Hydrologic Thermostat
When the silicate-rich rocks and minerals in Earth's interior are uplifted and exposed to Earth's surface, they dissolve. On a geologic time scale, this chemical weathering process ultimately creates a sink for CO2, thereby influencing global temperatures. Maher and Chamberlain (p. 1502, published online 13 March) developed a theoretical framework for understanding the fundamental relationship between weathering, tectonics, and the geological carbon cycle. The analysis suggests that temperature plays less of a role in regulating chemical weathering—which is dependent on the balance of tectonic uplift and erosion—than runoff on continents and the time that silicate minerals are exposed to fluids. Plateaus in weathering fluxes with increasing runoff or temperature allows for the stabilization of atmospheric CO2 despite high rates of uplift or erosion.
Abstract
Earth’s temperature is thought to be regulated by a negative feedback between atmospheric CO2 levels and chemical weathering of silicate rocks that operates over million-year time scales. To explain variations in the strength of the weathering feedback, we present a model for silicate weathering that regulates climatic and tectonic forcing through hydrologic processes and imposes a thermodynamic limit on weathering fluxes, based on the physical and chemical properties of river basins. Climate regulation by silicate weathering is thus strongest when global topography is elevated, similar to the situation today, and lowest when global topography is more subdued, allowing planetary temperatures to vary depending on the global distribution of topography and mountain belts, even in the absence of appreciable changes in CO2 degassing rates.
Despite substantial changes in solar luminosity, plate tectonics, and atmospheric composition, over billions of years temperatures on Earth have remained favorable for liquid water and, by extension, life (1). A requirement for maintaining such clement conditions is a chemical weathering process that converts atmospheric CO2 and silicate rocks to alkalinity and divalent cations, which are then buried on the seafloor as carbonate minerals (2–5). Chemical weathering rates cannot be out of balance with the supply of CO2 from volcanic and metamorphic sources for very long without catastrophic consequences (6). Fortunately, such imbalances have been infrequent. Yet, Earth’s climate has varied between warm ice-free conditions and cold extensively glaciated states, suggesting a climate system with variable regulation. The stability of Earth’s climate thus requires both a negative feedback between chemical weathering rates and temperature and a mechanism that allows the strength of the feedback, or extent of regulation, to vary (7). The strength of the feedback is dictated by the functional relationship between the weathering rate and climate, and when balanced against CO2 degassing rates, determines planetary temperatures (4–7). Several processes could allow the strength of the feedback to vary (8–12), suggesting that the mechanisms underlying one of the most profound features in the sculpting of Earth’s history remain unresolved.
We developed a mathematical framework that captures how the strength of the weathering feedback changes as a function of the tectonic regime (13). We linked the weathering rate per unit of area of continent to the interaction between runoff and tectonic processes. The two are linked by the balance between the time that water spends in the weathering zone (fluid travel time), which depends on runoff and flow path length, and the kinetics of mineral weathering, which are a function of composition, temperature, and erosion rate. The weathering flux to the oceans should be maximized when thermodynamic equilibrium between the dissolving and precipitating minerals is approached, resulting in a “thermodynamic limit” not included in previous models. Conversely, weathering fluxes are at a minimum when fluid travel times are short relative to the time required for weathering reactions to reach equilibrium (equilibrium time). In this formulation, weathering rates can increase more substantially in tectonically active than in inactive areas in response to changes in climate, as suggested by numerical models (7, 14).
The proposed model combines two equations: (1) a solute transport equation that quantifies weathering-derived solute as a function of the mean fluid travel time in a catchment and (2) an equation that relates the supply of fresh rock from erosion to the downward propagation of a weathering front. We calculate the solute concentration (C) as a function of the Damköhler number (Da) (15). The Damköhler number is a dimensionless number that compares the mean fluid travel time [Tf ≈ Lϕ/q(year)] to the time required to reach equilibrium [Teq ≈ Ceq/Rn(year)], where q[m/year] is runoff, the reactive flowpath length (Lϕ) is flowpath length [L(m)] times effective porosity (ϕ), Ceq(μmol/liter) is the “thermodynamic limit” (i.e., the maximum concentration), and Rn(μmol/liter/year) is the reaction rate (n, a specific mineral composition) (16). Because runoff is a key variable, we factor out runoff and introduce the Damköhler coefficient (Dw), which is modified to account for the supply of fresh minerals through erosion.
