Neogene continental denudation and the beryllium conundrum

Significance

Most weathering and denudation proxies are consistent with Cenozoic cooling being a consequence of increased CO₂ removal from the atmosphere by continental silicate weathering. Beryllium isotope ratios in the late Cenozoic seawater have been an exception that has been cited as falsifying this uplift–weathering hypothesis. This study presents a beryllium cycle model that reinterprets the beryllium isotope record and resolves the contradiction between the beryllium records and the other weathering proxies. The results are consistent with increased terrestrial erosion and weathering during the late Cenozoic. These results indicate an important role for geologic processes that compensate for CO₂ removal by continental weathering and prevent runaway cooling, such as enhanced oxidation of organic carbon, pyrite weathering, and/or reduced basalt weathering.

Abstract

Reconstructing Cenozoic history of continental silicate weathering is crucial for understanding Earth’s carbon cycle and greenhouse history. The question of whether continental silicate weathering increased during the late Cenozoic, setting the stage for glacial cycles, has remained controversial for decades. Whereas numerous independent proxies of weathering in ocean sediments (e.g., Li, Sr, and Os isotopes) have been interpreted to indicate that the continental silicate weathering rate increased in the late Cenozoic, beryllium isotopes in seawater have stood out as an important exception. Beryllium isotopes have been interpreted to indicate stable continental weathering and/or denudation rates over the last 12 Myr. Here we present a Be cycle model whose results show that variations in the ⁹Be weathering flux are counterbalanced by near-coastal scavenging while the cosmogenic ¹⁰Be flux from the upper atmosphere stays constant. As a result, predicted seawater ¹⁰Be/⁹Be ratios remain nearly constant even when global denudation and Be weathering rates increase by three orders of magnitude. Moreover, ¹⁰Be/⁹Be records allow for up to an 11-fold increase in Be weathering and denudation rates over the late Cenozoic, consistent with estimates from other proxies. The large increase in continental weathering indicated by multiple proxies further suggests that the increased CO₂ consumption by continental weathering, driven by mountain-building events, was counterbalanced by other geological processes to prevent a runaway icehouse condition during the late Cenozoic. These processes could include enhanced carbonate dissolution via pyrite weathering, accelerated oxidation of fossil organic carbon, and/or reduced basalt weathering as the climate cooled.

Over 3 decades ago, it was proposed that Cenozoic cooling was caused by a decline in atmospheric CO₂ due to accelerated silicate weathering on the continents, primarily driven by enhanced erosion following the Indian–Asian collision and uplift of the Himalayan–Tibetan region (1, 2). The premise that continental chemical weathering rates have been increasing since ∼40 Ma is supported by multiple ocean chemical proxies and numerous studies, including the carbonate compensation depth (2–4) and Sr (5, 6), Os (7), and Li isotopes (8). Although any individual weathering proxy can be interpreted in an alternative way (e.g., refs. 1, 9, 10), they are all consistent with the hypothesis of increased flux of continental material to the ocean over the late Cenozoic. In addition, sedimentary records also support up to a fourfold worldwide acceleration of erosion during the late Cenozoic (11, 12), although this interpretation may be biased by the increasing incompleteness of ocean sediment with age (13, 14). Moreover, bedrock thermochronometric cooling ages in the world’s mountainous regions also support a twofold increase in erosion rates during the past 8 Myr (15), although it has been suggested that the interpretation is also potentially biased by spatial erosion variability (16).

The primary argument against the idea that continental silicate weathering increased during the late Cenozoic is that continental silicate weathering rates need to be in close mass balance with volcanic degassing of CO₂, otherwise a runaway greenhouse or icehouse effect would occur within several million years of the input and output being imbalanced (17). This need for the input and output of CO₂ to the atmosphere to be balanced gave rise to the concept of the temperature–weathering feedback (18). Models that accept the physical evidence for enhanced weathering in mountainous regions posit that such a late Cenozoic increase must have been balanced by a decrease in silicate weathering rates elsewhere in the world in order to maintain the habitability of our planet (17, 19, 20). However, recent work has pointed to numerous other geological processes that impact the flux of carbon to the ocean–atmosphere reservoirs and thus could act as negative feedbacks within the global climate system.

For the ocean–atmosphere reservoir, there are three primary carbon sources: these are CO₂ degassing from volcanism and metamorphism (21, 22), the oxidative weathering of fossil organic carbon (23), and carbonate dissolution by sulfuric acid produced via pyrite oxidation (7, 24). There are four major carbon sinks: these are continental silicate weathering (25), subaerial basalt weathering (20), seafloor weathering (26), and organic carbon burial (27). Many studies have reconstructed the history and explored the controlling factors of these processes, and potential negative feedbacks, in addition to the temperature–weathering feedback, have been proposed. These proposed negative feedbacks include enhanced carbonate dissolution by sulfuric acid produced via pyrite oxidation (7), reduced subaerial basalt weathering (20, 28), slower seafloor basalt weathering (26), accelerated oxidation of fossil organic carbon (23), and decreased organic carbon burial (29) as the climate cooled. Indeed, observations suggest that the release rate of CO₂ from carbonate dissolution by sulfuric acid produced via pyrite oxidation has increased during the late Cenozoic (7), probably because increasing glacier activity and global erosion increase the weathering rate of pyrite (30). Modeling of Cenozoic seawater chemistry suggests that subaerial basalt weathering rates could have decreased during the late Cenozoic as the climate cooled (20), offsetting increased weathering in mountainous regions, since the subaerial basalt weathering rate is observed to be positively correlated with temperature (28). Seafloor weathering rates are generally lower under colder temperatures (26, 31). Therefore, they also should be decreasing during the late Cenozoic, resulting in a net flux of CO₂ to the ocean–atmosphere system. Under a cooling climate, increased glacier activity can also enhance the weathering of fossil organic carbon (23), creating another potential negative feedback by supplying additional carbon into the atmosphere during the late Cenozoic. All these studies suggest that accelerated CO₂ removal driven by increased continental silicate weathering in mountainous regions could have been balanced by one or more of a number of negative feedbacks operating within the geological carbon cycle. Collectively, these feedbacks could have maintained the habitability of our planet during the late Cenozoic. Our challenge here is in using the geologic record to determine exactly how these processes changed over the Cenozoic; only then will we arrive at an acceptable understanding of the operation of the global carbon cycle.

