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Nat Commun
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Nature Communications
2041-1723
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10.1038/s41467-024-51412-8
Article
Three-stage formation of cap carbonates after Marinoan snowball glaciation consistent with depositional timescales and geochemistry
http://orcid.org/0000-0003-2457-2890
Thomas Trent B. tbthomas@uw.edu

12
http://orcid.org/0000-0001-5646-120X
Catling David C. 12
1 https://ror.org/00cvxb145 grid.34477.33 0000 0001 2298 6657 Department of Earth and Space Sciences, University of Washington, Seattle, WA USA
2 https://ror.org/00cvxb145 grid.34477.33 0000 0001 2298 6657 Astrobiology Program, University of Washington, Seattle, WA USA
15 8 2024
15 8 2024
2024
15 705512 2 2024
6 8 2024
© The Author(s) 2024
2024
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At least two global “Snowball Earth” glaciations occurred during the Neoproterozoic Era (1000-538.8 million years ago). Post-glacial surface environments during this time are recorded in cap carbonates: layers of limestone or dolostone that directly overlie glacial deposits. Postulated environmental conditions that created the cap carbonates lack consensus largely because single hypotheses fail to explain the cap carbonates’ global mass, depositional timescales, and geochemistry of parent waters. Here, we present a global geologic carbon cycle model before, during, and after the second glaciation (i.e. the Marinoan) that explains cap carbonate characteristics. We find a three-stage process for cap carbonate formation: (1) low-temperature seafloor weathering during glaciation generates deep-sea alkalinity; (2) vigorous post-glacial continental weathering supplies alkalinity to a carbonate-saturated freshwater layer, rapidly precipitating cap carbonates; (3) mixing of post-glacial meltwater with deep-sea alkalinity prolongs cap carbonate deposition. We suggest how future geochemical data and modeling refinements could further assess our hypothesis.

A new formation mechanism is proposed to explain the presence and characteristics of “cap carbonates”: enigmatic rocks leftover from Snowball Earth events, during which Earth was globally ice-covered for millions of years in the distant past.

Subject terms

Geochemistry
Marine chemistry
Carbon cycle
Palaeoclimate
Astrobiology
100000001 National Science Foundation (NSF) DGE-1762114 100000104 National Aeronautics and Space Administration (NASA) 80NSSC21K0476 100000104 National Aeronautics and Space Administration (NASA) 80NSSC18K0829 issue-copyright-statement© Springer Nature Limited 2024
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pmcIntroduction

Earth’s Neoproterozoic Era (1 billion years ago to 538.8 million years ago) is marked by dramatic global climate change. Geologic evidence indicates two major glacial intervals where ice sheets reached low latitudes for millions of years (e.g., reviewed by Hoffman et al.1). These “snowball Earth” events2,3 are the Sturtian from 717 to 659 million years ago (Ma) and the Marinoan from ca 645 to 635 Ma. Together, these events bookend the Cryogenian Period (720–635 Ma).

The Cryogenian glacial intervals occurred alongside other global changes, including the appearance of the first large, complex organisms in Earth’s history in the subsequent Ediacaran Period4, an increase of atmospheric O2 relative to low levels in the mid-Proterozoic5, large excursions in the global carbon isotope record6, and the break-up of Rodinia and later assembly of Gondwana supercontinents7. All of these transitions occurred during or continued after the Cryogenian Period, which is only  ~2% of Earth’s 4.5-billion year history. Despite this temporal connection, the causes and the relationships between these global changes remain unclear.

Cap carbonates (CCs) probe Earth’s surface environment during, and immediately after, the Cryogenian. CCs are layers of limestone or dolostone up to ~200 meters thick that sharply overlie Sturtian and Marinoan glacial deposits in over 50 locations on all major Neoproterozoic continents (reviewed by Yu et al. 8). Carbonates record Earth’s surface conditions because they are sensitive to the chemistry of the atmosphere and ocean from which they precipitate. Thus, the sharp distinction between the glacial deposits and CCs is interpreted as an abrupt shift in Earth’s surface environment at the end of each Cryogenian glacial interval from cold, frozen conditions to hot conditions with a high partial pressure of atmospheric carbon dioxide, pCO23. In this scenario, continental weathering was inhibited during the glacial intervals, allowing volcanic CO2 to accumulate in the atmosphere and provide enough greenhouse warming to overcome the high albedo of Earth’s ice-covered surface, causing deglaciation. The post-glacial Earth then entered a high pCO2 but low albedo state in which continental weathering produced cations and carbonate ions (i.e. alkalinity) that drove rapid carbonate deposition2,3.

The above explanation for CC deposition is broadly consistent with the geologic evidence, but a complete explanation must answer several key questions. First, was the alkalinity source from continental weathering sufficient for the CCs? It is estimated that the global mass of the Marinoan CCs is over 1018 kg8. Enough alkalinity to generate this much carbonate must be supplied after the glacial interval. Second, what was the timescale of CC deposition? The interpretation of sedimentary structures, the presence of paleomagnetic reversals, and radiometric dating yield conflicting estimates that have yet to be resolved (Table 1). Third, what were the physical and chemical properties of the water body from which the CCs precipitated? After the Marinoan glaciation, the post-glacial ocean was subject to a large influx of glacial meltwater, sea level rise, and transgression onto the land. The deposition of the CCs was likely influenced by these changing ocean conditions.Table 1 Estimates for the age and timescale of Marinoan cap carbonate deposition

Radiometric Dating	
Age	Measurement location	Method	Geologic Formation	Reference	
632.50  ±  0.48 Ma	5 meters above top of CC	U-Pb	Doushantuo Formation, China	Condon et al.79	
632.3  ±  5.9 Ma	0.9 meters above top of CC	Re-Os	Sheepbed Formation, Canada	Rooney et al.80	
635.23  ±  0.57 Ma	Within CC, 2.3 meters above base	U-Pb	Doushantuo Formation, China	Condon et al.79	
634.57  ±  0.88 Ma	Base of CC	U-Pb	Nantuo Diamictite, China	Zhou et al.81	
636.41  ±  0.45 Ma	1 meter below base of CC	U-Pb	Cottons Breccia, Tasmania	Calver et al.82	
635.21  ±  0.59 Ma	~30 meters below base of CC	U-Pb	Ghuab Formation, Namibia	Prave et al.83	
635.5  ±  1.2 Ma	~30 meters below base of CC	U-Pb	Ghaub Formation, Namibia	Hoffmann et al.84	
Paleomagnetism	
Depositional Timescale	Description	Geologic Formation	Reference	
>1.25 Myr	5 polarity reversals in first 20 meters of CC	Mirassol d’Oeste Section, Brazil	Trindade et al.85	
>1.25 Myr	5 polarity reversals in first 20 meters of CC	Terconi Section, Brazil	Font et al.18	
>0.5 Myr	2 polarity reversals in first 9 meters of CC	Jebel Akhdar Section, Oman	Kilner et al.86	
>0.5 Myr	2 polarity reversals in first 12 meters of CC	Second Plain Section, Australia	Schmidt et al.87	
Sedimentology	
Depositional Timescale	Description	Geologic Formation	Review Reference	
103–104 yr	Rapid deglaciation and rapid deposition	Many	Hoffman et al.1	
>105 yr	Slow deglaciation and slow deposition	Many	Spence et al.16	
To calculate depositional timescale from paleomagnetic data, we assume 1 reversal occurred every 250 kyr, consistent with the Miocene, Jurassic, and Cambrian18. The sedimentological lines of evidence are broad interpretations of many CC formations across the literature.

CC cap carbonate.

Many explanations for CC deposition have been proposed, but none are complete. As summarized in Yu et al.8, suggestions include oceanic overturn9,10, continental weathering1,11, gas hydrate destabilization12,13, glacial meltwater plumes and subsequent ocean overturn14, sediment starvation15,16, microbial activity17,18, and calcareous loess19. Also summarized in Yu et al.8, these explanations all have unresolved deficiencies related to the physical and chemical conditions of the post-glacial ocean, the interpretation of the geologic evidence, and the predicted timescale of deposition.

Advances in our knowledge of the geologic carbon cycle and of Cryogenian conditions allow new tests of hypotheses for CC deposition.

Seafloor weathering has been recognized as a process in the geologic carbon cycle that has been important during some times in Earth’s history. Seafloor weathering occurs when seawater circulating through oceanic crust at low-temperatures reacts with constituents of basaltic rock (e.g., volcanic glass, olivine, and plagioclase) to release alkalinity in the form of Ca ions (e.g. reviewed by Coogan and Gillis20). Krissansen-Totton and Catling21 developed an empirically justified parameterization of seafloor weathering in a geologic carbon cycle model, and Krissansen-Totton et al.22 used this model to show that seafloor weathering may have been comparable in strength to continental weathering at some points in Earth’s history. The role of seafloor weathering in CC deposition has not been assessed. Previous global geologic carbon cycle models applied to Cryogenian glacial intervals used theoretical rate parameterizations that have proven inconsistent with recent experiments23, or they omit low-temperature seafloor weathering24–26.

The Marinoan CCs were likely deposited in a stratified, post-glacial ocean. The large volume of glacial meltwater following deglaciation should have created a distinct layer on top of the existing ocean. It has been proposed that the dolostone components of the CCs precipitated out of this layer14. This hypothesis is supported by geochemical measurements of the CCs, including 87Sr/86Sr and δ26Mg in multiple formations27–29 and a global analysis of Ca, Mg, Sr, and C isotopes30. A freshwater layer is consistent with 1D and 3D ocean models, which show that it could last for up to 105 years31,32. Thus, the evidence indicates that the meltwater layer must be considered in CC deposition; however, the previous global geologic carbon cycle models only consider whole-ocean chemistry.

Here, we investigate CC deposition with a geologic carbon cycle model that includes an empirically justified parameterization of seafloor weathering, explicit calculation of chemistry in the post-glacial meltwater layer, and other advances in our knowledge of both the geologic carbon cycle and Cryogenian conditions. Our model is applied to the Marinoan glaciation, but many aspects are likely applicable to the Sturtian and perhaps other glaciations. We identify a mechanism for Marinoan CC deposition that builds on previous explanations to answer the key questions mentioned above, and we find it is consistent with the global collection of CCs (See Supplementary Fig. S1).

Results

Climate evolution

We constructed a model for the evolution of the carbon content and marine alkalinity in Earth’s atmosphere and ocean before, during, and after the Marinoan glaciation (Fig. 1). We use a box model that evolves according to the processes of the geologic carbon cycle, which include continental silicate and carbonate weathering, volcanism, carbonate deposition, and seafloor weathering. In order to capture the unique climates of a glaciation event, we configure the model to address 4 distinct phases: the background Neoproterozoic phase, the syn-glacial phase, the post-glacial stratified ocean phase, and the post-glacial well-mixed ocean phase.Fig. 1 Schematic diagram of the box model used in this work, showing carbon (blue) and alkalinity (red) fluxes in the various model phases.

The basic model builds upon a previously data-validated model21,22 and consists of two boxes: one box for the combined atmosphere-ocean and one box for water in the seafloor rock pore-space, where seafloor weathering takes place. In the post-glacial stratified ocean phase, another box is included to explicitly account for a glacial meltwater layer. After calculating the aqueous chemistry in each box, the model calculates climate variables (e.g., ocean pH, surface temperature, and pCO2) and geologic processes (e.g., weathering rates, carbonate deposition rates). A complete description of these calculations is found in Methods and Supplementary Material.

