Leveraging ecosystems responses to enhanced rock weathering in mitigation scenarios

doi:10.21203/rs.3.rs-3145606/v1

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Leveraging ecosystems responses to enhanced rock weathering in mitigation scenarios

https://doi.org/10.21203/rs.3.rs-3145606/v1

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Carbon dioxide removal (CDR) is deemed necessary to attain the Paris Agreement's climate objectives. While bioenergy with carbon capture and storage (BECCS) has generated substantial attention, sustainability concerns have led to increased examination of alternative strategies, including enhanced rock weathering (EW). We analyse the role of EW under cost-effective mitigation pathways, by including the CDR potential of basalt applications from silicate weathering and enhanced ecosystem growth and carbon storage in response to phosphorus released by basalt. Using an integrated carbon cycle, climate and energy system model, we show that applying basalt to forests could triple the level of carbon sequestration induced by EW compared to an application restricted to croplands. EW reduces the costs of achieving the Paris Agreement targets, and alleviates the pressure on food prices by reducing the willingness to pay for bioenergy; however, it does not significantly reduce the use of BECCS, which remains a major cost-effective mitigation option. Further understanding requires improved knowledge of weathering rates through field testing.

Earth and environmental sciences/Climate sciences/Climate change/Climate-change mitigation

Earth and environmental sciences/Biogeochemistry

Physical sciences/Energy science and technology/Energy modelling

Parties to the Paris Agreement committed to keeping global warming well below 2°C, and to continuing their efforts to aim for 1.5°C of warming relative to the preindustrial level. Meeting this goal requires reducing emissions at an unprecedented pace to reach carbon neutrality by the middle of the century. Carbon dioxide removal (CDR) is known to be required to compensate for both temporary overshoots of carbon budgets and for residual emissions that may persist after emission reductions from all sectors. The longer the delay in emission reductions, the greater the need for CDR¹.

While bioenergy with carbon capture and storage (BECCS) and afforestation are so far the most widely explored carbon dioxide removal solutions², concerns have been raised regarding the technical feasibility and sustainability of BECCS at the scales envisaged in the mitigation scenarios assessed by the IPCC³. In particular, the amounts of biomass needed to reach sufficient CDR levels could have high impacts on water, land and nutrient use^4–6. Sustainable deployment of large-scale CDR thus requires the examination of alternative CDR portfolios ^7,8.

Enhanced weathering of basalt (EW) is an emerging and promising CDR that consists in amending soils with basalt dust^9–12. As basalt erodes, the minerals released react with CO₂ and sequester carbon for at least several hundred years¹³, a process called ‘geochemical CDR’. Unlike BECCS, EW does not disrupt existing land use and is usually assumed to be deployed on croplands ^1,9–12,14, that are accessible for transporting and spreading basalt. Furthermore, several co-benefits of croplands amendment with basalt have been highlighted: improvement of soils quality ¹⁵ which could enable a reduction of fertilisers use^16,17, improved plant health, and increased yields ^18,19. Moreover, EW stimulates biomass production through nutrients released during basalt dust dissolution, thereby increasing carbon sequestration and storage in natural ecosystems. This additional CO₂ removal process from EW is called ‘biotic CDR’ and has only recently been quantified. Biotic CDR could potentially double the global CDR of EW²⁰ (2–5 GtCO₂ per year ^4,12,14), yet non-agricultural application is not part of CDR portfolios in existing assessments ^1,2,8. While EW presents co-benefits for soils and ocean pH¹⁰, emissions associated with extracting, crushing and spreading basalt could partly offset the CDR potentials, depending on the underlying energy mix ^20,21.

