Extremely cold ocean temperatures in iron formation brine pools of snowball Earth

Domain: earth_science
Published: 2025-12-09
Editorial outcome: major_revision

Abstract
For these severe low-latitude “snowball Earth” glaciations, glacial deposits occurring on all continents is well-established. However, cold, salty, ice-covered oceans—a salient prediction of snowball Earth—is difficult to establish geologically. Here we demonstrate that anomalously high iron isotope values (δ56Fe) of snowball iron formation—never observed in earlier anoxic Archaean oceans—can be attributed to additional temperature-dependent fractionation in extremely cold brine pools in the snowball ocean. Experiments and modeled fractionations relevant to the precipitation of iron formation demonstrate temperature-dependent δ56Fe fractionation, where colder temperatures correspond with more positive δ56Fe. Assuming the ~0.9‰ differential in δ56Fe values of snowball iron formation in excess of those preceding the Great Oxidation Event is due to temperature-dependent fractionation, we calculate that the temperature of the iron formation brine pools was –15 ± 7 °C. Such cold snowball brine pools, colder than those in Antarctic margins today, represent Earth’s coldest recorded ocean temperatures.

Introduction
In addition to palaeomagnetic support for glacial deposits at low latitudes, snowball Earth is supported by geological evidence including glaciomarine sedimentary features, characteristic “cap carbonates”, and the reprisal of widespread iron formation (IF) deposition since its disappearance in the Palaeoproterozoic Era1–4 (Fig. 1). These Cryogenian iron formations (CIF) are mineralogically simple (predominantly composed of laminated hematite) and interbedded with glaciomarine deposits5,6. The occurrence of CIF during the Sturtian glaciation (ca. 717–660 Ma), the first of the two Neoproterozoic snowball Earth events, is attributed to the buildup of hydrothermally-derived ferrous iron (Fe2+) while the sink for oxidation by oxygenic photosynthesis was cut off by the ice-covered ocean1,7. A combination of reduced dissolved sulfate in river water due to a weakened hydrological cycle8 and mid-ocean ridges under less pressure due to sea-level fall (favoring a hydrothermal Fe>S ratio9) would have also tipped the relative balance in favor of Fe over S in the snowball ocean. Cyclostratigraphy constrains the duration of CIF deposition (for at least one well-studied unit, the Holowilena IF) to have lasted ~4 million years6.

Iron isotope values (δ56Fe) of CIF have previously been exclusively interpreted in terms of redox variability5,10. According to this framework, the oxidation of Fe2+ can result in the precipitation of Fe(III) (hydr)oxides that are enriched in isotopically heavy iron, and smaller degrees of partial oxidation (due to lower O2 availability) along a distillation pathway produce more strongly positive δ56Fe values in sedimentary rocks11,12. Importantly, CIF δ56Fe values exhibit a wide range of variability only observed in IF deposited prior to the transition to an oxidizing atmosphere during the Great Oxidation Event (GOE) (Fig. 2), suggesting an important environmental perturbation. However, the fact that CIF δ56Fe values are anomalously positive even in comparison to IF preceding the GOE challenges the interpretation that the extreme fractionation can be attributed to redox conditions alone.

Results
Alternatives to redox fractionation
We consider several possible alternative explanations for redox. Given the large amount of time elapsed between the pre-GOE and Cryogenian intervals being compared, it is possible that a secular shift in the sources of Fe to the oceans between these two times could account for some or all of the 0.94‰ shift from pre-GOE IF to the values in CIF. Nonetheless, a secular trend analysis yields a line with essentially zero slope (Supplementary Fig. 1), allowing us to reject a change in Fe sources in the oceans to explain the Cryogenian anomaly. It is also worth considering if the unique circumstances of the Cryogenian led to an unusual input of isotopically heavy Fe to the oceans at that time. Glacial erosion13–15 presumably led to the mechanical breakdown and chemical dissolution of a continental crust that could have been covered by isotopically heavy Fe oxides produced by a billion years or more of chemical weathering under an at least mildly oxidizing atmosphere. Such a hypothesized biased detrital input, perhaps, could have led to an unusually heavy source of Fe to the oceans at this time. However, detailed geochemistry, rock magnetism, and petrology all consistently demonstrate that while there is a small detrital contribution from magnetite, the main source of Fe in CIF was mostly a hydrothermal-derived chemical precipitate preserved as authigenic hematite laths6,16,17.