Transitions between model phases are imposed. A rigorous treatment of the transitions would require calculations beyond the scope of this work such as the complex movement of ice sheets subject to the ice-albedo instability or changes in the 3D circulation of the ocean. Thus, model transitions are not explicitly calculated, but they are informed by the literature. We instead focus on the major environmental and chemical conditions within each model phase.

We sample uncertain model parameters within their plausible value ranges. We follow Krissansen-Totton and Catling21 and Krissansen-Totton et al.22 to sample the key uncertain parameters in the geologic carbon cycle model. We also introduce extra parameters related to the glaciation, such as the size of the ice sheets, the continental shelf area during glaciation, and the composition of glacial meltwater.

By modeling the glaciation event in 4 distinct phases, we generate results that are self-consistent across the full range of potential climate states. The nominal model evolution through all phases is shown in Figs. 2 and 3. The model is run 3000 times to derive median values and confidence intervals while sampling uncertain parameters.Fig. 2 Climate evolution through all modeled phases noting that post-glacial Phase 3 is very compressed on a Myr timescale, so is expanded in Fig. 3.

The shaded regions are the 95% confidence intervals and the solid lines are the median model runs with randomly sampled parameters. Glaciation was terminated after 10 Myr and the stratified ocean was terminated after 100 kyr (tstrat = 105 years). Vertical dashed lines indicate boundaries between model phases, noting the two close vertical lines at 10 Myr and 10.1 Myr bounding post-glacial stratified ocean Phase 3. Horizontal dashed lines show modern values noted in the main text.

Fig. 3 Climate evolution in the stratified ocean Phase 3 from Fig. 2.

The shaded regions are the 95% confidence intervals and the solid lines are the median model runs with randomly sampled parameters. Post-glacial ocean stratification is assumed to last 100 kyr (tstrat = 105 years), indicated by the vertical dashed black line. A shows the evolution of atmospheric pCO2. B–E show the evolution of parameters related to the post-glacial meltwater layer in gray and the underlying ocean in color. Following stratification, the two reservoirs are combined and averaged.

The pre-glacial phase (Phase 1), given typical Neoproterozoic parameters, is characterized by a temperate or cool background climate. The 95% confidence interval for equilibrium atmospheric pCO2 is 1.6 × 10−4 to 5.5 × 10−3 bar, yielding surface temperatures of 274.4–291.6 K, ocean pH of 7.6–8.4, and ocean calcite saturation state of 3.3–5.2, which is reasonable given uncertainty in marine Ca2+ concentration in the Neoproterozoic (e.g.33–35). In the median model evolution, pCO2 is 5.9 × 10−4 bar and the ocean pH is 8.11, which is similar to the modern values of 4 × 10−4 bar and 8.1, respectively; however, the reduced solar luminosity allows for lower surface temperatures. The low surface temperature would leave Earth in a state that is potentially vulnerable to a snowball-causing climate perturbation.

During glaciation (Phase 2), pCO2 steadily rises while seafloor weathering supplies alkalinity to the subglacial ocean. With ice sheets covering the land and a slow hydrologic cycle, we assume that continental weathering either stops completely or is fixed at a rate several orders of magnitude below modern, following Lan et al.36. Seafloor weathering continues though, and causes alkalinity in the sub-glacial ocean to reach up to 0.035 mol eq kg−1, which is  ~14 times higher than modern seawater (2320 μmol eq kg−1;37, p. 131). The built up alkalinity does not result in widespread carbonate precipitation because high CO2 levels cause the ocean to be acidic, the ocean is cold, and the thick ice sheets eliminate most of the available shelf area for precipitation (though there is still some carbonate precipitation in the ocean crust). Thus, atmospheric pCO2 steadily rises as CO2 is supplied by subaerial and submarine outgassing. Note that we assume the atmosphere and ocean are in equilibrium despite widespread ice sheets, which is further justified in Methods.

We force the glaciation to end after 10 Myr, which is consistent with constraints on the duration of the Marinoan glaciation (see1, and references within). At the end of glaciation, pCO2 is 0.13–0.35 bar, consistent with estimates of the required pCO2 to cause global melting of 0.1–0.3 bar1,38,39. We do not include the complicated process of ice sheet melting in our model, because we focus on the evolution of geochemical parameters.

In the post-glacial stratified ocean (Phase 3), continental weathering rapidly supplies alkalinity to the meltwater layer (Fig. 3E) and CC deposition begins. In the nominal model, we assume that the lifetime of the meltwater layer, tstrat, is 105 years, but we also consider a scenario with tstrat = 104 years (Supplementary Figs. S2 and S3). The equilibration of the meltwater layer with the high CO2 atmosphere initially causes immediate and intense acidification. The acidification is then counteracted by alkalinity delivered from continental weathering in the hot, high CO2 conditions. Alkalinity supplied to the meltwater layer can cause the calcium-carbonate saturation state to reach over 70 before carbonate deposition can remove alkalinity at the same rate and balance the system. In the median model runs, carbonate deposition in the meltwater layer removes 0.04 and 0.16 bar CO2 in the first 104 and 105 years of stratification, respectively.

In the post-glacial well-mixed ocean (Phase 4), alkalinity is supplied to the surface from the deep ocean, CC deposition continues, and a steady state climate is eventually recovered. As mentioned above, seafloor weathering causes alkalinity to build up in the sub-glacial ocean during Phase 2. During Phase 3, this alkalinity remains trapped in the deep ocean under the meltwater layer. It is not until Phase 4, when the meltwater layer mixes with the underlying ocean, that this alkalinity is delivered to the surface ocean and contributes to carbonate precipitation on continental shelves. Note that in our model construction, the meltwater layer and the underlying ocean are abruptly mixed in a single timestep, which causes the discontinuity seen in some climate variables. This transition was probably more gradual and localized in reality, but we expect the ultimate evolution of the climate variables to be the same. In Phase 4, CO2 continues to be removed from the atmosphere on the timescale of the geologic carbon cycle, and the background Neoproterozoic steady state climate is generally recovered within 5 Myr of deglaciation.

Post-glacial carbonate deposition

Figures 4 and 5 show how carbonates are deposited after the glaciation event in the nominal model runs with tstrat = 104 and 105 years. Confidence intervals are derived from the model runs in Figs. 2 and 3 and in Supplementary Figs. S2 and S3.Fig. 4 Carbonate deposition rate and cumulative carbonate deposition after deglaciation in terms of mass for different lifetimes of the stratified ocean.

The end of the stratified ocean (Phase 3), tstrat, is indicated by the vertical dashed black lines. In A and B, tstrat = 104 years. In C and D, tstrat = 105 years. Horizontal dotted lines in B and D are minimum, median, and maximum estimates of the global mass of Marinoan cap carbonates from Yu et al.8: 4.2 × 1021, 9.3 × 1021, and 14.4 × 1021 g, respectively. The shaded regions are the 95% confidence intervals and the solid lines are the median model runs with randomly sampled parameters.

The carbonate deposition rate quickly rises in the first 10 kyr after deglaciation and reaches a maximum value 10 to 100 kyr after deglaciation (Fig. 4). For tstrat = 104 years, the median deposition rate peaks ~67 kyr after deglaciation, when the ocean is well-mixed (Phase 4). For tstrat = 105 years, the median deposition rate peaks ~25 kyr after deglaciation, when the ocean is still stratified (Phase 3). These results are due to the fact that the meltwater layer can reach a higher saturation state and faster deposition rate when it has a longer lifetime because more alkalinity can be delivered. When tstrat = 105 years, the second peak in deposition rate after the ocean mixes is probably unrealistic because it is due to the abrupt water mixing we impose in the model. In reality, the carbonate deposition rate would likely have been uniformly higher in the stratified ocean phase as the alkalinity from the deep ocean slowly mixed into the meltwater layer.

For context, post-glacial carbonate deposition peaks above 1017 g CaCO3 yr−1, 2 orders of magnitude higher than modern carbonate deposition on continental shelves ( ~1.4 × 1015 g CaCO3 yr−1;40). The post-glacial deposition rate is so high primarily because the saturation state in the meltwater layer reaches up to Ω = 70, compared to Ω = 3–5 at the surface of the modern ocean.

From the 95% confidence intervals for both values of tstrat, we predict that it took between 32 kyr and 591 kyr to produce the estimated minimum global mass of CCs (Fig. 4). In the median model runs, the time to deposit the CCs is 127 kyr and 162 kyr for tstrat = 104 and 105 yr, respectively. The timescales are similar despite differences in tstrat because the sources of alkalinity are the same: seafloor weathering during glaciation and continental weathering after glaciation. The alkalinity sources are the ultimate limiting factor for carbonate precipitation, and the timescale of deposition is set by the time it takes for them to saturate the whole ocean.

The proportion of the CCs deposited from the meltwater layer versus the well-mixed ocean depends on tstrat (Fig. 4). For tstrat = 104 years, the median total carbonate mass deposited in the meltwater layer is 3.3 × 1019 g, with 95% confidence interval of 3.3 × 1015 g to 1.4 × 1021 g. For tstrat = 105 years, the median is 2.5 × 1021 g and the 95% confidence interval is 3.2 × 1020 g to 9.4 × 1021 g. Most of the CCs are deposited after ocean mixing. Relative to the total carbonate mass deposited in the first 5 Myr after deglaciation, 0.13% and 9.83% of the CCs were deposited in the meltwater layer in the median model runs with tstrat = 104 and 105 yr, respectively.

For more direct relevance to the geologic record, we convert the mass of carbonates into a deposit thickness (Fig. 5). For a rough comparison, we assume constant sedimentation rates and that the total carbonate mass is evenly spread over a surface area equal to 2 times the modern continental shelf area to account for post-glacial sea level rise (See Methods). This calculation is somewhat qualitative because the dynamics of the depositional environments on post-glacial Earth were complex and subject to regional variability (e.g.41,42). In the median model runs, the peak deposition rate in a globally averaged CC deposit occurs 10.8 m and 2.6 m upsection for tstrat = 104 and 105 yr, respectively. In the 95% confidence interval for tstrat = 104 years,  < 0.001–8.12 m were deposited out of the meltwater layer. For tstrat = 105 years, the range is 1.84–53.68 m.Fig. 5 Carbonate deposition rate and cumulative carbonate deposition after deglaciation in terms of deposit thickness for different lifetimes of the stratified ocean.

The end of the stratified ocean (Phase 3), tstrat, is indicated by the vertical dashed black line in B and D. In A and B, tstrat = 104 years. In C and D, tstrat = 105 years. The shaded regions are the 95% confidence intervals and the solid lines are the median model runs with randomly sampled parameters. Confidence intervals do not align in A and C because they are originally time-based but are converted into height-based here.