This brings us back to beryllium. The Be isotope record in seawater has been used to test our current understanding of how the geological carbon cycle works (13, 32). Since the Be concentration in felsic crust is an order of magnitude higher than that in basalt and carbonate rocks (33), beryllium isotopes are regarded as a potential proxy for continental silicate weathering and are frequently used to trace continental silicate weathering (e.g., refs. 34, 35). The near constancy of the Be isotopic composition of late Cenozoic seawater has been used to argue against Neogene increases in continental denudation and weathering rates (13, 32, 35). Indeed, it is the only denudation and weathering proxy used to falsify the uplift–weathering hypothesis, and if this interpretation is true, it has important implications for the carbon cycle and the causes of the Ice Ages.

¹⁰Be is a cosmogenic isotope (t_1/2 =1.39 Ma), formed by spallation of nitrogen and oxygen in the upper atmosphere. It is mainly added to seawater through deposition from the atmosphere, and its production rate is assumed to be constant on multimillion-year timescales (35, 36). In contrast, ⁹Be is a stable isotope brought to the oceans via rivers when ⁹Be-bearing silicate minerals dissolve on the continents through weathering and erosion. Most of the riverine ⁹Be is removed by scavenging upon entering the coastal ocean (35). While the observation that the ¹⁰Be/⁹Be ratios in Neogene seawater have been roughly constant (13) has been interpreted to indicate the stability of continental denudation (13) and weathering (13, 32) rates, this conclusion relies on the assumption that the fraction of riverine Be that survives coastal scavenging and makes it to the open ocean has been nearly constant during the Neogene (32, 35). Recent research on the Be scavenging process in river estuaries (37) suggests this assumption may be invalid.

Here we consider how the variability of the coastal scavenging factor (${\text{φ}}_{\text{del}})$ can impact the interpretation of seawater ¹⁰Be/⁹Be as a proxy of continental denudation and weathering. Our model is motivated by the observation that inorganic particles enhance scavenging (37); thus, it is likely that as the continental denudation rate (defined as the sum of mass loss due to both physical erosion and chemical weathering per unit time per unit area of land) increases, the additional eroded inorganic material reaching the coastal ocean scavenges more dissolved ⁹Be. At the same time, an increase in denudation would increase the ⁹Be weathering flux, which is observed to be linearly correlated with denudation rates (33, 35). Thus, the response of ¹⁰Be/⁹Be in the open ocean to increasing denudation would depend on the competition between an accelerated ⁹Be flux from weathering and enhanced scavenging. For example, if an increase of ⁹Be due to weathering is entirely counterbalanced by enhanced scavenging as denudation increases, seawater ¹⁰Be/⁹Be ratios would not change. This effect has not been carefully considered in previous studies; rather, they have assumed that ${\text{φ}}_{\text{del}}$ is constant (32) or nearly constant, based on the further assumption that the partition coefficient is negatively correlated with suspended particle concentrations (35). In this study, we quantify how scavenging and weathering of Be would change in response to changes in denudation rates and, with these effects considered, interpret the late Cenozoic global denudation and Be weathering history from the Neogene seawater ¹⁰Be/⁹Be record.

Results and Discussion

The Model Predicts the Modern Ocean.

We have built a Be cycle model (details are presented in Materials and Methods) that calculates the effect of continental denudation variations on coastal scavenging by assuming a constant value for the Be partition coefficient (${\text{Kd}}_{\text{diss}}^{\text{Be}}$), unlike the previous model (35). Below we test the validity of this model by applying it to the present-day ocean, examining how well it predicts the dissolved ¹⁰Be/⁹Be ratio (¹⁰Be/⁹Be_oc) in each ocean basin. ¹⁰Be/⁹Be ratios are variable in the oceans because the Be residence time is 600 to 1,000 y (35, 36), shorter than the oceanic mixing time. For this test, we compare our model results to the ¹⁰Be/⁹Be ratios in the shallow water above the thermocline. We use this approach because Be isotopes in the surface waters of individual ocean basins reflect the mixing of the continental river flux (38) and the shallow advective flux from adjacent basins (39). Within individual basins, the upper ocean is well-mixed by ocean gyres on century timescales (40). In contrast, the deep water chemistry is controlled by the downward transport of the surface ocean dissolved load via the biological pump (38) and the deep advective flux from adjacent basins (35). Thus, although the late Cenozoic record of seawater ¹⁰Be/⁹Be was generated using Fe–Mn crusts in deep water (13), ¹⁰Be/⁹Be ratios in the upper ocean layers are the better test for our model accuracy because ¹⁰Be/⁹Be ratios in the upper ocean have a more direct link to the continental denudation flux.

