The evolution of Earth’s surficial Mg cycle over the past 2 billion years

Abstract

The surficial cycling of Mg is coupled with the global carbon cycle, a predominant control of Earth’s climate. However, how Earth’s surficial Mg cycle evolved with time has been elusive. Magnesium isotope signatures of seawater (δ²⁶Mg_sw) track the surficial Mg cycle, which could provide crucial information on the carbon cycle in Earth’s history. Here, we present a reconstruction of δ²⁶Mg_sw evolution over the past 2 billion years using marine halite fluid inclusions and sedimentary dolostones. The data show that δ²⁶Mg_sw decreased, with fluctuations, by about 1.4‰ from the Paleoproterozoic to the present time. Mass balance calculations based on this δ²⁶Mg_sw record reveal a long-term decline in net dolostone burial (NDB) over the past 2 billion years, due to the decrease in dolomitization in the oceans and the increase in dolostone weathering on the continents. This underlines a previously underappreciated connection between the weathering-burial cycle of dolostone and the Earth’s climate on geologic timescales.

A long Mg isotopic record of seawater reveals the link between weathering and burial of dolostones and Earth’s climate.

INTRODUCTION

Key external forcings of Earth’s climate, including solar luminosity, mantle outgassing intensity, and the composition and exposure of crustal rocks, have changed remarkably and irreversibly over geological time (1). Despite that, the Earth’s surficial temperature has remained within the habitable range for most of its history, which is believed to be regulated by atmospheric CO₂ levels through negative feedback in the carbonate-silicate cycles (2, 3). However, the exact mechanisms remain highly debated; some invoke weathering of silicates on continents (3, 4), whereas others emphasize reverse weathering on seafloors (5, 6). Addressing such problems requires the acquisition and interpretation of various secular records of different key elements for surficial processes both on land and in the oceans.

The surficial Mg cycle is interconnected by various processes, including continental weathering, high- and low-temperature alteration of oceanic crust, and formation of carbonates and clays on the seafloor. Through these interactions, the Mg cycle closely interacts with the geochemical cycles of carbon, calcium, and silicon (7–9). Despite its relevance to Earth’s habitability, quantitative studies of ancient surficial Mg cycles are challenging, particularly for the Precambrian periods (10). Previous attempts to reconstruct Mg cycles based on the compiled volume of sedimentary dolostones over geologic time (9) were hampered by the uneven preservation of carbonate rocks deposited in different environments and incomplete data for compilation, which worsened markedly for older records (11). Another record of Mg cycling is the Mg concentration in ancient seawater, recovered from fluid inclusions in halite (12), although the data are mainly restricted to the Phanerozoic Eon.

Magnesium isotopes are an effective tracer for surficial Mg cycles. Magnesium in the oceans is supplied from the weathering of silicates and Mg-bearing carbonates (mainly dolomite), which have a large difference in Mg isotope ratios [expressed in delta notation: δ²⁶Mg = (R_sample/R_standard − 1) × 1000, R = ²⁶Mg/²⁴Mg, the standard is DSM3]. The majority of igneous silicate rocks have similar δ²⁶Mg values that cluster around −0.25 ± 0.07‰, whereas carbonates have much lower values of δ²⁶Mg, commonly between −1 and −5‰ dependent on mineralogy, temperature, and precipitation kinetics (13). Thus, changes in the relative contribution of carbonate to silicate sources could lead to different Mg isotope compositions of Mg input into the oceans (14). Mg is removed from seawater via the formation of Mg-bearing carbonates and Mg-bearing silicates. Precipitation of dolomite and magnesian calcite [distinguished as high-Mg calcite and low-Mg calcite at a composition above and below 4 mol % MgCO₃ (15)] at ambient temperatures is associated with a fractionation factor (Δ²⁶Mg_min-aq = δ²⁶Mg_mineral − δ²⁶Mg_aqueous) of ~−2‰ or lower (16, 17), whereas uptake of aqueous Mg into silicates is generally associated with positive to zero Δ²⁶Mg_min-aq fractionation, depending on reaction temperature and mineralogy (13, 14). Consequently, a change in the relative contribution of the carbonate Mg sink relative to the silicate sink would also change the isotopic ratio of seawater Mg (8, 16). Therefore, Mg isotopes in seawater respond to changes in the balance between silicates and carbonates of the surficial Mg cycles, on both the source and sink sides. The geologic record of seawater δ²⁶Mg can thus be used to interrogate the long-term global carbonate-silicate cycles.

Several studies reconstructed the Mg isotope composition of seawater during the Cenozoic using biogenic calcite or aragonite (8, 18). Calcite and aragonite, however, are susceptible to diagenesis, thus their fidelity as Mg isotope archives for older geological times may require additional constraints (such as Ca isotopes) for verification (19). In contrast, Mg isotopes in dolomite have proven to be resistant to various postdepositional overprinting processes (20, 21). Dolostones are abundant in ancient marine sedimentary sequences, and the Mg isotope fractionation between dolomite and aqueous solution is well-constrained (16, 17). These features provide an opportunity to reconstruct the Mg isotope composition of ancient seawater. An alternative seawater Mg isotope archive is marine halite. Bedded halite from marine evaporites contains primary fluid inclusions, which preserve the Mg isotope composition of contemporaneous seawater (22). The advantage of halite is that seawater δ²⁶Mg values can be directly measured from fluid inclusions without the application of Mg isotope fractionation factors, because the precipitation of halite from evaporating seawater occurs before the precipitation of Mg-bearing evaporite minerals (22). Both the dolomite and halite records have certain limitations as seawater δ²⁶Mg archives, thus data screening is necessary. In practice, however, as shown in the following sections, the two records complement each other and place strong constraints on seawater δ²⁶Mg.

