Constraining the climate and ocean pH of the early Earth with a geological carbon cycle model

Significance

The climate and ocean pH of the early Earth are important for understanding the origin and early evolution of life. However, estimates of early climate range from below freezing to over 70 °C, and ocean pH estimates span from strongly acidic to alkaline. To better constrain environmental conditions, we applied a self-consistent geological carbon cycle model to the last 4 billion years. The model predicts a temperate (0–50 °C) climate and circumneutral ocean pH throughout the Precambrian due to stabilizing feedbacks from continental and seafloor weathering. These environmental conditions under which life emerged and diversified were akin to the modern Earth. Similar stabilizing feedbacks on climate and ocean pH may operate on earthlike exoplanets, implying life elsewhere could emerge in comparable environments.

Abstract

The early Earth’s environment is controversial. Climatic estimates range from hot to glacial, and inferred marine pH spans strongly alkaline to acidic. Better understanding of early climate and ocean chemistry would improve our knowledge of the origin of life and its coevolution with the environment. Here, we use a geological carbon cycle model with ocean chemistry to calculate self-consistent histories of climate and ocean pH. Our carbon cycle model includes an empirically justified temperature and pH dependence of seafloor weathering, allowing the relative importance of continental and seafloor weathering to be evaluated. We find that the Archean climate was likely temperate (0–50 °C) due to the combined negative feedbacks of continental and seafloor weathering. Ocean pH evolves monotonically from ${6.6}_{-0.4}^{+0.6}$ (2σ) at 4.0 Ga to ${7.0}_{-0.5}^{+0.7}$ (2σ) at the Archean–Proterozoic boundary, and to ${7.9}_{-0.2}^{+0.1}$ (2σ) at the Proterozoic–Phanerozoic boundary. This evolution is driven by the secular decline of pCO₂, which in turn is a consequence of increasing solar luminosity, but is moderated by carbonate alkalinity delivered from continental and seafloor weathering. Archean seafloor weathering may have been a comparable carbon sink to continental weathering, but is less dominant than previously assumed, and would not have induced global glaciation. We show how these conclusions are robust to a wide range of scenarios for continental growth, internal heat flow evolution and outgassing history, greenhouse gas abundances, and changes in the biotic enhancement of weathering.

Constraining the climate and ocean chemistry of the early Earth is crucial for understanding the emergence of life, the subsequent coevolution of life and the environment, and as a point of reference for evaluating the habitability of terrestrial exoplanets. However, the surface temperature of the early Earth is debated. Oxygen isotopes in chert have low δ¹⁸O values in the Archean (1). If this isotope record reflects the temperature-dependent equilibrium fractionation of ¹⁸O and ¹⁶O between silica and seawater, then this would imply mean surface temperatures around 70 ± 15 °C at 3.3 Ga (2). A hot early Earth is also supported by possible evidence for a low viscosity Archean ocean (3), and the thermostability of reconstructed ancestral proteins (4), including those purportedly reflective of Archean photic zone temperatures (5). Silicon isotopes in cherts have also been interpreted to infer 60–80 °C Archean seawater temperatures (6).

Alternatively, the trend in δ¹⁸O over Earth history has been interpreted as a change in the oxygen isotope composition of seawater (7), or hydrothermal alteration of the seafloor (8). Isotopic analyses using deuterium (9) and phosphates (10) report Archean surface temperatures <40 °C. Archean glacial deposits (ref. 11 and references therein) also suggest an early Earth with ice caps, or at least transient cool periods. A geological carbon cycle model of Sleep and Zahnle (12) predicts Archean and Hadean temperatures below 0 °C due to efficient seafloor weathering. An analysis combining general circulation model (GCM) outputs with a carbon cycle model predicts more moderate temperatures at 3.8 Ga (13). Resolving these conflicting interpretations would provide a better understanding of the conditions for the origin and early evolution of life.