Temperature-dependent iron isotope fractionation
In light of the uniquely positive CIF δ56Fe values that cannot be explained by redox nor other alternatives, we consider the temperature-dependent fractionation of δ56Fe associated with Fe (oxyhydr)oxide precipitation in cold, sub-ice shelf seawater. Arriving at a reliable fractionation factor is complicated by the possibility of kinetic isotope effects during Fe (oxyhydr)oxide precipitation, which will depend on a number of variables that control the rate and extent of Fe2+ oxidation, and are difficult to disentangle from equilibrium isotope fractionation in natural systems18. Thus, for the purposes of our study, we assume that any kinetic effects are either negligible or can be assumed to be constant across the record. Figure 3a shows theoretical calculated results of the isotopic Rayleigh fractionation relevant to the precipitation of IF (Methods). Based on the observed anomaly in excess of pre-GOE values (Fig. 2), an increase in δ56Fe value of +0.94‰ extrapolates to a temperature of –15.1±7°C (Fig. 3b; Methods for uncertainty estimate).

We first consider for comparison any other additional empirical constraints on snowball seawater temperature potentially available. Future work on CIF oxygen isotopes (δ18O) may provide an independent test, although the δ18O of hematite may be largely temperature-insensitive19 and subglacial meltwaters could have had very large δ18O heterogeneity. Cryogenian constraints from temperature-sensitive oxygen “clumped” isotopes are already available; although this method has typically only been used on relatively much younger, much better preserved carbonates, every effort has been made in the Cryogenian to carefully analyze only the most pristinely preserved carbonate successions. Although the absolute temperatures are uncertain in this case, the relative temperature difference between glacial and preglacial temperatures is determinable and is 26±10°C (ref. 20). Thus, if the temperature of the seawater during the Sturtian snowball was exactly –15°C as we have calculated, after adding the relative temperature difference 26°C to this, then the extrapolated pre-glacial temperature would have been 11°C. This estimate is actually quite close to the pre-glacial temperature of 9°C inferred from geological evidence in the form of the presence of temperature-sensitive ikaite21,22, where a cold climate before snowball is also corroborated by independent constraints23,24. Also, even if the ±10°C uncertainty of the aforementioned clumped isotopes constraint is considered20, along with the formation temperature of ikaite being ≤6°C, our reconstructed glacial seawater temperature would still range from –10°C to –30°C. This is consistent with our estimate of glacial seawater temperature derived from iron isotopes, which falls between –8°C and –22°C.

Methods
Data compilation
Iron isotope (δ56Fe) data from iron formation (IF) and ooidal ironstones were compiled from various data sources. Pre-1700 Ma δ56Fe data come from refs. 48,49. Those authors include anomalously positive δ56Fe from the ca. 3.46 Ga Marble Bar Chert of the Pilbara craton, originally interpreted as a primary signature indicative of a strongly anoxic Archaean ocean50. However, detailed petrography of the hematite-bearing chert has since revealed the presence of secondary hematite replacement, questioning the reliability of those data as a primary oceanographic signature51. Because of this complication, and because we only include bulk-rock δ56Fe data from iron-rich chemical sedimentary rocks (i.e., IF and ooidal ironstones) so as to compare similar datasets, the Marble Bar Chert data are excluded here. For comparison, δ56Fe data for ooidal ironstones at various ages between ca. 2 and 0.7 Ga from ref. 52 are also shown. Cryogenian iron formation (CIF) δ56Fe data were compiled for the Chuos Formation of Namibia5, the Fulu Formation45,53–56 and Xiafang Formation45 of South China, the Holowilena Ironstone of South Australia5,10, and the Kingston Peak Formation (Death Valley)57, the Rapitan Group (Northwest Territories, Canada)58, and the Tantonduk Iron Formation (Yukon–Alaska)10 of Laurentia.

Temperature and uncertainty estimation
δ56Fe isotope data are used to infer temperature ranges of the snowball ocean. Of the CIF δ56Fe data, those from the Fulu Fm are excluded due to the lack of direct evidence of glaciation and the suggestion that it occurs later in the Cryogenian than most CIF53. The 0.94‰ δ56Fe difference between the median δ56Fe values of pre-GOE IF and the CIF (excluding Fulu Fm) (Fig. 3; Supplementary Data 1) is taken as the magnitude of the temperature-dependent fractionation (assuming that positive anomalies below this Cryogenian-only threshold can be attributed to redox-sensitive fractionation related to anoxia). Median values are used given that both datasets being compared have heavy tailed distributions. As the δ56Fe difference between the two groups would be larger if means were used, this approach is also conservative. Including the Fulu Fm would only increase the δ56Fe difference (Supplementary Fig. 2), so its exclusion is the more conservative approach, in addition to the ambiguities surrounding its age and syn-glacial or interglacial association53.

