Critical zone processes limit alkalinity export from natural basaltic systems

EW is a strategy for long-term removal of CO₂ that seeks to mimic Earth’s natural carbon cycle through the addition of crushed volcanic rock, generally basalt, to agricultural fields^1,9. Weathering of basalt converts CO₂ in soil water to dissolved inorganic carbon, including both HCO₃⁻ (bicarbonate ion) and CO₃²⁻ (carbonate ion) that comprise carbonate alkalinity. If that alkalinity is transported to the oceans, it could modify ocean pH and promote the dissolution of atmospheric CO₂ into seawater, potentially moderating ocean acidification that results from increasing pCO₂ and ultimately removing CO₂ as calcium carbonate minerals². The ready availability of basaltic rocks, combined with the operational scale of agricultural systems, has been used to argue for potential CDR between 0.5 and 2.5 Gt year⁻¹ (refs. ^10,11). However, this scale of removal, and the diverse geochemical and hydrologic processes that will govern it, have not been assessed relative to well-established natural basaltic weathering rates.

Globally, weathering of silicate rocks transfers 0.52 ± 0.10 Gt CO₂ year⁻¹ from subaerial surfaces to the oceans¹². On the basis of analysis of global river data, mafic rock weathering accounts for approximately 15–30% of this long-term flux^13,14, or 0.08–0.18 Gt CO₂ year⁻¹ (Methods), highlighting the outsized role of volcanic provinces in the carbon cycle. EW seeks to mimic this process by applying basalt to soils and equating the alkalinity produced by weathering to a carbon removal value. However, global rates of natural basalt weathering are a factor of 8–30 times less than present estimates of EW CDR potential. The present basaltic CO₂ consumption rate integrated over the rest of the century is 3.4–5.0 Gt CO₂, which is 1.0–4.7% of the 105–335 Gt CO₂ target for removal of remaining cumulative emissions estimated as necessary to meet climate goals for 2100 by the Intergovernmental Panel on Climate Change (IPCC)¹⁵. Although EW seeks to amplify this natural flux, whether sufficient alkalinity can be generated to substantially exceed background rates, and thereby achieve measurable CDR, remains uncertain.

Assessing how much CO₂ could be sequestered by basalt amendment is challenging^16,17. The quantity of basalt added to soils in most studies is a small fraction of the native soil. Typically, 1–20 kg m⁻² are added to soil; for a soil treatment depth of 30 cm and soil density 1,300 kg m⁻³, the amendment comprises only 1–5% of the post-treatment soil mass. A common method of assessing the extent of EW in a treated agricultural field is to sample the soil down to a depth of 10–30 cm pre- and post-amendment. Although a variety of approaches has been presented, base cation loss is generally computed as the difference between the expected masses of Ca, Mg, Na and K and the observed values (typically compared with a control plot), equating the ‘missing’ base cations to the fraction of feedstock dissolved¹⁸. This sampling strategy requires careful statistical evaluation to address spatial variability, covariances and non-normal distributions^19,20.

Once the fraction dissolved is defined, base cations released by weathering are converted into a CDR potential, CDR_pot, using the Ca, Mg, Na and K losses from the basalt, often multiplied by a factor (roughly 1.7) representing the approximate short-term response of the ocean carbon system to the addition of alkalinity and dissolved inorganic carbon². This method assumes that: (1) all of the base cations are dissolved by the action of carbonic acid and generate alkalinity in stoichiometric proportion to base cation loss and (2) all of the alkalinity generated is transported to the oceans. EW calculations using the CDR_pot metric project up to 10 t CO₂ ha⁻¹ year⁻¹ potential uptake based on observation and models of base cation depletion from the amended soil layer^10,21. Yet the extent to which this potential uptake will be realized in most systems is unknown because other processes limit the generation and net export of alkalinity across the integrated soil–regolith–groundwater–stream water system, that is, the critical zone. Here we use observations from natural basaltic weathering systems to constrain alkalinity export and the processes that govern alkalinity transmission. We focus on the export of alkalinity from the critical zone, because unlike shallow soil data, it represents carbonate alkalinity that might reach the oceans and affect the global CO₂ balance on a durable (1,000-year) timescale²². We do not consider non-basalt silicate amendments, as they are not available in sufficient volumes or would require substantial transport and processing. We also do not consider other potential effects of basalt addition to soils, such as changes in soil nutrient supply, plant productivity or soil organic carbon storage.