In this study, we use Mg isotopes measured in marine dolostone and halite to generate a record of Mg isotope composition of seawater (δ²⁶Mg_sw) for the past 2 billion years. We compile a comprehensive Mg isotope dataset for marine sedimentary dolomite over the past 2 billion years, including 1809 analyses from 58 lithostratigraphic units reported in the literature and 425 additional analyses from 25 lithostratigraphic units in this study (Supplementary Materials, tables S1 and S2, and fig. S1). For the Phanerozoic, 103 marine halite samples from 37 lithostratigraphic units are also compiled, including 84 additional analyses from 29 lithostratigraphic units (Supplementary Materials and table S3). Halite samples are carefully selected based on geological and textural criteria to ensure that the fluid inclusions are primary and contain evaporated seawater (Supplementary Materials and fig. S2). In addition, only halites with ⁸⁷Sr/⁸⁶Sr ratios consistent with coeval seawater are included (Supplementary Materials and fig. S3). Non-seawater ⁸⁷Sr/⁸⁶Sr ratios in halite indicate notable contributions of non-marine waters to the enclosed evaporite basin, which could alter the seawater Mg isotope composition of the brine.

RESULTS

Seawater Mg isotope composition in the past 2 billion years

Marine dolostone samples show large variations in δ²⁶Mg values (−3.02 to −0.47‰) over the past 2 billion years (Fig. 1, A and B). However, histograms of data for six major geological time brackets show continuous decreases in the median, average, and overall range of dolostone δ²⁶Mg values through the Paleoproterozoic, Mesoproterozoic, Neoproterozoic, Paleozoic, Mesozoic, and Cenozoic (Fig. 1C). The Mg isotope variability of dolostones within a sedimentary unit mainly stemmed from the dolomitization processes (23, 24). Isotopic evolution of Mg in dolomitization fluids can occur along a diffusion/advection profile on a scale of meters to hundreds of meters (17, 25, 26) or across a carbonate platform on a scale of hundreds of kilometers (Supplementary Materials and figs. S4 and S5) or even within an enclosed basin on the continental scale (19, 27). Nonetheless, dolomitization invariably removes light Mg isotopes from the fluid, elevating the δ²⁶Mg value of the remaining fluid and the δ²⁶Mg values of dolomite precipitated from that fluid (23, 24). Therefore, δ²⁶Mg values of marine dolostones tend to be higher than the seawater-equilibrated δ²⁶Mg value, and the lowest δ²⁶Mg values of syn-depositional dolostones have the greatest possibility of approaching the seawater-equilibrated δ²⁶Mg values (19, 28).

Fig. 1. Summary of Mg isotope data from sedimentary archives.

(A) Mg isotope data from Phanerozoic dolostone and halite. Blue diamonds denote additional data for dolostones in this study, and open diamonds denote published data for dolostones. Red-filled circles denote additional data for halite in this study, and yellow-filled circles are published halite Mg isotope data. Dashed blue and red lines denote the reconstructed δ²⁶Mg_sw curves based on dolostones and halites, respectively. The dotted gray line shows the lower contour for the dolostone records. (B) Mg isotope records from dolostone and halite over the past 2 billion years. Legends are the same as in plot (A). (C) Histogram of δ²⁶Mg for dolostone over six geologic time intervals of the past 2 billion years.

To establish a curve of δ²⁶Mg_sw through time, a contour is extended between the lowest δ²⁶Mg values (hinge points) of the dolomite dataset in each time slice. We then apply a + 2‰ offset (i.e., the Mg isotope fractionation factor between dolomite and seawater) to the contour (Fig. 1). Data points that are abruptly higher than the neighboring hinge points may be caused by basin restriction effects. Such points are excluded because abrupt changes in δ²⁶Mg_sw are unlikely considering the long residence time of Mg in the oceans (i.e., ~10 million years presently). Small sample sets with n < 10 are not used to define the contour because they may not be representative of that period. The goal is to reconstruct long-term variations of δ²⁶Mg_sw but not sub-million-year scale perturbations of δ²⁶Mg_sw. The n = 10 threshold also ensures that the majority (i.e., > 50%) of our subdatasets of dolostones can be used for establishing the δ²⁶Mg_sw record for the past 2 billion years (fig. S6B).