The petrogenesis of IF follows a two-step pathway, i.e., the oxidation of aqueous Fe2+ to aqueous Fe3+ and precipitation of aqueous Fe3+ to Fe3+-(hydr)oxide45. Accordingly, the δ56Fe signature of IF involves a temperature-dependent equilibrium fractionation between aqueous Fe2+ and aqueous Fe3+ (refs. 59,60) and a subsequent kinetic fractionation during precipitation of aqueous Fe3+ to Fe (hydr)oxide11. The oxidation of aqueous Fe2+ to aqueous Fe3+ can reach isotopic equilibrium rapidly, resulting in enrichment of heavy iron isotope in aqueous Fe3+ (ref. 60). In the case of fast precipitation, the light iron isotope tend to be enriched in Fe3+-(hydr)oxides11. Collectively, the observed δ56Fe values of Fe (oxyhydr)oxides could be approximately considered to be controlled by the temperature-dependent equilibrium fractionation between aqueous Fe2+ and aqueous Fe3+, and the fraction of Fe(II) oxidation and precipitation rate. Currently, nothing is known about possible Fe(II)/Fe(III) mass balance differences between the pre-GOE and Cryogenian conditions, and is thus possibly worthy of investigative testing.

The equally large spread in δ56Fe values of both the pre-GOE IF (4.64‰) and CIF (4.49‰) can be well explained by the Rayleigh distillation model5,61 (Fig. 3a). The δ56Fe datasets with different aged intervals show distinct distributions (Supplementary Fig. 4). The dataset for the 3830–2310 Ma interval and CIF have the most similar frequency distributions and nearly identical δ56Fe ranges between minima and maxima (Fig. 3a; Supplementary Fig. 3). Although the petrogenesis of BIF is a two-stage process, assuming the precipitation rates at the time of IF in the two intervals (pre-GOE and Cryogenian) did not systematically differ, the systematic variation in Fe isotopes between these two intervals can be taken as to be derived mostly from temperature-dependent equilibrium fractionation. That is, the systematic increased δ56Fe values of the pre-GOE IF and CIF could mainly reflect the difference of temperature-dependent equilibrium between aqueous Fe2+ and aqueous Fe3+. Assuming that the ambient temperature at the time of the formation of the pre-GOE IF is 25°C (±10°C; ref. 52), the estimated temperature of the formation stage of the CIF is –15.1±7°C.

The largest source of uncertainty in our estimation is arguably the range of possible pre-GOE (largely Archaean) seawater temperatures that must be assumed for the relative temperature calculation. Recently, 18O/16O isotopes of marine carbonates and cherts have suggested a very hot Archaean ocean ranging from 50–85°C (ref. 62), or even hotter63. However, combined O and H isotopes suggest surface temperatures <40°C (ref. 64) and O isotopes of marine phosphates produce upper limits of only 26–35°C (ref. 65). Also, the repeated occurrence of glacial deposits at 3.5, 2.9, and 2.7 Ga are at odds with claims of a hot Archaean ocean and are more in line with the more temperature estimates66, leading to the range of 25°C (±10°C; ref. 52) we employ for our calculation.

If one were to include not only the uncertainty of the mean ocean temperature of the pre-GOE IF but also the uncertainties of both the large spread in δ56Fe values of the pre-GOE IF and CIF, then the resulting uncertainty is exceedingly large (>± 60°C), much of which is impossible parameter space for snowball exceeding freezing. However, based on both the similarity in their distributions (Supplementary Fig. 3) and the systematic increase in δ56Fe values of the pre-GOE IF and CIF (Fig. 2), we regard it reasonable to consider the error of the mean ocean temperature of the pre-GOE IF as the main source of uncertainty. Based on the theoretical equation of Fe isotopic fractionation in Fig. 3b, the uncertainty of the mean ocean temperature of the pre-GOE IF (±10°C) alone is thus propagated to derive the error of the estimated temperature of the formation stage of the CIF (±6.48°C).

Estimation of salinity
To estimate Sturtian salinity in this study, we utilized the Sr/Ba ratio of sediments, a newly developed geochemical indicator for evaluating palaeoceanographic salinity67. We find that the Sr/Ba ratios of syn-glacial CIF have spatially similar distribution characteristics to the modern ocean (Fig. 4), i.e., the Sr/Ba ratios are significantly lower in areas with strong nearshore freshwater influence (Fig. 4). This feature is clearly consistent with the glacial meltwater model of the CIF5, i.e., the median value of the Sr/Ba ratio is significantly lower at sites with low salinity where glacial meltwater input is high (ice-proximal) than at sites with low glacial meltwater input (ice-distal). Thus, the highest Sr/Ba value (6.2) in the CIF (Fig. 4) represents a Sr/Ba ratio that more closely represents marine sediments of this period. In contrast, modern marine sediments, which are less influenced by freshwater, have Sr/Ba ratios up to 1.4 (ref. 67) (Fig. 4).