Ocean pH is another important environmental parameter because it partitions carbon between the atmosphere and ocean and is thus linked to climate. Additionally, many biosynthetic pathways hypothesized to be important for the origin of life are strongly pH dependent (14–16), and so constraining the pH of the early ocean would inform their viability. Furthermore, bacterial biomineralization is favorable at higher environmental pH values because this allows cells to more easily attract cations through deprotonation (17). Arguably, low environmental pH values would be an obstacle to the evolution of advanced life due to biomineralization inhibition (18). Finally, many pO₂ proxies are pH dependent (19–21), and so understanding the history of pH would enable better quantification of the history of pO₂.

However, just as with climate, debate surrounds empirical constraints on Archean ocean pH. Empirical constraints are scant and conflicting. Based on the scarcity of gypsum pseudomorphs before 1.8 Ga, Grotzinger and Kasting (22) argued that the Archean ocean pH was likely between 5.7 and 8.6. However, others note the presence of Archean gypsum as early as 3.5 Ga (23); its scarcity could be explained by low sulfate (24). Blättler et al. (24) interpreted Archean Ca isotopes to reflect high Ca/alkalinity ratios, which in turn would rule out high pH and high pCO₂ values. Friend et al. (25) argued for qualitatively circumneutral to weakly alkaline Archean ocean pH based on rare Earth element anomalies.

Theoretical arguments for the evolution of ocean pH also disagree. By analogy with modern alkaline lakes, Kempe and Degens (26) argued for a pH 9–11 “soda ocean” on the early Earth, but mass balance challenges such an idea (27). Additionally, high pH oceans (>9.0) would shift the NH₃–NH₄⁺ aqueous equilibrium toward NH₃, which would volatilize and fractionate nitrogen isotopes in a way that is not observed in marine sediments (28). The conventional view of the evolution of ocean pH is that the secular decline of pCO₂ over Earth history has driven an increase in ocean pH from acidic to modern slightly alkaline. For example, Halevy and Bachan (29) modeled ocean chemistry over Earth history with prescribed pCO₂ and climate histories, and reported a monotonic pH evolution broadly consistent with this view. However, it has also been argued that seafloor weathering buffered ocean pH to near-modern values throughout Earth history (12).

On long timescales, both climate and ocean pH are controlled by the geological carbon cycle. The conventional view of the carbon cycle is that carbon outgassing into the atmosphere–ocean system is balanced by continental silicate weathering and subsequent marine carbonate formation (30, 31). The weathering of silicates is temperature and pCO₂ dependent, which provides a natural thermostat to buffer climate against changes in stellar luminosity and outgassing. This mechanism is widely believed to explain the relative stability of Earth’s climate despite a ∼30% increase in solar luminosity since 4.0 Ga (31).

A possible complimentary negative feedback to continental weathering is provided by seafloor weathering. Such weathering occurs when the seawater circulating in off-axis hydrothermal systems reacts with the surrounding basalt and releases cations, which then precipitate as carbonates in the pore space (32, 33). If the rate of basalt dissolution and pore-space carbonate precipitation depends on the carbon content of the atmosphere–ocean system via pCO₂, temperature, or pH, then seafloor weathering could provide an additional negative feedback (12).

The existence of a negative feedback to balance the carbon cycle on million-year timescales is undisputed. Without it, atmospheric CO₂ would be depleted, leading to a runaway icehouse, or would accumulate to excessive levels (34). However, the relative importance of continental and seafloor weathering in providing this negative feedback, and the overall effectiveness of these climate-stabilizing and pH-buffering feedbacks on the early Earth are unknown.

In this study, we apply a geological carbon cycle model with ocean chemistry to the entirety of Earth history. The inclusion of ocean carbon chemistry enables us to model the evolution of ocean pH and realistically capture the pH-dependent and temperature-dependent kinetics of seafloor weathering. This is a significant improvement on previous geological carbon cycle models (e.g., refs. 12 and 35) that omit ocean chemistry and instead adopt an arbitrary power-law dependence on pCO₂ for seafloor weathering which, as we show, overestimates CO₂ drawdown on the early Earth. By coupling seafloor weathering to Earth’s climate and the geological carbon cycle, we calculate self-consistent histories of Earth’s climate and pH evolution, and evaluate the relative importance of continental and seafloor weathering through time. The pH evolution we calculate is therefore more robust than that of Halevy and Bachan (29) because, unlike their model, we do not prescribe pCO₂ and temperature histories.