A second seawater Mg isotope archive, fluid inclusions in marine halite, is available for the Phanerozoic. Marine halites also exhibit variability in δ²⁶Mg values (−1.97 to 0.06‰; Fig. 1, A and B). This is because the bulk dissolution of halite is used for Mg isotope analysis of fluid inclusions. Measured δ²⁶Mg values are therefore complicated by possible soluble Mg-bearing evaporite mineral inclusions. For example, for the Late Miocene halite from Egypt, the measured δ²⁶Mg values vary from −1.63 to −0.78‰. These samples show a negative correlation between bulk Mg and K concentrations and δ²⁶Mg values (Supplementary Materials and fig. S7), indicating mixing of fluid inclusions and ²⁴Mg-enriched mineral inclusions. Detailed scanning electron microscopy (SEM) imaging confirms that polyhalite occurs in some halite samples (Supplementary Materials and fig. S8). Polyhalite is known to be enriched in light Mg isotopes (22). Note that although the entrapment of polyhalite could lower the measured δ²⁶Mg of bulk halite, this cannot alter the Mg isotope composition of evolved seawater during earlier stages of halite precipitation and brine evaporation, as has been quantified by thermodynamic simulation and isotope mass balance calculations (Supplementary Materials and fig. S9). To summarize, the δ²⁶Mg value measured from marine halite could be lower than contemporaneous seawater, and the highest δ²⁶Mg values from marine halite of a particular age can be used to define the lower boundary of the δ²⁶Mg_sw curve.

The dolomite-based δ²⁶Mg_sw curve is consistent with the upper contour of the halite-based δ²⁶Mg_sw curve within 0.2‰ for the Phanerozoic Eon (Fig. 1A). This consistency is crucial because marine dolostone and halite are totally independent seawater Mg isotope archives, and they are complementary as the dolomite-based δ²⁶Mg_sw value could be higher than the actual δ²⁶Mg_sw, whereas the halite-based δ²⁶Mg_sw could be lower than the actual δ²⁶Mg_sw. The reconstructed δ²⁶Mg_sw is around −0.8‰ in the Cenozoic, consistent with previous studies (8, 18). The δ²⁶Mg_sw increases with increasing age in the Mesozoic and reaches the peak Phanerozoic value, −0.3‰, around the Permian-Triassic boundary. The δ²⁶Mg_sw decreases to ~−0.7‰ during the Carboniferous and increases with age to ~−0.2‰ in the Cambrian.

The dolomite-based δ²⁶Mg_sw curve shows pronounced fluctuations in the Neoproterozoic that coincide with extreme climatic events such as the freezing and melting of Snowball Earth (29). The hinge points for the δ²⁶Mg_sw curve are sparser in the Proterozoic, particularly before 800 Ma, but they reveal an increasing trend of δ²⁶Mg_sw with increasing age, from −0.2 ± 0.2‰ during the Neoproterozoic, to 0 ± 0.2‰ during the Mesoproterozoic, to ≥ +0.5‰ in the early Paleoproterozoic (Fig. 1B). Considering that Earth was in the “Boring Billion” period between 800 and 1800 Ma marked by the lack of large sediment C isotope excursions (30) and orogenic quiescence (31), no marked perturbations in the surficial Mg cycle are expected to occur during this period. If so, the Monte Carlo modeling results show that the number of hinge points (n = 7) is sufficient to capture the trend of the δ²⁶Mg_sw curve during the Mesoproterozoic and early Paleoproterozoic (fig. S10). Additional Mg isotope data in the future will further refine the δ²⁶Mg_sw curve for the Proterozoic.

Overall, by combining two large Mg isotope datasets of dolomite and halite, we show that the Mg isotope composition of seawater changed notably during the past 2 billion years. The δ²⁶Mg_sw decreased from >+0.5‰ in the early Paleoproterozoic to a modern value of −0.8‰, with fluctuations during the Neoproterozoic and Paleozoic-Mesozoic transition. The present δ²⁶Mg_sw curve has limited temporal resolution (Fig. 1, A and B), and it is possible that finer-scale fluctuations in δ²⁶Mg_sw could be revealed with more data. Such refinement, however, is unlikely to change the overall statistical pattern of decreasing dolostone δ²⁶Mg in successively younger geological ages (Fig. 1C). The first-order observation, that the δ²⁶Mg_sw decreased by ~1.4‰ in the past 2 billion years, underlines fundamental changes in Earth’s surficial Mg cycles with time.

Secular changes in surficial Mg cycles constrained from δ²⁶Mg_sw

On the basis of the δ²⁶Mg_sw record, we next quantify how the surficial Mg cycle evolved over the past 2 billion years with a mass balance model. As described in the introductory paragraphs, the surficial Mg cycle is controlled by carbonate and silicate weathering expressed as riverine input to the ocean (14) and Mg removal as either carbonate minerals via dolomitization or silicate minerals through marine clay formation and alteration of oceanic crust (9, 14, 32). Note that when carbonate burial exceeds carbonate weathering, the excess carbonate burial would consume the alkalinity generated by silicate weathering and consequently remove CO₂ from the Earth’s surface (3, 4). Therefore, the imbalances between weathering and burial of Mg carbonates could induce net surficial carbon fluxes that might affect the Earth’s climate system. Thus, our model is particularly focused on calculating variations in the imbalances between Mg carbonate weathering and burial.

