Three-stage formation of cap carbonates after Marinoan snowball glaciation consistent with depositional timescales and geochemistry

Domain: earth_science
Published: 2024-08-15
Editorial outcome: minor_revision

Abstract
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.

Introduction
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” events 2,3 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 Period 4, an increase of atmospheric O2 relative to low levels in the mid-Proterozoic 5, large excursions in the global carbon isotope record 6, and the break-up of Rodinia and later assembly of Gondwana supercontinents 7. 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, pCO2. 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 deposition 2,3.

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 kg 8. 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.

Many explanations for CC deposition have been proposed, but none are complete. As summarized in Yu et al. 8, suggestions include oceanic overturn 9,10, continental weathering 1,11, gas hydrate destabilization 12,13, glacial meltwater plumes and subsequent ocean overturn 14, sediment starvation 15,16, microbial activity 17,18, and calcareous loess 19. 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 sometimes 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 Gillis 20). Krissansen-Totton and Catling 21 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 experiments 23, or they omit low-temperature seafloor weathering 24–26.

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 layer 14. This hypothesis is supported by geochemical measurements of the CCs, including 87Sr/86Sr and δ26Mg in multiple formations 27–29 and a global analysis of Ca, Mg, Sr, and C isotopes 30. A freshwater layer is consistent with 1D and 3D ocean models, which show that it could last for up to 105 years 31,32. 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.

The basic model builds upon a previously data-validated model 21,22 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 Catling 21 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.

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 (see 1, 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 bar 1,38,39. 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.

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 up section 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.

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.

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 meters 8, 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 hypothesis 1 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 end member 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 years 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 year 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 CC 50, 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 towards low 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 rose 11. 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 Shields 14; 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 studies 28,29,55,56 have measured 87Sr/86Sr along CC sections and found that they show a stepwise decrease from high to low values up section, 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 carbonates were precipitated out of mostly ocean water with lower, hydrothermally influenced 87Sr/86Sr. 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 measurements 30,56,57.

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.

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 Ga 21,22. 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-ocean, and one for water in the pore-space of the seafloor. The pore-space reservoir captures the chemistry of water circulating through 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:

d/dt Co = 1/Mo * (J(DICo - Cp) + Vtotal + Wcarb - Pshelf)
d/dt Ao = 1/Mo * (J(Ao - Ap) + 2Wsil + 2Wcarb - 2Pshelf)
d/dt Cp = 1/Mp * (J(Cp - DICo) - Ppore)
d/dt Ap = 1/Mp * (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 kg 60. 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−1 20; 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 levels 61,62. 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 cover 63,64. This assumption is justified for scenarios with complete ice cover as well since global averaged surface temperatures are predicted to be below 269.5 K 1.

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 is reached on timescales similar to the modern ocean 65. (2) A series of models have shown that the atmosphere and ocean are likely in equilibrium, and that this is the case even if there are large patches of open water 67. (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 glaciation 68. (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 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 sheets 55, 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 glaciation 25, 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/Amodshelf) 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/Amodshelf 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:

d/dt Cs = 1/Ms * (-K(DICs - Cd) + Vair + Wcarb - Pshelf - Osink)
d/dt As = 1/Ms * (-K(As - Ad) + 2Wsil + 2Wcarb - 2Pshelf)
d/dt Cd = 1/Md * (-K(Cd - DICs) - J(Cd - Cp) + Vridge + Osink)
d/dt Ad = 1/Md * (-K(Ad - As) - J(Ad - Ap))
d/dt Cp = 1/Mp * (J(Cp - Cd) - Ppore)
d/dt Ap = 1/Mp * (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 (Vridge), 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 Brown 74. 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 budget 37, 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 that the stratification lasts for tstrat = 104 or 105 years, consistent with 1D and 3D models of the post-glacial ocean 31,32. 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 by

Td = 269.5 + t/tstrat * (Ts + 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.