It is unlikely that such a high Sr/Ba ratio in the CIF can be interpreted as a rapid expansion in the Sr reservoir due to weathering or hydrothermal sources of Sr, but is more likely to result from the thickening of sea ice during this period that led to the concentration of seawater. This also brought about a consequent increase in seawater salinity. Therefore, using the linear relationship that exists between Sr/Ba ratio and modern seawater salinity, we can estimate the degree of seawater concentration during the snowball Earth period, which gives us the approximate salinity (152 psu) of the seawater at that time.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "I feel that the authors have done a good job at addressing my concerns. Although I would have liked to see bit more details about how the surges of oxidized glacial meltwater worked, it is a fair point that this topic has already been covered by the co-authors elsewhere. Thus, I am happy to accept the manuscript.", "reviewer_2": "This ms presents a very interesting observation that Fe isotope compositions of the Cryogenian BIF are among the heaviest in Earth’s history. As isotope fractionation is negatively correlated with temperature in general, this observation would imply that the temperature for Cryogenic BIF is extremely low, and this is what are the authors meant. However, BIF precipitates from water, and the freezing point of water is almost constant. Therefore, the fundamental reasoning of the ms is wrong. thus rejection is strongly suggested.", "reviewer_3": "Reviewers’ comments for revised manuscript entitled: “Extremely cold ocean temperatures during snowball Earth” by Lu et al. This study describes the use of temperature-dependent iron isotope fractionation of Cryogenian iron formations (CIF) to propose that the temperature of the Snowball oceans was -15˚C +/- 7˚C, and that marine ice was correspondingly very thick. The application of temperature-dependent Fe fractionation to ocean temperature reconstructions is of interest, especially for time periods when many of the proxies available for more recent Earth history cannot be applied. At the request of the Editor, we focused on the uncertainty and plausibility of the revised manuscript’s temperature reconstruction, and the authors’ responses to previous reviewers’ remarks.\n\nWe disagree with the manuscript’s overall conclusion that the reconstructed ocean temperatures apply to the global Cryogenian ocean. We do not dispute the temperature reconstructions; rather, we find that the framing of the environmental context of these results, and the subsequent ramifications for global snowball conditions, are not adequately supported by the arguments given. The claims made in this manuscript would benefit from greater exposition, perhaps in another journal conducive to longer manuscripts as suggested by previous Reviewer #2.\n\nLine numbers refer to the revised manuscript with integrated edits.\nCIF depositional settings. The authors note briefly (in lines 202-204) that CIF are associated with semi-restricted basins that may not have had a substantial connection to the open snowball ocean. The reviewers feel that it is more likely that the reconstructed temperatures are in fact capturing conditions in restricted basins. Note that the Holowilena Formation is found within Sturtian-age rift basins of the Adelaide Superbasin (see e.g. authors’ Ref. 17; Lloyd et al., Geological Magazine (2023)), and Neoproterozoic IF in general are typically associated with rift settings (authors’ Ref. 13). The authors dismiss a scenario in which the waters of these basins may have become isolated from the global ocean by the overflow of land-based glaciers, leading to the significantly higher salinity suggested by the Sr/Ba data (authors’ Ref. 5). The authors deem the isolation of Holowilena unlikely owing to the presence of submarine ridge volcanism (authors’ Ref. 46). However, none of the large scale volcanic events examined in authors’ Ref. 46 are in the geographic vicinity of Holowilena deposition. Furthermore, the authors have not addressed the possibility that smaller-scale hydrothermal vents supplying Fe could have been active within these rift basins, as they are e.g. in the modern Red Sea (van der Zwan et al., Communications Earth & Environment (2023)). Considering this omission of a more in-depth discussion, we argue that the authors do not sufficiently support their assertion that their findings are representative of the global ocean.\n\nSea water temperatures. The authors argue (lines 116-124) that the difference between their calculated glacial sea water temperature of -15˚C and an extrapolated preglacial temperature of 11˚C is consistent with a relative temperature difference of 26˚C between preglacial and glacial temperatures reconstructed from clumped oxygen isotopes (authors’ Ref. 25), and consistent with a preglacial temperature of 9˚C from ikaite (authors’ Ref. 26, 27). The reviewers feel that this part of the discussion does not adequately consider the broader range of environmental interpretations possible when the 95% confidence limits of the current study (yielding a range of sea water temperatures of -22˚C to -8˚C) are taken into consideration. Several questions arise:\n• What is the basis for extrapolating a reconstructed preglacial temperature of 11˚C?