The mathematical framework of the model is based on elemental and isotopic mass balance equations, an approach that has proven effective for studies of elements with long-residence times in seawater (8, 33, 34)

$$F_{\text{carb-in}}+F_{\text{sili-in}}=F_{\text{carb-out}}+F_{\text{sili-out}}$$ (1)

$${\mathrm{\delta }}_{\text{carb-in}}{F}_{\text{carb-in}}+{\mathrm{\delta }}_{\text{sili-in}}{F}_{\text{sili-in}}={\mathrm{\delta }}_{\text{carb-out}}{F}_{\text{carb-out}}+{\mathrm{\delta }}_{\text{sili-out}}{F}_{\text{sili-out}}$$ (2)

where F and δ represent the fluxes and isotopic compositions of Mg for the silicates (subscript: _sili) and carbonates (subscript: _carb) as influx (subscript: _-in) and outflux (subscript: _-out).

The above equations can be solved using a stochastic modeling approach. In the modeling, all the possible values for each F and δ parameter in the above equations are searched and tested by the Monte Carlo method. The fraction of each individual flux relative to the total Mg flux is first allowed to vary between 0 and 1 in the model calculation. For Mg isotope compositions of the influxes and outfluxes of carbonates (δ_carb-in and δ_carb-out) and silicates (δ_sili-in and δ_sili-out), estimates with realistic 2 sigma (95% confidence level) uncertainties under normal distribution are ascribed. Specifically, we note that the Mg isotope compositions of the outfluxes are controlled by the Mg isotope composition of seawater and the Mg isotope fractionation factors associated with carbonate precipitation and secondary silicate formation (i.e., δ_carb-out = δ_sw − Δ_carb-sw, δ_sili-out = δ_sw − Δ_sili-sw). δ_sw is reconstructed in this study, whereas Δ_carb-sw and Δ_sili-sw factors are provided in the literature. Details of the parameter settings for the mass balance equations and Monte Carlo modeling algorithms are provided in Materials and Methods and the Supplementary Materials.

We first numerically solve the elemental and isotopic mass balance equations for the modern Mg cycle (δ²⁶Mg_sw = −0.8‰). Infinite solutions of Mg influx and Mg outflux values for silicates and Mg carbonates (predominantly dolostones) exist (red dots in Fig. 2). However, these solutions define a broad linear trend in a cross plot of F_carb-in/F_Total-in versus F_carb-out/F_Total-out for each given δ²⁶Mg_sw value, regardless of the freedom in flux values (Fig. 2). In reality, F_carb-in/F_Total-in should have a much more restricted range. The contribution of silicate weathering to riverine input of Mg was estimated in several studies, which yielded a range of 0.41 to 0.52 (see Materials and Methods). When we further take the contribution of submarine weathering of silicates into consideration, the actual F_carb-in/F_total-in ratio for modern seawater is estimated to be 0.42 ± 0.08 (2σ). The Monte Carlo calculation results for such a distribution of F_carb-in/F_Total-in are shown by colored red contours in Fig. 2, and the corresponding F_carb-out/F_total-out is constrained to be 0.39 ± 0.26 (2σ, red histogram on the right side of Fig. 2), which agrees with the modern F_carb-out/F_total-out (0.27 to 0.52) estimated recently (35).

Fig. 2. Monte Carlo modeling results for global Mg cycles in the modern and the Paleoproterozoic.

Red and blue dots represent solutions of elemental and isotopic mass balance equations for a δ²⁶Mg_sw value of −0.8‰ (i.e., modern seawater) and + 0.6‰ (i.e., Paleoproterozoic seawater), respectively. For these solutions, F_carb-in/F_Total-in is allowed to vary between 0 and 1. However, in reality, F_carb-in/F_Total-in should have a limited range. A more realistic range of F_carb-in/F_Total-in is further defined by a normal distribution, and the corresponding F_carb-out/F_Total-out could be calculated accordingly (for details, see Materials and Methods). These refined ranges are shown as graded color contours in the main plots and histograms on the side plots. The red and blue circles are the average values of recalculated F_carb-in/F_Total-in and F_carb-out/F_Total-out ratios in the modern and Paleoproterozoic, respectively.

The same Monte Carlo method is applied to Paleoproterozoic seawater that has a δ²⁶Mg_sw value of 0.6‰; the numerical solutions are shown as blue dots in Fig. 2. The modeling results predominantly plot above the 1:1 line and show that F_carb-out/F_total-out was markedly greater than F_carb-in/F_total-in in seawater at 2000 Ma. This means that in the Paleoproterozoic, dolostone burial was higher than dolostone weathering flux. To quantify this imbalance in Mg surficial cycling, we define a parameter, Net Dolostone Burial (NDB), that represents the difference between the proportion of Mg removed by dolostone formation in total Mg outflux and the proportion of Mg supplied by dolostone weathering in total Mg influx (i.e., NDB = F_carb-out/F_total-out − F_carb-in/F_total-in). On the basis of the modeling results shown in Fig. 2, the NDB is estimated at 0.66 ± 0.19 (2σ). By contrast, modern oceans are in an approximate balance between F_carb-out/F_total-out and F_carb-in/F_total-in, with NDB ranging from −0.16 to 0.09, as the data points in the contoured area are close to the 1:1 line on Fig. 2. This implies that the modern global Mg cycle is near neutral in dolostone weathering and burial cycles, considering the uncertainty in the models. Therefore, the large difference between δ²⁶Mg_sw at 2 Ga and the modern δ²⁶Mg_sw shows that Earth’s surficial Mg cycles varied substantially over geological time.