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. We assume that the meltwater layer is in thermal equilibrium with the atmosphere. We expect that the meltwater layer is in chemical equilibrium with the atmosphere as well. First, the meltwater layer has a small volume relative to the ocean. Second, the meltwater layer is in direct contact with the atmosphere. Third, the meltwater layer is in a hot, high CO2 environment. Fourth, the meltwater layer is subject to vigorous mixing at the surface. 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 modern 75. 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 climates 76. 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 variable 41. If all of the ice on modern Earth was melted, it would result in at least 60 m of global sea level rise 77. Sea level rise due to thermal expansion in the post-glacial hothouse climate is predicted to be up to 8 m 32. Based on modern Earth’s hypsometry 78, 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 shelves 72. 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/Amodshelf = 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 diagenesis 30. Furthermore, a similar modeling study 25 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.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This is a valuable contribution that attempts to align physical and chemical properties of\nNeoproterozoic post-glacial “cap” carbonates with a revised, published global carbon cycle\nmodel, resulting in a hypothetical three-stage formation for all cap carbonates. The three\nenvisaged stages correspond to: (1) low-temperature seafloor weathering during glaciation\nthat generates deep-sea alkalinity; (2) renewed continental weathering supplies carbonate-\nsaturated freshwater, causing rapid precipitation of carbonate from surface waters\n(presumably above a stable pycnocline); and (3) mixing of post-glacial meltwater with deep-\nsea alkalinity that greatly prolongs carbonate deposition I in some areas. I agree in general\nwith this sequence (~Shields, 2005 scenario) and find the modelling approach taken to be\nrobust, but I don’t think that the authors have done a good enough job yet of showing how\nthese stages can be identified / evidenced in post-glacial carbonate successions. The one\nmajor problem I have with this study is the unwarranted assumption that quite different\nsets of deposits of different ages must have been produced by the same process. I recognise\nthat Cryogenian and even Neoproterozoic (including Ediacaran) \"caps\" are often conflated\nin the literature, but it muddies the waters. The scenario modelled here most closely\nresembles the Marinoan event, and this should be made explicit in the paper. Specific\nexamples of points, largely related to this issue follow:\nTitle: “… cap carbonates after Neoproterozoic Snowball Glaciations” presumes that\nlimestones deposited after the Sturtian ice age are intrisincally the same as dolostones\ndeposited after the Marinoan ice age, and what about the Ediacaran ice ages, of which there\nare at least two, and probably more? Please specify that you are referring here to end-\nCryogenian or Marinoan deposits.\nAbstract (lines 6-7): “Cap carbonates … are enigmatic rocks from this time: thick layers of\nlimestone or dolostone that overlie glacial deposits”. This does not describe cap carbonates\nadequately. Firstly, they are rarely “thick”, but are instead most commonly <5-10 metres in\nthickness, or in the case of Sturtian units absent. Secondly, is it warranted to throw post-\nSturtian limestones together with post-Marinoan dolostones, as cap carbonates? And if so,\nhow does the three-stage scenario work for post-Sturtian carbonates, which do not show\nthe same complexity as post-Marinoan carbonates? Marinoan cap carbonates exhibit what\nis widely interpreted to be a transgressive systems tract (cap dolostone), maximum flooding\nsurface (condensed horizon, limestone, barite fans, etc.) and highstand systems tract\n(limestone, which is only present in some regions), with some renewed transgression\npotentially caused by thermal expansion, e.g. Yang et al., 2017, in Geology). By comparison,\nSturtian caps are not well expressed. If present, they generally comprise limestone.\nLines 52-53 – again here, it seems that the authors are describing the post-Marinoan\nsituation, rather than the post-Sturtian.\nLine 58 – Shields (2005) invoked meltwater plumes to explain the stratigraphic architecture\nof post-Marinoan cap carbonates, with regionally distributed limestones formed following\noceanic overturn. Table 1 ignores the timescale constraints from the two-step transgression\nseen in many cap carbonate successions around the world (James et al., 2001 in Canadian\nJournal of Earth Science; Shields et al., 2007 in Precambrian Research), which if interpreted\nas a response to isostatic re-equilibration and/or thermal expansion upon mixing implies a\nshort (shorter than <20 Kyr) timescale for most cap dolostones at least.\nLines 76-84 – Although I agree with this interpretation, this is only relevant for the post-\nMarinoan cap dolostone, and is irrelevant both for any overlying \"cap\" limestone, and for\npost-Sturtian units.\nLine 124 – “yielding”. Line 125 – Is such a low calcite saturation state (~modern) reasonable\nfor a pre-skeletal ocean? This needs substantiation, as a common assumption is that it was\nfar higher in the absence of biologically controlled calcification, e.g. Arp et al., 2001, in\nScience).\nLines 135-137 – This is an interesting result, which would explain the lack of \"normal\"\nmarine carbonate during the glacial phases. However, would there not also be some\ncarbonate precipitation in the ocean crust?\nLines 152-154 – This initial precipitation (phase 3) is inferred to come as a result of alkalinity\nsupply during deglaciation, which is consistent with the transgressive nature of cap\ncarbonates. There is very little cross-referencing here between model and rock record, so\nthis aspect could be improved somewhat. Similarly:\nLines 159-161 – this is the \"cap limestone\" phase (Shields, 2005), which is thicker and\nregionally inhomogeneous, while the cap dolostone is generally thin and of global extent.\nLines 237-241 – pH is a useful prediction of the model, but no reference is made to the\nvarious boron isotope studies that have attempted to constrain post-glacial pH, e.g.\nKasemann et al. papers).\nLine 257-258 – An additional concern here is the definition of what constitutes a “cap\ncarbonate”? In this regard, I agree with the statement on lines 271-273 that carbonate\ndeposition continued for longer in favourable, likely low-latitude settings. In which case, it\nis hard to know just what constitutes the \"cap\"?\nLine 266 – “at least 32 Marinoan cap carbonates have been found globally (Yu et al., 2020)”\n– what does this mean? Presumably, this refers to named units, e.g. formations, but in any\ncase cap dolostones have been found worldwide wherever rocks of this age occur. Suggest\nrewording to make for a more meaningful statement.\nLines 285-286 – “should begin precipitating immediately after deglaciation” – but Marinoan\ncap carbonates are transgressive units, and so likely formed during deglaciation. This is\nconsistent with the bit below this part which outlines the short duration of the depositional\nhiatus, likely shorter than the time needed to melt thick ice sheets.\nLines 300-302 – This is the scenario outlined in Shields (2005), and approximates the change\nfrom dolostone to limestone in Marinoan cap carbonates.\nLines 309-312 – How is this estimated? Just by thickness, and assuming constant\nsedimentation rates?\nLines 315-316 – Although I’d agree that the model is broadly consistent with global mass\nand thickness of Marinoan cap carbonates, what about their mineralogies, and stratigraphic\narchitecture, relationship to relative sea level changes, etc? This needs more substantiation\nthan currently given, and a closer emphasis on the Marinoan record.\nLine 333 – What is Hoffman (2011) - not in reference list - and the “Glacial Lake Harland”\nhypothesis? In Hoffman (2011) in Sedimentology, Hoffman writes that he refers to the\nplumeworld as the ‘Glacial Lake Harland’ but it seems that the \"hypothesis\" here is precisely\nthe same? I note that in most post-2011 papers there is no mention of any GLH hypothesis,\nso I'm not quite sure that there are two separate hypotheses here?", "reviewer_2": "Thomas and Catlin propose that seafloor weathering provides an important alkalinity\ncontribution to cap carbonate formation in the aftermath of Snowball Earth. To assess this\nhypothesis they perform a series of geochemical modelling experiments. The authors find\nthat the addition of alkalinity production through seafloor weathering can explain the early\nand rapid carbonate precipitation in the glacial aftermath, reconciling issues with previous\nmodels of cap carbonate precipitation. As I mention in the line comments, I think the\nauthors could clarify that no much open ocean is needed to put the ocean and atmosphere\nin communication during the Snowball—I think it would be good for some clarification on\nthis point as many readers will likely misunderstand the implications for ice cover (which\nare actually not much). I would also argue that you need this additional sink of CO2 for the long\ndurations of the glaciations, particularly the Sturtian….\nThis is a well-written, novel, and totally solid contribution to our understanding of extreme\nclimate states in general and Snowball Earth in particular. Below are some small line\ncomments to clean up some questionable references. Otherwise, this paper should be\naccepted.\nLine comments:\n7: It is not clear that oxygen rose. Maybe at the very end. Also declined during the Sturitan.\n20: Cohen et al is wrong ref here. Doesn’t really need a reference.\n23-24: Wrong references for duration—could use Rooney et al., 2015 here.\n27: Wrong ref—Narbonne is referring to Ediacaran, not Cryogenian.\n28: I don’t think many people buy this anymore\n30: What does accretion of supercontinents mean? Accretion is a tectonic process that is\ndifferent from collision. Rewrite to assembly of Gondwana.\n33: Not entirely. The cap carbonate you are mostly referring to is actually basal Ediacaran in\nage.\n40: These are not ice ages, but a different planetary climate phenomena—ice ages refer to\nglacial maxima in orbitally driven glacial-interglacial cycles.\n354: I find this sentence a little misleading. LeHir showed that you only need a few hundred\nsquare km of open ice (size of Hawaii) to have equilibrium on million year timescales. It\nmight be worth clarifying here that you don’t need much.", "reviewer_3": "“Three-stage Formation of Cap Carbonates after Neoproterozoic Snowball Glaciations\nConsistent with Depositional Timescales and Geochemistry”\nThe manuscript details a newly updated carbon cycle model that is used to reconcile\nevidence for the formation of Neoproterozoic post-glacial cap carbonates. These distinctive\nunits have been a puzzle for many years, with a huge controversy about many aspects of\ntheir formation, including geochemistry, time-scale and sedimentology. In this study, the\nauthors suggest that they can account for many aspects of cap carbonate deposition\nincluding their mass, timescale and chemistry, by incorporating sea floor weathering into a\ncarbon cycle model. They suggest a process including post-glacial rapid carbonate\nprecipitation followed by seawater mixing and a more prolonged interval of carbonate\nformation.\nFirst, the paper is clear and well-written, the figures are good. Overall, the reasoning and\nmethods are presented well, and it’s commendable that the authors have been broad in\nconsidering the range of techniques applied to understanding the caps\n(geochron/sedimentology/chemistry etc.). It’s also great to see more detailed carbon cycle\nmodels being developed and applied to the Neoproterozoic.\nI’m not an expert myself in the details of this type of modelling, so I can’t comment\nauthoritatively to the methods itself- this would need to be addressed by another reviewer.\nHowever, I am very familiar with the geology and geochemistry of these cap carbonate units\n(and have also worked with carbon cycle modellers on this topic). Therefore my review\nconcentrates on these aspects of the study.\nOverall, I have several broad comments about reconciling the model with geological\nevidence. At present, the paper reads as a little un-nuanced in understanding the geological\nrecord of the Neoproterozoic. Unfortunately I think this and other aspects detract from the\nselling point of the study (solving the puzzle) and require further attention before\npublication. In light of these complications, I would suggest that short format might not be\nthe best way to present this study. Though I do certainly see the value in this approach,\nI think it needs to be better linked to the preserved geological record of cap carbonates.