High-alkalinity meltwater scenario

In the nominal model results, carbonate deposition does not begin until at least ~1 kyr after deglaciation. In this depositional hiatus, continental weathering has not yet supplied enough alkalinity to raise the saturation state of the meltwater high enough for rapid carbonate precipitation. This occurs for two reasons: (1) we assume that the initial alkalinity of the glacial meltwater is low, estimated from modern glacial waters, and (2) we do not explicitly model the global deglaciation, where meltwater from continental ice sheets would have traversed rocky terrain before entering the ocean. In reality, as the Earth was deglaciating, the water from the continental ice sheets would have weathered some of the rock and probably caused the initial alkalinity of the meltwater to be higher than we nominally assume.

Coupled climate and ice-sheet models indicate that the deglaciation process lasted ~2 kyr, due to the ice-albedo instability (e.g.43,44). We use our silicate weathering parameterization to calculate the delivery of alkalinity from melting glaciers during these 2 kyr. We assume that pCO2 is 0.1 bar and the surface temperature is 310 K during deglaciation. We fix the weatherability factor, fw = 1, and then vary the empirical factors in their standard ranges. This results in a maximum alkalinity delivery rate of 4.73 × 1015 mol eq yr−1 and a maximum meltwater alkalinity of 70,000 μmol eq kg−1 when integrated over 2 kyr. This is 70–100 times higher than our previous meltwater alkalinity assumption of 700–1000 μmol eq kg−1 based on modern glacial meltwater. Moreover, the true value may be even higher because the land surface was likely highly weatherable after enduring millions of years of rock-grinding glacier movement. Here we test this scenario by running our model with the higher initial meltwater alkalinity of 70,000 μmol eq kg−1.

The meltwater layer rapidly saturates and carbonates begin precipitating immediately after deglaciation in this scenario (Fig. 6). Here, deposition starts 100 years after deglaciation, which is essentially instantaneous in our model, since 100 years is the minimum timestep in this phase. On the other hand, the total timescale of CC deposition is similar to the baseline case. This is because the high-alkalinity meltwater scenario only adds alkalinity to the meltwater layer equivalent to 2 kyr of weathering, which is small relative to the 100 kyr timescale of full CC deposition in the baseline case.Fig. 6 Post-glacial carbonate deposition by mass in the high-alkalinity meltwater scenario.

The initial alkalinity of the meltwater in phase 3 is 70,000 μmol eq kg−1, compared to 700–1000 μmol eq kg−1 in the baseline case. The end of the stratified ocean (Phase 3), tstrat, is indicated by the vertical dashed black lines. In A and B, tstrat = 104 years. In C and D, tstrat = 105 years. Horizontal dotted lines in B and D are minimum, median, and maximum estimates of the global mass of Marinoan cap carbonates from Yu et al.8: 4.2 × 1021, 9.3 × 1021, and 14.4 × 1021 g, respectively. The shaded regions are the 95% confidence intervals and the solid lines are the median evolutions with randomly sampled parameters in 3000 model runs.

Additionally, the meltwater layer is much less acidic in this scenario (Supplementary Fig. S4). In the baseline case, the pH of the meltwater layer starts at  ~5 and then increases to  ~7 after 100 kyr. In the high alkalinity scenario, however, the pH of the meltwater layer starts over 7 and reaches close to 10 in some cases. This is a consequence of inorganic carbon speciation: when all else is held equal, increased alkalinity causes increased pH.

Comparison to geologic evidence

Here we compare our model results to several lines of evidence in the Marinoan CCs, which refers to the combination of (1) the cap dolostones, which are uniform in character, ubiquitous, and sit directly on top of Marinoan glacial deposits, and (2) the overlying limestones, which are more variable in character and thickness, and sit on top of the dolostones. Our conclusions are therefore most applicable to the Marinoan glaciation. However, some results may generalize to the Sturtian glaciation, which has CCs with notable differences from the Marinoan, such as being often far thinner or absent and generally limestone, not dolostone.

Our results are consistent with the global mass and thickness of the Marinoan CCs. As shown in Fig. 4, we find that enough alkalinity is generated in the post-glacial aftermath to explain the estimated global mass of CCs. The alkalinity source is a combination of continental and seafloor weathering, described above. Considering deposit thickness, we find that the observed global average CC thickness, ~11 meters8, is generally precipitated in under 200 kyr, while thicker sections can be deposited on longer timescales in model runs further from the median evolution (Fig. 5). This is consistent with the geologic record because there was likely significant regional variability in depositional environments (e.g.41,42) and some CCs are hundreds of meters thick, such as the Noonday Formation (e.g.45).

The timescale of CC deposition is constrained by three general types of evidence that have not been reconciled: radiometric dating, paleomagnetism, and sedimentology (Table 1). Although useful for determining absolute ages, the radiometric dating measurements cannot give a statistically significant estimate for the timescale of CC deposition due to the measurement uncertainty and scattered locations in different CCs. The presence of multiple paleomagnetic reversals in multiple sections is evidence for a depositional timescale on the order of 105 to 106 years, with uncertainty due to the unknown frequency of polarity reversals in the Neoproterozoic and the fidelity of the paleomagnetic data and their interpretations. Marinoan CCs also have unusual, heavily debated sedimentary structures. The standard Snowball hypothesis1 suggests that features like giant wave ripples and sheet-crack cements are present in CCs as a result of rapid deglaciation, implying depositional timescales of  ~103 to 104 years (e.g.14,46,47). However, these features have instead been interpreted as tepees and bedding expansion features that imply prolonged depositional timescales of ≥105 years (e.g.16,48,49).

Our results help reconcile the differing lines of evidence for the depositional timescale of the CCs.

First, we predict that the minimum global CC mass is deposited in 32 to 591 kyr in our nominal 95% confidence intervals. This result suggests that the global timescale of CC deposition was intermediate, with endmember scenarios for extremely rapid or prolonged deposition due to regional variability corresponding to model runs outside of the 95% confidence interval. So, we suggest that the sedimentary structures may reflect deposition on both short and long timescales. On one hand, deposition on timescales below 30 kyr may have occurred in regions with enhanced alkalinity delivery, where deposition can start as fast as 100 years after deglaciation (Fig. 6). On the other hand, deposition on timescales over 500 kyr can be reconciled by the fact that our modeled deposition rates remain higher than the baseline for over 2 Myr following deglaciation (Fig. 4). Considering the regional variability, it is likely that the overlying limestones in several sections experienced prolonged deposition in favorable environments—i.e., the Brazil, Oman, and Australian CCs—thus explaining the presence of the paleomagnetic reversals and some of the sedimentary structures.

Second, we predict that the peak carbonate deposition rate is achieved on timescales of 104 yrs after deglaciation (Figs. 4 and 6). We suggest that this can help reconcile evidence of both rapid and prolonged deposition. In our interpretation, the 103–104 yr timescale of CC deposition inferred from some of the sedimentary structures is an underestimate because it is assumed that the peak deposition rates lasted for the entirety of CC deposition. Perhaps some of the sedimentary structures indeed indicate peak deposition rates, but they did not last for the entirety of CC deposition, creating other sedimentary structures and recording paleomagnetic reversals as a result of longer deposition. This idea is consistent with our model results and a recent analysis of the Svalbard Marinoan CC50, which both indicate peak deposition rates occurring shortly after deglacation and then declining over time. The record of peak deposition rates can be further analyzed by comparing the distribution of sedimentary structures with respect to height to our qualitative deposition rates as a function of height (Fig. 5).

Third, our results are consistent with the contact between glacial deposits and CCs. In all Marinoan sections, there is sharp contact between CC and glacial unit (e.g.1), suggesting that the CCs precipitated during and immediately after deglaciation, with no hiatus (e.g.51). In the high-alkalinity meltwater scenario (Fig. 6), we show that there is no depositional hiatus (i.e. no more than ~100 years). In the baseline scenario with low initial meltwater alkalinity (which is biased toward slow deposition relative to the high-alkalinity meltwater scenario), the hiatus only lasts ~1 to ~10 kyr, which may be consistent with the evidence depending on sedimentation rates. Our model does not explicitly treat the dynamics of the deglaciation with respect to changing meltwater volume, regional variability, and weathering rates, so the two model scenarios cannot distinguish between syn-deglacial or post-deglacial deposition, but they are consistent with the general lack of a depositional hiatus, which has been a longstanding problem for CC explanations involving post-glacial continental weathering as an alkalinity source (see ref. 8).

Our results are also consistent with the general stratigraphy of the Marinoan CCs. Our model shows that CC deposition in the meltwater layer (Phase 3) is caused by alkalinity supply during and immediately after deglaciation, which is consistent with the transgressive nature of the Marinoan cap dolostones, deposited as sea levels rose11. Subsequent CC deposition in the well-mixed ocean (Phase 4) is consistent with the more variable and prolonged deposition of the overlying limestones, as outlined in the “cap limestone” phase of Shields14; here we have shown it is valid in a global geochemical model.

Several lines of geochemical evidence probe Marinoan post-glacial ocean stratification. The 87Sr/86Sr ratio in seawater is raised by continental weathering and lowered by hydrothermal input (e.g.52–54). Several studies28,29,55,56 have measured 87Sr/86Sr along CC sections and found that they show a stepwise decrease from high to low values upsection, indicated by the red lines in Fig. 7a. This decrease suggests that (1) first, CCs precipitate out of a glacial meltwater layer with elevated 87Sr/86Sr due to massive continental weathering, and then (2) second, the CCs precipitate out of a well-mixed ocean which has a lower 87Sr/86Sr that is closer to the typical modern ocean value. Thus, the height at which this stepwise decrease occurs should reflect the point at which the post-glacial ocean becomes well-mixed. This interpretation is further supported by other Ca, Mg, and Sr isotope measurements30,56,57.Fig. 7 Comparison of measured strontium isotopes and model results for determining the end of post-glacial ocean stratification.

A Measured 87Sr/86Sr offsets upsection in 5 cap carbonates. The red lines are the roughly inferred heights in the cap carbonate at which ocean stratification ends according to the mixing models of those who obtained and analyzed the data: Liu et al.28,29 (Mongolia), Liu et al.27 (Australia), and Wei et al.56 (Namibia, South China, and North China). Below the red lines, the cap carbonates were precipitated out of mostly glacial meltwater with elevated, continentally influenced 87Sr/86Sr. Above these lines, the cap carbonates were precipitated out of mostly ocean water with lower, hydrothermally influenced 87Sr/86Sr. B Model predictions for the height at which ocean stratification ends in the baseline scenario. These are effectively predictions for where the red lines should be. Results assuming tstrat = 104 years are on the left in blue, and assuming tstrat = 105 years are on the right in green. The filled squares are the median model predictions and the error bars are the 95% confidence interval corresponding to Fig. 5.

Our results are consistent with 87Sr/86Sr trends in CC sections. In Fig. 7b, we show our model results for the CC height at which ocean stratification ends. In the case with tstrat = 104 years, 0.18 meters of the CCs are deposited in the stratified ocean in the median model run; with tstrat = 105 years, this value increases to 14.36 meters. The 95% confidence intervals of these two cases incorporate the full range of Sr-inferred mixing heights. Our model is global, so it is likely that different places experienced different timescales of ocean stratification. For example, we would expect that the Mongolian deposit experienced 105 years or more of ocean stratification, the North China deposit experienced 104 years of ocean stratification or even less, and the Namibia, South China, and Australia deposits experienced an intermediate time between 104 and 105 years.