For the model–data comparison, we compile the published ¹⁰Be/⁹Be_sw ratios in the shallow water of North Pacific, South Pacific, North Atlantic, Indian, South Atlantic, Mediterranean, and Arctic Ocean (SI Appendix, Table S1). We use our model to calculate ¹⁰Be/⁹Be_sw in the shallow water, and we compare it to the observed shallow water ¹⁰Be/⁹Be_sw, measured in the top 1,000 m layer of modern seawater. The parameters used are listed in SI Appendix, Tables S2 and S3, and the modeling results are in SI Appendix, Table S4. The errors in the modeled ¹⁰Be/⁹Be_sw ratios are estimated by assigning 20% uncertainties to denudation rates, as in a previous model that assumed a constant coastal scavenging factor (${\text{φ}}_{\text{del}})$ (35) and considering measurement error of ¹⁰Be/⁹Be_sw and the Be concentration in the advective flux from adjacent basins. The model results show a close match to the observed ¹⁰Be/⁹Be_oc values in all the large basins. Moreover, our model reproduces the observed ¹⁰Be/⁹Be_sw better than the previous model that assumed constant ${\text{φ}}_{\text{del}}$ (35) (Fig. 1A), implying it is more accurate.

Fig. 1.

(A) Modeled vs. measured seawater ¹⁰Be/⁹Be ratios in waters at depths of <1,000 m (1 SD error bars). The circles and the diamonds represent our model results and those of the model assuming a constant φ_del, respectively. The black dashed line is the line of equality as a reference. Our results are closer to the equality line than those of the other model. (B) The comparison between φ_del, the fraction of riverine Be that survives scavenging and makes it to the ocean, as calculated by our model (open black bars), and the φ_del ranges that can fit the observed data (${\text{φ}}_{\mathit{del}}^{ob})$. The wider and narrower bands represent the inversely calculated ${\text{φ}}_{\mathit{del}}^{ob}$ ranges when 1 SD and 2 SD errors of observed ¹⁰Be/⁹Be are considered, respectively. The red line in B represents the constant φ_del value of 0.063 used by ref. 16. Our model predictions of φ_del are consistent with the ranges of ${\text{φ}}_{\mathit{del}}^{ob}$ constrained by measurements.

We also calculate the range of the coastal scavenging factor (${\text{φ}}_{\text{del}}$) for each ocean basin with our model (Materials and Methods) and then compare it to the ${\text{φ}}_{\text{del}}$ range that can reproduce the observed ¹⁰Be/⁹Be ratio of each ocean basin (${\text{φ}}_{\mathit{del}}^{ob}$).These results show that ${\text{φ}}_{\text{del}}$ ranges calculated by our model always match the $\begin{array}{l}{\text{φ}}_{\mathit{del}}^{ob}\\ \end{array}$ ranges inversely calculated (Materials and Methods) from the observed ¹⁰Be/⁹Be_sw values when 1 to 2 SDs are considered (Fig. 1B), demonstrating that the model reproduces the modern shallow ocean observations. These calculations suggest that ${\text{φ}}_{\text{del}}$ should not be assumed constant, given that there are large variabilities of ${\text{φ}}_{\mathit{del}}^{ob}$ in the ocean basins (Fig. 1B).

Response of ¹⁰Be/⁹Be Ratios to Changes in Denudation Rates.

The model’s success in reproducing the observed seawater ¹⁰Be/⁹Be ratios in different ocean basins shows that it captures how weathering input and scavenging effects in the coastal ocean control the distribution of present-day seawater Be isotope ratios. To understand the Neogene seawater ¹⁰Be/⁹Be record, we modeled how seawater ¹⁰Be/⁹Be ratios would change with fluctuations in continental denudation rates.

We ran the model under two scenarios. The first one is the present-day scenario. Under this scenario, we assume a positive correlation between the denudation rate (D_riv) and the physical erosion factor (α). Here α is a key parameter relating denudation to physical erosion and is defined as the ratio of the physical erosion rate to the total denudation rate in the drainage area of global ocean basins. In the present-day world, the relationship between D_riv and α can be described by a positive regression function of α = 0.142 × ln$({\text{D}}_{\text{riv}})$ + 0.028 (SI Appendix, Fig. S1). This α-denudation relationship mainly reflects control by the weathering of silicate igneous rock (details in the discussion in SI Appendix). During the weathering of igneous rock, the ratio of silicate weathering rate to denudation rate generally decreases with increasing denudation (41–43), resulting in a higher ratio of physical erosion to denudation rate. In the present-day scenario we combine the D_riv-α regression function and the model Eqs. 3 and 11 (in Materials and Methods) to calculate the response of the global ocean ¹⁰Be/⁹Be_oc to changes in global denudation rates.

We also ran our model under a reworked clay scenario, which assumes that recycling of sedimentary rock provides all the physical erosive flux. This scenario is important because Li and Nd isotopic evidence suggests that 60 to 90% of the global river sediment could be from erosion of old sedimentary rock (44, 45). The reworked clay scenario assumes that denudation of sedimentary rocks that are mainly composed of carbonate, evaporite, and clay minerals and devoid of fresh silicate minerals for weathering is primarily responsible for the transport of material to oceans. The higher fractions of sedimentary rock flux in the global denudation flux mean that the physical erosion factor (α) would be less sensitive to variations in D_riv, and α would become a constant when the fraction reaches 100% (SI Appendix). Thus, α is assumed to be constant in this model run. We ran this model using the same parameters as the present-day scenario, except for the physical erosion factor.

The model results under both scenarios show some common features. Under both model scenarios, when continental denudation rates are larger than 20 t/km²/yr, increased denudation rates result in an increase in the Be weathering flux (Fig. 2A), which is balanced by a decrease in the coastal scavenging factor (${\text{φ}}_{\text{del}}$; Fig. 2B), resulting in nearly constant ¹⁰Be/⁹Be_sw ratios (Fig. 2C). When D_riv increases from 20 to 10,000 t/km²/yr, the ¹⁰Be/⁹Be_sw ratios are always within the range between 0.97 × 10⁻⁷ and 1.6 × 10⁻⁷ under the present-day scenario and remain between 0.95 and 1.7 × 10⁻⁷ under the reworked clay scenario.