(1)where the fraction of fresh minerals, fw (= Xs/Xr), decreases with increasing soil age (Ts) or decreasing mineral supply rate (17–20) to moderate the maximum reaction rate (Rn,max). The minimum Teq occurs when the concentration of soil minerals (Xs) is equal to that of the original rock (Xr), or when Ts is very small, according to the following expression that is applicable to both steady-state (i.e., a balance between denudation and material supply) and transient landscapes
(2)where keff is the weathering rate constant, A is the specific surface area of the minerals, and m is the molar mass of the weathering minerals [(13), table S1]. At a given runoff, larger Dw values reflect more-efficient solute generation and systems that are closer to the thermodynamic limit. The final equation for solute production is
(3)where τ is a constant (= e2) [(13), figs. S1 to S3]. The weathering flux (W) is computed from Eq. (3) as C × q. Although we use SiO2(aq) as a proxy for weathering, Ca and Mg derived from silicate weathering would show the same behavior (13, 16). The solute production model does not capture all possible biogeochemical and climatic feedbacks that might operate on q, Ceq, keff, and Ts (3–6, 11). Some key parameters are also not well constrained by observations, and hence our assumptions require further evaluation as suitable data become available (21).
The maximum solute concentration occurs when the mean fluid travel time (Tf) exceeds the equilibrium time (Teq) at a given runoff. For example, consider a region on Earth at point 4 on Fig. 1, with short Tf and long Teq (22). If fresh minerals are supplied to the weathering zone, Teq decreases and solute concentrations increase, even with no change in Tf (point 3). As erosion increases and Teq becomes less than Tf, the thermodynamic limit is approached (point 1) and solute concentration remains fixed. At the thermodynamic limit, concentration does not vary with runoff, as observed for some rivers (23, 24). As declining surface uplift or erosion decreases the supply of fresh minerals from soil production, Teq will increase, resulting in lower solute concentration, even if Tf remains long (point 2). Hence, climate (through runoff) is mechanistically coupled to erosion through the operative physical length scales and thermodynamic limits.
(A) Hillslope cross-sections with variable slope, soil thickness, mineral abundance, and mean fluid travel time. Red arrows show the production of soil from bedrock (P) and soil removal by erosion (E) and chemical denudation (W). Dashed lines indicate the water table, whereas slope is distinguished by angles α and β, with α > β. Soil thickness and fw are equivalent for hillslopes 1, 2, and 4, whereas soil thickness is lower and fw higher for hillslope 3. Fresh bedrock above the water table decreases the Teq, so that Tf > Teq. (B) Evolution of SiO2(aq) as a function of Tf and Ts. The solid black line corresponds to weathering of fresh mineral, whereas light and stippled lines correspond to solute evolution for different Ts values. kyr, thousand years. Hillslope 1 (point 1) indicates a system at the thermodynamic limit where Tf > Teq, as compared to hillslopes 2 to 4, where Tf < Teq. Hillslopes 3 and 4 show how mineral supply (or fw) affects solute production, hillslopes 2 and 4 show how Tf affects solute production, and the greater relief of hillslope 1 as compared to that of 2 results in larger Lϕ.
This formulation requires that as Tf becomes shorter than Teq, solute concentrations decrease and solute fluxes plateau (Fig. 2). The Dw determines the runoff at which this plateau is reached. This relationship is observed in modern rivers draining active mountain ranges where high erosion and a rapid supply of fresh minerals result in short Teq, so that solute concentrations and fluxes are high (Fig. 2). These systems have Dw values greater than 0.03 m/year. In contrast, in tectonically inactive areas, such as large cratons, the solute concentrations and fluxes are smaller and Dw values lower, because the reduced supply of fresh minerals to the weathering zone increases Teq (25). The competition between Tf and Teq in modern river basins is evident by the large range of Dw values—about a factor of 100. Although we use SiO2(aq) as a proxy for weathering, Ca and Mg derived from silicate weathering would show the same behavior (16).
(A) SiO2(aq) for global rivers (8) as a function of runoff, compared to contours of Dw coefficients from 0.3 and 0.001 m/year, where 0.3 m/year corresponds to the global maximum Dw and Ceq. (B) SiO2(aq) fluxes. The range of Dw contours corresponds to either changes in Ts from 0 to 1 million years, Lϕ of 0.10 to 0.001 m, or variations in both. A Dw of 0.03 m/year (collisional/craton divide) corresponds to Lϕ of 0.1 m and Ts of 100,000 years. The 1:1 line for flux:discharge is the thermodynamic limit. Each river is shaded according to the erosional flux (assumed to reflect mineral supply to the weathering zone), using the total suspended sediment flux.