Our approach remains agnostic on unresolved issues, such as the history of continental growth, internal heat flow, and the biological enhancement of weathering, because we include a broad range of values for these parameters. Our conclusions are therefore robust to uncertainties in Earth system evolution. We find that a hot early Earth is very unlikely, and pH should, on average, have monotonically increased since 4.0 Ga, buffered somewhat by continental and seafloor weathering.

Methods

The geological carbon cycle model builds on that described in Krissansen-Totton and Catling (36). Here, we summarize its key features, and additional details are provided in the SI Appendix. The Python source code is available on GitHub at github.com/joshuakt/early-earth-carbon-cycle.

We model the time evolution of the carbon cycle using two separate boxes representing the atmosphere–ocean system and the pore space in the seafloor (Fig. 1 and SI Appendix A). We track carbon and carbonate alkalinity fluxes into and between these boxes, and assume that the bulk ocean is in equilibrium with the atmosphere.

Fig. 1.

Schematic of carbon cycle model used in this study. Carbon fluxes (Tmol C y⁻¹) are denoted by solid green arrows, and alkalinity fluxes (Tmol eq y⁻¹) are denoted by red dashed arrows. The fluxes into/out of the atmosphere–ocean system are outgassing, $F_{\text{out}}$, silicate weathering, $F_{\text{sil}}$, carbonate weathering, $F_{\text{carb}}$, and marine carbonate precipitation, $P_{\text{ocean}}$. The fluxes into/out of the pore space are basalt dissolution, $F_{\text{diss}}$, and pore-space carbonate precipitation, $P_{\text{pore}}$. Alkalinity fluxes are multiplied by 2 because the uptake or release of one mole of carbon as carbonate is balanced by a cation with a 2+ charge (typically Ca²⁺). A constant mixing flux, $J$ (kg y⁻¹), exchanges carbon and alkalinity between the atmosphere–ocean system and pore space.

Many of the parameters in our model are uncertain, and so we adopt a range of values (SI Appendix, Table S1) based on spread in the literature rather than point estimates. Each parameter range was sampled uniformly, and the forward model was run 10,000 times to build distributions for model outputs such as pCO₂, pH, and temperature. Model outputs are compared with proxy data for pCO₂, temperature, and carbonate precipitation (SI Appendix D).

Continental silicate weathering is described by the following function:

$$F_{\text{sil}}=f_{bio}{f}_{\mathrm{land}}{F}_{\text{sil}}^{\mathrm{mod}}{\left(\frac{{\text{pCO}}_2}{{\text{pCO}}_2^{\mathrm{mod}}}\right)}^{\alpha }\exp \left(\mathrm{\Delta }{T}_{\text{S}}/T_e\right)$$ [1]

Here, $f_{\text{bio}}$ is the biological enhancement of weathering (see below), $f_{\text{land}}$ is the continental land fraction relative to modern, $F_{\text{sil}}^{\mathrm{mod}}$ is the modern continental silicate weathering flux (Tmol y⁻¹), $\mathrm{\Delta }{T}_{\text{S}}=T_{\text{S}}-T_{\text{S}}^{\mathrm{mod}}$ is the difference in global mean surface temperature, $T_{\text{S}}$, relative to preindustrial modern, $T_{\text{S}}^{\mathrm{mod}}$. The exponent $\alpha$ is an empirical constant that determines the dependence of weathering on the partial pressure of carbon dioxide relative to modern, ${\text{pCO}}_2/{\text{pCO}}_2^{\mathrm{mod}}$. An e-folding temperature, $T_e$, defines the temperature dependence of weathering. A similar expression for carbonate weathering is described in SI Appendix A.

