been advocated to explain these excursions
(12, 13), we will show that the major features of the carbon isotope records are consistent with a seawater origin through the
action of the carbon cycle.
Indeed, a nondiagenetic origin for the carbon isotope excursion is supported by the fact that in individual regions, an excursion may be observed over 100’s of kilometers, mappable to the
same stratigraphic horizon, and with isotope trends independent
of sediment lithology (e.g., 14–16). The lateral extent and stratigraphic consistency of these excursions is difficult to reconcile
with a diagenetic origin. Furthermore, modeling shows that the
extent of isotopic alteration during diagenesis is highly dependant
on the mineralogy of both the initial and the altered sediment
(12). Isotope trends, however, transcend these differences (e.g.,
6, 14, 17), further arguing against a diagenetic origin for the
isotope signals.
Many of the large Neoproterozoic isotope excursions display
a relationship between the 18 O and 13 C of carbonate, which is
not easily explained with our current understanding of carbonate
isotope behavior in marine waters, and recent diagenetic models
have reproduced some of these 18 O and 13 C relationships (12).
5542–5547 ∣ PNAS ∣ April 5, 2011 ∣ vol. 108 ∣ no. 14
Clearly diagenesis has impacted the isotopic composition of
some Neoproterozoic carbonate rocks (11, 17). However, the
sedimentological arguments presented above, and the variable
diagenetic influence of 18 O and 13 C, as seen by major shifts in
δ18 OIC with no accompanying shift in δ13 CIC , speaks to a seawater
source for the major widespread carbon isotope anomalies
preserved in the Neoproterozoic isotope record (Fig. 1H and
Fig. S1C).
In previous discussions, the repeated oxidation of a huge
marine dissolved organic carbon (DOC) pool (more than 100
times the present size) has been used to explain the large negative
Neoproterozoic δ13 CIC excursions (10). While receiving wide
attention (4, 6, 16, 18), it is unclear with this model how the oxidation events are triggered, and the large isotope excursions
seemingly require more oxidant than can be supplied by the
atmosphere and ocean system (19). Therefore, we present a
unique carbon cycle model which accounts for the amplitude
and phasing of the late Neoproterozoic carbonate and inorganic
carbon 13 C records as observed through many of these anomalies,
and shows that at least a part of the 18 O excursions may also
have a nondiagenetic origin. Our model is forced by the input of
isotopically light methane and does not result in the same oxygen
demand as in previous models.
Observation of the Shuram-Wonoka Anomaly
We focus attention on the Shuram-Wonoka anomaly as this is
the largest, the most discussed, and the most challenging to
understand. Two well studied examples of this anomaly, which
are believed to be time contemporaneous (4, 17, 20), are reproduced in Fig. 1 [Oman (4)] and Fig. S1 [South China (6)]. From
available U-Pb isotope ages, this anomaly terminated just before
551 Ma, with a duration of 1 to 10 Ma (20), although some suggest that it may have been longer (4, 17). The two stratigraphic
sections are very similar geochemically, and they display the following common features: (i) each has δ13 CIC minimums of −8 to
−10‰ (Fig. 1C); (ii) each shows a general correlation between
δ13 CIC and δ18 OIC within the anomaly (Fig. 1H and Fig. S1C);
(iii) each shows a tendency for lower carbon isotope fractionation
(Δδ13 CIC-OC ) at lower values of δ13 CIC (Fig. 1G and Fig. S1B)
with a mean cross-plot slope of about 0.9; and (iv) there is hysteresis in the rate of change between Δδ13 CIC-OC and δ13 CIC with a
Author contributions: C.J.B. and D.E.C. designed research; C.J.B. and D.E.C. performed
research; C.J.B. and D.E.C. analyzed data; and C.J.B. and D.E.C. wrote the paper.
The authors declare no conflict of interest.
Freely available online through the PNAS open access option.
*The isotopic abundance ratio R ¼ ð13 C∕12 CÞ is used to define the isotopic composition as
δ ¼ 1;000½ðR − RSTD Þ∕RSTD , where RSTD is the abundance ratio for a standard sample.