About 6% of the Earth’s land surface is covered in basaltic or intermediate volcanics²³, providing a wealth of natural experiments that can inform our understanding of alkalinity export in the context of EW. Alkalinity export from a watershed represents the net yield of both dissolution reactions that generate dissolved base cations and alkalinity as well as acidification, precipitation and ion exchange reactions that act as sinks along subsurface flow paths. Many of these processes occur outside the shallow soil zone and cannot be assessed with data from near-surface soil sampling. By contrast, measurement of solutes exported from watersheds provides an integrative metric for CDR. Stream solute data must be corrected for atmospheric deposition and for hydrothermal inputs in active volcanic zones, in which high-temperature fluids and acidic gases can react with host rock to generate high solute fluxes that are unrelated to surface weathering processes^24,25. Dissolution of hydrothermal mineralization in altered basalts in both natural systems and EW amendments can be difficult to distinguish from weathering of existing primary minerals and may enhance apparent weathering rates²⁶. For example, rapid alteration of accessory minerals such as calcite present at the ≤1% level can dominate dissolution fluxes of Ca²⁺ and enhance apparent weathering rates without contributing to long-term CDR.

Compilation of watershed studies in which atmospheric and hydrothermal inputs can be reasonably constrained indicates that CO₂ uptake in natural volcanic watersheds is modest (Fig. 1). Median estimates range from 0.16 t CO₂ ha⁻¹ year⁻¹ to as high as approximately 1.0 t CO₂ ha⁻¹ year⁻¹ in the volcanically active Luzon and Bicol arcs of the Philippines. A broader synthesis of export from basaltic rivers globally²⁵ reported uptake rates of 0.18 t CO₂ ha⁻¹ year⁻¹ in inactive volcanic provinces and 0.90 t CO₂ ha⁻¹ year⁻¹ in active volcanic provinces. Collectively, the difficulty in correcting for hydrothermal inputs and bias that results from river sampling at base flow suggests that these values may be biased high (Methods). Nevertheless, these observed fluxes from catchments that are nominally underlain by basalt or basaltic andesite are substantially lower than the CDR_pot (4–12 t CO₂ ha⁻¹ year⁻¹) proposed for some EW deployments that have much smaller basalt loadings^18,21. This discrepancy highlights the importance of evaluating not only the generation of alkalinity through mineral dissolution but also the resulting alkalinity export.

The highest CDR rates known from natural watersheds occur in wet tropical settings with large inputs of fresh, reactive, fine-grained pyroclastic materials produced by recent voluminous eruptions²⁴ and high water infiltration rates. The 1991 eruption of Mount Pinatubo buried adjacent river valleys with up to 0.5 m of tephra, corresponding to mass loadings > 500 kg m⁻², and sedimentation rates approximately two orders of magnitude higher than pre-eruption levels persisted for more than 20 years post-eruption²⁷. The tephra size distributions (modes 0.25–2.00 mm) are similar to basalt used in EW trials (p80 = 0.27–1.80 mm)^28,29. The corresponding hydrochemical observations illustrate that estimated CO₂ uptake is high but variable (Fig. 1), reflecting the high reactivity of freshly erupted material, impacts from hydrothermal processes and strong hydrologic and geomorphic controls on weathering export. Thus, although basaltic catchments may differ operationally from agricultural EW deployments, the processes operating in basaltic catchments provide empirical insight into the efficiency of alkalinity transfer through a watershed.