The land fraction, $f_{\text{land}}$, and biological modifier, $f_{bio}$, account for the growth of continents and the biological enhancement of continental weathering, respectively. We adopt a broad range of continental growth curves that encompasses literature estimates (Fig. 2A and SI Appendix A). For our nominal model, we assume Archean land fraction was anywhere between 10% and 75% of modern land fraction (Fig. 2A), but we also consider a no-land Archean endmember (Fig. 2B).

Fig. 2.

Gray shaded regions are ranges assumed for selected model input parameters. (A) Range of continental growth curves assumed in our nominal model, $f_{\text{land}}$. Various literature estimates are plotted alongside the model growth curve (SI Appendix A). (B) Range of continental growth curves for an endmember of no Archean land; (C) range for biological enhancement of weathering histories, $f_{\text{bio}}$; and (D) range of internal heat flow histories, $Q$, compared with literature estimates (SI Appendix A).

To account for the possible biological enhancement of weathering in the Phanerozoic due to vascular land plants, lichens, bryophytes, and ectomycorrhizal fungi, we adopt a broad range of histories for the biological enhancement of weathering, $f_{bio}$ (Fig. 2C). The lower end of this range is consistent with estimates of biotic enhancement of weathering from the literature (37–39).

The dissolution of basalt in the seafloor is dependent on the spreading rate, pore-space pH, and pore-space temperature (SI Appendix A). This formulation is based on the validated parameterization in ref. 36. Pore-space temperatures are a function of climate and geothermal heat flow. Empirical data and fully coupled global climate models reveal a linear relationship between deep ocean temperature and surface climate (36). Equations relating pore-space temperature, deep ocean temperature, and sediment thickness are provided in SI Appendix A.

Carbon leaves the atmosphere–ocean system through carbonate precipitation in the ocean and pore space of the oceanic crust. At each time step, the carbon abundances and alkalinities are used to calculate the carbon speciation, atmospheric pCO₂, and saturation state assuming chemical equilibrium. Saturation states are then used to calculate carbonate precipitation fluxes (SI Appendix A). We allow calcium (Ca) abundance to evolve with alkalinity, effectively assuming no processes are affecting Ca abundances other than carbonate and silicate weathering, seafloor dissolution, and carbonate precipitation. The consequences of this simplification are explored in the sensitivity analysis in SI Appendix C. We do not track organic carbon burial because organic burial only constitutes 10–30% of total carbon burial for the vast majority of Earth history (40), and so the inorganic carbon cycle is the primary control.

The treatment of tectonic and interior processes is important for specifying outgassing and subduction flux histories. We avoid tracking crustal and mantle reservoirs because explicitly parameterizing how outgassing fluxes relate to crustal production and reservoirs assumes modern-style plate tectonics has operated throughout Earth history (e.g., ref. 12) and might not be valid. Evidence exists for Archean subduction in eclogitic diamonds (41) and sulfur mass-independent fractionation in ocean island basalts ostensibly derived from recycled Archean crust (42). However, other tectonic modes have been proposed for the early Earth such as heat-pipe volcanism (43), delamination and shallow convection (44), or a stagnant lid regime (45).

Our generalized parameterizations for heat flow, spreading rates, and outgassing histories are described in SI Appendix A. Fig. 2D shows our assumed range of internal heat flow histories compared with estimates from the literature. Spreading rate is connected to crustal production via a power law, which spans endmember cases (SI Appendix A). These parameterizations provide an extremely broad range of heat flow, outgassing, and crustal production histories, and do not assume a fixed coupling between these variables.

We used a 1D radiative convective model (46) to create a grid of mean surface temperatures as a function of solar luminosity and pCO₂. The grid of temperature outputs was fitted with a 2D polynomial (SI Appendix E). We initially neglect other greenhouse gases besides CO₂ and H₂O, albedo changes, and assumed a constant total pressure over Earth history. However, later we consider these influences, such as including methane (CH₄) in the Precambrian. The evolution of solar luminosity is conventionally parameterized (47).

Our model has been demonstrated for the last 100 Ma against abundant proxy data (36) and it can broadly reproduce Sleep and Zahnle (12) if we replace our kinetic formulation of seafloor weathering with their simpler CO₂-dependent expression (SI Appendix B). Agreement with ref. 12 confirms that the omission of crustal and mantle reservoirs does not affect our conclusions.