Throughout the text, δ13 CIC is the isotopic composition of carbonate carbon, δ13 COC is
the isotopic composition of organic carbon, Δδ13 CIC-OC (¼δ13 CIC − δ13 COC ) is the isotopic
fractionation between inorganic carbon and organic carbon, and δ18 OIC is the oxygen
isotopic composition of carbonate.
1
To whom correspondence may be addressed. E-mail: [email protected] or dec@
biology.sdu.dk.
This article contains supporting information online at www.pnas.org/lookup/suppl/
doi:10.1073/pnas.1101755108/-/DCSupplemental.
www.pnas.org/cgi/doi/10.1073/pnas.1101755108
A
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counter clockwise sense of rotation (Fig. 1G and Fig. S1B).
The high slope and hysteresis between Δδ13 CIC-OC and δ13 CIC
accompany several isotope excursions in the Cryogenian and
Ediacaran Periods of Earth history (10, 16).
Model
In our model, carbon isotope excursions are driven by the release
of methane to the atmosphere from sediment-hosted clathrates
formed beneath a low sulfate, high DOC ocean (we discuss
trigger mechanisms below). Photooxidation of DOC results in a
high flux of CO to the atmospheric, which lowers the concentration of the hydroxyl radical (•OH), which in turn increases the
residence time of methane in the atmosphere. This increase in
methane residence time is greater than would be accomplished
by just an increase in methane flux. The end result is high
atmospheric methane concentrations. Greenhouse warming from
the methane increases surface temperature and melts glacial ice,
which combine to produce a negative 18 O anomaly in precipitated
carbonates. The higher temperatures also accelerate the weathering of continental rocks, drawing down atmospheric CO2 .
Lower CO2 , in turn, reduces the isotope fractionation between
DIC and organic carbon during primary production (5), while
the δ13 COC is buffered by the large DOC reservoir. This cause
and effect chain of events is qualitatively consistent with all of the
observations. It was earlier suggested that methane release and
increased temperature drew down CO2 (21), possibly initiating
Bjerrum and Canfield
Neoproterozoic glaciations. Our model builds on this idea, but
goes much further in exploring the late Neoproterozoic carbon
cycle, and in explaining all of the major features of the preserved
carbon isotope records through the Shuram-Wonoka isotope
excursion.
Our model (fully described in the SI Text) is based on previous
isotope-based carbon cycle models (listed in refs. 7, 22), but
adds explicit reservoirs for marine DOC (10) and hydrate CH4
(23) (Fig. 2). We also add a simple time-dependent atmospheric
routine that calculates atmospheric CH4 , CO, and •OH concentrations (24). Most atmospheric chemistry models dealing with
methane oxidation in the deep past have modeled it as a steadystate process because of methane’s short residence time. However, the effective lifetime of a methane perturbation in chemically coupled systems is longer than the steady-state residence
time of methane as shown for the recent anthropogenic methane
increase (24, 25). When dealing with large perturbations as
studied here, this difference becomes even more important.
We follow previous studies in leaving out intermediate reactions
(24) and simplify the atmospheric reactions to:
i. CH4 þ •OH → … → CO…
ii. CO þ •OH… → CO2 …
iii. •OH þ X → …
Here, methane reacts with hydroxyl radicals, and the net reaction results in carbon monoxide and consumption of oxygen. CO
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Fig. 1. Observed and modeled stratigraphic changes in stable isotope compositions through the Shuram event (data from ref. 4). Observed (A) δ13 CIC ,
(C) δ13 COC , (E) Δδ13 CIC-OC ð¼ δ13 CIC -δ13 COC Þ. Tick line is five point running mean, color coded into specific stratigraphic intervals. (B, D, and F) is modeled
stable isotope compositions with y-axis scale on the right. (G) Cross plot (covariation) of observed δ13 CIC vs. Δδ13 CIC-OC . H) Cross plot of observed δ13 CIC
vs. δ18 OIC . The 8‰ shift in δ18 OIC with no significant shift in δ13 CIC (blue line) indicates an interval of variable diagenetic influence on δ18 OIC but not
δ13 CIC .