A common assumption underlying EW is that crushed basalt will have a greater overall dissolution rate compared with minerals in natural systems because comminution increases specific surface area (SSA)^1,10. However, water moving through volcanic catchments encounters reactive mineral surfaces along extended flow paths through soil, saprolite and fresh bedrock^30,31. The cumulative mineral surface area (SA) can therefore be substantial, even when individual substrates have lower SSAs (Extended Data Table 1). Notably, these same flow paths also expose weathering products to a wide range of secondary reactions that can attenuate alkalinity before export to reaching a stream.

The discrepancy between CO₂ uptake in natural volcanic systems and the larger values anticipated for EW can thus arise from a sequence of coupled chemical and hydrologic processes operating within a watershed. Dissolution reactions in the shallow soil zone determine the potential generation of alkalinity, whereas reactivity along subsurface flow paths, such as secondary mineral formation and ion exchange, dictate whether alkalinity ultimately survives transport through the landscape. The net alkalinity export therefore reflects the balance between weathering generation and downgradient attenuation within the watershed.

In EW studies, it is often assumed that grinding basaltic feedstock before application will lead to dissolution kinetics that are consistent with laboratory-derived kinetic rate laws for silicate hydrolysis⁹. Kinetic rate laws are typically defined according to an appropriation of transition state theory:

which defines the fractional rate of dissolution as the product of a mineral volume fraction (V_f), SA, kinetic rate constant (k) and a reaction affinity term (f(ΔG_rxn)) that describes the dependence on the departure from thermodynamic equilibrium.

Determining the effective SA for weathering can be challenging³². Specific SA is often assessed using gas adsorption techniques, such as the Brunauer–Emmett–Teller (BET) method, which are known to overpredict the SA that participates in mineral dissolution reactions³³. Also, BET SA measurements can be influenced by mineralogical heterogeneity and by the presence of high-SA alteration products such as clays and iron oxides³². A compilation of published measurements for crushed basalt shows that BET-measured SSA (SSA_BET) does not scale simply with grain size (Extended Data Figs. 1–3). Although very fine comminution (<100 μm) can increase measured SA, this relationship becomes weak at coarser grain sizes typically used in field applications. Experimental studies also report that dissolution rates of basaltic and olivine do not increase systematically with decreasing grain size or increasing BET-derived SA (ref. ³⁴). These observations underscore that the relationship between measured SA and observed reactivity remains uncertain, a long-standing challenge in quantifying natural weathering rates³³ and one that complicates efforts to extrapolate dissolution kinetics across scales¹⁷.

Although mineral dissolution with carbonic acid generates alkalinity, secondary aluminosilicate and oxyhydroxide precipitation reduce net alkalinity generation owing to the release of protons during hydrolysis reactions associated with secondary mineral precipitation, even when the secondary phase contains no base cations. In particular, hydrolysis of Al, Ti, Fe and Mn generates acidity that partially consumes alkalinity produced during primary silicate dissolution. Metal hydrolysis and secondary phase formation are ubiquitous in both natural and experimental basalt weathering systems and represent a fundamental constraint on net alkalinity export. For example, the dissolution of anorthite consumes eight protons:

If the Al and Si subsequently precipitate as kaolinite, six protons are released:

Combining reactions (2) and (3) yields a net consumption of two H⁺ per mole of anorthite dissolved. Although 1 mol of Ca²⁺ is released, inferring CO₂ removal directly from Ca²⁺ flux implicitly assumes that protons are supplied exclusively by carbonic acid and are not variably regenerated by secondary reactions. The protons involved in reaction (2) can be sourced from carbonic acid, strong acid inputs (for example, fertilizers), atmospheric inputs, mineral oxidation, exchangeable Al³⁺ and H⁺ on mineral surfaces and hydrolysis of metals. Consequently, cation export alone cannot directly reveal actual proton balance or source (for example, carbonic versus non-carbonic acid) during weathering.