To quantitatively understand how Earth’s surficial Mg cycles evolved through time, we extend the elemental and isotopic mass balance equations to the 2-billion-year record of δ²⁶Mg_sw from this study. For the Monte Carlo calculation, we assume that F_carb-in/F_total-in increased from 0.14 ± 0.04 at 2 Ga to 0.42 ± 0.04 at present or that F_carb-in/F_total-in could be any value between 0 and 1 and calculated the NDB over the past 2 billion years based on the δ²⁶Mg_sw curve using the abovementioned Monte Carlo method. The results not only confirm the decrease in NDB in the Mg cycle over the past 2 billion years but further imply that the decrease is not steady and monotonic (Fig. 3). A notable feature of the NDB trend is the large fluctuation between 330 and 250 Ma. The recognition of such fluctuation is due to higher data density during the Phanerozoic (Fig. 3B). The pattern of the average values of NDB through time is markedly similar to the δ²⁶Mg_sw curve, although the magnitude of the decline in NDB is smaller than that of δ²⁶Mg_sw. That is because the lowering of δ²⁶Mg_sw is produced by changes in NDB and by decreasing δ²⁶Mg of weathered dolostones, which confirms the sensitivity of Mg isotopes in seawater as a tracer of surficial Mg cycles.

Fig. 3. Monte Carlo modeling results quantitatively reveal how Earth’s surficial Mg cycles evolved through time.

Evolution of NDB (A) and data density (B) over the past 2 billion years (NDB = F_carb-out/F_total-out − F_carb-in/F_total-in). The black line is the average of Monte Carlo simulation results, and the yellow dashed lines denote the 1sd range of the simulation results.

DISCUSSION

In the classic view of the silicate-carbonate cycle, if carbonate burial exceeds carbonate weathering, then the excess carbonate burial consumes the alkalinity generated by silicate weathering and consequently removes CO₂ from the Earth’s surface (Eq. 3) (3).

$${\text{MgSiO}}_3+{\text{CO}}_2\to {\text{MgCO}}_3+{\text{SiO}}_2$$ (3)

In light of this, secular changes in NDB for the Earth’s surficial Mg cycles have a direct impact on CO₂ removal. An NDB of 0.66 ± 0.19 (2σ) at 2 billion years ago means that, for every 1 mol of Mg cycled on the Paleoproterozoic Earth’s surface, 0.66 ± 0.19 (2σ) mol of CO₂ was removed from the atmosphere by the imbalance between dolostone weathering and burial. In contrast, because the NDB at present is close to zero, the weathering and burial of Mg-bearing carbonates is balanced. Note that an NDB of zero does not mean that the surficial Mg cycles sequester zero CO₂ from the atmosphere. This is because hydrothermal alteration at mid-ocean ridges results in the removal of seawater Mg²⁺ and the release of Ca²⁺ from the basalts (3, 36), and precipitation of the excess Ca²⁺ from hydrothermal fluids as carbonates removes CO₂. The hydrothermal Mg flux is estimated to be up to 3.1 Tmol/year in the modern oceans, accounting for up to 56% of the total Mg outflux (8, 35). Therefore, presently, the Earth’s removal of CO₂ in the surficial Mg cycle is predominantly operated via an indirect route, i.e., through Mg-Ca exchange and subsequent CaCO₃ precipitation in the oceans. In contrast, direct dolostone precipitation was a major factor in CO₂ removal for Earth’s Mg surficial cycles at 2.0 Ga based on NBD. Therefore, the long-term interplay between Earth’s surficial Mg cycles and carbon cycles has evolved over the past 2 billion years.

Studies of the thermal history of Earth’s mantle suggest that volcanic degassing declined by twofold from 2000 to 500 Ma (37), while our modeling shows that the NDB decreased by a factor of three over the same period (Fig. 4A). This correlation suggests a possible link between NDB and Earth’s CO₂ cycles. In light of this, we further explore the response of the NDB to Earth’s climate during the Phanerozoic, when Earth’s climatic history is relatively well-reconstructed (38). As shown in Fig. 4B, in the past 500 Ma, there is a broad positive correlation between NDB and average global temperature. The two correlations in Fig. 4 suggest that NDB responded to, and/or participated in, the regulation of Earth’s climate over geological time. Considering the coupling of the Mg and C cycles, as illustrated in Eq. 3, it is possible that NBD has functioned as a geological thermostat.

Fig. 4. The linkages between Earth’s surficial Mg cycles and C cycles and climate.

(A) Correlation between relative volcanic degassing rate from 500 to 2000 Ma (37) and NDB. (B) Correlation between Phanerozoic global average temperature (38) and NDB. Modeling results are given for periods with measured dolostone δ²⁶Mg.