Fv
Org. C
Fwc
FCH4,esc
2Fwsi
4
Atmos.
CO2
2Fwsi
2Fwc
Fgex
(1-γ)j25
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Fwo
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Silicate
CaCO3
Atmos.
⋅OH
Atmos.
CH4
5
γj25
j35
γj23
Hydrate
CH4
3
Fbo
Fig. 2. Model reservoirs and fluxes as referred in Tables S1–S4 (online
SI Text). A simple time-dependent atmospheric chemistry model includes
CH4 , CO, •OH, and CO2 , where CH4 is oxidized by reaction with •OH. All fluxes
exiting a reservoir carry its isotopic signal except for fractionated fluxes.
Isotope fractionations result in an isotope flux from DOC to hydrate CH4 that
is (ðδ2 − Δch4 Þ × γ 0 j 23 ). The isotope flux from DIC to DOC is (δ1 − εo Þ × j 12 ),
where εo is fractionation between organic matter and dissolved CO2
(½CO2 aq ), plus the fractionation between ½CO2 aq and DIC (29–31). Note that
in steady-state, model DOC is respired to DIC, and but a small fraction of the
decomposition is by methanogenesis, where of only a small part of the
methane and CO2 flux (j 23 and j 25 ) enters the atmospheric CO2 and CH4
reservoirs. Importantly, DOC is photooxidized resulting in a flux of CO to
the atmosphere (j 26 ).
further consumes more •OH which results in a longer effective
lifetime for the methane perturbation in the coupled chemical
system than simple steady-state considerations would imply
(24). The simplicity of our time-dependent atmospheric chemistry permits us to semiquantitatively consider perturbation time
scales of over 10 kyr, a prerequisite for our modeling which spans
up to millions of years. We introduce a parameterization of
stratospheric methane photolysis and resultant •OH production.
For this purpose, we use a nonlinear source function of the •OH
radical dependent on methane concentration, which, for steady
state, we calibrate to the model results of Pavlov et al. (26) with
present day CO flux. In our standard calculation, we use a steady
CO flux to the atmosphere that is 5.2 times greater than the
present day flux resulting in a preevent residence time of atmospheric methane of 150 yr. This CO flux gives the best match to
the isotope record. A large CO flux is the expected consequence
of an ocean with more than 30 times present day levels of DOC.
This flux is because a large part of the CO flux today originates
from photooxidation of DOC in the surface ocean (27, 28). Other
reduced gases from the anoxic ocean could also have contributed
to the preevent reduction of •OH (e.g., 29).
It is important for our modeling that the methane concentration is high enough and its lifetime long enough to elevate
temperature for sufficient CO2 removal by weathering, and to
generate the observed timing of the isotope signal in the DIC reservoir. We initialize the model with reservoir sizes as shown in
Table S1, and weathering and burial fluxes as estimated for the
earliest Phanerozoic (7) modified to result in a relatively cooler
climate the ice-age-prone late Neoproterozoic time interval
(30, 31). The total preevent CH4 flux to the atmosphere is
assumed to be the same as the modern preanthropogenic flux.
A lower or higher preevent methane flux (0.2 to 1.5 times) does
not change our conclusions (see SI Text). Other reservoir sizes
and fluxes are set by an operator-assisted search to yield the best
model agreement with the isotope record.