Fig. 2.

Our model predictions on how (A) Be weathering rates, (B) the scavenging factor, and (C) ¹⁰Be/⁹Be_sw change as a function of continental denudation rates (D_riv). The star represents the modern level of global ¹⁰Be/⁹Be_sw and denudation. The blue band represents the range between the 16th and 84th percentile of ¹⁰Be/⁹Be in the late Cenozoic seawater.

In contrast, when denudation rates are lower than 20 t/km²/yr, ${\text{φ}}_{\text{del}}$ remains relatively stable as denudation rates increase (Fig. 2B) and thus cannot counterbalance the increase in riverine Be flux, leading to decreasing ¹⁰Be/⁹Be_sw ratios under both scenarios (Fig. 2C). As the denudation rate increases from 1 to 20 t/km²/yr, the modeled ¹⁰Be/⁹Be_sw under the present-day scenario and the reworked clay scenario decrease from 1.5 × 10⁻⁶ to 1.3 × 10⁻⁷ and from 1.5 × 10⁻⁶ to 1.7 × 10⁻⁷, respectively. Overall, our model predicts similar L-shaped relationships between ¹⁰Be/⁹Be_sw and continental denudation rates under both scenarios (Fig. 2C), indicating the results are not sensitive to assumptions about the relationship between α and denudation rate.

To further test whether the model predictions on the relationship between seawater ¹⁰Be/⁹Be and denudation rates are sensitive to changes in the values of the key parameters, we have done eight sensitivity tests by either doubling the surface area of the ocean (A_oc), the riverine drainage area (A_riv), the coastline length (CL), and the ¹⁰Be flux (F¹⁰Be _riv,oc) or decreasing the values of the four parameters by 50%. Only one parameter’s value is altered for each sensitivity test while keeping all the rest of the parameters unchanged. The details of how we did the sensitivity tests are presented in SI Appendix. The results suggest that the L-shaped relationship between seawater ¹⁰Be/⁹Be and denudation rates predicted by our model is insensitive to the values of input parameters (SI Appendix, Fig. S2).

The L-shaped relationships can best be explained by variations in the partition of beryllium between absorbed and dissolved phases as a function of denudation rates. The constant partition coefficient of beryllium means that the ratio of the concentration of absorbed Be in the suspended particles to the dissolved Be concentration in water is constant. Therefore, the percentage of absorbed Be in the total riverine Be flux depends on the mass ratio of suspended matter to water in rivers and estuaries. When the denudation rate is low, low concentrations of suspended matter cause the riverine Be flux to be dominated by the dissolved phase, which is not bound to the suspended matter and consequently is little affected by coastal scavenging. In this case, an increase in the riverine Be flux cannot be efficiently counterbalanced by scavenging by suspended matter, and ¹⁰Be/⁹Be_sw decreases significantly. As denudation rates increase, the concentration of suspended matter increases, the absorbed phase becomes dominant, and the scavenging process becomes powerful enough to offset the increase in the riverine Be flux, keeping ¹⁰Be/⁹Be_sw constant.

Neogene Denudation, Beryllium Weathering, and the Marine ¹⁰Be/⁹Be Record.

Using the model, we interpret the continental denudation and Be weathering history over the past 12 Myr from the ¹⁰Be/⁹Be_sw record. In order to generate a global record, given that each ocean basin has unique ¹⁰Be/⁹Be_sw values, we use the same approach as ref. 32; that is, we normalize the ¹⁰Be/⁹Be_sw record of each ocean basin to its modern ¹⁰Be/⁹Be_sw value and smooth the data with a 10-point running mean. The smoothed record (13) shows a near constancy (Fig. 3A) with an average value of 0.89 ± 0.3 (1σ). This uncertainty estimation of 34% is generally consistent with the estimation by ref. 13 that the North Pacific and North Atlantic records have uncertainties of 45 and 42%, respectively.

Fig. 3.

Be isotopes and constraints on denudation/Be weathering rates over the past 12 Myr. (A) The late Neogene normalized seawater ¹⁰Be/⁹Be record. The record is produced by normalizing ¹⁰Be/⁹Be records over the past 12 Myr to the present-day average for each basin ¹⁰Be/⁹Be_sw (gray circles), compiled by ref. 13. We note that the oldest data point in the ¹⁰Be/⁹Be_sw record is excluded due to its large measurement uncertainty. The black line represents the 10-point running mean, with the shaded area standing for the 1 SD error of the record. (B and C) The blue area marks the range of denudation/Be weathering rates compatible with the ¹⁰Be/⁹Be record, under the present-day (B) and the reworked clay (C) models. While the model shows that Be isotopes do not constrain the upper limit of the denudation rate (Fig. 2), here we assume the upper limit of denudation rate is 1,500 t/km²/yr, the maximum value observed in large river basins (SI Appendix, Table S5). We note that the modeling results cover nearly the entire figure, showing that Be isotopes are compatible with nearly all possibilities within the denudation range observed in large river basins. Dashed lines link the present-day denudation/Be weathering rates with the highest and lowest rates compatible with the models and show that the Be isotope data are consistent with both up to an 8.2-fold decrease (B and C) and a 10.9-fold increase (B) or a 5.7-fold increase (C) in denudation/Be weathering rates. Because denudation and Be weathering are linearly linked, all data can be referenced to either y axis. The modeling results are consistent with other estimates from the sediment volume record (12) and rock cooling ages (15).