\n• Mackey et al. (authors’ Ref. 25) concluded that “[m]ean glacial autochthonous dolomicrite Δ47 temperatures are 26 ± 10°C (95% CL) cooler than preglacial strata” and that “the preserved temperature and δ18O differences between low-latitude preglacial Tonian and synglacial Cryogenian dolomites are an imperfect reflection of primary temperature change and ice sheet expansion” owing to the influence of early diagenesis on preserved δ18O trends. Field et al (authors’ Ref. 27) notes that the 9˚C temperature associated with ikaite deposition is a maximum value, and has been more typically measured at <6˚C. What are the ramifications for the current study’s conclusions based on a reconstructed sea water temperature range of -15˚C ± 7˚C (the full range is important!) if the broader range of temperature constraints mentioned in Refs. 25-27 are taken into consideration?\n• The preglacial units cited in authors’ Refs. 25 and 26 are roughly contemporaneous in age and are both interpreted as low-latitude deposits, but their respective sea water temperature interpretations differ: Mackey et al. (authors’ Ref. 25) infer a warm preglacial period (approx. 30˚C warmer than “the glacial average,” which is not given a specific temperature range owing to inferred diagenetic effects), whereas Trower et al (authors’ Ref. 26) conclude that the preglacial interval was already cool leading into the Cryogenian (~9˚C). In order to best utilize these studies as supporting evidence for the current work, how would the authors reconcile these differences in interpretation?\n\nHigh salinity ramifications. The authors argue (lines 209-221) that a salinity of ~150 psu corresponding to sea water temperature of at least -11˚C (lines 143-147) and thicker sea ice (lines 193-194) implies a larger change in relative sea level than previously thought. If the global ocean had a salinity of ~150 psu, a simple back-of-the-envelope calculation suggests that would require a >75% reduction in volume compared to the modern ocean. Such a state should yield testable hypotheses regarding the large-scale erosion of continental margins and severe environmental impacts on life in the oceans at that time, and arguably, such impacts are at least as significant as an analytical finding of a sub-zero global ocean. However, the authors appear to reject significant glacial erosion for other reasons (lines 76-84), and do not address the significant challenges that high salinity would pose to life forms already impacted by extreme cold and (for photosynthetic organisms) limited light availability. The extent to which the current study’s extraordinary conclusions poses challenges to other lines of environmental interpretation should be presented in some greater detail, even if resolving any differences in interpretation are beyond the scope of the current manuscript.\n\nAdditional comments:\nLines 57-58: What are the bounds to a “wide range of variability” in del56Fe values as shown in Fig 1? While the range of values circa 2400 Ma is indeed broad (approx. 4.5 per mil), the time slice at ~700 Ma has roughly the same range (approx. 4.5 per mil), and the time slices at ~3000 Ma (range approx. 3.25 per mil) and ~1700 Ma (range approx. 2.9 per mil) are notably broader than the remaining ones shown.\nFig. 2: We are not convinced that the interpretation of this plot as indicating a lack of secular change in Fe sources to the oceans over 4000 Ma of Earth history is correct. The green line suggests a baseline del56Fe value of ~0.1 per mil, which appears a bit low given that the data points for many of the time slices skew more positively than this baseline value. It would be helpful to see the slope equation of the green line as well as a statistical analysis comparing the slope of the line to a line with slope = 0.\nLines 80-81: The statement, “However, firstly, the Fe isotopes of dissolved iron in modern East Antarctic glacial meltwater is strongly negative[16],” does not track as a rebuttal to the hypothesis that the unusually isotopically heavy Fe in CIF could have been the result glacial erosion. East Antarctica has a much different geologic history compared to the Cryogenian landscape, and therefore the negative Fe isotopes of Taylor Glacier’s subglacial waters, as described in authors’ Ref. 16, are likely not an appropriate contrast to the Cryogenian results.\nFig. 3a: The scale of the y axis of this figure makes interpreting the differences between the preGOE and Cryogenian distributions difficult. It would be helpful to include a simple statistical statement in the caption to assure readers that the difference is significant.\nLines 136-137: The authors argue that “strong support for a salinity-controlled freezing point comes from extremely cold temperatures of -13˚C recorded in analogous Antarctic brines (Ref. 31).” The geographic context of this -13˚C temperature (authors’ Ref. 31) is a buried Antarctic lake -- Lake Vida with salinity of 200 psu. The reviewers would argue that, from the standpoint of salinity and sea water temperature, citing Lake Vida as an analogous environment is supporting evidence for the CIF depositional settings as restricted basins, with no relation to global ocean conditions.\nFigure 4: The presentation of salinity in the plot would benefit from a second y axis indicating salinity as a psu value, for ease of comparison to the text discussion of salinity in terms of psu.