Results

Fig. 3 shows the evolution of the geological carbon cycle over Earth history according to our nominal model. Here, we have used our kinetic parameterization of seafloor weathering rather than the arbitrary pCO₂ power law adopted in previous studies (SI Appendixes A and B). We have also assumed a range of continental growth curves (Fig. 2A), a range of Phanerozoic biological weathering enhancements (Fig. 2C), and a range of temperature dependencies of weathering from ref. 36. Proxies for surface temperature, atmospheric pCO₂, and seafloor weathering flux are plotted alongside model outputs for comparison (SI Appendix D). For all results, both 95% confidence intervals and median values are plotted for key carbon cycle outputs. Median values are calculated at each time step, and consequently their evolution does not necessarily resemble the most probable time evolution of carbon cycle variables. In practice, however, most individual model realizations tend to track the median, at least qualitatively (SI Appendix A).

Fig. 3.

Nominal model outputs. Gray shaded regions represent 95% confidence intervals, and black lines are the median outputs. (A) Ocean pH with the 95% confidence interval from Halevy and Bachan (29) plotted with red dashed lines for comparison. Our model predicts a monotonic evolution of pH from slightly acidic values at 4.0 Ga to slightly alkaline modern values. (B) Atmospheric pCO₂ plotted alongside proxies from the literature. (C) Global outgassing flux. (D) Mean surface temperature plotted alongside glacial and geochemical proxies from the literature. Our model predicts surface temperatures have been temperate throughout Earth history. (E) Continental silicate weathering flux. (F) Seafloor weathering flux plotted alongside flux estimates from Archean altered seafloor basalt. dep, deposit.

We observe that modeled temperatures are relatively constant throughout Earth history, with Archean temperatures ranging from 271 to 314 K. The combination of continental and seafloor weathering efficiently buffers climate against changes in luminosity, outgassing, and biological evolution. This temperature history is broadly consistent with glacial constraints and recent isotope proxies (Fig. 3D). The continental weathering buffer dominates over the seafloor weathering buffer for most of Earth history, but in the Archean the two carbon sinks are comparable (SI Appendix, Fig. S1). Indeed, if seafloor weathering were artificially held constant, then continental weathering alone may be unable to efficiently buffer the climate of the early Earth—the temperature distribution at 4.0 Ga extends to 370 K, and the atmospheric pCO₂ distribution extends to 7 bar (SI Appendix, Fig. S3).

In our nominal model, the median Archean surface temperature is slightly higher than modern surface temperatures. If solar evolution were the only driver of the carbon cycle, then Archean temperatures would necessarily be cooler than modern temperatures; weathering feedbacks can mitigate this cooling but not produce warming. Warmer Archean climates are possible because elevated internal heat flow, lower continental land fraction, and lessened biological enhancement of weathering all act to warm to Precambrian climate. These three factors produce a comparable warming effect (SI Appendix, Fig. S17A and Appendix C), although the magnitude of each is highly uncertain and so temperate Archean temperatures cannot be uniquely attributed to any one variable.

Continental and seafloor weathering also buffer ocean pH against changes in luminosity and outgassing. Ocean pH increases monotonically over Earth history from 6.3–7.2 at 4.0 Ga, to 6.5–7.7 at 2.5 Ga, and to the modern value of 8.2. The broad range of parameterizations does not tightly constrain the history of atmospheric pCO₂, but the model pCO₂ outputs encompass paleosol proxies (Fig. 3B).

The results described above assume an Archean landmass fraction between 0.1 and 0.75 times the modern land fraction. Next, we consider the endmember scenario of zero Archean landmass. This is unrealistic because abundant evidence exists for Archean land (48). However, a zero land fraction case could represent a scenario where continental fraction is sufficiently small that continental silicate weathering becomes supply limited (e.g., ref. 49).