Alkalinity attenuation is further amplified when secondary minerals incorporate base cations. For example, under more alkaline conditions and assuming that the hydrolysis reactions are driven by carbonic acid, Ca-montmorillonite precipitation,

accompanied by the hydrolysis of aluminium

results in a 21% reduction in base cation export and 70% reduction in alkalinity yield. Together, example reactions (2)–(5) demonstrate that secondary mineral formation attenuates alkalinity export by regenerating acidity and sequestering weathering products along flow paths, reducing the fraction of silicate dissolution that can be exported as alkalinity.

In soils with high cation exchange capacity and low base saturation, divalent cations can exchange for monovalent ions or exchangeable acidity (that is, Al³⁺ and H⁺ at pH < 6), whereas at higher pH, added alkalinity is also partially consumed by the deprotonation of surface functional groups³⁵. Although this process is theoretically reversible if the system is re-acidified, in practice, re-acidification is often incomplete owing to agricultural management, limiting the recovery of added alkalinity.

Carbonate precipitation also plays an important role in limiting alkalinity export from watersheds:

Formation of calcite transfers half of the initial alkalinity to a potentially stable mineral form and returns half as CO₂, substantially reducing CDR_pot. Pedogenic carbonates tend to form in soil systems with high pH and/or negative water balance (precipitation − evapotranspiration)³⁶. Much of the world’s agricultural land occurs in regions with low but positive water balance values, in which soils are naturally high in nutrients and pH is neutral to slightly acid. In these regions, carbonates are unlikely to form within the soil solum but commonly form deeper in the vadose zone³⁷.

Tracking the fate of base cations and alkalinity along the soil-to-river continuum requires models that combine thermodynamic and kinetic constraints on mineral dissolution, ion exchange and precipitation and mass fluxes of water and gases³⁸. These mechanistic models provide insight into the emergent factors that contribute to the discrepancies between natural basalt systems and the values predicted for EW.

Secondary mineral formation is a pervasive but underappreciated sink for Si, Mg and Ca in basaltic systems. Nearly all rivers in a global database are supersaturated with respect to Na, Mg and Ca-smectites⁶. Major ion chemistry and Si, Ca and Mg isotope mass balances demonstrate substantial retention of Si, Ca and Mg in basaltic systems, including the Philippines, Iceland, Guadeloupe, Reunion and Hawai‘i (Methods and Supplementary Information). In Icelandic catchments, inverse modelling indicates that 30–67% of Ca, 45–81% of Mg and 90–95% of Si from silicate weathering inputs to the critical zone are taken up in secondary minerals⁷. Comparable behaviour is observed at the 30 m scale in the Landscape Evolution Observatory mesocosm in which 69–90% of dissolved Ca, Mg and Si are retained over hydrologic timescales of days to weeks, based on solute chemistry, dissolved δ³⁰Si mass balance and observations of secondary mineral formation^8,39.

Together, these observations indicate that substantial dissolution products are retained along flow paths, probably as neoformed secondary minerals, substantially reducing the efficiency with which weathering-derived solutes are transmitted to streams (Extended Data Table 2). As a result, base cation release from the shallow soil zone does not necessarily translate to downstream alkalinity export or inferred CO₂ removal (Extended Data Table 3).

The window for evaluating secondary minerals extends beyond the zone of feedstock application, including groundwater aquifers. Soil pH conditions vary widely across both natural volcanic landscapes and managed agricultural systems³⁶ and therefore do not provide a consistent basis for assuming greater or lesser secondary mineral formation in either setting. Active plant uptake and recycling of nutrients can substantially affect the upper 10–30 cm of soil profiles. Substantial root and microbial respiration increases pCO₂ and lowers soil pH at shallow depths and chelation delays the onset of secondary mineral saturation^40,41. Accumulated weathering products are displaced downward by fluid flow, delaying critical saturation. In basaltic weathering profiles, it is not uncommon to see moderate- and low-solubility elements such as Al, rare-earth elements and Zr transported downward by about 0.5 to several metres, at which they are reprecipitated⁴² (Fig. 2). These depth-dependent patterns integrate shallow soil processes dominated by dissolution with deeper regolith processes dominated by approach to equilibrium and mineral neosynthesis.