As opposed to earlier models (10), the DOC concentration in
our model does not change significantly over time and therefore
has no significant contribution to the δ13 CIC isotope excursion
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of the oxidant balance of the surface environment. Two paths
of CH4 to the atmosphere are included in our model. One path
is a direct result of methane escaping the ocean from DOC
remineralization; the other path is through the methane hydrate
reservoir and is calculated from the reservoir size and its estimated residence time (32). It is assumed that the DOC remineralization rate and the fraction of organic matter decomposed
by methanogenesis is proportional to the atmospheric O2 concentration, and that half of the methane produced reenters the
hydrate reservoir. While the form of our parameterization of
DOC decomposition pathways and the choice of absolute values
is unconstrained, the extent to which organic carbon oxidation
proceeds by methanogenesis should be related to the volume
of anoxic waters and sediments, which is a function of atmospheric oxygen concentration and other factors. The relationship
we use between atmospheric O2 and methanogenesis has the
effect of increasing the duration of the isotope excursion. Finally,
we assume that organic matter decomposing below the ocean
mixed layer equilibrates isotopically with the DOC pool before
removal, and organic carbon is then removed with the isotopic
composition of the DOC (e.g., 6).
Recent studies suggest that increases in N2 O release to the
atmosphere could influence the methane cycle through ozone
reduction and an increase in the production of •OH (25). This
production could partially offset increases in methane concentrations, as modeled here, which result from increased marine
DOC concentrations and elevated atmospheric CO fluxes.
Indeed, the N2 O flux to the atmosphere might be expected to
increase with an anoxic ocean under low atmospheric oxygen as
assumed here (33, 34). We recognize that this N2 O effect on
atmospheric methane residence time may have some significance
in Neoproterozoic atmospheres, but find it unconstrained with
the current unknowns in the N2 O cycle.
Results and Discussion
Our model reproduces the major carbon isotopic features of
the Shuram-Wonoka anomaly with the net liberation of about
2.7 × 1018 moles of methane over a period of 1 million years
(Fig. 3 and Fig. S2). The model also generates the trends between
δ13 CIC and Δ13 CIC-OC including a counter clockwise sense of
rotation (compare Fig. 4A with Fig. 1G). The hysteresis in this
relationship provides indications of cause and effect and the relative timing of events in the carbon cycle as related to flux rates,
reaction rates, and reservoir sizes. Initially, fractionation during
photosynthesis (Δ13 CIC-OC ) decreases, along with the isotopic
composition of the marine DIC pool (δ13 CIC ), as CO2 is removed
by weathering. Later, the isotopic composition of the marine
DIC pool (δ13 CIC ) increases more slowly than the increases in
fractionation (Δ13 CIC-OC ) as the CO2 sink during weathering
approaches equilibrium with the CH4 source /sinks in the atmosphere, with an enhanced methane cycle due to lower oxygen
levels.
The Shuram-Wonoka anomaly also displays a general relationship between the 18 O and 13 C of carbonate (Fig. 1H and
Fig. S1C). This relationship has proven difficult to explain with
a seawater origin for the isotope signals, and has provided the
entrance point for discussions of a diagenetic origin for the preserved isotopic record (12, 13). Our model, produces a relationship between carbonate δ18 O and δ13 CIC (Fig. 4B), where the
δ18 O signal is generated through a combination of temperature
changes and glacial melt (in response to increasing temperature)
(see SI Text). Temperature and the pH effect on 18 O fractionation in carbonate contributes about 2.5‰ of the isotope signal,
while glacial melt contributes variably to the signal depending
on how this contribution is parameterized. In our model, the
glacial input is regulated assuming a linear decrease in glacial
volume as temperature increases (cf. 18). The best fit to the
isotope record is only approached with a very big preevent
Bjerrum and Canfield
200
200
Hydrate
18
(× 10 mole)
E
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ice volume, ∼3 times that of the peak Quaternary period. If the
temperature sensitivity to CO2 and CH4 changes was much higher than that in our model, by analogy with model attempts to
reconcile observations during the Paleocene-Eocene Thermal
Maximum (35, 36), a greater 18 O effect would be observed. Consequently, a smaller glacial volume would be needed to match
the 18 O carbonate excursions in the isotope record. The amount
of glacial ice during the Shuram-Wonoka event is poorly constrained, but the event is within an ice-age-prone time interval
(30, 31), and there is some indication of glacial diamictites correlating to the Shuram-Wonoka anomaly (37). Finally, the temperature in the extratropics may have increased by 50% more
than the global mean temperature increase (38) (thin dashed
line, Fig. 4B). This increase is viewed as a maximal temperature
effect on the 18 O record, assuming that most of the ShuramWonoka sections were preserved in extratropical regions.