\n1) Marinoan focus. The paper focuses on the (shorter) timescale and (more extensive) cap\ncarbonate features relevant to the late Cryogenian Marinoan glaciation. This is important,\nbut if the authors wish to be able to suggest their model addresses cap carbonate\ndeposition more broadly, then they would also need to be able to explain the Sturtian (and\neven the Gaskiers) caps. If their model can explain carbon cycling through the two major\nglaciations and their aftermaths, I would be more supportive of publishing it in short\nformat/high impact journal. However the focus on only one of the events detracts from this\nbroader view.\nHow can you then link the different duration and variable expressions of the cap carbonates\nbetween the two glaciations using your model? In particular, the Sturtian is a much longer\nglaciation with mostly, very thin cap carbonate deposition (e.g. cm-scale, up to units that\nlook like Marinoan caps). These caps are also regionally spatially heterogeneous and depth\ndependant. This geological evidence suggests that both broader (e.g. Sturtian vs. Marinoan\nocean chem/redox/timing/tectonics) and more focused (e.g. local) effects both play\nimportant roles in the thickness and style of cap carbonate formation. While the model here\ndoesn’t have to solve everything of course, it needs to be able to explain at least the\ndifference between Sturtian and Marinoan caps. This aspect is arguably one of the most\nconfusing parts of the puzzle.\n2) Specifically, the authors do not include ice-sheet melting or ocean circulation in the\nmodel. As the authors suggest, these are obviously a very complex processes and I imagine\nwould be difficult to integrate into a model. However, in this case I think the lack of these\nprocesses being incorporated (based on previous models and interpretations) biases the\nstudy towards the rapid cap formation scenario. This is because if the timescale of de-\nglaciation is prolonged, the dynamics of the ice melt and its mixing in the ocean become\nmore important, rather than a single melt event. This timeframe changes the rate and\namount of freshwater melt entering the ocean, changing the size and timing and possibly\nthe existence of a freshwater lens—which forms a large part of the model interpretation\nhere. Could a model run could be set up to test if the meltwater influx was pulsed,\nprolonged and to see if a stratified meltwater lens did not necessarily develop? Maybe this\nis the other end of the spectrum of reality, but it seems important to include given the\nweight placed on the existence of ocean stratification in the model and discussion. At\npresent if feels like the whole interpretation relies on this point, but I think the geological\nand geochemical evidence for a meltwater lens is equivocal. Especially as cap carbonates\nalso precipitate in very deep water too (e.g. sections with no sedimentary structures except\nlamination that are basinward of turbidite facies). Despite many years of work, I still don’t\nreally think have a good enough understanding of the impact of meltwater on the system\nduring and after glaciation.\n3) The peak ‘depositional rate’ of carbonate generated in the model at ~2-10m up section\n(Lines 200-208) is not in agreement with where carbonate deposition is concentrated in\npreserved Marinoan cap carbonates. Generally they have higher carbonate concentration\nimmediately or ~<1m above the base which declines upwards after several few metres or so\nof high carbonate concentration. Higher carbonate precipitation could also be linked to the\nformation of sheet cracks and tepees in some cap hypotheses (e.g. the condensed models\nwhich suggest force of crystallisation for dolomite precipitation; Wallace et at., 2019,\nPrecambrian Research). These features are also commonly around the base of the\nsequences, with some variability. Though you have provided these estimates, I’d suggest\nthis is a good place where you can use the geology to test and refine your model. Just a note\ntoo that cap carbonates are also not necessarily composed of 100% carbonate. In shale\nbasins like Australia and Svalbard, the caps can be only 50-70% carbonate, where as in\ncarbonate basins like Namibia, the cap is almost entirely dolomite. Can you use some\nexamples of this from sedimentology papers to test your results here?\n4) Thickness of cap carbonate. As a carbonate sedimentologist, I suggest that there is a\nbias in the literature to measure the true thickness of the cap carbonate as higher than it\nactually is, in carbonate basins. The Noonday (Line 251) and Rasthof are two examples of this. Each\nhas a basal member of only ~2-10m or so which is a commonly a laminated dolomite like a\ntypical cap carbonates (e.g. Le Ber et al., 2013, Sedimentary Geology). The additional 100’s\nmetres thickness in these sections are simply carbonate reefs or buildups developed on top\nof the cap carbonate and are unrelated to the deglaciation--or at least in the short term\n(<My). I suspect the thickness estimates, nicely compiled in Yu et al., 2020, would show no\nsubstantials equatorial trend if paleo-depth and post-glacial microbial carbonate buildups\nwere accounted for.\n5) Likewise, estimates of the speed of deglaciation are subjective- fast rates have been\nsuggested in Paul Hoffman’s Snowball Earth hypothesis, and based on tidal cycles by Myrow\nand others, 2018. But these rates are questioned (e.g. see Fairchild et al., 2023, Depositional\nRecord), and the sequence that Paul Myrow looked at is generally understood to be syn-\nglacial (e.g. see early work by George Williams). In reality, there are no really precise\nestimates of the timing of deglaciation, either from geochron or sedimentology. The timing\nof cap carbonate precipitation is the same. The magnetic reversals are an interesting one–\nmore work needs to be done though (without ruining any important outcrops). I think that\nthese do have real potential to suggest a longer timeframe but it is hard to say how long.\nPerhaps the authors should test two scenarios with longer and shorter rates of deglaciation\nand discuss these- especially in relation to the existence of a meltwater lens as my comment\nabove.\n6) The section on sedimentary structures is needs developing better with a broader\nliterature review. Under the snowball theory, structures in the cap are interpreted as giant\nwave ripples and sheet crack cements (Hoffman et al., 2017 for summary). These are both\nare interpreted to be the result of rapid deposition. However, I think it’s fair to say that\nmost sedimentologists would regard these structures as tepees and bedding expansion\nfeatures, both of which imply long timescales of formation (e.g. hardgrounds, Wallace et al.,\n2019; Fairchild et al., 2023, Depositional Record). In these papers, the cap carbonates of\nAustralia and Svalbard also record abundant ~cm scale turbidite layers with erosive bases\nand flute marks, also more consistent with longer estimates of formation—though not\nnecessarily proving them. Turbidite facies have also been documented in the Namibian\nsequence (e.g. Domack and Hoffman, 2017 GSA Bulletin).\nFurther, the base of the cap carbonate is not always sharp, and not always after\ndeglaciation, and therefore not always consistent with the interpretation of post-meltwater\ncap carbonate formation in this manuscript. Dropstones are occasionally found in the basal\ncap carbonate (e.g. Le Heron, 2020 Geology; I think also Jon Giddings found some in the\nFlinders Ranges but I can’t find the exact citation). In another example, in Namibia at\nFransfontein Ridge, there is a unit of laminated dolomite and dropstone beds, the Bethanis\nMb. which transitionally underlies the Keilberg cap carbonate (Domack and Hoffman, 2017).\nThis dropstone dolomite marks the beginning of dolomite precipitation (which also appears\nto dolomitise several metres of the underlying limestone diamict), suggesting that dolomite\nprecipitation occurs during deglaciation in some places. I think these authors might have\ninterpreted this differently, but it is certainly a distinct change to a dolomite mineralogy\nassociated with deglaciation that I would suggest represents the start of dolomite cap\nprecipitation. Though not published, in a recent fieldtrip I have seen the cap carbonates\ninterbedded with the glacial sediments over ~<a1m-scale and also at 10’s metres scale at\nthe top of both of the Marinoan and Sturtian the glacial sequences in South Australia. In\nyour model, you can account for cap precipitation after melting, but can it also demonstrate\ndolomite precipitation beginning during deglaciation?\n7) Precipitation versus sedimentation. The sedimentology of the cap carbonates (e.g.\nwork by Noel James, Malcolm Wallace, Jon Giddings and Ian Fairchild for example),\nindicates that the carbonates are a mix of authigenic, precipitated dolomite (e.g.\nmicrocrystalline and nodular dolomite) and detrital carbonate (e.g. peloids), which are\ncemented by dolomite. There is discussion about the original mineralogy and importance\nof precipitation vs. deposition in these units, though often both modes of formation are\nevident. In your model, do you assume precipitation is totally from pore water, and what\ntype of carbonate do you model to precipitate? (both aragonite and calcite are mentioned\nin methods- I get that it’s difficult to model dolomite kinetics). How would the results\nchange if you used different interpretations about styles of deposition- e.g. water column,\npore-water or detrital? Maybe this information is available in the supp data, but it would be\ngood to have more information about this in the manuscript.\n8) A big focus of the model appears to be sub-marine weathering, but it would be valuable\nto better define this in the manuscript rather than the supp data. When I was researching\nthis aspect for a paper on Mg cycling, it seemed like this is unfortunately quite poorly\nunderstood, even in modern settings, and it would be different again in anoxic Precambrian\nwater. I therefore disagree with your assumption that this would be the same in the\nNeoproterozoic (anoxic ocean, supercontinent breakup) as to the modern.\nOne of my broader concerns with using modelling to address the Snowball Earth scenario\nis that the timescales involved (e.g. >50My) make it difficult to run models of detailed\ndynamics through glaciation and deglaciation due to processing power- e.g. 57 Myr GCM\nruns. On the other hand, carbon cycle models can deal with these long timescales better,\nbut then can’t realise some of the detailed processes which may have very important\nimpacts on the state of the ocean-atmosphere at smaller time intervals (like ice dynamics,\nmeltwater-seawater interaction etc). Though the authors do mention some assumptions, I\nthink the authors need to be clearer about the caveats of their model in this way--how\nmuch of it is based on interpretations and an assessment of how much these more\ncomplex processes would change the results if included. Some of these aspects are\ndiscussed but I think some aspects need further justification.\nLine 265. This statement is unfair, as the amount of studies looking at paleomag in cap\ncarbonates is limited, and the lack of evidence for magnetic reversals is not a result of them\nnot being present in the rocks, but just that no one has tested all the deposits.\nJust a final note too that Sr/Sr results from non-pure dolomitic cap carbonates (e.g.\nAustralia, Svalbard etc.) are tricky to interpret. Not only is dolomite almost impossible to\ndissolve without dissolving non-carbonate components, but also the caps differ in their\ncarbonate mineralogy and carbonate concentration, biasing these comparisons between\ndifferent locations.\nOverall, I wouldn’t say that I agree that this model reconciles all the different evidence\nabout the cap carbonates but I do think the paper is well-presented and interesting. This is\na pretty heavily debated topic and I still don’t think we have figured it out. The model has\npotential to be a tool for the Neoproterozoic climate change more broadly and therefore it\nwould be good to see it developed further with more consideration to the geology.\nI note that some of the information I’m referring to has not been published (after some\nsignificant career interruptions on my end). If the authors are interested at looking at some\nof this unpublished information in revising the manuscript, I’d be happy to share it.\nAshleigh Hood, University of Melbourne"}, "author_response": "Response to referees for manuscript entitled:\n“Three-stage Formation of Cap Carbonates after Marinoan Snowball\nGlaciation Consistent with Depositional Timescales and Geochemistry”\nWe thank the reviewers for volunteering their time and providing constructive comments\nthat have improved this manuscript. Our responses are below. Reviewer comments are in\nnormal typeface and our replies are in blue. Changes made in the manuscript are in bold.