\nLines 194-195: The manuscript cites Tziperman et al [Ref. 40] as an example of a global circulation model that predicted the Snowball global ocean was covered with ~1-km-thick sea ice, and the authors suggest this may represent an underestimate given the reconstructed sea water temperatures of this study. However, Tziperman et al. utilized a two-dimensional global ice flow model that assumes at the outset that sea ice must be very thick, and Tziperman et al. concede that their model “ignores many known important factors such as thermodynamic, optical effects, dust and dust transport, and is therefore meant as a process study focusing on one specific effect, rather than a realistic simulation of Neoproterozoic ice thickness.” To date, these reviewers are not aware of any three-dimensional global climate model -- which incorporates all aspects of Earth’s climate system (not just sea ice) -- that has developed ~1 km-thick sea ice as an emergent response to snowball-type climate forcings. Note e.g. that Liu et al (authors’ Ref. 52) do not indicate more than ~20-26 m total sea ice thickness for Snowball Earth climate simulations using the CCSM3 global climate model (their Figs. 6, 13a and A2).\nSupplementary Fig. 3: It seems as if the signs of the x axis are reversed. In figure 1 of the paper, the Cryogenian samples have a positive skew, but in this figure they have a negative skew.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Response: We greatly appreciate the reviewer’s repeated consideration of our manuscript and their positive assessment of it this last round.\nRevision: To address the reviewer’s additional request, and in light of comments by new Reviewers 3/4, we added a new final figure that should also help elucidate the meltwater discharge model that Reviewer #1 also hoped to see more detail on. Details provided later below.\nResponse: The statement that “the freezing pint of water is almost constant” is incorrect with regards to basic thermodynamics. Salinity can significantly reduce freezing point. As we have not only demonstrated temperature-dependent fractionation suggesting very negative ocean temperatures, but also demonstrated strongly elevated salinity that such a cold freezing temperature would require, our two findings are internally consistent, not to mention consistent with one might expect in a Cryogenian iron formation brine pool (see revisions based on Reviewers 3/4 below).\nRevision: We thank Reviewers 3/4 for helping us realize—actually in line with much of the past work of some of our co-authors—that the CIF d56Fe temperature and salinity estimates are not representative of the global ocean, but rather a globally distributed CIF depositional setting, including the following criteria:\n(i) Near ice grounding line\n(ii) Restriction\n(iii) Brine pools\nThis critical revision greatly increases the specificity and certainty of our result, and provides an internally consistent result for both the extreme cold and extreme salinity of the CIF during snowball Earth. Thus, our method+result remained unchanged, but the context has modified the implications, which still offer critical insights into glaciomarine settings distributed globally during snowball Earth and the unique reprisal of iron formation. Here are some of the revisions that have been made to address this major revision:\n(i) The title has been modified (bold) to “Extremely cold ocean temperatures in iron formation brine pools of snowball Earth”\n(ii) Both the Abstract setup and finish have been modified (bold):\nSetup: “However, cold, salty, ice-covered oceans—a salient prediction of snowball Earth—is difficult to establish geologically.”\nFinish: “…we calculate that the temperature of the iron formation brine pools was –15 ± 7˚C. Such cold snowball brine pools, colder than those in Antarctic margins today, represent Earth’s coldest recorded ocean temperatures.”\n(iii) A new Figure 1 now shows an updated paleogeographic reconstruction showing the globally distributed occurrences of CIF, underlying that while our result is not emblematic of the global ocean, it represents a globally significant depositional setting during the snowball Earth, with implications for potential refugia for the survival of life during extreme glaciation.\n(iv) The Discussion has essentially been nearly entirely rewritten to accommodate this slight, but not subtle, shift in the scope of our interpretation of the d56Fe-based T estimate.\n(v) Previous Figure 5—comparison with oxygen-isotope-based surface T estimates—which was only referred to in one sentence in the text, and not commented on by Reviewers 3/4, was removed. It did not contribute too much additional support and, since adding a new final figure on brines and a CIF brine production model for snowball, we thought it would be better not to distract from the main message.\n(vi) Instead, a new final figure (Fig. 6) has been added that drives home the new take-home message that the d56Fe-based T estimate of seawater relates to iron formation brine pools. Figure 6a compares the snowball T estimates and modern ones from Antarctic brines. Figure6b provides a geologic model for how such cold, salty snowball brines might have been developed in Cryogenian iron formation depositional settings.\nWe cannot thank the reviewers enough for being firm on what our result does and doesn’t mean. We hope you agree that the substantially revised, and much more focused manuscript still provides an innovative geochemical method and a geologically important result for better understanding the severe conditions of Cryogenian climate as viewed through its unique iron formation.\nResponse: We believe this is already explained quite clearly in the main text:\n“Although the absolute temperatures are uncertain in this case, the relative temperature difference between glacial and preglacial temperatures is determinable and is 26 ˚C (Mackey+20_AGUAdv1). Thus, if the temperature of the seawater during the Sturtian snowball was exactly –15 ˚C as we have calculated, then the extrapolated pre-glacial temperature would have been 11 ˚C…”\n–15˚C + 26˚C = 11˚C\nRevision: The text has nonetheless been slightly modified to make this even more clear. A since-published study corroborating, independently of ikaite, a cold climate before snowball (Trower+25_GEO2) has also been added.