Here we analyse how the application of EW on crop fields and forests affect mitigation pathways using a new hard-linked carbon-cycle, climate and energy system model that considers geochemical and biotic CDR and associated energy requirements within a single framework. We quantified the potential CDR from EW for ambitious climate mitigation pathways and the subsequent reduction in reliance on BECCS. The addition of EW to the CDR portfolio of mitigation technologies can make ambitious climate targets achievable with lower mitigation costs²². We thus examined how EW affects mitigation costs, energy consumption and temperature pathways over the 21st century in four climate target cases: 1.5°C scenarios with low overshoot (up to 0.2°C) and high overshoot (no limit) and 2.0°C scenarios with no overshoot and with high overshoot (no limit). All three overshoot scenarios achieve the respective temperature target by 2100. In our 1.5°C low overshoot scenario, we allow a higher overshoot than what is defined as low overshoot scenarios in IPCC AR6 (up to 0.1°C); as the latter would lead to very large unrealistic short-term demand reductions in our model ^23,24. By taking advantage of our energy-climate modelling framework, we further highlight key uncertainties that influence the role of EW for climate mitigation.

We developed a new version of the partial-equilibrium energy model GET7.1^25,26, which we integrated with the aggregated carbon cycle, atmospheric chemistry and climate model (ACC2^27,28). The resulting coupled model GET-ACC2 (Fig. 1) quantifies least-cost pathways where low-carbon technologies, CDR, and abatement measures for CH₄ and N₂O are deployed to mitigate climate change. The net present value of the social surplus (i.e. the sum of consumers surplus minus the energy costs, discounted at a 5% rate) is maximised with perfect foresight, leading to a preference for late spending, including late abatement.

We also developed an EW module and coupled it with the carbon cycle module of GET-ACC2, where the dissolution of basalt directly removes atmospheric CO₂, and delivers phosphorus to the soil which stimulates the net primary production (NPP). The increase in terrestrial carbon storage is the difference between NPP and CO₂ released from heterotrophic respiration, which are resolved in ACC2 on a global-annual-mean basis. We emulated the phosphorus stimulation of NPP through the release of phosphorus from basalt by using an output of ORCHIDEE-CNP²⁹, a global biosphere model that resolves phosphorus cycling, in order to quantify the geochemical (abiotic) and biotic CDR from basalt applied to forest ecosystems.

To address parametric uncertainty, we sampled uncertain parameters, such as equilibrium climate sensitivity (ECS), technology costs and diffusion constraints, and EW parameters (see methods & SI.2). When ECS exceeds 3.7°C, keeping global warming below 1.7°C is infeasible with GET-ACC2. Consequently, we set ECS at 3°C for the 1.5°C scenario with low overshoot, while ECS is varied between 2°C and 4.7°C³⁰ in all other scenarios. Unless otherwise noted, the reported results represent the mean of simulations performed on this set of parameter samples.

Enhanced weathering deployment

Under each climate target case, we assessed the following three CDR portfolios: i) BECCS only (No EW), ii) BECCS with EW on croplands only (EW on CL), and iii) BECCS with EW on croplands and forest areas (EW on CL + FA). In the latter, we assumed that basalt could be spread over forest areas, yet with a significant energy and cost penalty compared to croplands. The cost-effective magnitude of CDR from EW deployment is very contrasted across climate target scenarios (Fig. 2): EW is more used to achieve 1.5°C than to achieve 2°C, and it is also used more in high-OS than in low-OS scenarios.

The EW application only on croplands approaches its full potential in the 1.5°C high OS scenario with an annual CDR peak of 4.5 GtCO₂ per year (mean projection: some values in the sample are below the maximum potential) and a 165 GtCO₂ accumulated removal. Here, we assume no limit to basalt dust production although its growth rate is limited (to 10–20% per year). The maximum CDR potential by EW on croplands thus depends on the application rate of basalt (15 kg/m²), the area of suitable croplands with sufficiently warm and rainy climate, 7.9Mkm², i.e. a third of global croplands¹⁴, and the weathering rate (1–26% per year). The maximum cropland CDR is 4.9 GtCO₂ per year, consistent with other estimates assuming unlimited basalt supply^12,31. Allowing basalt application also on forests more than triples the EW-induced CDR, with a peak of 18.5 GtCO₂ per year and 522 GtCO₂ cumulatively in the 1.5°C with high OS scenario.