Using this dataset, we estimate the Neogene history of denudation and weathering rates from the normalized ¹⁰Be/⁹Be_sw record under both the present-day and reworked clay scenarios. For these estimations, we used an inversion approach based on a Monte Carlo method adopted from ref. 46 (Materials and Methods). This approach allows us to search all model solutions within certain ranges of model parameters. In our calculation, the range of denudation within which we solve the model for the denudation history is from 0 to 1,500 t/km²/yr. The upper limit of ${\text{D}}_{\text{riv}}$ is set as the greatest denudation rate in large river basins with drainage area larger than 5 × 10⁵ km², which is observed in the Huanghe River, one of the Tibet-draining rivers (SI Appendix, Table S5).

Under the present-day scenario the ¹⁰Be/⁹Be_sw record is consistent with up to a 10.9-fold increase in continental denudation and Be weathering rates over the last 12 Myr, and using the reworked clay scenario, it is consistent with up to a 5.7-fold increase. This range of results allows for increases in continental denudation far beyond the range of estimates from the sediment record (12) and rock cooling ages (15), which support a fourfold and twofold increase in continental denudation rates, respectively.

Interestingly, the model results for the present-day and reworked clay scenarios also show that both scenarios are consistent with up to an 8.2-fold decrease in the continental denudation and Be weathering rates over the last 12 Myr. The largest magnitude of decrease occurs if the continental denudation rate decreased from 1,500 t/km²/yr to the modern level during the past 12 Myr (although note that a global denudation rate of 1,500 t/km²/yr is currently the world’s highest value in large southeast Asian rivers and would likely only occur when mountain-building events similar to Himalayan orogeny happen all over the world). These results show that the Neogene ¹⁰Be/⁹Be_sw record is consistent with a large range of continental denudation and Be weathering rates (Fig. 3 B and C) including both significant increases and decreases. We emphasize that this simply reflects how insensitive the ¹⁰Be/⁹Be_sw ratio is to the variations in continental denudation rates as discussed earlier.

Resolution of the Be Weathering Conundrum.

Our results resolve an important conundrum—namely, why the constancy of the ¹⁰Be/⁹Be proxy record has been seemingly at odds with numerous other proxies that, to a first order, indicate enhanced denudation and weathering rates likely occurred in the late Cenozoic. The apparent contradiction between Be and the other proxies is a consequence of the strong impact of coastal scavenging on the ⁹Be flux, while this effect has only a minor impact on other proxies (e.g., Sr and Li isotopes) which are truly dissolved ions and not absorbed by suspended matter in the water (47). Moreover, while coastal scavenging impacts the ⁹Be flux to the open ocean, it has only a small effect on the flux of ¹⁰Be from the upper atmosphere because nearly all oceanic ¹⁰Be comes directly from the atmosphere and not riverine sources (35). As a result, the ¹⁰Be/ ⁹Be values of the open ocean are buffered from the effects of increased continental denudation. From these results it also follows that the Be record cannot be used to falsify the hypothesis that weathering rates have increased over the late Cenozoic (e.g., refs. 1, 2).

Potential Forcing Mechanisms for the Acceleration of Continental Silicate Weathering.

Although our model solves the Be weathering conundrum, the forcing mechanism for the acceleration of continental silicate weathering during the late Cenozoic is still under debate. Most studies agree that the global physical erosion increased during the late Cenozoic (e.g., refs. 12, 15, 20, 32). However, the relationship between silicate weathering and physical erosion is generally believed to be complicated (48–50). Under low physical erosion rates, silicate weathering is limited by the supply of fresh silicate minerals by physical erosion, resulting in a positive correlation between weathering and physical erosion (48, 50). Under high physical erosion rates, modeling of the silicate weathering process and observations in small watersheds suggest that the supply of silicate minerals is sufficient and no longer the limiting factor of the silicate weathering rate, which is instead limited by climatic factors (48, 49, 51). The weathering regimes under low and high physical erosion rates are called supply-limited and weathering-limited regimes, respectively (24).

In order to test how observations on larger scales compare with those in small watersheds, we next explore the relationship between physical erosion rates and silicate weathering, both in larger rivers and on subcontinental scales. For this purpose, we use the riverine dissolved Si flux as a measure for silicate weathering rates to avoid potential interferences from carbonate weathering. Milliman and Farnsworth (52) have divided the world’s land into 11 subcontinental regions and estimated the Si weathering and physical denudation rate of these regions and the islands of Indonesia. Using the dataset, we find that silicate weathering and physical erosion are always positively coupled, even when denudation rates are higher than 2,000 t/km²/yr on the subcontinental scale (Fig. 4A).

Fig. 4.

The correlation between Si weathering and physical erosion rate (A) on the continental scale and (B) in global large river basins. The red dot represents Huanghe River, which is excluded in the regression analysis. The subcontinental-scale Si weathering and physical erosion rates are from ref. 52, and the Si weathering rate and physical erosion rates in large river basins are cited from ref. 25 and ref. 52, respectively.

The positive correlation between silicate weathering and physical erosion is also observed in large river basins for the whole range of physical erosion rates in the dataset, spanning from 0 to 2,000 t/km²/yr (Fig. 4B). Large rivers generally have floodplains, which the small basins do not have. We propose that the apparent contradiction between the weathering regimes of small and large river basins can be explained by weathering in floodplains. Many studies suggest that floodplains act as reactors to further dissolve the silicate minerals provided by mountain erosion (53–56). Therefore, with floodplains, physical erosion can further increase silicate weathering resulting in higher physical erosion thresholds between the two weathering regimes and consequently a stronger positive coupling between silicate weathering and physical erosion that is not as obvious or prevalent in small mountainous catchments. Some evidence supporting this argument comes from the Huanghe River. The riverbed of the Huanghe River is several meters higher than its surrounding floodplains in its lower reaches, an unusual situation caused by its high sediment load and low river discharge. Thus, the Huanghe River cannot receive any weathering flux from its floodplains, and the expected correlation between silicate weathering flux and physical erosion rate in Huanghe River falls apart. Of all the large rivers shown in our global database (Fig. 4B), the Huanghe River is the only one that does not follow the positive correlation trend between silicate weathering and physical erosion. From these observations we suggest that floodplain weathering may be the key mechanism that couples silicate weathering and physical erosion at high physical erosion rates. Therefore, it is likely that enhanced physical erosion by mountain building accelerated continental silicate weathering via upland and floodplain weathering, leading to a decline in atmospheric CO₂ and climate cooling during the late Cenozoic (1, 2).