Discussion

In the above sections, we have presented a global model for the deposition of CCs after the Marinoan glaciation. This model is consistent with geologic evidence regarding the global mass and thickness of the CCs, the timescale of their deposition, and their deposition in a post-glacial stratified ocean. Our results could be summarized as the “Seafloor weathering-Continental weathering-Ocean Mixing (SCOM)” mechanism for CC deposition (Fig. 8).Fig. 8 Schematic diagram of the “Seafloor weathering-Continental weathering-Ocean Mixing (SCOM)” mechanism for cap carbonate deposition.

The SCOM mechanism has 3 phases. First, seafloor weathering in high CO2, acidic conditions during the glaciation supplies alkalinity to the sub-glacial ocean. Second, intense continental weathering supplies alkalinity to the post-glacial meltwater layer and CCs begin precipitating. Third, the eventual mixing of the meltwater layer and the deep ocean supplies alkalinity to the surface and CCs continue precipitating.

The SCOM mechanism explains Marinoan CC deposition on a global scale and was likely subject to regional variability. For example, post-glacial sea level rise was likely highly regionally variable (e.g.41,42), runoff rates from continental weathering depend on regional topography, and the duration of ocean stratification likely depends on regionally varying currents. These important regional distinctions explain how individual CCs could deviate from our median model predictions, but even the most unique CCs are broadly consistent with our 95% confidence intervals. We therefore propose that Marinoan CC deposition on a global scale was primarily driven by the SCOM mechanism.

The SCOM mechanism draws from several previous hypotheses for CC deposition. In the plumeworld hypothesis14, it was proposed that CCs rapidly precipitate out of a stable glacial meltwater layer with alkalinity generated from a variety of sources. Many others have hypothesized that rapid continental weathering would have supplied the necessary alkalinity to the ocean to generate the CCs (e.g.11,38). Deep ocean upwelling of alkalinity—derived from the degradation of organic matter, not seafloor weathering—has also been suggested9,10. While these hypotheses are plausible and have been extensively studied individually, they struggle to explain the timescale of deposition, the required alkalinity source, and other geologic evidence8. With the SCOM mechanism, we self-consistently combine and refine these hypotheses to show that it is consistent with the geologic evidence on a global scale. The key improvements presented here include the previously unconsidered alkalinity source of seafloor weathering, the explicit calculation of aqueous chemistry in the glacial meltwater layer and subsequent mixed ocean, and the rigorous calculation of the geologic carbon cycle.

There are several caveats and limitations on the SCOM mechanism from both the geologic record and our modeling approach. First, transitions between phases are imposed in our model due to their complexity; for example, the deglacial transition would require a careful treatment of ice sheet dynamics and climate, and the ocean mixing transition would require GCM-like treatment of 3D ocean dynamics. We do, however, provide a sensitivity study to explore the effect of a prolonged deglaciation (Supplementary Section C2). In the most extreme endmember, this may increase the time required for CC deposition by up to 90 kyrs, but does not change our main conclusions. Further discussion of forcing model transitions and sensitivities are found in Supplementary Section C. Second, our model is global, and does not explicitly capture regional behavior, which is important for interpretation of individual CCs. Third, compilation of the global CC record is subject to variability in interpretation and measurement, which may cause biases (e.g., toward thicker CC sections than are actually present or toward overinterpetation of paleomagnetic data). Future studies on the model transitions, the implications for regional behavior, and improved global interpretation of the CC record can improve or test the SCOM mechanism and are encouraged.

There are many other lines of geologic evidence that can be used to test the SCOM mechanism, including ocean pH proxies of boron isotopes (e.g.58) and rare Earth element distributions59, styles of carbonate deposition within CCs, sedimentation rates and carbonate concentrations as a function of height within CCs, developing proxies that probe alkalinity in the subglacial ocean, and more radiosotope dates from multiple CCs (preferably at the top and bottom of the same section). Additionally, comparisons to the record of Sturtian CCs may provide insights into how the two major Cryogenian glaciations differed (e.g., the effect of disparate glacial durations) and their implications on the evolution of Earth’s surface. In this work we have shown that the SCOM mechanism is broadly consistent with the global characteristics of Marinoan CCs, but future studies making more detailed, regional comparisons to the above evidence are suggested.

Methods

We model the evolution of the carbon content and marine alkalinity in Earth’s atmosphere and ocean as it is subject to processes of the geologic carbon cycle before, during, and after a global glaciation event. Our model is based on previous geologic carbon cycle models that have been rigorously validated against Earth’s last 100 Myr and applied as far back as 4 Ga21,22. In order to capture the unique climate of the Cryogenian glaciations, we modify the model accordingly and separate it into 4 distinct configurations (Fig. 1): the background Neoproterozoic phase, a syn-glacial phase, a post-glacial stratified ocean phase, and a post-glacial well-mixed ocean phase.

Key aspects of the model are described below. Additional information is in the Supplementary Material. The calculation of the baseline carbon cycle fluxes, aqueous chemistry, and climate is in Supplementary Section A. Calibration and benchmarking of the model against the modern and post-glacial Earth is in Supplementary Section B. Further description of transitions between model phases and a sensitivity study are in Supplementary Section C.

Phase 1: Background Neoproterozoic

The goal of phase 1 is to find the background climate in the Neoproterozoic era before any glaciation events occur. In this phase, there are two model reservoirs: one for the combined atmosphere and ocean, and one for water in the pore-space of the seafloor. The pore-space reservoir captures the chemistry of water circulating through the the upper portion of the oceanic crust, which is important for investigating the impact of seafloor weathering. The time evolution of carbon chemistry in these reservoirs is described by the following set of equations:1 dCodt=1Mo−J(DICo−Cp)+Vtotal+Wcarb−PshelfdAodt=1Mo−J(Ao−Ap)+2Wsil+2Wcarb−2PshelfdCpdt=1Mp−J(Cp−DICo)−PporedApdt=1Mp−J(Ap−Ao)+2Wsea−2Ppore.

Here, C is the concentration of inorganic carbon with units mol C kg−1 and A is the carbonate alkalinity with units mol eq kg−1 where the subscript o and p indicate the ocean-atmosphere and pore-space reservoirs, respectively. Cp is equal to the dissolved inorganic carbon (DIC) of the pore-space. Co is the sum of DIC in the ocean and the carbon content in the atmosphere, given by Co = DICo + pCO2 × s, where s is a scaling factor equal to the total number of moles C per bar in the atmosphere divided by the mass of the ocean, s = 1.8 × 1020/Mo, and pCO2 is in bar. We assume that the masses of the ocean and pore-space water are equal to their modern values, respectively given by Mo = 1.35 × 1021 kg and Mp = 1.35 × 1019 kg60. J is the water mass flux between the deep ocean and pore-space, which has been estimated by balancing crustal heat fluxes: J = 0.6–2 × 1016 kg yr−120; this is equivalent to the entire ocean circulating through the pore space every 70 to 250 kyrs.

The remaining terms are fluxes of carbon (mol C yr−1) and alkalinity (mol eq yr−1) due to processes of the geologic carbon cycle: Vtotal is the sum of volcanic outgassing from subaerial and mid-ocean ridge sources, Wcarb is continental carbonate weathering, Wsil is continental silicate weathering, Wsea is seafloor weathering, Pshelf is carbonate precipitation on the continental shelf, and Ppore is carbonate precipitation in the pore-space. Calculation of these fluxes is in Supplementary Section A.

Phase 2: Syn-glacial

Starting from the background Neoproterozoic climate, we impose a glaciation event. In the syn-glacial phase, we calculate the time-dependent evolution of the geologic carbon cycle until a threshold for deglaciation is reached. The equations in (1) are still the governing equations of this phase, but they are modified in several ways, described below.

With the presence of a large global ice sheet, sea level should fall significantly and the global mass of the liquid ocean should decrease. Hoffman et al.1 estimate ocean volume change during glaciation by summing continental and sea ice volumes under various dust accumulation rates and pCO2 levels61,62. We explore the range of estimates and assume a decrease in ocean volume of 10% to 30% relative to the modern ocean. To calculate the immediate increase in dissolved species concentration from a shrinking ocean, we assume that no conservative cations (e.g., Ca2+) are trapped in the ice during freezing. Thus, the ocean alkalinity and dissolved inorganic carbon increase relative to the background Neoproterozoic values by the same relative proportion that the ocean volume decreases.

The 2D and 3D ocean circulation models of Ashkenazy et al.63,64 show that the sub-glacial ocean should have had vigorous convective mixing under the ice cover, causing it to be isothermal and chemically well-mixed. Thus, we continue to use a single box in our model to represent the ocean. We assume that the syn-glacial ocean had a uniform and constant temperature of 269.5 K, regardless of pCO2, which is indicated by ocean models with complete ice cover63,64. This assumption is justified for scenarios with incomplete ice cover as well since global averaged surface temperatures are predicted to be below 269.5 K1.

We nominally assume that the atmosphere and sub-glacial ocean were in equilibrium with respect to inorganic carbon speciation and aqueous chemistry during the glaciation. Several lines of evidence support this assumption: (1) It has been shown that atmosphere-ocean equilibrium with respect to CO2 can be reached on million year timescales with only 103 km2 open ocean65. Areas of open ocean likely exceeded this threshold via geothermal heat production and lava flows alone, as the modern area of emerged active hydrothermal systems (1.5 × 106 km2) is 3 orders of magnitude greater than what is required for equilibration66. (2) Sedimentological evidence, oxygen isotopes, and sulphur isotopes of the Svalbard Marinoan glacial deposits indicate that ice sheets were sensitive to orbital forcing as pCO2 rose, creating extensive patches of open water67. (3) Geochemical measurements of carbon, nitrogen, and iron in the Nantuo Formation suggest there was aerobic nitrogen cycling in surface waters and swaths of open ocean at mid-latitudes during glaciation68. (4) Approximately 25% of global volcanic outgassing of CO2 occurs at underwater mid-ocean ridges on the modern Earth (69, p. 203). CO2 bubbles from this volcanism would directly equilibrate with the subglacial ocean regardless of ocean-atmosphere equilibrium. Combined, this evidence indicates that a chemically isolated atmosphere and ocean is unlikely.

In order to determine the minimum timestep for modeling this phase, we must estimate how long it takes for the atmosphere-ocean equilibrium to be reached. Le Hir et al.65 showed that only 3000 km3 of open ocean is required for full ocean CO2 diffusion on the order of several millions of years. When combined with the efficient mixing of the subglacial ocean, it is reasonable to assume that equilibrium would be reached on timescales similar to the modern ocean. We conservatively assume equilibration takes 100 times longer than the modern time, and thus our minimum model timestep during this phase is 100,000 years.

During widespread ice sheet coverage on land, continental weathering rates are expected to have been significantly reduced or completely stopped. We nominally assume that there was no continental weathering during glaciation; however, we do test our model with the incorporation of low, constant weathering rates calculated in Lan et al.36. Their models estimate that the continental silicate weathering rate was 3.3–22 × 108 mol eq yr−1 and that the continental carbonate weathering rate was 8–18 × 108 mol C yr−1, both of which are several orders of magnitude lower than their modern rates of  ~8 × 1012 mol eq yr−1 70 and  ~11 × 1012 mol C yr−1 71, respectively. Our parameterization of seafloor weathering and pore-space carbonate deposition remains unchanged through this time period.