\nSincerely,\nTrent B. Thomas (tbthomas@uw.edu) and David C. Catling\nDepartment of Earth and Space Sciences\nUniversity of Washington, Seattle, WA\nReviewer #1 (Remarks to the Author):\n1. This is a valuable contribution that attempts to align physical and chemical properties of\nNeoproterozoic post-glacial “cap” carbonates with a revised, published global carbon\ncycle model, resulting in a hypothetical three-stage formation for all cap carbonates. The\nthree envisaged stages correspond to: (1) low-temperature seafloor weathering during\nglaciation that generates deep-sea alkalinity; (2) renewed continental weathering supplies\ncarbonate-saturated freshwater, causing rapid precipitation of carbonate from surface\nwaters (presumably above a stable pycnocline); and (3) mixing of post-glacial meltwater\nwith deep-sea alkalinity that greatly prolongs carbonate deposition I in some areas. I agree\nin general with this sequence (~Shields, 2005 scenario) and find the modelling approach\ntaken to be robust, but I don’t think that the authors have done a good enough job yet of\nshowing how these stages can be identified / evidenced in post-glacial carbonate\nsuccessions. The one major problem I have with this study is the unwarranted assumption\nthat quite di]erent sets of deposits of di]erent ages must have been produced by the same\nprocess. I recognise that Cryogenian and even Neoproterozoic (including Ediacaran) \"caps\"\nare often conflated in the literature, but it muddies the waters. The scenario modelled here\nmost closely resembles the Marinoan event, and this should be made explicit in the paper.\nSpecific examples of points, largely related to this issue follow:\nWe thank the reviewer for the constructive feedback on our manuscript. We have made\nchanges in the manuscript to address the general comments above: (1) we have added\nclearer comparison to existing geologic evidence and suggested more avenues to compare\nour model results/predictions to the geologic record, and (2) we have made it explicit that\nour model applies to the Marinoan glaciation throughout the manuscript including a\nrevised title. We have individually addressed all comments below.\n2. Title: “… cap carbonates after Neoproterozoic Snowball Glaciations” presumes that\nlimestones deposited after the Sturtian ice age are intrisincally the same as dolostones\ndeposited after the Marinoan ice age, and what about the Ediacaran ice ages, of which\nthere are at least two, and probably more? Please specify that you are referring here to end-\nCryogenian or Marinoan deposits.\nThe title has been edited to specify the Marinoan cap carbonates.\n3. Abstract (lines 6-7): “Cap carbonates … are enigmatic rocks from this time: thick layers\nof limestone or dolostone that overlie glacial deposits”. This does not describe cap\ncarbonates adequately. Firstly, they are rarely “thick”, but are instead most commonly <5-\n10 metres in thickness, or in the case of Sturtian units absent. Secondly, is it warranted to\nthrow post-Sturtian limestones together with post-Marinoan dolostones, as cap\ncarbonates? And if so, how does the three-stage scenario work for post-Sturtian\ncarbonates, which do not show the same complexity as post-Marinoan carbonates?\nMarinoan cap carbonates exhibit what is widely interpreted to be a transgressive systems\ntract (cap dolostone), maximum flooding surface (condensed horizon, limestone, barite\nfans, etc.) and highstand systems tract (limestone, which is only present in some regions),\nwith some renewed transgression potentially caused by thermal expansion, e.g. Yang et al.,\n2017, in Geology). By comparison, Sturtian caps are not well expressed. If present, they\ngenerally comprise limestone.\nWe have removed the word “thick” and been explicit that the model addresses post-\nMarinoan cab carbonates.\n4. Lines 52-53 – again here, it seems that the authors are describing the post-Marinoan\nsituation, rather than the post-Sturtian.\nCorrected here and throughout the main text to specify the Marinoan.\n5. Line 58 – Shields (2005) invoked meltwater plumes to explain the stratigraphic\narchitecture of post-Marinoan cap carbonates, with regionally distributed limestones\nformed following oceanic overturn. Table 1 ignores the timescale constraints from the two-\nstep transgression seen in many cap carbonate successions around the world (James et\nal., 2001 in Canadian Journal of Earth Science; Shields et al., 2007 in Precambrian\nResearch), which if interpreted as a response to isostatic re-equilibration and/or thermal\nexpansion upon mixing implies a short (shorter than <20 Kyr) timescale for most cap\ndolostones at least.\nThank you for pointing this out. We have added descriptions in the main text to account for\nthis (line 61 and paragraph starting line 329). We have simplified the sedimentology\nevidence in Table 1 as a result of this comment and other comments from Reviewer 3 to\ngive a broader, easier to understand overview of inferred depositional timescales.\n6. Lines 76-84 – Although I agree with this interpretation, this is only relevant for the post-\nMarinoan cap dolostone, and is irrelevant both for any overlying \"cap\" limestone, and for\npost-Sturtian units.\nWe have corrected in the main text to specify the dolomitic components of the Marinoan\ncap carbonates.\n7. Line 124 – “yielding”.\nCorrected in main text.\n8. Line 125 – Is such a low calcite saturation state (~modern) reasonable for a pre-skeletal\nocean? This needs substantiation, as a common assumption is that it was far higher in the\nabsence of biologically controlled calcification, e.g. Arp et al., 2001, in Science).\nConstraints on the marine Ca2+ concentration in the Neoproterozoic are uncertain, which\nmakes the marine calcite saturation state in the Neoproterozoic uncertain as well.\nThere are several estimates for Ca2+ concentration in the literature that do not agree but\nare not inconsistent with low calcite saturation. For example, Arp et al. (2001) infer that the\nmarine Ca2+ concentration must have been at least 19 mmol/L at ~570 Ma based on the\npresence of calcareous stromatolites from this time. Hill et al. (2000) analyze fluid\ninclusions from >830 Ma and infer a marine Ca2+ concentration of 9-12 mmol/L. Spear et\nal. (2014) analyze gypsum-before-halite evaporites equivalent in age to the Hill et al.\nanalysis and place a lower limit on marine Ca2+ of 6 mmol/L. This gives a range of Ca2+\nconcentration of 6 to over 19 mmol/L in the Neoproterozoic ocean compared to ~10\nmmol/L in the modern ocean.\nOur prediction here is reasonable given the uncertainty in marine Ca2+, the fact that the\nconstraints encompass the modern value, and that we are predicting a steady-state\nbackground climate on which transient excursions in Ca2+ and saturation state can occur\nbut would not be captured if they are below the 1 Myr timescale of the geologic carbon\ncycle.\nWe have updated the main text to reflect the above points.\n9. Lines 135-137 – This is an interesting result, which would explain the lack of \"normal\"\nmarine carbonate during the glacial phases. However, would there not also be some\ncarbonate precipitation in the ocean crust?\nYes, thank you for catching this. We have updated the main text to mention this point.\n10. Lines 152-154 – This initial precipitation (phase 3) is inferred to come as a result of\nalkalinity supply during deglaciation, which is consistent with the transgressive nature of\ncap carbonates. There is very little cross-referencing here between model and rock record,\nso this aspect could be improved somewhat. Similarly:\nWe have addressed this point in the main text by adding a new paragraph in section 2.4\n(line 329) to compare our model results to the stratigraphy of the cap carbonates.\n11. Lines 159-161 – this is the \"cap limestone\" phase (Shields, 2005), which is thicker and\nregionally inhomogeneous, while the cap dolostone is generally thin and of global extent.\nWe have addressed this point in the main text by adding a new paragraph in section 2.4\n(line 329) to compare our model results to the stratigraphy of the cap carbonates.\n12. Lines 237-241 – pH is a useful prediction of the model, but no reference is made to the\nvarious boron isotope studies that have attempted to constrain post-glacial pH, e.g.\nKasemann et al. papers).\nWe have edited the main text to suggest future comparison to boron isotope and other pH\nproxy studies (final paragraph in main text, line 406).\n13. Lines 257-258 – An additional concern here is the definition of what constitutes a “cap\ncarbonate”? In this regard, I agree with the statement on lines 271-273 that carbonate\ndeposition continued for longer in favourable, likely low-latitude settings. In which case, it\nis hard to know just what constitutes the \"cap\"?\nWe have corrected this in the manuscript to refer to the overlying limestones. We have also\nadded a new paragraph at the start of section 2.4 (line 254) to clarify what we refer to when\nwe say cap carbonate.\n14. Line 266 – “at least 32 Marinoan cap carbonates have been found globally (Yu et al.,\n2020)” – what does this mean? Presumably, this refers to named units, e.g. formations,\nbut in any case cap dolostones have been found worldwide wherever rocks of this age occur.\nSuggest rewording to make for a more meaningful statement.\nWe ended up removing this sentence entirely after rewriting this section to provide a more\nbalanced discussion of the geologic record.\n15. Lines 285-286 – “should begin precipitating immediately after deglaciation” – but\nMarinoan cap carbonates are transgressive units, and so likely formed during deglaciation.\nThis is consistent with the bit below this part which outlines the short duration of the\ndepositional hiatus, likely shorter than the time needed to melt thick ice sheets.\nCorrected in the main text.\n16. Lines 300-302 – This is the scenario outlined in Shields (2005), and approximates the\nchange from dolostone to limestone in Marinoan cap carbonates.\nWe have addressed this in the main text by adding a new paragraph in section 2.4 (line 329)\nto compare our model results to the stratigraphic architecture of the cap carbonates and\ndirectly reference Shields (2005).\n17. Lines 309-312 – How is this estimated? Just by thickness, and assuming constant\nsedimentation rates?\nYes, this estimate directly corresponds to the thickness profiles shown in Figure 5. We have\nadded this description to the caption of Figure 7 and specified that constant sedimentation\nrates were assumed in the main text (line 211).\n18. Lines 315-316 – Although I’d agree that the model is broadly consistent with global\nmass and thickness of Marinoan cap carbonates, what about their mineralogies, and\nstratigraphic architecture, relationship to relative sea level changes, etc? This needs more\nsubstantiation than currently given, and a closer emphasis on the Marinoan record.\nWe have addressed this in the main text by adding a new paragraph in section 2.4 (line 329)\nto compare our model results to the stratigraphic architecture of the cap carbonates and\ndirectly reference Shields (2005). We have also suggested several future studies related to\nthese topics in the final paragraph of the main text.\n19. Line 333 – What is Ho]man (2011) - not in reference list - and the “Glacial Lake Harland”\nhypothesis? In Ho]man (2011) in Sedimentology, Ho]man writes that he refers to the\nplumeworld as the ‘Glacial Lake Harland’ but it seems that the \"hypothesis\" here is\nprecisely the same? I note that in most post-2011 papers there is no mention of any GLH\nhypothesis, so I'm not quite sure that there are two separate hypotheses here?\nThe Ho]man 2011 reference has been removed from the main text.\nReviewer #2 (Remarks to the Author):\n1. Thomas and Catlin propose that seafloor weathering provides an important alkalinity\ncontribution to cap carbonate formation in the aftermath of Snowball Earth. To assess this\nhypothesis they perform a series of geochemical modelling experiments. The authors find\nthat the addition of alkalinity production through seafloor weathering can explain the early\nand rapid carbonate precipitation in the glacial aftermath, reconciling issues with previous\nmodels of cap carbonate precipitation. As I mention in the line comments, I think the\nauthors could clarify that no much open ocean is needed to put the ocean and atmosphere\nin communication during the Snowball—I think it would be good for some clarification on\nthis point as many readers will likely misunderstand the implications for ice cover (which\nare actually not much). I would also argue that you need this additional sink of CO2 for the\nlong durations of the glaciations, particularly the Sturtian….\nThis is a well-written, novel, and totally solid contribution to our understanding of extreme\nclimate states in general and Snowball Earth in particular. Below are some small line\ncomments to clean up some questionable references. Otherwise, this paper should be\naccepted.\nWe thank the reviewer for the constructive feedback on our manuscript. We provide a\ndetailed discussion of atmosphere-ocean equilibrium during the snowball in our methods\nsection, which we have now referenced in the main text (line 146). We have also removed\nthe misleading sentence in comment 10, below.\nLine comments:\n2. 