Fig. 4 shows model outputs for the zero land fraction case. When continental weathering drops to zero, seafloor weathering increases dramatically to balance the carbon cycle (Fig. 4F). This is largely a consequence of the temperature-dependent feedback of seafloor weathering. The climate warms by 10–15 K (Fig. 4D) before the temperature-dependent seafloor weathering flux is sufficiently large to balance the carbon cycle. Even in this extreme case, the median Archean temperature is ∼305 K, and the upper end of the temperature distribution at 4 Ga only extends to ∼328 K, excluding a “hot” Archean of 60–80 °C. Archean pCO₂ (and pH) are slightly higher (lower) in the zero land case, but the seafloor weathering feedback is still an effective buffer.

Fig. 4.

No Archean land endmember scenario. Panels A–F, lines, and, shadings are the same as in Fig. 3. (E) Continental weathering drops to zero in the Archean, but (F) seafloor weathering increases due to its temperature dependence to balance the carbon cycle. This causes an increase in surface temperature in the Archean, (D) but conditions are still temperate throughout Earth history. The evolution of (A) ocean pH and (B) pCO₂ are similar to the nominal model. dep, deposit.

Finally, we investigated whether the inclusion of methane as a Precambrian greenhouse gas would substantially change our results. Fig. 5 shows model outputs where we have assumed 100 ppm Proterozoic methane and 1% Archean methane levels (SI Appendix E). The temperature changes are smaller than what might be expected if only methane levels were changing. This is because pCO₂ drops in response to the imposed temperature increase—pCO₂ must drop otherwise weathering sinks would exceed source fluxes. The pCO₂ distribution at 4.0 Ga is shifted downward relative to the nominal case with no other greenhouse cases, and ocean pH increases in response to this pCO₂ drop. Note that for parts of parameter space where CO₂/CH₄ ≳ 0.2 (50), our temperatures should be considered upper limits because a photochemical haze would form, cooling the climate (SI Appendix E).

Fig. 5.

Default continental growth range with imposed 100 ppm methane in the Proterozoic and 1% methane in the Archean. Panels A–F, lines, and, shadings are the same as in Fig. 3. (D) Temperature increases sharply in the Archean due to methane, but by less than what would be expected if pCO₂ were unchanged. In practice, there is a compensating decrease in atmospheric pCO₂, (B) which must occur to balance the carbon cycle. Otherwise temperatures would be too high and weathering sinks would exceed outgassing sources. Because pCO₂ is lower, Archean pH values are closer to circumneutral (A). dep, deposit.

Thus, even with considerable warming from an additional greenhouse gas, the median temperature at 4.0 Ga is below 300 K, and the temperature distribution extends to 320 K, again excluding a hot Archean. SI Appendix, Fig. S7 shows the results for the most extreme case of no Archean land and high methane abundances. Even in this extreme scenario, the seafloor weathering flux successfully buffers the climate to a median 4.0 Ga value of ∼310 K. Archean pH values are closer to circumneutral when methane is included due to lower pCO₂, but there is still a monotonic evolution in pH over Earth history.

Discussion

Previously, Sleep and Zahnle (12) modeled the evolution of the geological carbon cycle over Earth history and reported the Hadean and Archean mean surface temperatures below 0 °C, unless atmospheric methane abundances were very high. In contrast, we find that Archean temperatures were likely temperate, regardless of methane abundances. This disparity can be ascribed to the differing treatments of seafloor weathering. Sleep and Zahnle (12) did not include ocean chemistry in their model (they effectively fix pH), and were thus forced to parameterize seafloor weathering using a power-law pCO₂ dependence with a fitted exponent. This parameterization overestimates the role of Archean seafloor weathering. Experiments with basalt dissolution reveal a weak pH dependence and a moderate temperature dependence, but no direct pCO₂ dependence (see discussion in ref. 36).