There should be few neritic environments for carbonate deposition in the syn-glacial ocean. Sea level is expected to have dropped by over 500 m during glaciation due to the size and extent of the ice sheets55, so the syn-glacial sea level should be too low to support carbonate deposition on continental shelves given that they are generally not deeper than 200 m on modern Earth. However, evidence has been found for syn-glacial carbonate deposition during the Sturtian glaciation25, indicating that some carbonate depositional environments must have persisted through global glaciation, potentially on the continental slopes. This motivates us to allow carbonate deposition during glaciation. We continue to use the baseline parameterization to calculate the deposition rate, but we reduce the ratio of syn-glacial continental shelf area to modern (Ashelf/Ashelfmod) to account for the decrease in depositional environments. On the modern Earth, the surface area of continental shelves is 3.22 × 107 km2 and of continental slopes is 1.96 × 107 km2 72; the removal of continental shelves results in a 62% decrease in depositional area. Thus, we explore a range of Ashelf/Ashelfmod values from 0.3 to 0.5 to simulate the elimination of deposition on continental shelf environments during glaciation.

Phase 3: Post-glacial Stratified Ocean

After the syn-glacial phase ends, the model transitions to the post-glacial stratified ocean phase. This phase is time-dependent and spans from the end of the glaciation until the ocean becomes well-mixed.

To account for the post-glacial ocean stratification, we alter the Neoproterozoic background model for atmosphere and ocean chemistry by splitting the whole-ocean box into two boxes: one box contains the atmosphere and meltwater layer, and the other contains the deep ocean. We follow Boudreau et al.73 to design the basic framework of the 2-box model. The time evolution of carbon chemistry is now described by the following set of equations:2 dCsdt=1Ms−K(DICs−Cd)+Vair+Wcarb−Pshelf−OsinkdAsdt=1Ms−K(As−Ad)+2Wsil+2Wcarb−2PshelfdCddt=1Md−K(Cd−DICs)−J(Cd−Cp)+Vridge+OsinkdAddt=1Md−K(Ad−As)−J(Ad−Ap)dCpdt=1Mp−J(Cp−Cd)−PporedApdt=1Mp−J(Ap−Ad)+2Wsea−2Ppore.

The model now tracks carbon and alkalinity in three boxes: the surface ocean meltwater layer (s), the deep ocean (d), and the pore-space (p). C is still the concentration of inorganic carbon and A is still carbonate alkalinity. Cs contains the sum of the DIC in the surface ocean and the carbon in the atmosphere, Cs = DICs + pCO2 × s, and s is adjusted to reflect the mass of the surface ocean meltwater layer, s = 1.8 × 1020/Ms. J is the water mass flux between the deep ocean and pore-space, and is unchanged from the Neoproterozoic background configuration. K is the water mass flux between the surface and deep ocean. The volcanic outgassing flux is now split into a subaerial component (Vair) and mid-ocean ridge component (Vair), which are 75% and 25% of the total volcanic flux, respectively (69, p. 203). Finally, Osink is the flux of sinking organic carbon from the surface to the deep ocean.

We assume that the deep ocean retains the same DIC and alkalinity as the final results from the sub-glacial ocean in phase 2. On the other hand, we must make assumptions about the initial chemical properties of the glacial meltwater. To determine the alkalinity, we use compositional measurements of modern glacial meltwater, compiled in Brown74. The compilation includes 22 different measurements of glacial meltwater from around the world, including both land and sea glaciers. The average alkalinity from the minimum and maximum bounds of these measurements is 700-1000 μmol eq kg−1. We take this as the starting alkalinity for the post-glacial surface ocean. We then assume that the meltwater is immediately equilibrated with the atmosphere to calculate the DIC.

We assume the total post-glacial ocean mass is equal to the modern day ocean mass, as we did in phase 1. This assumption is justified because modern Earth’s glaciers are responsible for only ~2% of the total water budget37, so even if they were completely melted in the post-glacial hothouse climate they would not significantly change the mass of the ocean. The mass of the meltwater layer is 10–30% of the global ocean mass, consistent with the ice volume in phase 2. The deep ocean makes up the rest of the total mass.

We assume the glacial meltwater layer remains chemically distinct from the deep ocean for a variable amount of time after deglaciation. We assume the stratification lasts for tstrat = 104 or 105 years, consistent with 1D and 3D models of the post-glacial ocean31,32. These models form the basis for the assumptions we make to simulate the post-glacial ocean. First, we nominally assume that there is no mixing between the meltwater layer and the deep ocean (K = 0) during stratification. Second, we assume that the meltwater layer is in thermal equilibrium with the surface, as the melting glacial water is quickly heated at the surface before sinking deeper into the layer. Third, we assume that the deep ocean temperature warms linearly during the time of stratification. As is shown in the models, the ocean eventually recovers to a well-mixed state with a surface temperature for which our baseline deep ocean temperature parameterization applies. Thus, the deep ocean temperature (Td) evolution is described by3 Td=269.5+ttstratagradTs+bint−269.5

where 269.5 K is the temperature of the sub-glacial ocean, t is the time after glaciation, and the term in the parenthesis is the difference between the deep ocean temperature calculated via the baseline parameterization and the sub-glacial ocean temperature.

The minimum timestep for this phase is set by the time it takes for chemical equilibrium to be reached between the meltwater layer and the atmosphere. We expect this to be shorter than the modern timescale for several reasons. First, the meltwater originates at the surface in small parcels as it melts. We expect that the meltwater should reach atmospheric equilibrium as soon as it is produced due to the high surface area to volume ratio of the parcels and their direct exposure to the atmosphere. Second, the meltwater layer contains only the upper portion of the ocean. Mixing at the surface is more vigorous than deep ocean mixing due to e.g. wind-driven perturbation and should lead to faster equilibration. This mixing is enhanced when paired with an estimated 22% increase in runoff relative to modern75. Third, and most importantly, there is simply less water to equilibrate. The meltwater layer has a water mass that is 10-30% of the modern ocean. Combining these arguments, we indeed assume that equilibration in the meltwater layer is faster than in the modern ocean. We nominally assume this equilibration happens in 100 years, which is the minimum allowable timestep for phase 3.

We apply our baseline continental weathering parameterizations to the post-glacial environment. The post-glacial environment likely had a high CO2 atmosphere, leading to high surface temperatures and a rapid hydrologic cycle. Le Hir et al.75 investigated the post-glacial climate using the FOAM General Circulation Model and the WITCH weathering model to estimate continental weathering rates as a function of pCO2. As shown in Supplementary Section B, our standard continental weathering parameterization aligns with and encompasses the rates from the more detailed models in Le Hir et al.75. The spread in our derived rates is mainly a product of the weatherability factor, fw, which was varied from 0.5 to 1.5. Narrowing this range can more closely align our predicted rates with those from Le Hir et al.75 but may not be justified given all the uncertain factors that determine fw.

We apply the baseline carbonate deposition parameterization, which was originally developed for the Neoproterozoic pre- and post-glacial climates76. The post-glacial shelf area relative to modern is needed in order to apply this parameterization. In the post-glacial climate, the eustatic sea level should be higher in general due to total ice melting and thermal expansion (e.g.32), but regional-scale sea level change is highly variable41. If all of the ice on modern Earth was melted, it would result in at least 60 m of global sea level rise77. Sea level rise due to thermal expansion in the post-glacial hothouse climate is predicted to be up to 8 m32. Based on modern Earth’s hypsometry78, a 70 m rise in sea level would cover about 1.5 × 107 km2 of land, which is equivalent to  ~50% of the area of modern continental shelves72. Using this as the basis for our calculation, post-glacial shelf area would have been 1.5 times larger than the modern area. Thus, we explore the range of values Ashelf/Ashelfmod=1−2.

We nominally assume that all carbonate precipitation chemistry is based on calcite and aragonite. Post- and syn-glacial snowball Earth carbonates are frequently dolomitic in composition; however, recent isotopic evidence suggests the cap carbonates were deposited as calcium carbonate and later altered to dolomite via marine diagenesis30. Furthermore, a similar modeling study25 shows that the geochemical evolution of the ocean during and after the Sturtian glaciation is not sensitive to the difference in carbonate chemistries based on using calcite, magnesite, or dolomite as the representative carbonate mineral. Thus, we believe our assumption is justified for modeling the large scale features of the geologic record such as the total mass and depositional timescale of the Cryogenian carbonates.

Because we have split the ocean box into surface and deep components, we now include an organic carbon export flux from the surface ocean to the deep ocean, following Boudreau et al.73. The modern global rate of organic carbon export is on the order of 100 Tmol yr−1 37. We expect carbon export in the post-glacial ocean to be greatly diminished for two reasons: (1) total biomass in the Precambrian era should have been less than in the modern day, and (2) the abrubt swings of temperature, ocean pH, and unfrozen ocean area should have exterminated a large portion of existing biomass. Nevertheless, we explore a range of values for carbon export in the post-glacial ocean: Osink = 50–200 Tmol yr−1. We assume that all carbon exported from the surface is regenerated in the deep ocean.

Phase 4: Post-glacial well-mixed ocean

After the post-glacial stratified ocean phase is terminated, the model transitions to the post-glacial well-mixed ocean phase. This phase is time-dependent and spans from the end of the stratified ocean until the background climate state is recovered. The model configuration in phase 4 is almost identical to phase 1. The only difference is the increase in assumed shelf area due to sea level rise, described in phase 3. Phase 4 is terminated when a steady state background climate is reached and the model run is complete.

Supplementary information

Supplementary Information

Peer Review File

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-024-51412-8.

Acknowledgements

T.B.T. acknowledges funding from the NSF GRFP (DGE-1762114). D.C.C. acknowledges support from NASA Exobiology Program grant no. 80NSSC21K0476. This work is supported in part by the Virtual Planetary Laboratory, a member of NASA NExSS, funded via the NASA Astrobiology Program (Grant 80NSSC18K0829).

Author contributions

T.B.T. and D.C.C. designed the project and wrote the manuscript. T.B.T. performed the modeling and analysis.

Peer review

Peer review information

Nature Communications thanks Ashleigh Hood, Francis Macdonald, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

The datasets corresponding to this study and code to reproduce all figures are available at Zenodo (10.5281/zenodo.12786460).

Code availability

The GOOSE model code developed and used in this work is persistently available at Zenodo (10.5281/zenodo.12786460) and on the lead author’s GitHub (github.com/trentagon).