Although dissolution may be enhanced within a shallow zone in which EW feedstock is applied, the cascade of secondary reactions spans many metres along subsurface flow paths. A study in a basaltic aquifer found that 40% of the CO₂ reacted in the critical zone remained long term in older groundwater and a further 10–30% precipitated as calcite as pCO₂ was reduced under closed system conditions⁴³. Thermodynamic analyses of basaltic groundwaters in Hawai‘i, Brazil and Iceland indicate that Ca and Mg concentrations are controlled by metastable equilibria among smectite and zeolite assemblages^30,44,45. Secondary mineral precipitation and cation removal occur along subsurface flow paths, including the deeper critical zone, even where near-surface waters are initially undersaturated^44,46. This behaviour highlights the need to consider chemical evolution along the entire reactive path.

Water flux and its role in fostering weathering and redistribution of weathering products and alkalinity is central to quantification of EW carbon sinks. For surface-controlled dissolution, increases in flushing rate are not matched by increases in alkalinity generation, which are limited by mineral dissolution rates (Fig. 3). The resulting dilution is clearly detectible in basaltic catchments, in which HCO₃⁻ decreases as river discharge (Q) increases. Systematic analysis of a large number of basaltic catchments⁶ demonstrated that, at very high runoff, dissolved CO₂ export reached a plateau near 0.7 t CO₂ ha⁻¹ year⁻¹, reflecting increasing dilution, whereas the median maximum weathering flux was around 0.22 t CO₂ ha⁻¹ year⁻¹ (Fig. 1b). The strong dependence of alkalinity concentrations on discharge implies that sampling at base flow will result in a considerable overestimate of stream alkalinity export (Extended Data Fig. 4). Reliable estimates of export require that watersheds be monitored over the full range of hydrologic variability. Other temporally dynamic factors, including mixing of waters of different ages and sources, complicate the observed relationships. Given the large variability observed in watershed HCO₃–Q relationships, substantial shifts in cations or alkalinity are required to detect shifts in weathering even in small catchments. Also, travel times of water can vary from weeks to decades depending on the topography, climate and the permeability structure of a catchment, such that signals from EW may be dispersed and delayed many years before reaching downgradient wells and river networks.

The capacity for EW alkalinity export is further constrained by both land use and individual river chemistry. Global croplands occupy about 10% of exorheic basin area^47,48 and only a fraction of those lands are hydrologically connected to river networks or otherwise suitable for EW. In the upper Mississippi basin, effective hydrologic recharge is ≤0.25 m year⁻¹ (ref. ⁴⁹); at steady state, moving the equivalent of 2.5 t CO₂ ha⁻¹ year⁻¹ CDR through the soil column to groundwater and streams would imply mean soil solution alkalinity ≥ 22 meq l⁻¹, outside plausible ranges. In many agricultural regions, rivers are saturated with respect to carbonate minerals, reducing the potential that alkalinity will be conservatively transmitted to the oceans³. Because the alkalinity flux is the product of HCO₃⁻ and Q (Figs. 1b and 3), realizing predicted CDR_pot would require alkalinity export from treated regions to increase by 1 to 2 orders of magnitude over present levels. Global discharge in response to future warming is predicted to increase by around 6% (ref. ⁵⁰), thus increased alkalinity concentrations would need to provide almost all of this increased flux.