Conclusion

A model describing the response of seawater ¹⁰Be/⁹Be ratios to changes in continental denudation rates that, unlike previous models, assumes a constant partition coefficient of Be between dissolved and adsorbed phases shows an excellent match between modeled and observed ¹⁰Be/⁹Be records in the modern oceans. Furthermore, the model predicts that fluctuations in the riverine ⁹Be flux into the coastal ocean are largely counterbalanced by scavenging of ⁹Be; this results in nearly constant ¹⁰Be/⁹Be ratios in seawater even when global denudation and Be weathering rates increase by three orders of magnitude. With increasing denudation and Be weathering rates, ¹⁰Be/⁹Be ratios in seawater thus reach nearly constant values in the oceans and thereby become insensitive as a proxy of denudation rates. Nevertheless, the model results can be used to set constraints on the potential magnitude of an increase in denudation rates over the late Cenozoic. The Neogene ¹⁰Be/⁹Be_sw record is consistent with nearly an 11-fold increase in global continental denudation rates, allowing for increases far beyond the range of estimates from other denudation proxies (12, 15).

The results here solve the contradiction between the Be record and modern observations that show a significant correlation between denudation rates and silicate weathering rates on a global scale. In the present day, >50% of denudation occurs in the steepest mountainous regions (57), accounting for ∼10% of the Earth’s surface. Therefore, during the late Cenozoic, when the area of mountainous regions (58, 59) and consequently denudation rates was increasing, we should expect that continental silicate weathering also increased. The Be record is in fact consistent with such an increase.

Our results provide important information on how the geological carbon cycle works. From a carbon mass balance perspective, assuming that the CO₂ degassing rate is relatively constant during the late Cenozoic (21), the increasing continental silicate weathering and CO₂ consumption rates must be compensated by other carbon cycle processes. A number of likely possibilities exist, including climate-modulated carbon release by carbonate dissolution via pyrite weathering (30), oxidation of fossil organic carbon regulated by glacier activity (23), and variability of CO₂ consumption due to the temperature dependence of subaerial and seafloor basalt weathering (26, 28). In other words, the increase in CO₂ consumption by continental silicate weathering could be counterbalanced by enhanced carbon release or reduced carbon consumption by carbonate dissolution via pyrite weathering, organic carbon weathering, and/or basalt weathering, maintaining a close mass balance of the carbon cycle. The important point is that with the modeling results we present, there is no robust geologic evidence for constant (or decreasing) continental silicate weathering rates as climate cooled in the late Cenozoic. We thus rule out the possibility that the weathering of felsic continental silicate minerals acted as the Earth’s thermostat during the late Cenozoic (60). On the contrary, our results suggest that Earth’s habitability is likely maintained by multiple thermostats operating within the totality of the planetary carbon cycle, at least during periods of extensive mountain building on Earth’s surface during the Phanerozoic.

Materials and Methods

Partition Coefficients and the Particle Concentration Effect.

How one treats coastal marine scavenging processes is key to interpreting the evolution of ¹⁰Be/⁹Be ratios in Cenozoic seawater. Therefore, knowledge of the behavior of the partition coefficient ${\text{Kd}}_{\text{diss}}^{\text{Be}}$, that is, the ratio of the concentration of Be adsorbed on suspended particles ([Be]_reac, in mg/kg) to its concentration in the dissolved load ([Be]_diss, in mg/L), is critical. Consider an adsorption reaction, where ∼X represents an adsorption site on suspended particles; [∼X] represents the concentration of Be if all the available particle adsorption sites in a volume of water are occupied by Be atoms (mg Be/L); XBe is a Be ion bound to ∼X, [XBe], and represents the actual concentration of adsorbed Be per unit volume of water (mg Be/L); and total suspended solids (TSS) is the mass of solid particles per unit volume (kg/L) (61): [Be]_reac = $\frac{\left[\text{XBe}\right]}{\text{TSS}}$. Given the adsorption reaction Be_diss + ∼X = XBe, the equilibrium constant K_eq is

$${\text{Kd}}_{\text{eq}}^{}=\frac{\left[\text{XBe}\right]}{\left[\sim \text{X}\right]*\left[\text{Be}\right]\text{diss}},$$ [1]

and the partition coefficient, ${\text{K}}_{\text{diss}}^{\text{Be}}$, is

$${\text{Kd}}_{\text{diss}}^{\text{Be}}=\frac{\left[\text{Be}\right]\text{reac}}{\left[\text{Be}\right]\text{diss}}=\frac{\left[\text{XBe}\right]}{\text{TSS}*\left[\text{Be}\right]\text{diss}}=\frac{\left[\text{XBe}\right]}{\left[\sim \text{X}\right]*\left[\text{Be}\right]\text{diss}}*\frac{\left[\sim \text{X}\right]}{\text{TSS}}=\frac{\left[\sim \text{X}\right]}{\text{TSS}}*K_{\text{eq}}.$$ [2]

In this case, ${\text{K}}_{\text{diss}}^{\text{Be}}$ is not expected to change with suspended particle concentrations, because K_eq and $\frac{\left[\sim \text{X}\right]}{\text{TSS}}$ are both constants, and $\frac{\left[\sim \text{X}\right]}{\text{TSS}}$ is the mass of Be that can be scavenged per unit mass of suspended particles (mg Be/kg of particles), which is a function of the number of potential adsorption sites. Nevertheless, the particle concentration effect (PCE), which is the notion that the value of ${\text{K}}_{\text{diss}}^{\text{Be}}$ decreases with increasing suspended particle concentrations, has been accepted by numerous studies based on observations (61–64). The apparent contradiction between the expected constancy of ${\text{Kd}}_{\text{diss}}^{\text{Be}}$ (61) and observed PCEs (61–64) has been shown to disappear in studies that employ ultrafiltering methods to effectively remove colloidal phases (65–67). In such experiments, nearly constant partition coefficients have been observed, showing that PCEs are measurement artifacts from taking the colloid phase mistakenly as the dissolved phase.