Looking at different formations recording the ShuramWonoka anomaly, the relationship between δ18 O and δ13 C shows
different slopes and even different starting 18 O compositions,
but with similar δ13 C (12). Some of the δ18 O differences could
be explained by temperature deviations from the global mean
at the site of deposition, or by post depositional alteration of
the δ18 O in some cases. Generally, δ18 O is much more susceptible
to alteration than δ13 C (12) (e.g., blue trend in Fig. 1H, and part
of purple—red trend in Fig. S1C). Our modeling is not intended
to dismiss the possible significance of diagenesis in generating
the carbonate 18 O record. Rather, we carefully propose that some
of the coupled changes between the 13 C and 18 O record could
have resulted from the natural operation of the carbon cycle.
The isotope event in our model develops on the same time
scale as the release of the methane, and on the order of 0.5–1
million years, with a return to preevent conditions after 2.5 Myr.
Bjerrum and Canfield
This time scale can increase by increasing the total methane
liberated and decreasing the preevent CO flux, but if we liberate
the same amount of methane more slowly, the amplitude of the
model isotope event is smaller than observations, and the correlation slope in the carbon isotope cross plot is too steep (see
SI Text). Overall, the duration of our model event and its match
to observations is governed by the interplay between the •OH
removal rate, which increases the methane residence time in
the atmosphere, the amount of methane released, and its rate
of degassing as well as the size of the DIC and DOC reservoirs.
Over the time scale of the event, we simulate a stratigraphic
column (Fig. 1) assuming that sedimentation rate is proportional
to silicate and carbonate weathering and furthermore assuming
that sediment discharge is proportional to runoff and temperature (39), with runoff as a weak linear function of global mean
temperature (40, 41). Depending on the lithology underlying
the local drainage basin and whether head-water regions are glaciated, the sedimentary succession would be between 50–1,000 m
thick in good agreement with observed ranges (Fig. 1 and Fig. S1)
(4, 6, 37).
The methane released in our model amounts to 3 to 30 times
more methane than estimated for the modern day hydrate reservoir (42). This amount of methane, however, is not unrealistic
given: (i) that the methane reservoir size should increase sharply
with lowered concentrations of dissolved oxygen in marine bottom waters (42), and that bottom water anoxia was common in
the late Ediacaran (43, 44), (ii) Ediacaran marine sulfate concentrations were much lower than now (44, 45) allowing more organic carbon mineralization by methanogenesis, and (iii) 2.7 × 1018
moles of methane correspond to a methane hydrate volume of
3.8 × 105 km3 , which is 2 to 19 times lower than estimates of
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Fig. 3. Modeled carbon cycle, climate and isotope changes (5) as a result of increased methane hydrate degassing in the Neoproterozoic. (A) Atmospheric
pCO2 , (B) methane, (C) global mean temperature deviation (ΔT ) from preevent T ¼ 13.5 °C, (D) DIC (solid line) and organic carbon reservoir sizes [DOC,
dashed line, starting concentration set at ∼25 times present day concentration (square)], (E) methane hydrate reservoir size (circle range and mean
estimate for Earth today), (F) atmospheric O2 change relative to PAL, (G–I) isotope composition of carbonate carbon (δ13 CIC ), organic matter carbon
(δ13 COC ), and their isotope difference Δδ13 CIC-OC .
10
13
δ C IC (‰)
5
A
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10
Fig. 4. (A) Cross plot of modeled δ13 CIC vs. Δδ13 CIC-OC (5). Counter clock
rotation as in observations (Fig. 1B). (B) Cross plot of δ13 CIC vs. Δδ18 OIC ,
where Δδ18 OIC is the deviation from the preevent δ18 OIC ; (i) thin blue line
is for temperature contribution to δ18 OIC ; (ii) thick colored line as (i) with
4‰ contribution from big melting ice volume; (iii) thin blue dashed line
as (ii) with 1.5× extratropical amplification of mean temperature change.