Large changes in alkalinity levels in rivers will be difficult to achieve because of precipitation of carbonates. The global average riverine HCO₃⁻ concentration¹² is 1.8 mmol l⁻¹, with some rivers in agricultural regions as high as 5–6 mmol l⁻¹ (Extended Data Fig. 4), compared with typical ranges in basaltic catchments⁶ of between 0.1 and 3.0 mmol l⁻¹. Some model-based studies conclude that riverine processes would only weakly attenuate alkalinity generated by EW, based on assumptions that substantial carbonate precipitation requires strong supersaturation (saturation index > 1) and that it occurs primarily within stream channels⁵¹. These assumptions are not fully consistent with watershed-scale observations of δ⁴⁴Ca and δ⁸⁸Sr. In several river systems, the stable isotope data imply substantial removal of Ca (about 70%), implying that extensive carbonate precipitation can take place in the deeper vadose zone, in groundwater and in riparian settings not included in channel-focused models (Methods and Extended Data Fig. 5).

Alkalinity export from natural active volcanic catchments, characterized by abundant, permeable and highly reactive lavas, pyroclastic deposits and tephra and by mass loadings that greatly exceed EW applications, provides a field-based reference for evaluating CDR from EW. Data from experimental mesocosms further confirm that substantial fractions of dissolved base cations and alkalinity generated by weathering in the shallow surface environment are retained or consumed in the subsurface and not exported to streams.

By contrast, most present EW assessment relies on the widely used metric of base cation depletion in the upper soil, reported directly or used with a multiplier to calculate CDR_pot (refs. ^18,52). This approach may capture weathering in the near-surface soil but it does not account for critical zone alkalinity sinks, including clay precipitation, carbonate precipitation and ion (proton) exchange. Assessment of near-surface chemistry does not capture the full range of processes that ultimately control carbon fluxes at the watershed scale, the minimum scale necessary to supply alkalinity to the oceans.

Evidence from natural basaltic systems, experimental mesocosms and the limited number of field-scale EW studies that report alkalinity suggest that present CDR_pot estimates may overestimate the fraction of alkalinity that escapes the critical zone and contributes to durable CDR^17,53. We suggest that EW strategies should be evaluated in a source-to-sink context that accounts for the full suite of chemical and transport processes at appropriate timescales.

Global CO₂ uptake from silicate and basalt rock weathering

Global silicate weathering is estimated from river chemical fluxes with values from 0.525 to 0.612 Gt CO₂ year⁻¹ (refs. ^12,14,54). An estimate that sought to balance weathering fluxes with marine carbonate deposition fluxes is near the lower end of this range⁵⁵. Estimating the fraction of silicate weathering contributed by basaltic rocks is complicated by varied rock classification and insufficient data on both river and groundwater fluxes in volcanic terranes^13,25,30,56. Estimates vary from 15 to 35% (refs. ^13,14,24), with overall basalt weathering fluxes in the range 0.084–0.180 Gt CO₂ year⁻¹ depending on assumptions, or about 0.3% of anthropogenic emissions⁵⁷.

Alkalinity fluxes from basaltic watersheds

River solute data were compiled from several published sources (Supplementary Information). When available, we used titration alkalinity, otherwise alkalinity was calculated by charge balance: Alk = 2[Ca⁺⁺] + 2[Mg⁺⁺] + [Na⁺] + [K⁺] − [Cl⁻] − 2[SO₄⁼] − [NO₃⁻] ≅ [HCO₃⁻] + 2[CO₃⁼]. Where time series data were available, we established a discharge-weighted concentration and used the geometric mean discharge (Q_geo) to compute the watershed flux, as Q is often log-normally distributed in smaller watersheds. In other cases, we used mean annual discharge estimates. The accuracy and bias of watershed flux calculations are almost always affected by lack of concentration and discharge (C–Q) data at sufficiently high frequency⁵⁸.