7: It is not clear that oxygen rose. Maybe at the very end. Also declined during the\nSturitan.\nWe have corrected this in the main text.\n3. 20: Cohen et al is wrong ref here. Doesn’t really need a reference.\nThe Cohen et al. reference has been removed from the main text.\n4. 23-24: Wrong references for duration—could use Rooney et al., 2015 here.\nThe references (Kirschvink 1992, Ho]man 1998) here are for the phrase “snowball Earth”\nand the first proposal of the idea that the Earth was completely frozen. The evidence\nrelated to the duration is reviewed in Ho]man et al. 2017, which is also cited just before\nthis sentence. Rooney et al., 2015 is cited later in the manuscript.\n5. 27: Wrong ref—Narbonne is referring to Ediacaran, not Cryogenian.\nCorrected in the main text.\n6. 28: I don’t think many people buy this anymore\nWe have corrected this in the main text.\n7. 30: What does accretion of supercontinents mean? Accretion is a tectonic process that\nis di]erent from collision. Rewrite to assembly of Gondwana.\nWe have corrected this in the main text.\n8. 33: Not entirely. The cap carbonate you are mostly referring to is actually basal Ediacaran\nin age.\nWe have corrected this in the main text.\n9. 40: These are not ice ages, but a di]erent planetary climate phenomena—ice ages refer\nto glacial maxima in orbitally driven glacial-interglacial cycles.\nWe have corrected this in the main text here and throughout.\n10. 354: I find this sentence a little misleading. LeHir showed that you only need a few\nhundred square km of open ice (size of Hawaii) to have equilibrium on million year\ntimescales. It might be worth clarifying here that you don’t need much.\nWe have removed this sentence in the main text in agreement with this comment and also\nto allow more space for discussion of other topics raised by reviewers. We also note that\nthe calculations done by LeHir are discussed in the methods section in some detail,\nconsistent with this comment.\nReviewer #3 (Remarks to the Author):\n0. “Three-stage Formation of Cap Carbonates after Neoproterozoic Snowball Glaciations\nConsistent with Depositional Timescales and Geochemistry”\nThe manuscript details a newly updated carbon cycle model that is used to reconcile\nevidence for the formation of Neoproterozoic post-glacial cap carbonates. These\ndistinctive units have been a puzzle for many years, with a huge controversy about many\naspects of their formation, including geochemistry, time-scale and sedimentology. In this\nstudy, the authors suggest that they can account for many aspects of cap carbonate\ndeposition including their mass, timescale and chemistry, by incorporating sea floor\nweathering into a carbon cycle model. They suggest a process including post-glacial rapid\ncarbonate precipitation followed by seawater mixing and a more prolonged interval of\ncarbonate formation.\nFirst, the paper is clear and well-written, the figures are good. Overall, the reasoning and\nmethods are presented well, and it’s commendable that the authors have been broad in\nconsidering the range of techniques applied to understanding the caps\n(geochron/sedimentology/chemistry etc.). It’s also great to see more detailed carbon cycle\nmodels being developed and applied to the Neoproterozoic.\nI’m not an expert myself in the details of this type of modelling, so I can’t comment\nauthoritatively to the methods itself- this would need to be addressed by another reviewer.\nHowever, I am very familiar with the geology and geochemistry of these cap carbonate\nunits (and have also worked with carbon cycle modellers on this topic). Therefore my\nreview concentrates on these aspects of the study.\nOverall, I have several broad comments about reconciling the model with geological\nevidence. At present, the paper reads as a little un-nuanced in understanding the geological\nrecord of the Neoproterozoic. Unfortunately I think this and other aspects detract from the\nselling point of the study (solving the puzzle) and require further attention before\npublication. In light of these complications, I would suggest that short format might not be\nthe best way to present this study. Though I do certainly see the value in this approach,\nI think it needs to be better linked to the preserved geological record of cap carbonates.\nWe thank the reviewer for the constructive feedback on our manuscript. We have made\nseveral large scale changes in the manuscript to address the general comment raised\nabove and we have overhauled much of the comparison to the geologic record to be\nclearer and more accurate.\n1) Marinoan focus. The paper focuses on the (shorter) timescale and (more extensive) cap\ncarbonate features relevant to the late Cryogenian Marinoan glaciation. This is important,\nbut if the authors wish to be able to suggest their model addresses cap carbonate\ndeposition more broadly, then they would also need to be able to explain the Sturtian (and\neven the Gaskiers) caps. If their model can explain carbon cycling through the two major\nglaciations and their aftermaths, I would be more supportive of publishing it in short\nformat/high impact journal. However the focus on only one of the events detracts from this\nbroader view.\nHow can you then link the di]erent duration and variable expressions of the cap\ncarbonates between the two glaciations using your model? In particular, the Sturtian is a\nmuch longer glaciation with mostly, very thin cap carbonate deposition (e.g. cm-scale, up\nto units that look like Marinoan caps). These caps are also regionally spatially\nheterogeneous and depth dependant. This geological evidence suggests that both broader\n(e.g. Sturtian vs. Marinoan ocean chem/redox/timing/tectonics) and more focused (e.g.\nlocal) e]ects both play important roles in the thickness and style of cap carbonate\nformation. While the model here doesn’t have to solve everything of course, it needs to be\nable to explain at least the di]erence between Sturtian and Marinoan caps. This aspect is\narguably one of the most confusing parts of the puzzle.\nWe have clarified in the title, abstract, and main text that our model applies to the\nMarinoan glaciation and the associated cap carbonates. An explanation for the cap\ncarbonates of the Marinoan alone is still a major advancement (in agreement with\nReviewers 1 and 2) considering that they are more abundant and well-expressed in the\ngeologic record than the Sturtian CCs and still lack consensus on their formation after\nextensive debate in the literature. Additionally, our work can serve as a basis for better\nunderstanding the unique aspects of the Sturtian CCs that would not correspond to the\nformation mechanism we have proposed here.\nWe have added to the main text to suggest future studies related to comparing and\ncontrasting the formation of Sturtian and Marinoan CCs. Because this would be a research\nproject rather than a mere extension of this paper, it is best left to future work.\n[Comment 2 and 5 grouped together below]\n2) Specifically, the authors do not include ice-sheet melting or ocean circulation in the\nmodel. As the authors suggest, these are obviously a very complex processes and I\nimagine would be di]icult to integrate into a model. However, in this case I think the lack of\nthese processes being incorporated (based on previous models and interpretations) biases\nthe study towards the rapid cap formation scenario. This is because if the timescale of de-\nglaciation is prolonged, the dynamics of the ice melt and its mixing in the ocean become\nmore important, rather than a single melt event. This timeframe changes the rate and\namount of freshwater melt entering the ocean, changing the size and timing and possibly\nthe existence of a freshwater lens—which forms a large part of the model interpretation\nhere. Could a model run could be set up to test if the meltwater influx was pulsed,\nprolonged and to see if a stratified meltwater lens did not necessarily develop? Maybe this\nis the other end of the spectrum of reality, but it seems important to include given the\nweight placed on the existence of ocean stratification in the model and discussion. At\npresent if feels like the whole interpretation relies on this point, but I think the geological\nand geochemical evidence for a meltwater lens is equivocal. Especially as cap carbonates\nalso precipitate in very deep water too (e.g. sections with no sedimentary structures except\nlamination that are basinward of turbidite facies). Despite many years of work, I still don’t\nreally think have a good enough understanding of the impact of meltwater on the system\nduring and after glaciation. 5) Likewise, estimates of the speed of deglaciation are\nsubjective- fast rates have been suggested in Paul Ho]man’s Snowball Earth hypothesis,\nand based on tidal cycles by Myrow and others, 2018. But these rates are questioned (e.g.\nsee Fairchild et al., 2023, Depositional Record), and the sequence that Paul Myrow looked\nat is generally understood to be syn-glacial (e.g. see early work by George Williams). In\nreality, there are no really precise estimates of the timing of deglaciation, either from\ngeochron or sedimentology. The timing of cap carbonate precipitation is the same. The\nmagnetic reversals are an interesting one–more work needs to be done though (without\nruining any important outcrops). I think that these do have real potential to suggest a longer\ntimeframe but it is hard to say how long. Perhaps the authors should test two scenarios\nwith longer and shorter rates of deglaciation and discuss these- especially in relation to the\nexistence of a meltwater lens as my comment above.\nThank you for bringing up these points about the deglaciation transition. We have\nperformed additional model runs where we test a prolonged deglacial transition with both\nlinear and pulsed melting that causes the mass of the meltwater layer, weathering rates,\nand surface temperature to change over time. We have included these model runs (Figures\nS7-S10) in the supplementary material section C2 and referenced them in the main text.\nAs described in detail there, we find that the prolonged deglaciation does not have a strong\nimpact on our main conclusions. When we modified the nominal model scenario to\ninclude prolonged deglaciation, it increased the minimum amount of time for CC\ndeposition from ~40 kyr to ~110 kyr but it did not increase the upper bound of CC\ndeposition of ~500 kyr. Considering that the prolonged deglaciation with very little\nmeltwater alkalinity is the extreme endmember scenario, we conclude that our main\nresults still hold but with additional context, which we have added in the main text.\nWe believe that the sections added to the main text and supplementary material\nsu]iciently address the comment above, but we would also like to add the following:\nFirst, the presence of the meltwater layer is e]ectively part of the SCOM hypothesis.\nTherefore, if the meltwater layer never existed, the SCOM hypothesis in its current form\nwould be wrong. Modifications to the hypothesis could be made since other aspects would\nremain valid (e.g., enhanced marine alkalinity during the snowball), but exploring a\nscenario where the meltwater layer doesn’t exist is separate from what we propose in this\npaper.\nSecond, we believe the evidence that the meltwater layer did exist is stronger than\nequivocal. As cited in the main text, there are now many lines of geochemical evidence that\nfavor the existence of a meltwater layer: Sr, Mg, Ca, and C isotopes (see main text\nparagraph starting line 79). Also, the original interpretation of the stratigraphic architecture\nas an indicator of the meltwater layer has not been disproven (Shields 2005). Also, models\npredict its existence in both 1D and 3D (Yang et al. 2017; Ramme & Marotzke 2022; see line\n~85).\n3) The peak ‘depositional rate’ of carbonate generated in the model at ~2-10m up\nsection (Lines 200-208) is not in agreement with where carbonate deposition is\nconcentrated in preserved Marinoan cap carbonates. Generally they have higher\ncarbonate concentration immediately or ~<1m above the base which declines upwards\nafter several few metres or so of high carbonate concentration. Higher carbonate\nprecipitation could also be linked to the formation of sheet cracks and tepees in some cap\nhypotheses (e.g. the condensed models which suggest force of crystallisation for dolomite\nprecipitation; Wallace et at., 2019, Precambrian Research). These features are also\ncommonly around the base of the sequences, with some variability. Though you have\nprovided these estimates, I’d suggest this is a good place where you can use the geology to\ntest and refine your model. Just a note too that cap carbonates are also not necessarily\ncomposed of 100% carbonate. In shale basins like Australia and Svalbard, the caps can be\nonly 50-70% carbonate, where as in carbonate basins like Namibia, the cap is almost\nentirely dolomite. Can you use some examples of this from sedimentology papers to test\nyour results here?