Color coding as in Fig. 1 and 3. Open circles and crosses are observed values
from (4, 6), respectively.
the volume available for hydrate formation in the modern ocean
(23, 32).
Our model results lend support to the hypothesis that the
Shuram-Wonoka anomaly, and the associated isotopic signatures,
were generated by the massive release of methane from clathrate
hydrates. Indeed, if this release was the case, our model makes
several testable predictions. First, the anomaly was rather short
in duration, probably closer to 2 million years than 10 million
years. The semiquantitative assessment is based on the idea that
the maximum clathrate reservoir cannot greatly exceed the
hydrate volume we modeled and still allow for considerable nonhydrate pore volume, as is typical in sediments containing clathrates (46). Second, the nadir of the anomaly should be associated
with an average temperature maximum some 10–15 °C above preanomaly levels. Third, the anomaly would have been associated
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with a slight reduction in atmospheric oxygen concentrations of
about 0.1 present atmospheric level (PAL) relative to preanomaly
levels.
The oxidant requirement in our model event is much less
than previous models (10, 18), which ascribed the event to the
extensive oxidation of a large DOC reservoir. As highlighted
elsewhere (19), these models require more oxidant than would
have been available as O2 in the atmosphere and sulfate in
the oceans, both of which are thought to be in low concentration
at the time (45, 47). Furthermore, high DOC concentrations
in the deep ocean would have resulted in high surface DOC
as required by the time scales of ocean mixing (1,000 yr) and
the much longer residence time of a large DOC reservoir. It is
also unclear what could trigger the oxidation of high surface
(and deep) DOC concentrations as atmospheric O2 would always
have been in contract with surface-water DOC.
The Trezona anomaly within the Cryogenian Period (∼720
to 635 Ma) just precedes the δ13 C event of the Marinoan glaciation, and records δ13 C values down to −9‰ with trends between
δ13 CIC and Δ13 CIC-org similar to the Shuram-Wonoka anomaly
(16). We believe the Trezona anomaly, together with the ShuramWonoka anomaly modeled here, provide evidence for an
unusually large role for methane in the carbon cycle of the
Cryogenian and Ediacaran Periods of the Neoproterozoic. We
cite a number of converging factors. Widespread ocean anoxia
enhanced rates of anaerobic organic carbon degradation, while
low sulfate concentrations increased the significance of methanogenesis in anaerobic carbon mineralization. Enhanced marine
DOC concentrations, a source of atmospheric CO, may have accompanied increased marine productivity in relation to accelerated weathering from the evolution of lichens (48). Furthermore,
periodic low temperatures during this ice-age-prone time (31)
increased the stability zone of methane hydrates in sediments
allowing more to form. Perhaps lower temperatures during the
Cryogenian and Ediacaran Periods distinguished this time from
the rest of the Precambrian, where ocean anoxia and low sulfate
concentrations were also prevalent. Once formed, factors like
dike swarm emplacement in organic rich sediments, a sharp drop
in sea level, and/or a transient increase in temperature could
result in the destabilization of existing hydrates and methane
release. Once this destabilization happens, the greenhouse warming associated with the methane generates a positive feedback
encouraging further methane release.
ACKNOWLEDGMENTS. We thank Galen Halverson for input and comments.
Input on an earlier version of this paper from Daniel Rothman helped us
in shaping our ideas and model, and they sharpened the paper tremendously.
We thank Jim Kasting and Lee Kump for constructive reviews. This study
was carried out at the Nordic Center for Earth Evolution funded by the
Danish National Research Foundation and with additional funding from
the Danish Natural Science Research Council (FNU).
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PNAS ∣
April 5, 2011 ∣
vol. 108 ∣
no. 14 ∣
5547