Phanerozoic global environmental records are compiled in Fig. 5 to explore the NDB geo-thermostat. The NDB curve shows broad correlations (or anticorrelations) with records of continental glaciation, global sea level, and average global surface temperature over the Phanerozoic. When Earth was in ice-house climate states (i.e., low-latitude glaciation, low sea level, and low average temperature), lower sea levels led to the exposure of carbonate platforms which increased carbonate weathering. Since dolomite precipitation is suppressed at lower temperatures (39), less Mg was removed by dolomitization in seawater during ice-house climates. These two processes produced the decrease in NDB (i.e., lower F_carb-out/F_total-out but higher F_carb-in/F_total-in), which prevented a further decline in atmospheric CO₂ (Fig. 5) and created effective negative feedback to low atmospheric CO₂ levels and low surficial temperatures.

Fig. 5. Comparison of Earth’s surficial Mg cycles with other global environmental records.

Temporal variations in NDB over the Phanerozoic compared to temporal variations in atmospheric CO₂ concentration (78, 79), average global temperature (38), relative sea-level (80), and paleo-latitude of continental glaciation (81).

The dolostone weathering-and-burial cycle is not the only component of the Earth’s surficial Mg cycle. Another component of the Earth’s surficial Mg cycle that has climatic consequences is the Mg-Ca exchange at the mid-ocean ridges with subsequent CaCO₃ precipitation (3, 36). In addition, the surficial Ca cycle via Ca-silicate weathering and subsequent Ca carbonate burial is critical in balancing Earth’s carbon cycle (40). Quantification of the complete surficial Ca cycle in geological history is beyond the scope of this Mg isotope investigation. Nonetheless, the 1:1 molar ratio of Mg:Ca in dolomite stoichiometry means that the changes in NDB reconstructed in this study can be used to understand the portion of the Ca cycle involved in dolomite weathering and burial. Other parts of the surficial Ca cycle, such as limestone weathering and burial, are out of the reach of Mg isotope tracers. However, 60 to 80% of carbonate was buried as dolostone during the Proterozoic (41, 42). For comparison, the fraction of dolostone burial to the total carbonate burial fluctuated markedly between 2 and 90% in the Phanerozoic, with an estimated bulk average of 30 to 50% (43–45). Therefore, sedimentary records also show that the relative influence of the Mg cycle (compared with the Ca cycle) on atmospheric CO₂ was stronger in the Proterozoic than the Phanerozoic, which is also in accordance with the NDB trend based on Mg isotopes.

Clay formation in marine sediments or “reverse weathering” (46, 47) has been proposed as a geological thermostat (47–49). It should be noted, however, that such a thermostat mainly functioned during the Precambrian, because the rise of marine siliceous organisms resulted in low Si concentrations in the Phanerozoic oceans (50) that suppressed the reverse weathering thermostat (47). A recent study suggested that high dissolved Si is favorable for dolomite formation (51). Thus, the higher Si content in Precambrian oceans (50) may have contributed to the higher proportion of dolostones in Proterozoic carbonate sediments compared to Phanerozoic carbonates. A holistic understanding of the secular evolution of the Earth’s atmospheric CO₂ requires quantitative constraints on the surficial cycles of Mg, Ca, and Si. The calculated NDB in the past 2 billion years in this study represents one further step in understanding Earth’s long-term surficial cycles.

MATERIALS AND METHODS

Analytical methods

This study performs Mg isotope analysis on halite and dolostone samples. X-ray diffraction analysis of bulk dolostone powder helps screen dolomite-dominated samples for Mg isotope analysis. SEM–energy-dispersive x-ray spectroscopy (EDS) analysis of halite samples is used to identify trace amounts of Mg-bearing evaporite minerals. Sr isotope analysis of halite provides an effective way to identify non-marine signals. All analyses are done at facilities at the State Key Laboratory of Mineral Deposit Research, Nanjing University, China.

Sample preparation

Halite samples are first cleaned by wiping with lint-free paper towels (Kimwipes); about 1- to 2-g sample is scraped off by a tungsten carbide scraper and subsequently ultrasonically cleaned in anhydrous ethanol (>99.7%) for 5 min. After the sample is cleaned and dried, it is dissolved in 12 ml of deionized water (18.2 megohm cm) as a stock solution (22, 52). The dolostone samples are ground into 200 mesh in a precleaned agate mortar. About 10 mg of powder is weighed and dissolved in 5 ml of 1.5 M HAC (CH₃COOH) in a Teflon beaker. Then, the dolostone sample solution is placed on a hotplate (96°C) for about 12 hours for digestion.

Mineral analyses

The mineralogy of the dolostone samples is determined by a Rigaku RAPID II or a Bruker D8 Advance x-ray diffractometer. The Rigaku RAPID II instrument operates at 50 kV and 90 mA on a rotating Mo anode x-ray source; the Bruker D8 Advance instrument runs at 40 kV and 40 mA with a Cu anode x-ray source. X-ray diffraction data processing and mineral identification are performed using Jade 6.5 software. The relative abundance of dolomite (104), calcite (104), and quartz (101) is estimated from the area of characteristic diffraction peaks (53). Textural analysis of the halite samples is performed on a Hitachi SU1510 Variable Pressure SEM, and the chemical compositions are characterized using EDS equipped with SEM.