\nResponse: Clumped isotope thermometry faces significant challenges in reconstructing original water temperatures during carbonate deposition due to pervasive diagenetic alteration. However, the paleogeographic context provides a critical constraint: both Svalbard and Death Valley occupied proximal low-latitude positions before, during, and after the Sturtian glaciation. Leveraging this spatial and temporal coherence, we utilize two key parameters:\n(1) A documented 26°C temperature difference between these coeval sites under a shared thermal history (McKay+23_AGUAdv1), and\n(2) The presence of pre-glacial ikaite. This mineral's stability constrains maximum water temperatures in these low-latitude regions to ≤9°C, with typical conditions below 6°C (Field+17_MinMag3).\nIntegrating these constraints permits estimation of glacial carbonate deposition temperatures. Calculations suggest values as low as -17°C, potentially reaching -20°C. Notably, this estimated range (-17°C to -20°C) falls within the independently derived low-latitude aquatic temperature envelope of -8°C to -22°C established through our iron isotope proxy.\nRevision: We thank Reviewers 3/4 again for pointing out that the depositional context of CIF is not only important for interpreting their extremely cold temperatures, but also their extremely high salinity. That is, modifying the interpretation from the global ocean to the globally distributed CIF ice-grounding line brine pools resolves the certainty and nuance of our result. Please note that the Discussion has essentially been nearly entirely rewritten to accommodate this slight, but not subtle, shift in the scope of our interpretation of the d56Fe-based T estimate. Specifically here, too, we appreciated the point about the implied reduction in ocean volume that provides an important prediction to consider—which we have incorporated essentially verbatim, thanks. We also have addressed how modern analogs for CIF of sub-ice shelf Antarctic brines help understand the severe cold and salinity, as well as not precluding such a setting as a refugium for at least microbial life during severe snowball conditions. Thanks for all of the suggestions, most of which have been incorporated in the revision.\nResponse: With all due respect to the reviewers, we stand by this sentence as written. Perhaps the reviewers misread it, as the CIF interval is to ~700 Ma timescale; and this sentence is pointing out exactly what the reviewers noted: the comparable large variability of the ca. 2400 and 700 Ma time slices. (Meanwhile, the variability at 1700 Ma is not nearly as large and relies on only 3 [arguably outlier] data, unlike the aforementioned time slices.)\nResponse: While we appreciate the suggestion to compare this line with free slope to a line with slope = 0, we have already done so, and double-checked again, and the two lines are visually indistinguishable from each other.\nResponse: Furthermore, to make this point more quantitatively clear, we have added the miniscule slope of the free-slope line to the figure caption, which is m = 5 x 10-14, or effectively zero. Nonetheless, in light of the reviewers saying not finding this figure terribly convincing for the point it is used to make, we have opted to move it back into the supplementary information (from whence it came)—also, since we have added two new figures to address other more salient points.\nRevision: Although we may disagree that Taylor glacier is not a bad analog for Cryogenian, since we already have another line of argument here, we have just removed this disputed one.\nResponse: Excellent suggestion. The following has been added to the figure caption:\n“A Mood test for equal medians yields a p value of 8.5 x 10-9, which is <<<0.05, indicating that the null hypothesis can be rejected and that the two medians are strongly statistically distinct.”\nResponse: Many thanks, again, for making this point because it has pushed us to critically revise the context and main implication of our method+result, shifting from our previous argument of the “global ocean” to now the “globally distributed CIF snowball brine pools.” As detailed elsewere, this revision is expressed throughout the revised manuscript in a multitude of edits that improve its accuracy and therefore also its certainty. Please note that the Discussion has essentially been nearly entirely rewritten to accommodate this slight, but not subtle, shift in the scope of our interpretation of the d56Fe-based T estimate.\nResponse: While we appreciate the suggestion, and would enact it if we could, there is no direct conversion available for converting Sr/Ba ratio proxy to salinity (psu units). This nonetheless do not detract from our ability to compare the ~4 times difference in Sr/Ba CIF ratios with those in the modern ocean to yield at least a broad estimate of CIF brine pool salinity.\nRevision: But, yes, this section on salinity has been clearly revised in order to focus on CIF brine pools during snowball and not the global snowball ocean.\nRevision: We appreciate the reviewers’ knowledge of snowball sea-ice thickness models. As the focus of this paper—thanks to your insightful feedback—has been redirected away from “global ocean” implications, such text has been altogether removed or revised with these comments in mind. Please note that the Discussion has essentially been nearly entirely rewritten to accommodate this slight, but not subtle, shift in the scope of our interpretation of the d56Fe-based T estimate.