Before calculation of alkalinity, flux stream data were corrected for atmospheric input using either local (if available) or seawater X/Cl⁻ ratios. For example, Na* = [Na⁺]_river − (Na/Cl)_precip × [Cl⁻]_river. Where available, we used strontium isotope mass balances as a check for correcting atmospheric inputs or sedimentary carbonate inputs. In active volcanic zones, samples with high [SO₄⁼] or SO₄⁼/Cl⁻ were screened out as having hydrothermal contributions. Some samples that do not carry anomalous sulfate still seem to be anomalously high in dissolved solutes, as sulfate may have been partially consumed by other reactions. If rocks in the watershed were previously altered by temperature hydrothermal fluids, they may contain alteration minerals such as zeolites and carbonates that can weather readily, thus contributing a ‘relict’ hydrothermal signal to the stream solute load. This signal can be difficult to quantify and correct for²⁶. Consequently, it is likely that some values from active volcanic regions overestimate the true low-temperature weathering signal.

Cation retention estimates

One estimate of the fraction of a partially soluble element j that is retained in the critical zone is given by

This assumes that the dissolution step of volcanic rock weathering is congruent and that sodium is not notably lost to adsorption or precipitation, that is, is conservative. Generally, Si/Na, Ca/Na and Mg/Na in stream fluxes are low relative to the source rock, implying sequestration or retention of silica and base cations in the weathering⁸ (Extended Data Table 2). Similarly, we can estimate cation losses in river sediment clay mineral fraction by comparing the river clay fraction compositions to the bedrock composite. We computed mass transfer coefficients as:

in which C_j is the concentration of a mobile element j such as Mg, Ca or Si, C_i is the concentration of an immobile element i (here Ti or Nb) and the subscripts wea and br refer to the weathered regolith or river sediment clay fraction and bedrock parent material, respectively. τ_i,j < 0 indicates loss of element j relative to the parent material. Then:

Retention of Mg and Si based on comparing the clay fraction of river sediments from Luzon Island (Philippines) agree well with the solute derived estimates. For Ca, \({f}_{{\rm{retained}}}^{{\rm{Ca}}}\) based on the clay data is lower than from the solute data. Some Ca is very likely retained as secondary carbonates, with most stream pHs in the range 7.0–8.6 (ref. ²⁴). The evidence of strong incongruency of weathering in these locations is consistent with inferences from δ²⁶Mg, δ³⁰Si and Ge/Si data^{39,59,60,61,62,63}.

The Landscape Evolution Observatory has three 30 × 11 × 1-m artificial hillslopes with fresh basalt loadings of 15,900 kg m⁻² with mean SSA = 0.92 m⁻² g⁻¹ and is irrigated from above according to a controlled schedule^64,65. Solutions were sampled at the bottom seepage face^8,39 and transit time distributions calculated by modelling random precipitation forcing with deuterium-labelled water⁶⁶. Alkalinity was determined by direct measurement of dissolved inorganic carbon and cation mass balances with equation (7); inferences of secondary mineral formation are supported by mineral saturation calculations and δ³⁰Si data^8,39,64.

SAs measured on basaltic materials

A common assumption in studies of EW is that grinding the rock feedstock will increase SA and therefore reaction rate (for example, equation (1)). This has led to the perception that basalt weathering rates in EW experiments will ‘be greatly accelerated’ relative to natural systems⁵². The transition state theory rate formulation predicts a proportional dependence on SA and on k_r, such that model predictions are heavily influenced by the assessment of SA. For EW, mechanical comminution is a primary lever on the total weathering flux by increasing SA. For geometrically smooth particles, geometric-specific SA should scale inversely with particle size during comminution, such that the surface increases in proportion to L₁/L₂, in which L₁ is the characteristic size of the parent grain and L₂ is the size after crushing. BET SSA data can be a useful basis of comparison but are not equivalent to the ‘reactive surface area’ that should be used with equation (1) to compute dissolution rates³². Available BET SA data as a function of grain size for basaltic materials do not show a simple dependence and are not well predicted by some particle size models that have been used for EW^10,67 (Extended Data Figs. 1 and 2). The reactivity of any rock substrate depends on its mineralogical composition as well as how its surface characteristics may evolve over time and water–rock interaction. For example, older basalt surfaces can be passivated or otherwise reacted, thus decreasing reactivity^68,69. Basalts used for EW are commonly altered at least to some degree and can contain substantial carbonate⁷⁰ that could bias weathering rate calculations high as well as other secondary alteration phases (zeolites and clays, among others)²⁹ that should react more slowly than primary basaltic minerals and glass. SSA data from natural basalts that have not been crushed or ground overlap substantially with crushed basalts that have been used or proposed for EW applications (Extended Data Fig. 3). Together, available SSA and mineralogical data as well as data on reaction rates as a function of grain size^34,71 do not provide an obvious basis that basalts used in EW should be more reactive than natural occurrences.