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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References

1. Hoffman PF Snowball Earth climate dynamics and Cryogenian geology-geobiology Sci. Adv. 2017 3 e1600983 10.1126/sciadv.1600983 29134193
Hoffman, P. F. et al. Snowball Earth climate dynamics and Cryogenian geology-geobiology. Sci. Adv. 3, e1600983 (2017).29134193
2. Kirschvink, J. L. Late Proterozoic low-latitude global glaciation: the snowball Earth. The Proterozoic biosphere: a multidisciplinary study. (Cambridge University Press, 1992).
3. Hoffman PF A Neoproterozoic Snowball Earth Science 1998 281 1342 1346 10.1126/science.281.5381.1342 9721097
Hoffman, P. F. A Neoproterozoic Snowball Earth. Science 281, 1342–1346 (1998).9721097
4. Narbonne GM THE EDIACARA BIOTA: Neoproterozoic Origin of Animals and Their Ecosystems Annu. Rev. Earth Planet. Sci. 2005 33 421 442 10.1146/annurev.earth.33.092203.122519
Narbonne, G. M. THE EDIACARA BIOTA: Neoproterozoic Origin of Animals and Their Ecosystems. Annu. Rev. Earth Planet. Sci. 33, 421–442 (2005).
5. Planavsky NJ A case for low atmospheric oxygen levels during Earth’s middle history Emerg. Top. Life Sci. 2018 2 149 159 10.1042/ETLS20170161 32412619
Planavsky, N. J. et al. A case for low atmospheric oxygen levels during Earth’s middle history. Emerg. Top. Life Sci. 2, 149–159 (2018).32412619
6. Kaufman A Knoll A Neoproterozoic variations in the C-isotopic composition of seawater: stratigraphic and biogeochemical implications Precambrian Res. 1995 73 27 49 10.1016/0301-9268(94)00070-8 11539552
Kaufman, A. & Knoll, A. Neoproterozoic variations in the C-isotopic composition of seawater: stratigraphic and biogeochemical implications. Precambrian Res. 73, 27–49 (1995).11539552
7. Cordani UG Brito-Neves BB D’Agrella-Filho MS From Rodinia to Gondwana: A Review of the Available Evidence from South America Gondwana Res. 2003 6 275 283 10.1016/S1342-937X(05)70976-X
Cordani, U. G., Brito-Neves, B. B. & D’Agrella-Filho, M. S. From Rodinia to Gondwana: A Review of the Available Evidence from South America. Gondwana Res. 6, 275–283 (2003).
8. Yu W Algeo TJ Zhou Q Du Y Wang P Cryogenian cap carbonate models: a review and critical assessment Palaeogeogr., Palaeoclimatol., Palaeoecol. 2020 552 109727 10.1016/j.palaeo.2020.109727
Yu, W., Algeo, T. J., Zhou, Q., Du, Y. & Wang, P. Cryogenian cap carbonate models: a review and critical assessment. Palaeogeogr., Palaeoclimatol., Palaeoecol. 552, 109727 (2020).
9. Grotzinger JP Knoll AH Anomalous Carbonate Precipitates: Is the Precambrian the Key to the Permian? PALAIOS 1995 10 578 10.2307/3515096 11542266
Grotzinger, J. P. & Knoll, A. H. Anomalous Carbonate Precipitates: Is the Precambrian the Key to the Permian? PALAIOS 10, 578 (1995).11542266
10. Knoll AH Bambach RK Canfield DE Grotzinger JP Comparative Earth History and Late Permian Mass Extinction Science 1996 273 452 457 10.1126/science.273.5274.452
Knoll, A. H., Bambach, R. K., Canfield, D. E. & Grotzinger, J. P. Comparative Earth History and Late Permian Mass Extinction. Science 273, 452–457 (1996).
11. Hoffman PF Schrag DP The snowball Earth hypothesis: testing the limits of global change Terra Nova 2002 14 129 155 10.1046/j.1365-3121.2002.00408.x
Hoffman, P. F. & Schrag, D. P. The snowball Earth hypothesis: testing the limits of global change. Terra Nova 14, 129–155 (2002).
12. Kennedy, M. J., Christie-Blick, N. & Sohl, L. E. Are Proterozoic cap carbonates and isotopic excursions a record provided by Columbia University Academic Commons of gas hydrate destabilization following Earth’s coldest intervals? Geology 29, 443–446 (2001).
13. Kennedy M Mrofka D von der Borch C Snowball Earth termination by destabilization of equatorial permafrost methane clathrate Nature 2008 453 642 645 10.1038/nature06961 18509441
Kennedy, M., Mrofka, D. & von der Borch, C. Snowball Earth termination by destabilization of equatorial permafrost methane clathrate. Nature 453, 642–645 (2008).18509441
14. Shields GA Neoproterozoic cap carbonates: a critical appraisal of existing models and the plumeworld hypothesis Terra Nova 2005 17 299 310 10.1111/j.1365-3121.2005.00638.x
Shields, G. A. Neoproterozoic cap carbonates: a critical appraisal of existing models and the plumeworld hypothesis. Terra Nova 17, 299–310 (2005).
15. Kennedy MJ Christie-Blick N Condensation origin for Neoproterozoic cap carbonates during deglaciation Geology 2011 39 319 322 10.1130/G31348.1
Kennedy, M. J. & Christie-Blick, N. Condensation origin for Neoproterozoic cap carbonates during deglaciation. Geology 39, 319–322 (2011).
16. Spence GH Le Heron DP Fairchild IJ Sedimentological perspectives on climatic, atmospheric and environmental change in the Neoproterozoic Era Sedimentology 2016 63 253 306 10.1111/sed.12261
Spence, G. H., Le Heron, D. P. & Fairchild, I. J. Sedimentological perspectives on climatic, atmospheric and environmental change in the Neoproterozoic Era. Sedimentology 63, 253–306 (2016).
17. Nédélec A Affaton P France-Lanord C Charrière A Alvaro J Sedimentology and chemostratigraphy of the Bwipe Neoproterozoic cap dolostones (Ghana, Volta Basin): A record of microbial activity in a peritidal environment Comptes Rendus Geosci. 2007 339 223 239 10.1016/j.crte.2005.06.002
Nédélec, A., Affaton, P., France-Lanord, C., Charrière, A. & Alvaro, J. Sedimentology and chemostratigraphy of the Bwipe Neoproterozoic cap dolostones (Ghana, Volta Basin): A record of microbial activity in a peritidal environment. Comptes Rendus Geosci. 339, 223–239 (2007).
18. Font E Nédélec A Trindade RIF Moreau C Fast or slow melting of the Marinoan snowball Earth? The cap dolostone record Palaeogeogr., Palaeoclimatol., Palaeoecol. 2010 295 215 225 10.1016/j.palaeo.2010.05.039
Font, E., Nédélec, A., Trindade, R. I. F. & Moreau, C. Fast or slow melting of the Marinoan snowball Earth? The cap dolostone record. Palaeogeogr., Palaeoclimatol., Palaeoecol. 295, 215–225 (2010).
19. Retallack GJ Neoproterozoic loess and limits to snowball Earth J. Geol. Soc. 2011 168 289 308 10.1144/0016-76492010-051
Retallack, G. J. Neoproterozoic loess and limits to snowball Earth. J. Geol. Soc. 168, 289–308 (2011).
20. Coogan LA Gillis KM Low-Temperature Alteration of the Seafloor: Impacts on Ocean Chemistry Annu. Rev. Earth Planet. Sci. 2018 46 21 45 10.1146/annurev-earth-082517-010027
Coogan, L. A. & Gillis, K. M. Low-Temperature Alteration of the Seafloor: Impacts on Ocean Chemistry. Annu. Rev. Earth Planet. Sci. 46, 21–45 (2018).
21. Krissansen-Totton J Catling DC Constraining climate sensitivity and continental versus seafloor weathering using an inverse geological carbon cycle model Nat. Commun. 2017 8 15423 10.1038/ncomms15423 28530231
Krissansen-Totton, J. & Catling, D. C. Constraining climate sensitivity and continental versus seafloor weathering using an inverse geological carbon cycle model. Nat. Commun. 8, 15423 (2017).28530231
22. Krissansen-Totton J Arney GN Catling DC Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model Proc. Natl Acad. Sci. 2018 115 4105 4110 10.1073/pnas.1721296115 29610313
Krissansen-Totton, J., Arney, G. N. & Catling, D. C. Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model. Proc. Natl Acad. Sci. 115, 4105–4110 (2018).29610313
23. Le Hir G Goddéris Y Donnadieu Y Ramstein G A geochemical modelling study of the evolution of the chemical composition of seawater linked to a "snowball" glaciation Biogeosciences 2008 5 253 267 10.5194/bg-5-253-2008
Le Hir, G., Goddéris, Y., Donnadieu, Y. & Ramstein, G. A geochemical modelling study of the evolution of the chemical composition of seawater linked to a "snowball" glaciation. Biogeosciences 5, 253–267 (2008).
24. Penman DE Rooney AD Coupled carbon and silica cycle perturbations during the Marinoan snowball Earth deglaciation Geology 2019 47 317 320 10.1130/G45812.1
Penman, D. E. & Rooney, A. D. Coupled carbon and silica cycle perturbations during the Marinoan snowball Earth deglaciation. Geology 47, 317–320 (2019).
25. Hood AVS Neoproterozoic syn-glacial carbonate precipitation and implications for a snowball Earth Geobiology 2022 20 175 193 10.1111/gbi.12470 34528380
Hood, A. V. S. et al. Neoproterozoic syn-glacial carbonate precipitation and implications for a snowball Earth. Geobiology 20, 175–193 (2022).34528380
26. Fang Y Xu H Coupled dolomite and silica precipitation from continental weathering during deglaciation of the Marinoan Snowball Earth Precambrian Res. 2022 380 106824 10.1016/j.precamres.2022.106824
Fang, Y. & Xu, H. Coupled dolomite and silica precipitation from continental weathering during deglaciation of the Marinoan Snowball Earth. Precambrian Res. 380, 106824 (2022).
27. Liu C Wang Z Raub TD Geochemical constraints on the origin of Marinoan cap dolostones from Nuccaleena Formation, South Australia Chem. Geol. 2013 351 95 104 10.1016/j.chemgeo.2013.05.012
Liu, C., Wang, Z. & Raub, T. D. Geochemical constraints on the origin of Marinoan cap dolostones from Nuccaleena Formation, South Australia. Chem. Geol. 351, 95–104 (2013).
28. Liu C Wang Z Raub TD Macdonald FA Evans DAD Neoproterozoic cap-dolostone deposition in stratified glacial meltwater plume Earth Planet. Sci. Lett. 2014 404 22 32 10.1016/j.epsl.2014.06.039
Liu, C., Wang, Z., Raub, T. D., Macdonald, F. A. & Evans, D. A. D. Neoproterozoic cap-dolostone deposition in stratified glacial meltwater plume. Earth Planet. Sci. Lett. 404, 22–32 (2014).