Modeling Seawater ¹⁰Be/⁹Be from Meteoric and Denudation Input.

A general beryllium isotope mass balance equation can be written, based on the discussion in the main text:

$${}_{}{}^{10}\text{B}\text{e}/{}_{}{}^9\text{B}{\text{e}}_{\text{sw}}{ }_{}=\frac{\left(\frac{{\text{A}}_{\text{oc}}}{{\text{A}}_{\text{riv}}}\right){*\text{F}}_{\text{oc}}^{{10}_{\text{Be}}}+{\text{φ}}_{\text{del}}*{\text{F}}_{\text{riv}}^{{10}_{\text{Be}}}}{{\text{φ}}_{\text{del}}{*\text{D}}_{\text{riv}}*\left[{}_{}{}^9\text{B}\text{e}\right]\text{cc}*\left({\text{f}}_{\text{reac}}^{9_{\text{Be}}}+{\text{f}}_{\text{diss}}^{9_{\text{Be}}}\right)},$$ [3]

where ¹⁰Be/⁹Be_sw is the seawater Be isotope ratio; ${\text{F}}_{\text{oc}}^{{10}_{\text{Be}}}$ and ${\text{F}}_{\text{riv}}^{{10}_{\text{Be}}}$ are the average meteoric ¹⁰Be flux of ¹⁰Be per unit area over the ocean surface and the continent, respectively; $[{}_{}{}^9\text{B}\text{e}]\text{cc}$ is the ⁹Be concentration in the continental crust; A_oc is the surface area of the oceans; A_riv is the drainage area of rivers; $({\text{f}}_{\text{reac}}^{9_{\text{Be}}}+{\text{f}}_{\text{diss}}^{9_{\text{Be}}})$ is the sum of the reactive and dissolved fractions of the total riverine ⁹Be flux (35, 68); and D_riv is the denudation rate, which is the mass of eroded material per unit time per unit area of land. Beryllium weathering rates can be simply calculated as F(⁹Be_riv) = ${\text{D}}_{\text{riv}}*[{}_{}{}^9\text{B}\text{e}]\text{cc}*\left({\text{f}}_{\text{reac}}^{9_{\text{Be}}}+{\text{f}}_{\text{diss}}^{9_{\text{Be}}}\right)$. ${\text{φ}}_{\text{del}}$ is the scavenging factor, describing the fraction of the riverine Be flux that survives scavenging in the coastal oceans.

We try to calculate ${\text{φ}}_{\text{del}}$. Let M be the beryllium content per unit volume of water (in mg/L). The amount of beryllium absorbed to unit mass of particles (C_reac, in mg/mg) can be calculated as

$${\text{C}}_{\text{reac}}=\frac{{\text{M}*\text{Kd}}_{\text{diss}}^{\text{Be}}}{1+{\text{Kd}}_{\text{diss}}^{\text{Be}}*\text{x}}.$$ [4]

Here x represents the particle concentration in coastal water (mg/L). As scavenging goes on, x decreases, and the beryllium absorbed to the falling particles is removed. The removal rate of beryllium can be calculated as

$${\text{dM/dt}=-\text{C}}_{\text{reac}}*\text{dx/dt}.$$ [5]

Solving this differential equation with Eq. 4, we have

$$\text{M}\left(\text{x}\right){=\text{C1}*\text{e}}^{\text{C2}}{*(1+\text{K}}_{\text{diss}}^{\text{Be}}*\text{x}).$$ [6]

Here C1 and C2 are both constants. When the particle concentration (x) decreases to 0, the beryllium still present in the water survives the scavenging and reaches the open ocean. The proportion of beryllium that survives and reaches the open ocean (${\text{φ}}_{\text{del}})$ equals the ratio of the M value at x = 0 to the M value at x = x(initial):

$${ \text{Φ}}_{\text{del}}=\frac{\text{M}\left(0\right)}{\text{M}\left(\text{x}\left(\text{initial}\right)\right)}.$$ [7]

Here x(initial) represents the initial particle concentration in coastal oceans. This value should be set by the mixing of river water and coastal water. Consider the particle flux (i.e., the physical erosive flux, F) from rivers that reaches the coastal water mass with a volume of V, then x(initial) can be calculated as

$$\text{x}\left(\text{initial}\right)= \text{F/V}.$$ [8]

By introducing the physical erosion factor (α), which is the ratio of physical erosion rate to the denudation rate (D_riv), we have

$${\text{F}= \text{D}}_{\text{riv}*}{\text{α}*\text{A}}_{\text{riv}}.$$ [9]

As V is proportional to the coastline length (CL, in km), we have

$$\text{V}=\text{k}*\text{CL}.$$ [10]

Here k is a constant. Combining Eqs. 7–10, we have

$${\text{φ}}_{\text{del}}=\frac{1}{1+\frac{{\text{Kd}}_{\text{diss}}^{\text{Be}}{*\text{D}}_{\mathit{riv}}{* \text{α}*\text{A}}_{\mathit{riv}}}{k*CL}}.$$ [11]

We can now calculate the ¹⁰Be/⁹Be ratio of seawater as a function of continental denudation rates with Eqs. 3 and 11.