δ ⁴⁴Ca and δ ⁸⁸Sr constraints on carbonate removal

The stable isotopes of Ca and Sr are generally strongly fractionated by carbonate precipitation, leading to their use as a constraint on watershed-scale carbonate removal. An early estimate based on δ⁸⁸Sr data suggested that at least 40% of carbonate is removed from global large river systems, but with notable uncertainties⁷². In other watershed systems, δ⁴⁴Ca and δ⁸⁸Sr indicate up to 70% Ca removal that is poorly correlated with river carbonate saturation^73,74 (Extended Data Fig. 5). The lack of correlation is consistent with the hypothesis that carbonate precipitation primarily takes place in the deeper vadose zone³⁷, groundwaters^44,46,75,76, during riparian zone degassing⁷⁷ and potentially in reservoirs^78,79, rather than the main river stem. Carbonate precipitation can occur within the river if supersaturation is sufficient, typically under low-flow conditions⁸⁰.

Alkalinity export from EW field trials

Direct measurements of alkalinity export from EW field trials are at present sparse. Across the small number of published field and mesocosm studies, basalt amendments ranging from about 100 to 200 t ha⁻¹ have produced inferred alkalinity export equivalent to roughly 0–0.15 t CO₂ ha⁻¹ year⁻¹, with most estimates clustered below 0.1 t CO₂ ha⁻¹ year⁻¹ and frequently statistically indistinguishable from zero. In high-rainfall tropical systems (about 2,000 mm mean annual precipitation), large basalt additions (approximately 150–200 t ha⁻¹) have yielded either no resolvable increase in stream alkalinity flux⁴ or small subsurface alkalinity signals measured at 1.25 m depth⁵, corresponding to a minor carbon uptake rate of 0.026 t CO₂ ha⁻¹ year⁻¹ that is not statistically resolvable from zero. Other multiyear field experiments report similarly low apparent CDR rates based on alkalinity export (<0.1 t CO₂ ha⁻¹ year⁻¹)⁵³, whereas mesocosm studies observe basalt dissolution without detectable alkalinity export⁸¹. At a site in a Mediterranean climate that had 107 t ha⁻¹ of basalt and olivine amendments, soil-solution alkalinity increases equivalent to about 0.12–0.15 t CO₂ ha⁻¹ were observed in the upper 30 cm; both weathering and export in this system may have been limited by water availability and there are no data on export below 30 cm (ref. ⁸²).

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Authors and Affiliations

1. Cornell University, Ithaca, NY, USA

   L. A. Derry

2. Institut de Physique du Globe de Paris, Paris, France

   L. A. Derry

3. Stanford University, Stanford, CA, USA

   K. Maher

4. University of California, Santa Barbara, CA, USA

   O. A. Chadwick

Contributions

L.A.D., K.M. and O.A.C. all contributed to the conceptualization of the paper. L.A.D. and K.M. assembled data and carried out calculations. L.A.D., K.M. and O.A.C. contributed to writing.

Corresponding author

Correspondence to L. A. Derry.

Competing interests

The authors declare no competing interests.

Peer review information

Nature thanks Susan Brantley, Evan Ramos and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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