29. Liu C Wang Z Macdonald FA Sr and Mg isotope geochemistry of the basal Ediacaran cap limestone sequence of Mongolia: Implications for carbonate diagenesis, mixing of glacial meltwaters, and seawater chemistry in the aftermath of Snowball Earth Chem. Geol. 2018 491 1 13 10.1016/j.chemgeo.2018.05.008
Liu, C., Wang, Z. & Macdonald, F. A. Sr and Mg isotope geochemistry of the basal Ediacaran cap limestone sequence of Mongolia: Implications for carbonate diagenesis, mixing of glacial meltwaters, and seawater chemistry in the aftermath of Snowball Earth. Chem. Geol. 491, 1–13 (2018).
30. Ahm A-SC An early diagenetic deglacial origin for basal Ediacaran “cap dolostones” Earth Planet. Sci. Lett. 2019 506 292 307 10.1016/j.epsl.2018.10.046
Ahm, A.-S. C. et al. An early diagenetic deglacial origin for basal Ediacaran “cap dolostones”. Earth Planet. Sci. Lett. 506, 292–307 (2019).
31. Yang J Jansen MF Macdonald FA Abbot DS Persistence of a freshwater surface ocean after a snowball Earth Geology 2017 45 615 618 10.1130/G38920.1
Yang, J., Jansen, M. F., Macdonald, F. A. & Abbot, D. S. Persistence of a freshwater surface ocean after a snowball Earth. Geology 45, 615–618 (2017).
32. Ramme L Marotzke J Climate and ocean circulation in the aftermath of a Marinoan snowball Earth Climate 2022 18 759 774
Ramme, L. & Marotzke, J. Climate and ocean circulation in the aftermath of a Marinoan snowball Earth. Climate 18, 759–774 (2022).
33. Hill AC Cotter KL Grey K Mid-Neoproterozoic biostratigraphy and isotope stratigraphy in Australia Precambrian Res. 2000 100 281 298 10.1016/S0301-9268(99)00077-7
Hill, A. C., Cotter, K. L. & Grey, K. Mid-Neoproterozoic biostratigraphy and isotope stratigraphy in Australia. Precambrian Res. 100, 281–298 (2000).
34. Arp G Reimer A Reitner J Photosynthesis-Induced Biofilm Calcification and Calcium Concentrations in Phanerozoic Oceans Science 2001 292 1701 1704 10.1126/science.1057204 11387471
Arp, G., Reimer, A. & Reitner, J. Photosynthesis-Induced Biofilm Calcification and Calcium Concentrations in Phanerozoic Oceans. Science 292, 1701–1704 (2001).11387471
35. Spear N Analyses of fluid inclusions in Neoproterozoic marine halite provide oldest measurement of seawater chemistry Geology 2014 42 103 106 10.1130/G34913.1
Spear, N. et al. Analyses of fluid inclusions in Neoproterozoic marine halite provide oldest measurement of seawater chemistry. Geology 42, 103–106 (2014).
36. Lan, Z. et al. Massive Volcanism May Have Foreshortened the Marinoan Snowball Earth. Geophys. Res. Lett. 49(6), 10.1029/2021GL097156 (2022).
37. Pilson, M. E. Q.An Introduction to the Chemistry of the Sea. 10.1017/CBO9781139047203 Cambridge University Press, 2 edition, December (2012). ISBN 978-0-521-88707-6 978-1-139-04720-3. https://www.cambridge.org/core/product/identifier/9781139047203/type/book
38. Higgins, J. A. and Schrag, D. P. Aftermath of a snowball Earth. Geochem. Geophys. Geosyst. 4(3), 10.1029/2002GC000403 (2003).
39. Pierrehumbert RT High levels of atmospheric carbon dioxide necessary for the termination of global glaciation Nature 2004 429 646 649 10.1038/nature02640 15190348
Pierrehumbert, R. T. High levels of atmospheric carbon dioxide necessary for the termination of global glaciation. Nature 429, 646–649 (2004).15190348
40. Iglesias-Rodriguez MD Progress made in study of ocean’s calcium carbonate budget Eos, Trans. Am. Geophys. Union 2002 83 365 375 10.1029/2002EO000267
Iglesias-Rodriguez, M. D. et al. Progress made in study of ocean’s calcium carbonate budget. Eos, Trans. Am. Geophys. Union 83, 365–375 (2002).
41. Creveling JR Mitrovica JX The sea-level fingerprint of a Snowball Earth deglaciation Earth Planet. Sci. Lett. 2014 399 74 85 10.1016/j.epsl.2014.04.029
Creveling, J. R. & Mitrovica, J. X. The sea-level fingerprint of a Snowball Earth deglaciation. Earth Planet. Sci. Lett. 399, 74–85 (2014).
42. Irie Y Nakada M Okuno J Bao H Nonmonotonic Postdeglacial Relative Sea Level Changes at the Aftermath of Marinoan (635 Ma) Snowball Earth Meltdown J. Geophys. Res.: Solid Earth 2019 124 9373 9394 10.1029/2018JB017260
Irie, Y., Nakada, M., Okuno, J. & Bao, H. Nonmonotonic Postdeglacial Relative Sea Level Changes at the Aftermath of Marinoan (635 Ma) Snowball Earth Meltdown. J. Geophys. Res.: Solid Earth 124, 9373–9394 (2019).
43. Hyde WT Crowley TJ Baum SK Peltier WR Neoproterozoic ‘snowball Earth’ simulations with a coupled climate/ice-sheet model Nature 2000 405 425 429 10.1038/35013005 10839531
Hyde, W. T., Crowley, T. J., Baum, S. K. & Peltier, W. R. Neoproterozoic ‘snowball Earth’ simulations with a coupled climate/ice-sheet model. Nature 405, 425–429 (2000).10839531
44. Myrow PM Lamb MP Ewing RC Rapid sea level rise in the aftermath of a Neoproterozoic snowball Earth Science 2018 360 649 651 10.1126/science.aap8612 29674430
Myrow, P. M., Lamb, M. P. & Ewing, R. C. Rapid sea level rise in the aftermath of a Neoproterozoic snowball Earth. Science 360, 649–651 (2018).29674430
45. Petterson R Prave AR Wernicke BP Fallick AE The Neoproterozoic Noonday Formation, Death Valley region, California Geol. Soc. Am. Bull. 2011 123 1317 1336 10.1130/B30281.1
Petterson, R., Prave, A. R., Wernicke, B. P. & Fallick, A. E. The Neoproterozoic Noonday Formation, Death Valley region, California. Geol. Soc. Am. Bull. 123, 1317–1336 (2011).
46. Allen PA Hoffman PF Extreme winds and waves in the aftermath of a Neoproterozoic glaciation Nature 2005 433 123 127 10.1038/nature03176 15650730
Allen, P. A. & Hoffman, P. F. Extreme winds and waves in the aftermath of a Neoproterozoic glaciation. Nature 433, 123–127 (2005).15650730
47. Hoffman PF Macdonald FA Sheet-crack cements and early regression in Marinoan (635Ma) cap dolostones: Regional benchmarks of vanishing ice-sheets? Earth Planet. Sci. Lett. 2010 300 374 384 10.1016/j.epsl.2010.10.027
Hoffman, P. F. & Macdonald, F. A. Sheet-crack cements and early regression in Marinoan (635Ma) cap dolostones: Regional benchmarks of vanishing ice-sheets? Earth Planet. Sci. Lett. 300, 374–384 (2010).
48. Fairchild IJ Kennedy MJ Neoproterozoic glaciation in the Earth System J. Geol. Soc. 2007 164 895 921 10.1144/0016-76492006-191
Fairchild, I. J. & Kennedy, M. J. Neoproterozoic glaciation in the Earth System. J. Geol. Soc. 164, 895–921 (2007).
49. Wallace MW Hood AVS Fayle J Hordern ES O’Hare TF Neoproterozoic marine dolomite hardgrounds and their relationship to cap dolomites Precambrian Res. 2019 328 269 286 10.1016/j.precamres.2019.04.026
Wallace, M. W., Hood, A. V. S., Fayle, J., Hordern, E. S. & O’Hare, T. F. Neoproterozoic marine dolomite hardgrounds and their relationship to cap dolomites. Precambrian Res. 328, 269–286 (2019).
50. Fairchild IJ Bao H Windmill RJ Boomer I The Marinoan cap carbonate of Svalbard: Syngenetic marine dolomite with 17O-anomalous carbonate-associated sulphate Depositional Rec. 2023 9 482 507 10.1002/dep2.201
Fairchild, I. J., Bao, H., Windmill, R. J. & Boomer, I. The Marinoan cap carbonate of Svalbard: Syngenetic marine dolomite with 17O-anomalous carbonate-associated sulphate. Depositional Rec. 9, 482–507 (2023).
51. Domack EW Hoffman PF An ice grounding-line wedge from the Ghaub glaciation (635 Ma) on the distal foreslope of the Otavi carbonate platform, Namibia, and its bearing on the snowball Earth hypothesis GSA Bull. 2011 123 1448 1477 10.1130/B30217.1
Domack, E. W. & Hoffman, P. F. An ice grounding-line wedge from the Ghaub glaciation (635 Ma) on the distal foreslope of the Otavi carbonate platform, Namibia, and its bearing on the snowball Earth hypothesis. GSA Bull. 123, 1448–1477 (2011).
52. Davis AC Bickle MJ Teagle DAH Imbalance in the oceanic strontium budget Earth Planet. Sci. Lett. 2003 211 173 187 10.1016/S0012-821X(03)00191-2
Davis, A. C., Bickle, M. J. & Teagle, D. A. H. Imbalance in the oceanic strontium budget. Earth Planet. Sci. Lett. 211, 173–187 (2003).
53. Vance D Teagle DAH Foster GL Variable Quaternary chemical weathering fluxes and imbalances in marine geochemical budgets Nature 2009 458 493 496 10.1038/nature07828 19325631
Vance, D., Teagle, D. A. H. & Foster, G. L. Variable Quaternary chemical weathering fluxes and imbalances in marine geochemical budgets. Nature 458, 493–496 (2009).19325631
54. Allègre CJ The fundamental role of island arc weathering in the oceanic Sr isotope budget Earth Planet. Sci. Lett. 2010 292 51 56 10.1016/j.epsl.2010.01.019
Allègre, C. J. et al. The fundamental role of island arc weathering in the oceanic Sr isotope budget. Earth Planet. Sci. Lett. 292, 51–56 (2010).
55. Liu Y Peltier WR Sea level variations during snowball Earth formation: 1. A preliminary analysis: SNOWBALL EARTH SEA LEVEL J. Geophys. Res.: Solid Earth 2013 118 4410 4424 10.1002/jgrb.50293
Liu, Y. & Peltier, W. R. Sea level variations during snowball Earth formation: 1. A preliminary analysis: SNOWBALL EARTH SEA LEVEL. J. Geophys. Res.: Solid Earth 118, 4410–4424 (2013).
56. Wei G-Y Ca and Sr isotope constraints on the formation of the Marinoan cap dolostones Earth Planet. Sci. Lett. 2019 511 202 212 10.1016/j.epsl.2019.01.024
Wei, G.-Y. et al. Ca and Sr isotope constraints on the formation of the Marinoan cap dolostones. Earth Planet. Sci. Lett. 511, 202–212 (2019).
57. Wang, J., Jacobson, A. D., Sageman, B. B. and Hurtgen, M. T. Application of the δ44/40Ca-δ88/86Sr multi-proxy to Namibian Marinoan cap carbonates. Geochimica et Cosmochimica Acta, page S0016703723001941, 10.1016/j.gca.2023.04.023 April (2023). ISSN 00167037. URL https://linkinghub.elsevier.com/retrieve/pii/S0016703723001941