Element analyses

A small fraction of the stock solution from the halite and dolostone samples is extracted and diluted to 4 ml in 2% double-distilled HNO₃. The concentrations of elements (such as Mg, Ca, and Sr) are measured using the inductively coupled plasma optical emission spectrometer (ICP-OES; Skyray ICP-3000). Calibration curves for a series of gravimetrically prepared commercially available multi-element standards with linear correlation coefficients (R²) are better than 0.999. A 1 parts per million (ppm) multi-element standard is bracketed every 10 samples to monitor and correct the instrument drift. The long-term external accuracy (2RSD, two times relative standard deviation) of elemental analysis is better than 10% (22, 52).

Isotope analyses

Mg isotope analyses

On the basis of the stock solution concentration measured by ICP-OES, an aliquot of the sample containing approximately 20 μg of Mg is used for Mg isotope analysis. To remove sodium, the halite sample is pre-enriched in Mg by precipitation of Mg(OH)₂ before undergoing the ion-exchange procedures (22). Halite and dolostone samples are further purified by cationic resin (AG50W-X12 and X8) together; see (21) for the process. After column chemistry treatments, Mg recovery is better than 95%, and the total matrix elements are less than 1% of Mg.

Mg isotopes are measured on a Thermo Fisher Scientific NEPTUNE Plus multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS) or a Nu 1700 Sapphire MC-ICP-MS. Both instruments operate on a standard low resolution, wet plasma mode. The sample solution is introduced at an uptake rate of 100 μl/min. The method of standard-sample-standard bracketing is used to correct the instrumental drift and mass bias. Each Mg isotope ratio measurement consists of 50 cycles of 4-s integrations. Two pure Mg stock solutions [HPS909104: produced by High Purity Standards Company; A-Mg: prepared by dissolution guaranteed reagent Mg(NO₃)₂ solid] serve as in-house bracketing Mg standards. Although there is a difference in the on-machine concentration of pure Mg between the two instruments (Nu 1700: 0.5 ppm; Neptune: 1 ppm), the sample concentration is required to match the standard (the difference less than 10%) in the respective analysis processes. Moreover, the δ²⁶Mg value of the in-house bracketing Mg standards [δ²⁶Mg_HPS909104 = −0.67 ± 0.13‰, n = 47, (54); δ²⁶Mg_A-Mg = −3.25 ± 0.06‰, n = 107] relative to international standard DSM3 is well-calibrated. Analytical accuracy is monitored by international Mg isotope standards DSM3 and Cambridge1. The International Association for the Physical Sciences of the Oceans (IAPSO) seawater and United States Geological Survey (USGS) rock (DTS-2) standards are processed along with samples to verify the accuracy of chemical procedures. The measured δ²⁶Mg values of the standards (table S4) match the published values (13, 54), and the long-term external analytical precision was better than ±0.1‰.

Sr isotope analyses

An aliquot of the halite stock solution containing approximately 500 ng Sr is extracted for Sr isotope analyses. The Sr-spec resin is used to purify the sample (55). The sample is loaded in 3 N HNO₃, and Sr is collected with 0.05 N HNO₃. The USGS rock (AGV-2) and IAPSO seawater standards are treated as unknown samples to monitor the analysis procedure. Strontium isotope analysis is performed using a Finnigan Triton thermal ionization mass spectrometer. At the beginning of every analytical sequence, the international standard NIST 987 (⁸⁷Sr/⁸⁶Sr = 0.710228 ± 0.000033, 2σ = 100) is measured to verify the instrument status. With exponential law, the Sr isotope data are normalized to ⁸⁶Sr/⁸⁸Sr = 0.1194. All the measured ⁸⁷Sr/⁸⁶Sr ratios of standards (table S4) are consistent with published values (21, 52, 56).

Isotopic mass balance model based on a Monte Carlo approach

The model framework

The primary sources of Mg in the ocean include silicate weathering and carbonate weathering. The major outputs are dolomitization, low-temperature and high-temperature alteration of basalt, and authigenic clay formation (8). For simplification, we use a single symbol sil-out to represent all the processes that uptake Mg from seawater into silicate minerals, including low-temperature and high-temperature alteration of basalt and authigenic clay formation. Similarly, carb-out, carb-in, and sil-in represent dolomitization, carbonate weathering, and silicate weathering, respectively. By assuming that the Mg cycle is at steady state [a treatment that has been universally applied in relevant studies for Li (33, 57), Mg (8, 35, 58), K (59, 60), Mo (61–63), and U (64–67)], we have

$$F_{\text{carb-in}}+F_{\text{sili-in}}=F_{\text{carb-out}}+F_{\text{sili-out}}$$ (4)

$${\mathrm{\delta }}_{\text{carb-in}}{F}_{\text{carb-in}}+{\mathrm{\delta }}_{\text{sili-in}}{F}_{\text{sili-in}}={\mathrm{\delta }}_{\text{carb-out}}{F}_{\text{carb-out}}+{\mathrm{\delta }}_{\text{sili-out}}{F}_{\text{sili-out}}$$ (5)

where F represents the Mg fluxes and δ stands for isotopic compositions of the Mg flux for the major components that participate in the Mg cycle.