\nAs noted in the main text, our method of calculating the height of the deposits is\nqualitative. It assumes a global average deposition rate over an area twice the modern\ncontinental shelf area and constant sedimentation rates. It assumes constant density of\nthe carbonates and does not consider sedimentary processes, compaction, or anything\nelse. The main purpose of this simple approach was to (1) provide a basic comparison to\nCC sections as a function of height and (2) to estimate how much carbonate is deposited in\nphase 3 vs phase 4 to make the Sr isotope comparison later (Fig 7).\nIt is unclear in the literature where the highest carbonate concentration in CC sections is. If\nthe carbonate concentration remains high for several meters above the base, that is\nconsistent with our qualitative estimate of peak deposition rate at ~2 meters above the\nbase. Moreover, it is claimed that higher carbonate precipitation is linked to sheet cracks\nand tepees in some hypotheses. In Wei et al. (2019; Earth and Planetary Science Letters)\nFigure 1, the Etoto CC has sheet crack cements and tepees up to ~6 m, the Jiulongwan CC\nhas the same up to ~3 m, and the Wushi CC has the same up to ~1.6 m. In Liu et al. (2014;\nEarth and Planetary Science Letters) Figure 2, the Mongolia CC has giant wave ripples\n(which, as comment 6 says, are subject to interpretation and are probably tepees) up to\n~6m, and the Australia CC has the same up to ~4m. Taken together, the presence of these\nsedimentary structures places high sedimentation rates 1.6-6m above the base, which is\nconsistent with our reported range.\nWe agree with the comments that comparison to these lines of evidence, including the\npercent carbonate in the cap, is a worthwhile endeavor that can further test our\nhypothesis. However, a useful comparison would require a more detailed\nsedimentation/compaction model. We have suggested these studies in the main text as\nfuture work (Line 310 and paragraph starting line 406).\n4) Thickness of cap carbonate. As a carbonate sedimentologist, I suggest that there is a\nbias in the literature to measure the true thickness of the cap carbonate as higher than it\nactually is, in carbonate basins. The Noonday (Line 251) and Rasthof are two examples of\nthis. Each has a basal member of only ~2-10m or so which is a commonly a laminated\ndolomite like a typical cap carbonates (e.g. Le Ber et al., 2013, Sedimentary Geology). The\nadditional 100’s metres thickness in these sections are simply carbonate reefs or buildups\ndeveloped on top of the cap carbonate and are unrelated to the deglaciation--or at least in\nthe short term (<My). I suspect the thickness estimates, nicely compiled in Yu et al., 2020,\nwould show no substantials equatorial trend if paleo-depth and post-glacial microbial\ncarbonate buildups were accounted for.\nThank you for pointing this out.\nFirst, we have added a paragraph in the main text (line 254) to specify that we are referring\nto both aspects of Marinoan CCs – the cap dolostones and the overlying limestones, which\nis consistent with the Yu et al. compilation.\nSecond, we model the system evolution for several Myr after deglaciation and find that the\nbackground climate isn’t recovered until ~5 Myr. So we can still compare to the overlying\nlimestones in the thicker formations if deposition took longer than 1 Myr following\ndeglaciation.\nThird, our claim about regional variability in depositional environments is not a claim of\nequatorial trends. We are claiming, based on the cited papers (Creveling and Mitrovica\n2014; Irie et al. 2019), that regional variability in sea level rise, based on local topography\nand ocean dynamics, would create variability in depositional environments. Thus, we do\nnot rely on an equatorial trend in Yu et al.\nFourth, although this bias exists, this is the best compilation we are aware of and is still\nuseful for comparing to our model on a global scale. We have added a caveat in the main\ntext (line 402) that this thickness bias might exist.\n6) The section on sedimentary structures is needs developing better with a broader\nliterature review. Under the snowball theory, structures in the cap are interpreted as giant\nwave ripples and sheet crack cements (Ho]man et al., 2017 for summary). These are both\nare interpreted to be the result of rapid deposition. However, I think it’s fair to say that most\nsedimentologists would regard these structures as tepees and bedding expansion features,\nboth of which imply long timescales of formation (e.g. hardgrounds, Wallace et al., 2019;\nFairchild et al., 2023, Depositional Record). In these papers, the cap carbonates of\nAustralia and Svalbard also record abundant ~cm scale turbidite layers with erosive bases\nand flute marks, also more consistent with longer estimates of formation—though not\nnecessarily proving them. Turbidite facies have also been documented in the Namibian\nsequence (e.g. Domack and Ho]man, 2017 GSA Bulletin).\nFurther, the base of the cap carbonate is not always sharp, and not always after\ndeglaciation, and therefore not always consistent with the interpretation of post-meltwater\ncap carbonate formation in this manuscript. Dropstones are occasionally found in the\nbasal cap carbonate (e.g. Le Heron, 2020 Geology; I think also Jon Giddings found some in\nthe Flinders Ranges but I can’t find the exact citation). In another example, in Namibia at\nFransfontein Ridge, there is a unit of laminated dolomite and dropstone beds, the Bethanis\nMb. which transitionally underlies the Keilberg cap carbonate (Domack and Ho]man,\n2017). This dropstone dolomite marks the beginning of dolomite precipitation (which also\nappears to dolomitise several metres of the underlying limestone diamict), suggesting that\ndolomite precipitation occurs during deglaciation in some places. I think these authors might\nhave interpreted this di]erently, but it is certainly a distinct change to a dolomite\nmineralogy associated with deglaciation that I would suggest represents the start of\ndolomite cap precipitation. Though not published, in a recent fieldtrip I have seen the cap\ncarbonates interbedded with the glacial sediments over ~<a1m-scale and also at 10’s\nmetres scale at the top of both of the Marinoan and Sturtian the glacial sequences in South\nAustralia. In your model, you can account for cap precipitation after melting, but can it also\ndemonstrate dolomite precipitation beginning during deglaciation?\nWe thank the reviewer for pointing this out. We have rewritten most of the section on\nsedimentary structures in accord with this comment, with the following general\nimprovements:\n§ We have been more specific with respect to dolostone vs limestone mineralogies\n§ We have been more balanced in the interpretation of sedimentary structures\n§ We have a more detailed treatment of syn-deglacial vs post-deglacial carbonate\ndeposition\n§ We have added comparison to the stratigraphic architecture and transgressive\nnature of the CCs\nWe have also simplified table 1 by removing individual lines of sedimentological evidence\nand instead focusing on the broad interpretation. There are too many individual (and\nconflicting) interpretations to include, so we instead cite the two major competing\nhypotheses to indicate that sedimentological features can be interpreted to indicate rapid\nor slow deposition.\n7) Precipitation versus sedimentation. The sedimentology of the cap carbonates (e.g.\nwork by Noel James, Malcolm Wallace, Jon Giddings and Ian Fairchild for example),\nindicates that the carbonates are a mix of authigenic, precipitated dolomite (e.g.\nmicrocrystalline and nodular dolomite) and detrital carbonate (e.g. peloids), which are\ncemented by dolomite. There is discussion about the original mineralogy and importance\nof precipitation vs. deposition in these units, though often both modes of formation are\nevident. In your model, do you assume precipitation is totally from pore water, and what\ntype of carbonate do you model to precipitate? (both aragonite and calcite are mentioned\nin methods- I get that it’s di]icult to model dolomite kinetics). How would the results\nchange if you used di]erent interpretations about styles of deposition- e.g. water column,\npore-water or detrital? Maybe this information is available in the supp data, but it would be\ngood to have more information about this in the manuscript.\nIn our model of shelf carbonate deposition, we assume that carbonates precipitate out of\nthe water column and are deposited on the seafloor, as developed in Ridgwell et al. (2003)\nfor the Neoproterozoic and used in many subsequent modeling studies. Because the focus\nof our model is on the global chemistry of the ocean and climate, we do not have to specify\nthe style of deposition beyond the fact that carbon and alkalinity are removed from the\nocean. In our model of seafloor weathering, we assume carbonates precipitate in cracks\nand veins in the ocean crust, as observed today.\nIn our model, the deposition of calcite vs aragonite is contained within the n parameter of\nsupplementary equation 13. We explore the range n = 1.0 – 2.5 when running the model to\nconsider deposition of both calcite and aragonite in di]erent proportions (Opdyke and\nWilkinson 1993). This parameterization has been benchmarked and validated against data\nfrom the Cenozoic (Krissansen-Totton and Catling 2017). We further note that in the main\ntext Methods section (line 608) we discuss this assumption, reproduced below:\n“We nominally assume that all carbonate precipitation chemistry is based on calcite and\naragonite. Post- and syn-glacial snowball Earth carbonates are frequently dolomitic in\ncomposition; however, recent isotopic evidence suggests the cap carbonates were\ndeposited as calcium carbonate and later altered to dolomite via marine diagenesis (Ahm\net al. 2019). Furthermore, a similar modeling study (Hood et al. 2022) shows that the\ngeochemical evolution of the ocean during and after the Sturtian glaciation is not sensitive\nto the difference in carbonate chemistries based on using calcite, magnesite, or dolomite\nas the representative carbonate mineral. Thus, we believe our assumption is justified for\nmodeling the large scale features of the geologic record such as the total mass and\ndepositional timescale of the Cryogenian carbonates.”\nPut simply, the di]erent styles of deposition are below the resolution of our model because\nwe chiefly consider the global removal of carbon and alkalinity from carbonate deposition.\nBeyond that, we remain agnostic to the specific style in which they sediment on the\nseafloor. Varying the styles may impact our CC height calculations, but as we are clear\nabout in the text, that specific model is very simple and meant for qualitative comparison\nonly.\nA future study in which our model results are used as the basis for a detailed model of the\ndeposition and sedimentology is an exciting avenue for future research, which we now\nmention in the main text (paragraph starting line 406).\n8) A big focus of the model appears to be sub-marine weathering, but it would be\nvaluable to better define this in the manuscript rather than the supp data. When I was\nresearching this aspect for a paper on Mg cycling, it seemed like this is unfortunately quite\npoorly understood, even in modern settings, and it would be di]erent again in anoxic\nPrecambrian water. I therefore disagree with your assumption that this would be the same\nin the Neoproterozoic (anoxic ocean, supercontinent breakup) as to the modern.\nOne of my broader concerns with using modelling to address the Snowball Earth scenario\nis that the timescales involved (e.g. >50My) make it di]icult to run models of detailed\ndynamics through glaciation and deglaciation due to processing power- e.g. 57 Myr GCM\nruns. On the other hand, carbon cycle models can deal with these long timescales better,\nbut then can’t realise some of the detailed processes which may have very important\nimpacts on the state of the ocean-atmosphere at smaller time intervals (like ice dynamics,\nmeltwater-seawater interaction etc). Though the authors do mention some assumptions, I\nthink the authors need to be clearer about the caveats of their model in this way--how\nmuch of it is based on interpretations and an assessment of how much these more\ncomplex processes would change the results if included. Some of these aspects are\ndiscussed but I think some aspects need further justification.\nOur understanding of seafloor weathering on modern Earth is incomplete, like many\naspects of the Earth system, but there have been many recent advancements (e.g.\nreviewed in Coogan and Gillis 2018; Annual Reviews). The parameterization of seafloor\nweathering used in this model incorporates these advances, empirical results from the\nlaboratory, and has been benchmarked and validated against data from the Cenozoic\n(Krissansen-Totton and Catling 2017, Krissansen-Totton et al. 2018). We also vary a wide\nrange of empirical parameters associated with our treatment of seafloor weathering in\norder to account for the uncertainty.