58. Kasemann SA Prave AR Fallick AE Hawkesworth CJ Hoffmann K-H Neoproterozoic ice ages, boron isotopes, and ocean acidification: Implications for a snowball Earth Geology 2010 38 775 778 10.1130/G30851.1
Kasemann, S. A., Prave, A. R., Fallick, A. E., Hawkesworth, C. J. & Hoffmann, K.-H. Neoproterozoic ice ages, boron isotopes, and ocean acidification: Implications for a snowball Earth. Geology 38, 775–778 (2010).
59. Lin, P.-C. and Catling, D. C. The Rare Earth Element Distribution in Marine Carbonates as a Potential Proxy for Seawater pH on Early Earth. Am. J. Sci. 324, 10.2475/001c.118215 (2024).
60. Caldeira K Long-term control of atmospheric carbon dioxide; low-temperature seafloor alteration or terrestrial silicate-rock weathering? Am. J. Sci. 1995 295 1077 1114 10.2475/ajs.295.9.1077
Caldeira, K. Long-term control of atmospheric carbon dioxide; low-temperature seafloor alteration or terrestrial silicate-rock weathering? Am. J. Sci. 295, 1077–1114 (1995).
61. Goodman JC Strom DC Feedbacks in a coupled ice-atmosphere-dust model of the glacial Neoproterozoic “Mudball Earth”: SNOWBALL DUST DYNAMICS J. Geophys. Res.: Atmospheres 2013 118 11,546–11,557 10.1002/jgrd.50849
Goodman, J. C. & Strom, D. C. Feedbacks in a coupled ice-atmosphere-dust model of the glacial Neoproterozoic “Mudball Earth”: SNOWBALL DUST DYNAMICS. J. Geophys. Res.: Atmospheres 118, 11,546–11,557 (2013).
62. Benn DI Orbitally forced ice sheet fluctuations during the Marinoan Snowball Earth glaciation Nat. Geosci. 2015 8 704 707 10.1038/ngeo2502
Benn, D. I. et al. Orbitally forced ice sheet fluctuations during the Marinoan Snowball Earth glaciation. Nat. Geosci. 8, 704–707 (2015).
63. Ashkenazy Y Dynamics of a Snowball Earth ocean Nature 2013 495 90 93 10.1038/nature11894 23467167
Ashkenazy, Y. et al. Dynamics of a Snowball Earth ocean. Nature 495, 90–93 (2013).23467167
64. Ashkenazy Y Gildor H Losch M Tziperman E Ocean Circulation under Globally Glaciated Snowball Earth Conditions: Steady-State Solutions J. Phys. Oceanogr. 2014 44 24 43 10.1175/JPO-D-13-086.1
Ashkenazy, Y., Gildor, H., Losch, M. & Tziperman, E. Ocean Circulation under Globally Glaciated Snowball Earth Conditions: Steady-State Solutions. J. Phys. Oceanogr. 44, 24–43 (2014).
65. Le Hir G Ramstein G Donnadieu Y Goddéris Y Scenario for the evolution of atmospheric pCO2 during a snowball Earth Geology 2008 36 47 10.1130/G24124A.1
Le Hir, G., Ramstein, G., Donnadieu, Y. & Goddéris, Y. Scenario for the evolution of atmospheric pCO2 during a snowball Earth. Geology 36, 47 (2008).
66. Dessert C Dupré B Gaillardet J François LM Allègre CJ Basalt weathering laws and the impact of basalt weathering on the global carbon cycle Chem. Geol. 2003 202 257 273 10.1016/j.chemgeo.2002.10.001
Dessert, C., Dupré, B., Gaillardet, J., François, L. M. & Allègre, C. J. Basalt weathering laws and the impact of basalt weathering on the global carbon cycle. Chem. Geol. 202, 257–273 (2003).
67. Mitchell RN Orbital forcing of ice sheets during snowball Earth Nat. Commun. 2021 12 4187 10.1038/s41467-021-24439-4 34234152
Mitchell, R. N. et al. Orbital forcing of ice sheets during snowball Earth. Nat. Commun. 12, 4187 (2021).34234152
68. Song, H. Mid-latitudinal habitable environment for marine eukaryotes during the waning stage of the Marinoan snowball glaciation. Nat. Commun. 14, 1564 (2023).
69. Catling, D. and Kasting, J. F.Atmospheric evolution on inhabited and lifeless worlds. (Cambridge University Press, Cambridge, 2017).
70. Moon S Chamberlain CP Hilley GE New estimates of silicate weathering rates and their uncertainties in global rivers Geochimica et. Cosmochimica Acta 2014 134 257 274 10.1016/j.gca.2014.02.033
Moon, S., Chamberlain, C. P. & Hilley, G. E. New estimates of silicate weathering rates and their uncertainties in global rivers. Geochimica et. Cosmochimica Acta 134, 257–274 (2014).
71. Hartmann J Jansen N Dürr HH Kempe S Köhler P Global CO2-consumption by chemical weathering: What is the contribution of highly active weathering regions? Glob. Planet. Change 2009 69 185 194 10.1016/j.gloplacha.2009.07.007
Hartmann, J., Jansen, N., Dürr, H. H., Kempe, S. & Köhler, P. Global CO2-consumption by chemical weathering: What is the contribution of highly active weathering regions? Glob. Planet. Change 69, 185–194 (2009).
72. Harris PT Macmillan-Lawler M Rupp J Baker EK Geomorphology of the oceans Mar. Geol. 2014 352 4 24 10.1016/j.margeo.2014.01.011
Harris, P. T., Macmillan-Lawler, M., Rupp, J. & Baker, E. K. Geomorphology of the oceans. Mar. Geol. 352, 4–24 (2014).
73. Boudreau BP Middelburg JJ Sluijs A van der Ploeg R Secular variations in the carbonate chemistry of the oceans over the Cenozoic Earth Planet. Sci. Lett. 2019 512 194 206 10.1016/j.epsl.2019.02.004
Boudreau, B. P., Middelburg, J. J., Sluijs, A. & van der Ploeg, R. Secular variations in the carbonate chemistry of the oceans over the Cenozoic. Earth Planet. Sci. Lett. 512, 194–206 (2019).
74. Brown GH Glacier meltwater hydrochemistry Appl. Geochem. 2002 17 855 883 10.1016/S0883-2927(01)00123-8
Brown, G. H. Glacier meltwater hydrochemistry. Appl. Geochem. 17, 855–883 (2002).
75. Le Hir G The snowball Earth aftermath: Exploring the limits of continental weathering processes Earth Planet. Sci. Lett. 2009 277 453 463 10.1016/j.epsl.2008.11.010
Le Hir, G. et al. The snowball Earth aftermath: Exploring the limits of continental weathering processes. Earth Planet. Sci. Lett. 277, 453–463 (2009).
76. Ridgwell AJ Kennedy MJ Caldeira K Carbonate Deposition, Climate Stability, and Neoproterozoic Ice Ages Science 2003 302 859 862 10.1126/science.1088342 14593177
Ridgwell, A. J., Kennedy, M. J. & Caldeira, K. Carbonate Deposition, Climate Stability, and Neoproterozoic Ice Ages. Science 302, 859–862 (2003).14593177
77. Frederikse T The causes of sea-level rise since 1900 Nature 2020 584 393 397 10.1038/s41586-020-2591-3 32814886
Frederikse, T. et al. The causes of sea-level rise since 1900. Nature 584, 393–397 (2020).32814886
78. Eakins, B. W. & Sharman, G. F. Hypsographic Curve of Earth’s Surface from ETOPO1, NOAA National Geophysical Data Center, Boulder, CO, 2012. https://www.ncei.noaa.gov/sites/g/files/anmtlf171/files/2023-01/Hypsographic%20Curve%20of%20Earth%E2%80%99s%20Surface%20from%20ETOPO1.pdf.
79. Condon D U-Pb Ages from the Neoproterozoic Doushantuo Formation, China Science 2005 308 95 98 10.1126/science.1107765 15731406
Condon, D. et al. U-Pb Ages from the Neoproterozoic Doushantuo Formation, China. Science 308, 95–98 (2005).15731406
80. Rooney AD Strauss JV Brandon AD Macdonald FA A Cryogenian chronology: Two long-lasting synchronous Neoproterozoic glaciations Geology 2015 43 459 462 10.1130/G36511.1
Rooney, A. D., Strauss, J. V., Brandon, A. D. & Macdonald, F. A. A Cryogenian chronology: Two long-lasting synchronous Neoproterozoic glaciations. Geology 43, 459–462 (2015).
81. Zhou C Huyskens MH Lang X Xiao S Yin Q-Z Calibrating the terminations of Cryogenian global glaciations Geology 2019 47 251 254 10.1130/G45719.1
Zhou, C., Huyskens, M. H., Lang, X., Xiao, S. & Yin, Q.-Z. Calibrating the terminations of Cryogenian global glaciations. Geology 47, 251–254 (2019).
82. Calver CR Globally synchronous Marinoan deglaciation indicated by U-Pb geochronology of the Cottons Breccia, Tasmania, Australia Geology 2013 41 1127 1130 10.1130/G34568.1
Calver, C. R. et al. Globally synchronous Marinoan deglaciation indicated by U-Pb geochronology of the Cottons Breccia, Tasmania, Australia. Geology 41, 1127–1130 (2013).
83. Prave AR Condon DJ Hoffmann KH Tapster S Fallick AE Duration and nature of the end-Cryogenian (Marinoan) glaciation Geology 2016 44 631 634 10.1130/G38089.1
Prave, A. R., Condon, D. J., Hoffmann, K. H., Tapster, S. & Fallick, A. E. Duration and nature of the end-Cryogenian (Marinoan) glaciation. Geology 44, 631–634 (2016).
84. Hoffmann K-H Condon DJ Bowring SA Crowley JL U-Pb zircon date from the Neoproterozoic Ghaub Formation, Namibia: Constraints on Marinoan glaciation Geology 2004 32 817 10.1130/G20519.1
Hoffmann, K.-H., Condon, D. J., Bowring, S. A. & Crowley, J. L. U-Pb zircon date from the Neoproterozoic Ghaub Formation, Namibia: Constraints on Marinoan glaciation. Geology 32, 817 (2004).
85. Trindade RIF Font E D’Agrella-Filho MS Nogueira ACR Riccomini C Low-latitude and multiple geomagnetic reversals in the Neoproterozoic Puga cap carbonate, Amazon craton Terra Nova 2003 15 441 446 10.1046/j.1365-3121.2003.00510.x
Trindade, R. I. F., Font, E., D’Agrella-Filho, M. S., Nogueira, A. C. R. & Riccomini, C. Low-latitude and multiple geomagnetic reversals in the Neoproterozoic Puga cap carbonate, Amazon craton. Terra Nova 15, 441–446 (2003).
86. Kilner B Niocaill C Brasier M Low-latitude glaciation in the Neoproterozoic of Oman Geology 2005 33 413 10.1130/G21227.1
Kilner, B., Niocaill, C. & Brasier, M. Low-latitude glaciation in the Neoproterozoic of Oman. Geology 33, 413 (2005).
87. Schmidt PW Williams GE McWilliams MO Palaeomagnetism and magnetic anisotropy of late Neoproterozoic strata, South Australia: Implications for the palaeolatitude of late Cryogenian glaciation, cap carbonate and the Ediacaran System Precambrian Res. 2009 174 35 52 10.1016/j.precamres.2009.06.002
Schmidt, P. W., Williams, G. E. & McWilliams, M. O. Palaeomagnetism and magnetic anisotropy of late Neoproterozoic strata, South Australia: Implications for the palaeolatitude of late Cryogenian glaciation, cap carbonate and the Ediacaran System. Precambrian Res. 174, 35–52 (2009).