\nRevision: Hawkeye. Thanks for the attention to detail. Indeed, the signs of the x-axis were reversed and have been corrected.\nResponse: We commend both Nature Communications for such a wise program and you (and your mentor) for encouraging the art of (helpful!) critical peer review early on."}, {"round": 2, "reviewer_comments": {"reviewer_3": "Reviewers’ comments on second revision of manuscript now entitled: “Extremely cold ocean temperatures in iron formation brine pools of snowball Earth” by Lu et al. The authors have made extensive revisions in response to previous comments, and the latest revision of this manuscript presents a more defensible interpretation of their temperature-independent iron isotope results. However, we do have some additional comments.\n\nLine numbers refer to the second revised manuscript with integrated edits.\nSea water temperatures. The authors have added (lines 159-166) some additional text and a new reference to expand upon the point previously made, about the consistency between Mackey et al.’s (authors’ ref. 26) preglacial and glacial temperature difference in relative terms, and a preglacial and glacial temperature difference based on the author’s reconstruction and a formation temperature of 9˚C of ikaite. While this clarifying language and the new reference are welcome, the authors did not quite address our previous comment suggesting that the full range of possible interpretations need to be addressed. To be more explicit:\nLine 161 mentions that the relative temperature difference identified by Mackey et al. is 26˚C (no ± error stated). However, Mackey et al. described this difference as 26˚C ± 10˚C. Given that the typical formation temperature of ikaite in nature is <6˚C (authors’ ref. 28), the authors’ analogy holds best as long as Mackey et al.’s relative temperature difference falls somewhere between 16 and 21˚C (to accommodate a ≤6˚C formation temperature of ikaite) and the authors’ reconstructed temperature lies between -22˚C and -10˚C.\nWe suggest, in the interest of full transparency, that the Mackey et al. error bounds are made explicit in the discussion. This would not detract from the authors’ argument, and could in fact be of interest as an additional constraint to Mackey et al.\n\nSea ice thickness. The authors state that increasing δ56Fe isotopes upsection provides “strong support for a ‘hard’ snowball Earth” (line 322), and that the general occurrence of CIF at low latitudes is consistent with “their isotopic signature of thick sea ice” (line 324) that is “incompatible with ‘slushball’ or ‘waterbelt’ solutions involving open ocean in equatorial regions with high sublimation” (lines 325-326). Given that “CIF are generally thought to have been deposited in semi-restricted basins” (lines 225-226), and the δ56Fe isotopes are a proposed proxy for sea water temperature and not sea ice thickness, we find that these closing lines make broad statements about the temperature and sea ice cover of the tropical ocean away from continental margins that are not supported by the information provided in the current study. We contend that the use of “strong” and “incompatible” are not appropriate terms considering the limited scope of the evidence provided. We suggest the use of less definitive language. In our opinion the evidence i) “provides support for a ‘hard’ snowball Earth” and ii) is unable to address the presence (or absence) of a ‘slushball’ or ‘waterbelt’.\n\nAdditional comments:\nFig. 5: Typo in the figure labeling, should read “-9˚C, McMurdo brines”\nFig 5 caption: The authors refer to a contrast between the reconstructed temperatures of the current study and an ambient snowball ocean temperature of -5.5˚C, authors’ ref. 51 (lines 264-265). Since ref. 51 is not yet publicly available, it is unclear what the source of the -5.5˚C value is, and whether that refers to an average temperature of the entire global ocean or just some portion of it (e.g., upper ocean). Further information is necessary to evaluate this statement.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Revision: Excellent suggestion. We will incorporate the error (±10°C) you mentioned. Furthermore, if we take this error into account, along with the formation temperature of ikaite being ≤6˚C, our reconstructed glacial seawater temperature would still range from –10˚C to –30˚C. This is consistent with our estimate of glacial seawater temperature derived from iron isotopes, which falls between –8°C and –22°C. This qualification has been added to the revised text.\nRevision: Fair point. Point taken, and excellent suggestion for revision. The final two lines of the manuscript have been revised accordingly:\n“Increasing magnetic susceptibility associated with an increasing abundance of hematite that corresponds closely with increasing 56Fe values upsection1 can therefore be attributed with colder temperatures of glacial advance. This collective observation provides support for a “hard” snowball Earth, where oxidation for CIF deposition only occurred from surges of oxidized continental-derived meltwater2, but is unable to address the presence (or absence) of a “soft” snowball or ‘waterbelt’3,4.”\nRevision: Good eye. Fixed.\nRevision: Good point and smart request. Both points of information are now provided in this addition to the caption, as well as an additional reference that is key to the Hoffman textbook calculation:\n“Estimate for global snowball ocean is based on slight pressure-based freezing-point depression from the overlying sea glacier, under a range of salinities and water depths (or equivalent ice thicknesses)5,6.”"}]

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