The change from a CO₂-dependent parameterization to a temperature-dependent parameterization means the seafloor weathering feedback better stabilizes climate against increasing luminosity. For a purely temperature-dependent weathering feedback, decreasing luminosity does not change climate, as the weathering flux must remain constant to maintain carbon cycle balance. Instead, CO₂ adjusts upwards to maintain the same temperature at lower insolation. In contrast, for a purely CO₂-dependent weathering feedback, a decrease in solar luminosity will result in a temperature decrease (see also SI Appendix B). In short, the pH-dependent and temperature-dependent seafloor weathering parameterization we apply stabilizes climate and prevents a globally glaciated early Earth. This result is broadly consistent with a single time point at 3.8 Ga that calculated equilibrium surface temperatures using a GCM and geological carbon cycle model (13).

The only way to produce Archean climates below 0 °C in our model is to assume the Archean outgassing flux was 1–5× lower than the modern flux (SI Appendix, Fig. S12). However, dramatically lowered Archean outgassing fluxes contradict known outgassing proxies and probably require both a stagnant lid tectonic regime and a mantle more reduced than zircon data suggest, which lowers the portion of outgassed CO₂ (SI Appendix C). Moreover, even when outgassing is low, frozen climates are not guaranteed (SI Appendix, Fig. S12).

Our model gives a monotonic evolution of ocean pH from 6.3–7.7 in the Archean (95% confidence), to 6.5–8.1 (95% confidence) in the Proterozoic, and increasing to 8.2 in the modern surface ocean. This history is broadly consistent with that of Halevy and Bachan (29) (Figs. 3 and 4). Halevy and Bachan (29) tracked Na, Cl, Mg, and K exchanges with continental and oceanic crust, and related these fluxes to the thermal evolution of the Earth. Minor constituents such as HS, NH₃, Fe²⁺, and SO₄^2- were also considered. However, they prescribe many features of the carbon cycle rather than apply a self-consistent model as we have done here. Specifically, they imposed pCO₂ to ensure near-modern temperatures throughout Earth history. Consequently, the explicit temperature dependence of both seafloor and continental weathering were omitted. Additionally, subduction and outgassing were assumed to be directly proportional, a limited range of heat flow histories were adopted, and continental silicate weathering was described using an overall pCO₂ power-law dependence with no allowance for changing land fraction or biogenic enhancement weathering. Thus, the uncertainty envelopes for the early Earth ocean pH are underestimated in ref. 29 as can be seen by their uncertainty diminishing further back in time. Good agreement with the results of ref. 29 confirms that the details of ocean chemistry are of secondary importance to pH evolution, and that the monotonic evolution of pH is instead driven by solar luminosity evolution, buffered by enhanced continental and seafloor weathering under high pCO₂ conditions. The two models also agree because the carbon cycle buffers to near-modern temperatures, allowing the constant temperature assumption of ref. 29, but there is no way of knowing the effectiveness of the buffer without a self-consistent model of the carbon cycle.

One caveat for our results is that the ocean chemistry is incomplete. Specifically, Ca abundances in the ocean and pore space are controlled entirely by alkalinity fluxes from continental and seafloor weathering. In reality, Ca abundances are modulated by other processes such as the hydrothermal exchange of Ca and Mg in the seafloor, dolomitization, and clay formation (51). To explore whether neglecting these processes would affect our results we conducted sensitivity tests with a large ensemble of Ca evolutions (SI Appendix C). High Archean Ca abundances might be expected to produce more acidic oceans because carbonate abundances are lower for the same saturation state. However, this effect is buffered by decreases in Ca and CO₃²⁻ activity coefficients (complexing), and so model outputs look very similar to our nominal model for a broad range of Ca abundance trajectories (SI Appendix, Fig. S9).

In our nominal climate model, we did not include the effects of changing atmospheric pressure or albedo changes. These effects are likely to be modest compared with the other sources of uncertainty in our model. Lower surface albedo from a reduced Archean land fraction can contribute at most 5 W/m² of radiative forcing (52), which would cause only a few degrees of warming. Halving Archean total pressure—as has been suggested by paleopressure proxies (53)—would cool the Earth by ∼5 K because of the loss of pressure broadening, thereby offsetting the lower land fraction (54). Changes in cloud cover could, in principle, induce larger warming, but the required conditions for >10 K warming are highly speculative (52). In any case, the effects of pressure changes and albedo changes are unlikely to affect our conclusions because the temperature changes they induce will be compensated by pCO₂ variations to balance the carbon cycle. Sensitivity analyses where massive amounts of Archean warming are imposed (+30 K) still result in temperate surface temperatures because of this pCO₂ compensation (SI Appendix, Fig. S10).