Then, for ease of programming, we divide the two sides of the equation by the total flux that goes into the ocean (i.e., F_carb-in + F_sili-in) and let f_carb-in represent the fraction of the Mg flux derived from carbonate weathering in the total Mg input flux, and f_carb-out stands for the fraction of Mg in seawater deposited as carbonates. The two equations can be simplified to

$$\begin{array}{c}{\mathrm{\delta }}_{\text{carb-in}}{f}_{\text{carb-in}}+{\mathrm{\delta }}_{\text{sili-in}}(1-f_{\text{carb-in}})=\\ {\mathrm{\delta }}_{\text{carb-out}}{f}_{\text{carb-out}}+{\mathrm{\delta }}_{\text{sili-out}}(1-f_{\text{carb-out}})\end{array}$$ (6)

Here, δ_carb-out and δ_sili-out are functions of the Mg isotopic composition of seawater (δ_sw)

$${\mathrm{\delta }}_{\text{carb-out}}={\mathrm{\delta }}_{\text{sw}}+{\mathrm{\Delta }}_{\text{carb-out}}$$ (7)

$${\mathrm{\delta }}_{\text{sili-out}}={\mathrm{\delta }}_{\text{sw}}+{\mathrm{\Delta }}_{\text{sil-out}}$$ (8)

With Eqs. 6 to 8, we built a model that calculates how the Mg cycle evolves with the record of the Mg isotopic composition of seawater.

Model parameters

In this section, we describe how we quantify the model parameters. Considering that Mg, sourced from carbonate weathering (F_carb-in), is dominated by dolomite (68), and in the long-run, dolomite weathering is congruent, δ_carb-in is set to be the weighted average of δ²⁶Mg of the previously deposited dolostones, which are compiled in Fig. 1 of the main text. The fraction of dolostone that remains on the continent (R) is estimated from a time-dependent decay function following (11)

$$R=e^{-0.001T}$$ (9)

Here, T (in Ma) is the time elapsed since the deposition of dolostone. The δ²⁶Mg of the dolostone is calculated from the Mg isotopic composition of seawater by assuming a fractionation factor of −1.5 ± 0.2‰ (1 SD). Then, δ_carb-in is determined as the R-weighted average of δ²⁶Mg of the weathered dolostones; calculation results are shown in fig. S11A. Considering that silicate weathering is associated with clay formation that generally enriches heavy Mg isotopes, δ_sili-in is assumed to be close to, but slightly lighter than, the δ²⁶Mg of the bulk silicate earth (13), with a value of −0.4 ± 0.1 ‰ (1 SD). For the calculation of δ_carb-out with Eq. 7, Δ_carb-out is estimated to be ~−1.5‰ with 1 SD of 0.2‰ (16). The fractionation involved in the alteration of seafloor basalt and formation of authigenic marine clays varies substantially, ranging from 0 to 1.6‰ (17, 35). To cover this range and account for uncertainty, we assume that Δ_sil-out is 0.8 ± 0.4‰ (1 SD).

The quantification of f_carb-in is more complicated. In the modern world, estimates of the fraction of Mg flux derived from silicate weathering vary considerably, ranging from 0.48 to 0.59 (8, 40, 68, 69). Accordingly, f_carb-in ranges from 0.41 to 0.52. Another factor that affects the quantification of f_carb-in is marine silicate weathering, which has drawn increasing attention recently (70–72). On the basis of a methane generation estimate ranging from 7 to 300 × 10¹² mol/year (73, 74), Wallmann et al. (72) estimated that the CO₂ consumption rate by marine silicate weathering is 5 to 20 × 10¹² mol/year. Using an updated methane generation flux of ∼1.2 × 10¹² mol/year (75), the estimate of marine silicate weathering is revised to 1 to 4 × 10¹² mol/year (71). The latter is close to the estimate of 1× 10¹²mol/year by (76) based on the global authigenic Ca carbonate flux. Therefore, in this study, we use 1 to 4 × 10¹² mol/year as the best estimate of the global marine silicate weathering rate, which is 8.5 to 34.1% of the subaerial silicate weathering rate (77). Assuming silicate weathering follows the same stoichiometries in both terrestrial and marine environments, f_carb-in ranges from 0.34 to 0.50 if we consider the marine silicate weathering flux. In other words, a f_carb-in value of 0.42 ± 0.04 (1 SD) is used for the modern.

During Earth’s history earlier than 3 Ga, f_carb-in is assumed to be 0 because carbonates cannot be exposed to weathering without tectonic uplift (73, 74). For any time between 0 and 3 Ga, we assume that f_carb-in increased from 0 to the modern value, with an SD of 0.1. In other words, if t represents age (in Ma), we have

$$f_{\text{carb-in}}=0.42–0.42*t/3000$$

The curve of f_carb-in is presented in fig. S11B. For δ_sw at a specific time, we estimate the δ_sw value with linear interpolation, assuming that the δ_sw record has a 1 SD uncertainty of 0.1 (fig. S11C).

Supplementary Materials

This PDF file includes:

Supplementary Text

Figs. S1 to S15

Tables S1 to S4

Legends for data files S1 and S2

Other Supplementary Material for this manuscript includes the following:

Data files S1 and S2

Auxiliary References