The increase in EW-induced CDR resulting from the application of basalt on forests, in addition to croplands, is due to two factors: the additional area for basalt application, and the biotic CDR in forest. Their contributions vary depending on scenarios; for example, in the 1.5°C with high OS scenario, the increase in CDR due to the additional area is more pronounced because cropland application is at full potential. Furthermore, the share of the biotic CDR is proportionally lower at high application levels because the phosphorus stimulation of forest NPP gradually saturates, thereby limiting the biotic CDR potential. This limit explains why biotic CDR by EW varies less than geochemical CDR by EW among different scenarios.

Impact of enhanced weathering on mitigation scenarios

Policy costs

EW provides flexibility, not only by replacing more expensive mitigation measures but also by allowing abatement to be delayed. This reduces the costs of achieving climate objectives, here quantified as the net present value of policy cost (the energy system costs plus the loss of consumer surplus) compared to a baseline without climate policy (Fig. 3, see also Fig. S4 for energy demand reduction and SI3 for annual costs). Abatement is mainly delayed in OS scenarios: in our forward-looking optimisation model, the greater the future opportunity for negative emissions is, the lower the near-term abatement and the discounted costs. Therefore, applying EW on croplands and forest areas reduces policy costs most significantly in the high OS scenarios, by 25% in the 1.5°C scenario with high OS, against 12% in the 1.5°C scenario with low OS. In the latter case, the rapid reduction required over the next decade is too early for basalt to be used on a large scale, and relies largely on a severe contraction in the demand. The application of EW on croplands only has a weaker impact, in particular in the 2°C scenario without OS where it reduces policy costs by only 1.2%.

The increasing stringency of climate policies across the 21st century is reflected by the endogenous carbon price (Fig. 3). EW reduces it, on average, by 45% if applied on croplands and forests in the 1.5°C with high OS scenario, and by 25% when applied on croplands. When aiming at 2°C, EW reduces it by 10%. But if application over croplands only is considered, the carbon price is only reduced by 3%. Thus, applying EW on crop fields helps to reduce the efforts required to achieve the most ambitious climate objectives but is not a game-changer when aiming at the 2°C target. Overall, EW pays off more when aiming at 1.5°C than when aiming at 2°C, and more with OS than without, corresponding to its level of use.

As a consequence of delaying abatement and changing the net emission pathways, EW increases the peak temperature level in high OS scenarios: from 1.88°C without EW to 1.98°C with EW in the 1.5°C case, and from 2.13°C to 2.20°C in the 2°C case (Fig. 3). This behaviour depends on the assumed discount rate, and is strongly reduced with a lower discount rate of 2% (Fig. S2, S3).

Reduction of BECCS

Reducing the reliance on BECCS for achieving negative emissions could limit the deployment of bioenergy crops and alleviate the threats they pose to food security, water and nutrient resources and biodiversity³². Therefore, it is of interest to analyse if EW and BECCS are complementary or in competition with each other. EW does not directly compete with BECCS for resources: BECCS provides energy while EW uses energy, and EW could be applied on bioenergy crops areas. BECCS are used in all our mitigation scenarios to supply electricity and heat, but also hydrogen (for transportation, and industrial processes) when high levels of negative emissions are required. We found that adding EW to the CDR portfolio increases the total CDR level but reduces the use of BECCS which becomes partially superfluous (Fig. 2). The reduction in BECCS per tonne of EW-induced CDR is higher in low or no OS scenarios than in high OS scenarios, where BECCS and EW rather add up.

By reducing the dependence on bioenergies, the EW could also reduce the pressure on food prices, reduce land rents and the market incentive to cultivate food or bioenergy crops in pristine areas. Due to the competition for land³³, food prices should increase with biomass prices³⁴, which reflect the willingness to pay for bioenergy and increase with carbon prices. Applying EW on croplands and forests reduces biomass prices by up to 35% in the 1.5°C scenario with high OS (Fig. 4), and cuts the use of bioenergy by up to 15%. Limiting EW to croplands reduces these effects. In summary, EW only partially replaces BECCS, but reduces the demand for bioenergy.