\nAs noted in the comment, there are pros and cons for all types of models applied to\nSnowball Earth. While GCMs can resolve detailed processes on short timescales, they\ncannot resolve changes over long timescales (which are especially important for a Myr\nscale event like Snowball Earth) due to limits on computational power. They also su]er\nfrom the fact that they require precise information and parameterizations that are not\nknown in the Neoproterozoic (e.g., topography, ocean bathymetry) to calculate their high-\nresolution output.\nThe virtue of a global model like ours is that it is relatively “low resolution”, modeling the\nglobal chemistry and climate as a single box. This level of resolution not only allows us to\ncapture the long timescales of the event, but it is also consistent with the level of\nknowledge we have of the Neoproterozoic Earth system. Moreover, we have used the high-\nresolution models of Snowball Earth (e.g., 3D studies of post-glacial ocean stratification,\ndeglaciation threshold, and ice sheet melting/sea level rise) to inform our model when\npossible. We have added to the main text to clarify the caveats of our modeling approach\nand suggested areas where it can be improved (line 390).\nLine 265. This statement is unfair, as the amount of studies looking at paleomag in cap\ncarbonates is limited, and the lack of evidence for magnetic reversals is not a result of them\nnot being present in the rocks, but just that no one has tested all the deposits.\nWe ended up removing this sentence from the main text when making large scale edits to\nthis section, consistent with this comment.\nJust a final note too that Sr/Sr results from non-pure dolomitic cap carbonates (e.g.\nAustralia, Svalbard etc.) are tricky to interpret. Not only is dolomite almost impossible to\ndissolve without dissolving non-carbonate components, but also the caps di]er in their\ncarbonate mineralogy and carbonate concentration, biasing these comparisons between\ndi]erent locations.\nWe agree that the Sr/Sr isotopes are di]icult to interpret and subject to uncertainty. We\nrelied on the published measurements and associated interpretations to make this\ncomparison in our model.\nOverall, I wouldn’t say that I agree that this model reconciles all the di]erent evidence\nabout the cap carbonates but I do think the paper is well-presented and interesting. This is\na pretty heavily debated topic and I still don’t think we have figured it out. The model has\npotential to be a tool for the Neoproterozoic climate change more broadly and therefore it\nwould be good to see it developed further with more consideration to the geology.\nWe agree that this model does not reconcile all the di]erent evidence about CCs. Our goal\nis to show that this model is novel and broadly consistent with many lines of evidence on a\nglobal scale, and to suggest future work that can be used to test it. We thank the reviewer\nfor the thoughtful, constructive comments that greatly improved the manuscript in these\nregards.\nI note that some of the information I’m referring to has not been published (after some\nsignificant career interruptions on my end). If the authors are interested at looking at some\nof this unpublished information in revising the manuscript, I’d be happy to share it.\nWe have cited your personal communication on line 315/316 regarding the presence of\ninterbedding between CCs and glacial units. Please let us know if there is a better citation\nor a di]erent course of action you’d like us to take.\nAshleigh Hood, University of Melbourne\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors have done a good job addressing the reviewers' critique, and I have a few\nremaining points only.\n1) Line 45-46 - This sentence implies that the connection between cap carbonates and\nsnowball earth comes from Kirschvink, but my understanding is that this linkage was first\nmade in Hoffman et al., 1998. Probably needs both references.\n2) In figures 2 and 3, the x-axis header \"million years since glaciation\" is confusing. Shouldn't\nthis be \"...since glacial onset\"?\n3) Line 173, not just gradual but also localised?\n4) Lines 185-186 - this statement does not really explain why. Needs a bit more explanation\nI believe.\n5) Lines 210-211 - as the dolostone layer is global, and overlying limestone (where present)\nis highly localised, I'm not sure how relevant this would be? Perhaps needs clarification...\n6) Line 286 - goes some way to explaining why dropstones are rare to absent in Marinoan\ncap carbonates (see below)\n7) Lines 314-318. I don't agree with this summary, which seems to have gone a bit awry due\nto a reviewer's unpublished observations. Dropstones in cap carbonates? Le Heron et al\n(2020) report putative dropstones from a post-Sturtian carbonate unit, and so is not\nrelevant here. Domack and Hoffman (2011) describe the Ghaub diamictite in great detail\nbut do not really address the issue of dropstones in cap carbonates directly - dolomitisation\ncommonly occurs after deposition so I'm not sure whether dolomitisation of underlying or\nassociated units implies synchroneity between glaciogenic deposition and dolomitisation.\nInterbedding needs more of a reference than a personal communication considering just\nhow much has been published on cap dolostones. My understanding of the authors' results\nis that they are perfectly consistent with precipitation during latter stages of deglaciation\ncontinuing into post-glacial time, and that this is consistent with the sedimentology. In\nshort, I'd would urge caution not to overinterpret the sedimentology in what is primarily a\nmodelling study. Perhaps the authors could turn this around by suggesting what evidence\nmight help to test the timeframe proposed here?\nReviewer #2 (Remarks to the Author):\nI am still happy with the manuscript and would still like to see it published. The authors have\ndone a nice job addressing the reviews, but it is unfortunate that there are still some\npresentation issues that would help the manuscript. Particularly, the title is weak and not\nparticularly informative. The contribution is that the authors point out that seafloor\nweathering provides an important alkalinity contribution to cap carbonate formation. Why\ndon’t the authors just say that with a title like: “The contribution of seafloor weathering to\ncap carbonate formation in the aftermath of the Marinoan Snowball Earth glaciation”? Or\nthe SCOM that you emphasize in the text?\nThe first sentence of the abstract is weak. Delete and try again. The second and third\nsentences are also weak—what attributes do the cap carbonates fail to explain? This is\nvague, and many people would argue that the cap carbonates are in fact the predicted\nresult of high CO2 and alkalinity in a Snowball aftermath. Get rid of abbreviations in\nabstract.\nLine 34: How do cap carbonates probe?\nLine 41: Williams 1979 is a weird reference here—if you don’t have Snowball you don’t have\na hysteresis. Why not cite one of Hoffman’s papers?\nLine 52: The evidence for paleomagnetic reversals is weak. These are mostly patchy\noverprints and are hugely overinterpreted, but the literature has not been critical enough\non this point.\nLine 58: I’m not convinced by your claim that these are not complete or sufficient, but OK. I\nwould just motivate instead by the fact that none of these models account for seafloor\nweathering, which was likely the major player on the carbon cycle during the Snowball,\nand cite LeHir.\nTable 1: The Kilner pmag is demonstrably an overprint (see Rowan and Tate 2010 AGU\nposter). I would argue all of the Australia and Brazil data also fail to demonstrate that the\nproposed reversals are symmetric and are not overprints or excursions. Each component\nneeds confidence tests with magnetic mineralogy clearly defined. I understand that this is\nbeyond the scope of this work, but I would suggest adding some caution and not spend too\nmuch time trying to explain these timescales.\n113: I think it would be helpful to be specific in the main text about the reactions involved in\nseafloor weathering to produce alkalinity. Many of the readers will not know what these\nreactions are, and they should not have to go to the SM. Just add a one-paragraph easy\nexplanation of seafloor weathering with a couple of reactions.\n132: Krissansen-Totten et al., 2018 have a low sensitivity of seafloor weathering to pH. How\ndoes this model compare? It seems like this should be addressed directly because in LeHir\nit is the pH dependence that is critical for seafloor weathering. Where Krissansen-Totten\nemphasizes the T control on seafloor weathering and low pH dependence to create an\nArchean silicate weathering feedback, this paper seems to go back to the strong pH\ndependence—what is the difference?\n270: One reviewer had an issue with the use of the Noonday Formation as it includes units\nother than the cap. This can be resolved by just referring here to the Sentinal Peak Member\nof the Noonday Formation, which as pointed out by Petterson does in fact form an ~100 m\nreef in some locations.\n277: And the fidelity of the palemagnetic data and their interpretations.\n361: Why not use this for title?\nReviewer #3 (Remarks to the Author):\nThanks to the authors for revising the manuscript and taking the comments on board. I have\nbeen unable to find enough time to do a thorough re-review due to field teaching\ncommitments, but I provide a few minor notes here for consideration please.\nOverall, I thank the authors for taking their work and consideration in addressing the\ncomments. I am happy with the revisions, and I think this will make a nice addition to the\nliterature to spur further discussion. Even though I do not agree totally with the\nmechanisms suggested for cap carbonate formation in the paper, I think that the carbon\ncycle model developed here is a good approach and is useful for future studies to build on.\nA few minor notes:\nSection Lines 285-312 on reconciling fast and slow depositional rates. This has some new\nadditions to the text based on the reviews. I do like the idea of this section, and I think\ncertainly there was a variation in precipitation rate through the caps as the authors suggest\n(peak precipitation close to the base and declining upwards). However, I don’t think you\ncan directly reconcile the sedimentary structures aspect of this new text, based on a\ndepositional rate. This is because in one scenario you are dealing with deposition of water-\ncolumn precipitates/sediment (wave ripples) and in the other (teepees) you are dealing\nwith in situ authigenic precipitation (not water column deposition). These processes would\nrespond different to the evolving seawater chemistry as one is seafloor-immediate\nsubsurface. It’d suggest perhaps removing the emphasis on the sedimentary structures\naspect of this discussion in this regard, but using just the stratigraphy to present this idea.\n(As a practical note, perhaps the post-glacial cap-shale sequences are best at showing up\nthe timing and maximum of carbonate precipitation rather than the basins with ongoing\ncarbonates above the cap?)\nFor the section on the different theories for cap carbonate precipitation, an earlier\nreference for ‘sediment starvation’ models to cite too is either Kennedy, 1996 or Kennedy\nand Christie-Blick 2011.\nI think at this point I’d rather not include the pers. comm in Line 315 please, as it is a\nstudent project and we are still in the middle of the study. Thanks for your consideration of\nthis in the comments.\nAsh Hood, University of Melbourne\nSecond response to referees for manuscript entitled:\n“Three-stage Formation of Cap Carbonates after Marinoan Snowball\nGlaciation Consistent with Depositional Timescales and Geochemistry”\nWe thank the reviewers for volunteering their time and providing constructive comments\nthat have improved this manuscript. Our responses are below. Reviewer comments are in\nnormal typeface and our replies are in blue. Changes made in the manuscript from this\nrevision are in bold italics while changes from the first revision remain in bold.\nSincerely,\nTrent B. Thomas (tbthomas@uw.edu) and David C. Catling\nDepartment of Earth and Space Sciences\nUniversity of Washington, Seattle, WA\nReviewer #1 (Remarks to the Author):\nThe authors have done a good job addressing the reviewers' critique, and I have a few\nremaining points only.\n1) Line 45-46 - This sentence implies that the connection between cap carbonates and\nsnowball earth comes from Kirschvink, but my understanding is that this linkage was first\nmade in HoUman et al., 1998. Probably needs both references.\nAdded HoUman et al., 1998 reference.\n2) In figures 2 and 3, the x-axis header \"million years since glaciation\" is confusing.\nShouldn't this be \"...since glacial onset\"?\nUpdated in all figures.\n3) Line 173, not just gradual but also localised?\nAdded the word “localized” in the text.\n4) Lines 185-186 - this statement does not really explain why. Needs a bit more explanation\nI believe.\nAdded “because more alkalinity can be delivered” in the text.\n5) Lines 210-211 - as the dolostone layer is global, and overlying limestone (where present)\nis highly localised, I'm not sure how relevant this would be? Perhaps needs clarification...