Correction for Advection Flux from Adjacent Ocean Basins.

Next, we try to quantify the effect of advection flux on the seawater ¹⁰Be/⁹Be ratios. This is important because dissolved beryllium in shallow ocean water is derived from the continental beryllium input via rivers and the advective water flux of beryllium from adjacent ocean basins. ¹⁰Be/⁹Be_oc is determined by the mixture of these two endmembers:

$${}_{}{}^{10}\text{B}\text{e}/{}_{}{}^9\text{B}{\text{e} }_{\text{shallow}}=\frac{{}_{}{}^{10}\text{B}{\text{e}}_{\text{denudation}}+{}_{}{}^{10}\text{B}{\text{e}}_{\text{advection}}}{{}_{}{}^9\text{B}{\text{e}}_{\text{denudation}}+{}_{}{}^9\text{B}{\text{e}}_{\text{advection}}},$$ [12]

which can be rewritten as

$${[\frac{{}_{}{}^{10}\text{B}\text{e}}{{}_{}{}^9\text{B}\text{e}}]}_{\text{shallow}}={[\frac{{}_{}{}^{10}\text{B}\text{e}}{{}_{}{}^9\text{B}\text{e}}]}_{\text{denudation}}*\text{f}{}_{}{}^9\text{B}{\text{e}}_{\text{denudation}}+{[\frac{{}_{}{}^{10}\text{B}\text{e}}{{}_{}{}^9\text{B}\text{e}}]}_{\text{advection}}*(1-\text{f}{}_{}{}^9\text{B}{\text{e}}_{\text{denudation}}),$$ [13]

where $\text{f}{}_{}{}^9\text{B}{\text{e}}_{\text{denudation}}$ represents the fraction of riverine ⁹Be in the total ⁹Be input and can be calculated as

$$\text{f}{}_{}{}^9\text{B}{\text{e}}_{\text{denudation}}=\frac{{\text{φ}}_{\text{del}}{*\text{D}}_{\text{riv}}*\left[{}_{}{}^9\text{B}\text{e}\right]\text{cc}*\left({\text{f}}_{\text{reac}}^{9_{\text{Be}}}+{\text{f}}_{\text{diss}}^{9_{\text{Be}}}\right)}{({\text{φ}}_{\text{del}}{*\text{D}}_{\text{riv}}*\left[{}_{}{}^9\text{B}\text{e}\right]\text{cc}*\left({\text{f}}_{\text{reac}}^{9_{\text{Be}}}+{\text{f}}_{\text{diss}}^{9_{\text{Be}}}\right)+{\text{F}}_{\text{avd}}*{\left[\text{Be}\right]}_{\text{oc}}}.$$ [14]

Here F_avd is the advection water fluxes from adjacent ocean basins, and${\left[\text{Be}\right]}_{\text{sw}}$ is the Be concentration in the shallow layer in the ocean basins. With Eqs. 12–14, the influence of the advection flux on the seawater ¹⁰Be/⁹Be can be evaluated. With both continental inputs and the advection flux considered, the ¹⁰Be/⁹Be of modern seawater can be calculated. The results are presented in Fig. 1 and SI Appendix, Table S4.

Calculating the Modern Scavenging Factor and Cenozoic Denudation and Weathering.

To estimate the scavenging factors in the modern ocean that fit the modern seawater ¹⁰Be/⁹Be (${\text{φ}}_{\mathit{del}}^{ob})$, we used an inversion approach based on a Monte Carlo method adopted from ref. 46. For each Monte Carlo calculation, we calculate seawater ¹⁰Be/⁹Be with the parameter listed in SI Appendix, Table S2, a random value between 0 and 1 of ${\text{φ}}_{\mathit{del}}^{ob}$, and random values of the advection flux, the seawater Be concentration, and the ¹⁰Be/⁹Be of advective Be within the observed range of the three parameters (SI Appendix, Table S3) and then compare the calculated seawater ¹⁰Be/⁹Be with the measured ¹⁰Be/⁹Be in seawater. If they match, the random value of ${\text{φ}}_{\mathit{del}}^{ob}$ is saved as a valid solution. We repeat the calculations until the range of ${\text{φ}}_{\mathit{del}}^{ob}$ becomes stable, which indicates the full range of ${\text{φ}}_{\mathit{del}}^{ob}$ is obtained.

Similarly, for the calculation of Cenozoic denudation and the Be weathering history, we assume the highest denudation rate observed in the large river basins (i.e., about 1,500 t/km²/yr) is the upper limit of the Cenozoic continental denudation rates. For each Monte Carlo calculation, a random value between 0 and 1,500 t/km²/yr for the continental denudation rate is used to calculate the seawater ¹⁰Be/⁹Be, which is compared with the Cenozoic record of seawater ¹⁰Be/⁹Be. The random values of denudation rates that can match the calculated seawater ¹⁰Be/⁹Be to the record are saved as model solutions. The calculations are repeated until the full range of continental denudation rates fitting the record is obtained. Then the Be weathering history is generated as F(⁹Be_riv) = ${\text{D}}_{\text{riv}}*\left[{}_{}{}^9\text{B}\text{e}\right]\text{cc}*\left({\text{f}}_{\text{reac}}^{9_{\text{Be}}}+{\text{f}}_{\text{diss}}^{9_{\text{Be}}}\right)$.

Data Availability

The MATLAB codes used in the study are available at GitHub, https://github.com/shileigeo/Bemodel. All other study data are available in the article and SI Appendix.