To change solute fluxes in rivers requires altering Lϕ, Teq, and/or runoff via tectonic and/or climatic events. For example, the construction of a mountain belt will alter all three of these parameters through the development of relief, an increased supply of fresh minerals (26, 27), and increased runoff due to orographically induced precipitation (28). During initial mountain building, fresh rock exposed to the weathering zone shortens Teq and increases solute concentrations (Fig. 3A). When mountains reach sufficient height to create orographic rainfall, solute fluxes will increase further with additional runoff. Even if thin soils result in short Tf in upland areas, the creation of upland topography may result in the deposition of reactive floodplains (29, 30), a decrease in Teq, and possibly an increase in Tf. Once the mountain belt reaches a physical steady state, no additional increase in chemical weathering is possible without a change in runoff. Finally, as tectonism wanes, reducing mineral supply to the weathering zone, solute fluxes decrease and complete the cycle.
(A) The inset depicts how an enhanced supply of fresh mineral from increasing erosion, combined with global cooling and decreased runoff, results in a decrease in weathering fluxes from the cratons (points 1 to 2, minus sign, pink wedge), whereas solute fluxes increase in mountains (points 1 to 3, plus sign, gray wedge), so that weathering fluxes (and global CO2 levels) could remain at near-modern levels, depending on the area occupied by different weathering regimes. (B) Colored bars and gray wedges show the change in solute flux for a doubling of runoff for mountainous regions (blue), the global average (purple), and cratons (green), with the corresponding percent change in solute flux per °C of increase. Gray lines are contours of Dw as in Fig. 2.
The atmospheric heat budget of Earth is driven by the fluxes of atmospheric greenhouse gases, primarily CO2. Silicate weathering is the dominant mechanism that sequesters CO2 over geologic time scales (2). We propose that the removal of CO2 is regulated by the intensity of the hydrologic cycle, rather than directly by temperature. Increases in global mean temperatures (GMTs) are associated with more precipitation and attendant changes in runoff (31), although climate model predictions vary widely. A climate model study of the response of runoff to increased GMT found an increase in runoff of 6.8 to 2.3%/°C between high- and low-latitude rivers, respectively (31). Because the effects of global warming on runoff will not be distributed evenly across latitudes, we use the maximum runoff sensitivity of 6.8%/°C GMT, so that a doubling of runoff occurs with a temperature increase of 15°C. Assuming that temperature affects only runoff (supplementary text and figs. S7 and S8), changes in solute fluxes for a doubling of runoff across low-relief regions, active tectonic regions, and the global average indicate the differential climate sensitivity (Fig. 3B). Weathering fluxes in basins with moderate erosion rates, which represent a large portion of Earth’s surface today (32), show minimal change. In contrast, active high-relief regions near the thermodynamic limit are the most sensitive to climatic changes (27), because higher Dw values afford a large change in runoff before maximum solute flux is achieved.
The order-of-magnitude difference in climate sensitivity between inactive and active tectonic regions may dramatically alter the global weathering feedback. The climate-weathering feedback is strongest in rapidly eroding regions near the thermodynamic limit, as shown by the wedges in Fig. 3B. In low-relief areas, the climate feedback is weaker, because solute fluxes plateau when Teq exceeds Tf. During times of global warming and amplification of the hydrologic cycle, weathering fluxes will increase disproportionately between tectonically active and inactive areas, with high-relief tectonic areas providing proportionally more alkalinity to the oceans. At a given CO2 degassing rate, global temperature is thus determined by the differential sensitivity of mountainous and low-relief areas to runoff, and will vary depending on the distribution of erosional regimes and mountain belts (Fig. 3A). This feature of our model allows weathering rates and atmospheric CO2 to stabilize at different levels but prevents runaway CO2 consumption during active tectonic periods, due to the enhanced climate sensitivity. Similarly, periods of warming and the attendant increases in runoff will drive weathering rates upward, particularly in mountainous regions. The solute production model explains the observed correlation between erosion and chemical weathering fluxes (8, 26), while preserving the negative feedback between silicate weathering rates and global temperature.
Supplementary Materials
www.sciencemag.org/content/343/6178/1502/suppl/DC1
Materials and Methods
Supplementary Text
Figs. S1 to S8
Table S1
References and Notes
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- Acknowledgments: The paper benefitted greatly from the reviews provided by several anonymous reviewers. This work was supported by the U.S. NSF (EAR-1254156 to K.M.). Data used in this study come from previously published studies, and the details of the model are provided in the supplementary materials.