\nYes, the characteristics of the cap carbonates are variable from section to section, likely\ndue to high regional variability at the time of formation. Here we provide a global average\nheight because we are comparing to the global collection of cap carbonates. This is useful\nfor qualitatively comparing our results to the geologic record and is required to make the\ncomparison to Sr isotopes that we show in Figure 7. We describe the relationship between\nour global model results and the regional variability of the cap carbonates in detail\nthroughout the discussion section.\n6) Line 286 - goes some way to explaining why dropstones are rare to absent in Marinoan\ncap carbonates (see below)\nAddressed below.\n7) Lines 314-318. I don't agree with this summary, which seems to have gone a bit awry due\nto a reviewer's unpublished observations. Dropstones in cap carbonates? Le Heron et al\n(2020) report putative dropstones from a post-Sturtian carbonate unit, and so is not\nrelevant here. Domack and HoUman (2011) describe the Ghaub diamictite in great detail\nbut do not really address the issue of dropstones in cap carbonates directly -\ndolomitisation commonly occurs after deposition so I'm not sure whether dolomitisation of\nunderlying or associated units implies synchroneity between glaciogenic deposition and\ndolomitisation. Interbedding needs more of a reference than a personal communication\nconsidering just how much has been published on cap dolostones. My understanding of\nthe authors' results is that they are perfectly consistent with precipitation during latter\nstages of deglaciation continuing into post-glacial time, and that this is consistent with the\nsedimentology. In short, I'd would urge caution not to overinterpret the sedimentology in\nwhat is primarily a modelling study. Perhaps the authors could turn this around by\nsuggesting what evidence might help to test the timeframe proposed here?\nCorrected in the main text line 317.\nReviewer #2 (Remarks to the Author):\nI am still happy with the manuscript and would still like to see it published. The authors\nhave done a nice job addressing the reviews, but it is unfortunate that there are still some\npresentation issues that would help the manuscript. Particularly, the title is weak and not\nparticularly informative. The contribution is that the authors point out that seafloor\nweathering provides an important alkalinity contribution to cap carbonate formation. Why\ndon’t the authors just say that with a title like: “The contribution of seafloor weathering to\ncap carbonate formation in the aftermath of the Marinoan Snowball Earth glaciation”? Or\nthe SCOM that you emphasize in the text?\nThe first sentence of the abstract is weak. Delete and try again. The second and third\nsentences are also weak—what attributes do the cap carbonates fail to explain? This is\nvague, and many people would argue that the cap carbonates are in fact the predicted\nresult of high CO2 and alkalinity in a Snowball aftermath. Get rid of abbreviations in\nabstract.\nWe have elected to keep the title of the paper as is. While the importance of seafloor\nweathering is an important part of our paper, it is only one of several aspects of the three-\nstage formation mechanism for cap carbonate formation that we propose. For example, we\nhave also shown how the post-glacial meltwater layer is important and its eventual mixing\nwith the deep ocean may newly explain some timescale-related evidence. We have also\nconstructed a self-consistent global model for the carbon cycle to calculate the evolution\nof climate variables through all phases of a snowball, which allowed us to find the three-\nstage SCOM mechanism to begin with. We believe our current title captures these points\nand the take home message of the paper as concisely as possible. We would ideally like to\ninclude more details about the SCOM mechanism in the title, but it would make the title\ntoo long, so we have included a brief description in the abstract.\nWe have edited the abstract to strengthen the first few sentences and removed\nabbreviations.\nLine 34: How do cap carbonates probe?\nThis question is answered 2 sentences later:\n“Carbonates record Earth’s surface conditions because they are sensitive to the chemistry\nof the atmosphere and ocean from which they precipitate. Thus, the sharp distinction\nbetween the glacial deposits and CCs is interpreted as an abrupt shift in Earth’s surface\nenvironment at the end of each Cryogenian glacial interval from cold, frozen conditions to\nhot conditions with a high partial pressure of atmospheric carbon dioxide, pCO2 (HoUman\net al., 1998).”\nLine 41: Williams 1979 is a weird reference here—if you don’t have Snowball you don’t have\na hysteresis. Why not cite one of HoUman’s papers?\nChanged citation to HoUman et al., 1998.\nLine 52: The evidence for paleomagnetic reversals is weak. These are mostly patchy\noverprints and are hugely overinterpreted, but the literature has not been critical enough on\nthis point.\nAlthough this may be true, we rely on what is included in the published peer-reviewed\nliterature. We have added to a sentence to caution against overinterpreting the\npaleomagnetic data later in the manuscript, see line 403.\nLine 58: I’m not convinced by your claim that these are not complete or suUicient, but OK. I\nwould just motivate instead by the fact that none of these models account for seafloor\nweathering, which was likely the major player on the carbon cycle during the Snowball,\nand cite LeHir.\nAs mentioned in this paragraph, further details about why these hypotheses are not\nsuUicient is described in Yu et al., 2020. We provide a brief summary of what is found there\nin the final sentence of the paragraph:\n“Also summarized in Yu et al. (2020), these explanations all have unresolved deficiencies\nrelated to the physical and chemical conditions of the post-glacial ocean, the\ninterpretation of the geologic evidence, and the predicted timescale of deposition.”\nThe next paragraph is about seafloor weathering and how it has not been assessed in\nrelation to the cap carbonates.\nTable 1: The Kilner pmag is demonstrably an overprint (see Rowan and Tate 2010 AGU\nposter). I would argue all of the Australia and Brazil data also fail to demonstrate that the\nproposed reversals are symmetric and are not overprints or excursions. Each component\nneeds confidence tests with magnetic mineralogy clearly defined. I understand that this is\nbeyond the scope of this work, but I would suggest adding some caution and not spend too\nmuch time trying to explain these timescales.\nAlthough this may be true, we rely on what is included in the published peer-reviewed\nliterature. We have added to a sentence to caution against overinterpreting the\npaleomagnetic data later in the manuscript, see line 403.\n113: I think it would be helpful to be specific in the main text about the reactions involved in\nseafloor weathering to produce alkalinity. Many of the readers will not know what these\nreactions are, and they should not have to go to the SM. Just add a one-paragraph easy\nexplanation of seafloor weathering with a couple of reactions.\nWe provide a brief description of seafloor weathering in the introduction and we have now\nadded some text to include the minerals and ions involved in the reactions at line 71.\n132: Krissansen-Totten et al., 2018 have a low sensitivity of seafloor weathering to pH. How\ndoes this model compare? It seems like this should be addressed directly because in LeHir\nit is the pH dependence that is critical for seafloor weathering. Where Krissansen-Totten\nemphasizes the T control on seafloor weathering and low pH dependence to create an\nArchean silicate weathering feedback, this paper seems to go back to the strong pH\ndependence—what is the diUerence?\nThe temperature vs pH dependence of seafloor weathering is an important factor in the\ngeologic carbon cycle, but the comparison of our results to Krissansen-Totten et al., 2018\n(KT18) is not informative. KT18 model the Earth system without ice sheets, so the\ntemperature and pH dependence of seafloor weathering can be evaluated throughout\nEarth history and diUerent times can be sensibly compared.\nThe climate state we model, where Earth is covered in ice sheets, dramatically diUers in the\nfact that the sub-glacial ocean is assumed to be isothermal at a temperature that does not\nchange with time, there is essentially no alkalinity delivery to the ocean from continental\nweathering, continental shelf area for carbonate deposition is greatly reduced, and more.\nThe seafloor weathering parameterization we use is certainly sensitive to temperature and\npH, but when combined with these diUerences in the climate state that also impact\nseafloor weathering, it is diUicult to distinguish which ocean variable (T or pH) is more\nimportant, especially when considering temperature doesn’t change during the ice-\ncovered phase. Thus, a comparison to KT18 is not informative.\nAdditionally, the Le Hir et al. parameterization of seafloor weathering is based on\ntheoretical rate parameterizations and is inconsistent with recent experiments, so is\nentirely diUerent from our parameterization.\n270: One reviewer had an issue with the use of the Noonday Formation as it includes units\nother than the cap. This can be resolved by just referring here to the Sentinal Peak Member\nof the Noonday Formation, which as pointed out by Petterson does in fact form an ~100 m\nreef in some locations.\nWe have removed this sentence from the main text.\n277: And the fidelity of the palemagnetic data and their interpretations.\nCorrected in the main text.\n361: Why not use this for title?\nWe have elected to keep the title of the paper as is, for reasons described above.\nReviewer #3 (Remarks to the Author):\nThanks to the authors for revising the manuscript and taking the comments on board. I\nhave been unable to find enough time to do a thorough re-review due to field teaching\ncommitments, but I provide a few minor notes here for consideration please.\nOverall, I thank the authors for taking their work and consideration in addressing the\ncomments. I am happy with the revisions, and I think this will make a nice addition to the\nliterature to spur further discussion. Even though I do not agree totally with the\nmechanisms suggested for cap carbonate formation in the paper, I think that the carbon\ncycle model developed here is a good approach and is useful for future studies to build on.\nA few minor notes:\nSection Lines 285-312 on reconciling fast and slow depositional rates. This has some new\nadditions to the text based on the reviews. I do like the idea of this section, and I think\ncertainly there was a variation in precipitation rate through the caps as the authors suggest\n(peak precipitation close to the base and declining upwards). However, I don’t think you\ncan directly reconcile the sedimentary structures aspect of this new text, based on a\ndepositional rate. This is because in one scenario you are dealing with deposition of water-\ncolumn precipitates/sediment (wave ripples) and in the other (teepees) you are dealing\nwith in situ authigenic precipitation (not water column deposition). These processes would\nrespond diUerent to the evolving seawater chemistry as one is seafloor-immediate\nsubsurface. It’d suggest perhaps removing the emphasis on the sedimentary structures\naspect of this discussion in this regard, but using just the stratigraphy to present this idea.\n(As a practical note, perhaps the post-glacial cap-shale sequences are best at showing up\nthe timing and maximum of carbonate precipitation rather than the basins with ongoing\ncarbonates above the cap?)\nWe have elected to leave this section unchanged. In this paragraph we suggest how our\nmodel results may explain some of the sedimentary structures. This suggestion can be\nevaluated in future work with a greater focus on sedimentation and deposition. It is\npossible that this comment is correct and that the sedimentary structures are a\nconsequence of depositional style that is not included in our model. However, it is also\npossible that the style of deposition may have changed in response to ocean chemistry, or\nthat the interpretation of the sedimentary structures in general may change in the future.\nWe put forth this section in hopes that future work can address this problem quantitatively.\nFor the section on the diUerent theories for cap carbonate precipitation, an earlier\nreference for ‘sediment starvation’ models to cite too is either Kennedy, 1996 or Kennedy\nand Christie-Blick 2011.\nAdded in the main text.\nI think at this point I’d rather not include the pers. comm in Line 315 please, as it is a\nstudent project and we are still in the middle of the study. Thanks for your consideration of\nthis in the comments.\nWe have removed your personal communication and edited this section in accordance\nwith comments from Reviewer 1.\nAsh Hood, University of Melbourne"}]

Decision letter