Although our model outputs are broadly consistent with paleosol proxies and glacial constraints, some disagreement occurs with selected seafloor weathering proxies. Proxies for seafloor carbonate precipitation were estimated by using the average carbonate abundances in Archean oceanic crust, scaled by the model spreading rate at that time multiplied by an assumed carbonatization depth (SI Appendix D). Our modeled seafloor carbonate precipitation fluxes agree with that of Nakamura and Kato (55) and Shibuya et al. (56), but undershoot crustal carbonate abundances reported by Shibuya et al. (57) and Kitajima et al. (58). It is difficult to construct a balanced carbon cycle model with seafloor weathering fluxes in excess of 100 Tmol C/y as these latter two studies imply, and so the discrepancy may be because those oceanic crust samples are not representative of global carbonatization flux, or because some of the carbonate is secondary. The only way to approach the carbonate abundances reported by Shibuya et al. (57) and Kitajima et al. (58) is to impose very high Archean outgassing (e.g., up to 60× the modern flux; SI Appendix, Fig. S11), but even then the fit is marginal. If high Archean crustal carbonate estimates were truly primary, then Archean outgassing would have been very high, and so Earth’s internal heat flow would have decreased dramatically over Earth’s history, contrary to Korenaga (59).

We conclude that current best knowledge of Earth’s geologic carbon cycle precludes a hot Archean. Our results are insensitive to assumptions about ocean chemistry, internal evolution, and weathering parameterizations, so a hot early Earth would require some fundamental error in current understanding of the carbon cycle. Increasing the biotic enhancement of weathering by several orders of magnitude as proposed by Schwartzman (60) does not produce a hot Archean because this is mathematically equivalent to zeroing out the continental weathering flux (Fig. 4). In this case the temperature-dependent seafloor weathering feedback buffers the climate of the Earth to moderate temperatures (SI Appendix, Fig. S14). Dramatic temperature increases (or decreases) due to albedo changes also do not change our conclusions due to the buffering effect of the carbon cycle (see above). If both continental and seafloor weathering become supply limited (e.g., refs. 49 and 61), then temperatures could easily exceed 50 °C. However, in this case the carbon cycle would be out of balance, leading to excessive pCO₂ accumulation within a few hundred million years unless buffered by some other, unknown feedback.

Conclusions

The early Earth was probably temperate. Continental and seafloor weathering buffer Archean surface temperatures to 0–50 °C. This result holds for a broad range of assumptions about the evolution of internal heat flow, crustal production, spreading rates, and the biotic enhancement of continental weathering. Even in extreme scenarios with negligible subaerial Archean land and high methane abundances, a hot Archean (>50 °C) is unlikely. Sub-0 °C climates are also unlikely unless the Archean outgassing flux was unrealistically lower than the modern flux.

The seafloor weathering feedback is important, but less dominant than previously assumed. Consequently, the early Earth would not have been in a snowball state due to pCO₂ drawdown from seafloor weathering. In principle, little to no methane is required to maintain a habitable surface climate, although methane should be expected in the anoxic Archean atmosphere once methanogenesis evolved (ref. 62, chap. 11).

Ignoring transient excursions, the pH of Earth’s ocean has evolved monotonically from ${6.6}_{-0.4}^{+0.6}$ at 4.0 Ga (2σ) to ${7.0}_{-0.5}^{+0.7}$ at 2.5 Ga (2σ), and 8.2 in the modern ocean. This evolution is robust to assumptions about ocean chemistry, internal heat flow, and other carbon cycle parameterizations. Consequently, similar feedbacks may control ocean pH and climate on other Earthlike planets with basaltic seafloors and silicate continents, suggesting that life elsewhere could emerge in comparable environments to those on our early planet.