Impacts on energy use

EW generally requires smaller energy input than other CDR options, such as direct air carbon capture and storage. The energy use of EW can be divided in three components: mining and grinding of basalt (here, a size of 20µm was assumed¹⁴) which consumes fuel and electricity, transport to application sites which increases the freight demand, and spreading of basalt dust requiring fuel if tractors are used (for crop fields for instance) and aviation fuel if basalt is spread on forests (see methods).

The final energy intensity of EW per ton of CO₂ sequestered depends on the level of EW deployment, and thus on the scenario (Fig. 5). In crop fields, the final energy input increases with basalt application because the most accessible fields are used first and more remote areas require more energy due to longer transport distances. Therefore, if basalt is only applied on crop fields, the final energy use per tCO₂ removed varies between 1.4 GJ/tCO₂ in the 2°C without OS where EW is less applied, and 2.5 GJ/tCO₂ in the 1.5°C scenario with high OS. In forests, CO₂ removal per ton of basalt is higher than on croplands due to the biotic effect but it decreases with increasing application, whereas energy use per ton of basalt varies little because the areas chosen first are those most stimulated by phosphorus, rather than the nearest ones. The application on forest areas therefore reduces the energy intensity in the 2°C scenario without OS (1.3 GJ/tCO₂), but increases it in the 1.5°C scenario with high OS (4.3 GJ/tCO₂) due to the saturation of the biotic effect. For comparison, direct air carbon capture and storage would typically require 4 to 12.4 GJ/tCO₂^35,36 depending on the technology used.

Electricity and aviation fuel are the predominant energy carriers used for EW, which uses 9% of the projected electricity production, and 36% of the projected aviation fuel until 2100 in the 1.5°C with high OS scenario. The emissions from EW depend on the energy sources used, and thereby on the carbon price. In the low OS scenarios, the share of kerosene among the aviation fuel used for basalt application is higher than in the high OS scenarios where higher carbon prices at the time of basalt application on forests lead to a switch to hydrogen. Moreover, since a share of this hydrogen is produced from BECCS, the net basalt supply emissions are negative in the 1.5°C scenario with high OS. Conversely, in the 2°C scenario the carbon price is lower, kerosene continues to be used, and the EW-related emissions offset 7.9% of the CDR (Fig. 5).

Uncertainty analysis

CDR plays a critical role in mitigation pathways developed by IAMs despite low technology readiness of the majority of CDR technologies. Thus, uncertain costs and scalability³⁷ calls for an analysis of the impact of related underlying model assumptions on our results. Besides, costs of competing technologies³⁸ or low discount rates³⁹ have notably been shown to affect uncertainties on the role of CDR.

To gain insight into uncertainties related to the key parameters of our model, we analysed the sensitivity of our results by using the Morris method^40,41. It quantifies the mean and standard deviation of the variations of an output variable resulting from increasing the value of a single parameter over a representative sample of all parameter values (see methods). A positive mean indicates that the output increases with a higher parameter value. A large standard deviation shows that this effect depends on other parameters values. This method is applied to analyse the sensitivity of EW and BECCS deployment to key model parameters, as shown in Fig. 6 (complete set in SI.2).

The parameters that increase the efficiency of EW tend to reduce the use of BECCS, and vice versa, so that EW and BECCS appear as competing technologies or substitutes. CDR use also increases with the costs of other mitigation technologies, such as wind, solar or nuclear energy: a decrease in their costs reduces the carbon price and therefore the incentive for CDR³⁸. Similarly, increasing the system flexibility such as the maximal rate at which the installed capacity of technologies can grow, or the price-elasticity of the demand, generally reduces the use of CDR. The use of CDR further depends on the climate uncertainty, as assessed through the ECS and other related parameters³⁰.

We found that the uncertainty related to the physical processes of EW (weathering rate, geochemical capture rate, and the phosphorus-led NPP increase) strongly influence the magnitude of EW CDR, it is less impacted by the uncertainties of parameters surrounding the energy requirements of EW. The sensitivity of EW deployment to energy requirements is higher in the overshoot scenarios, where the energy cost of basalt application is higher.

Weathering rates in soils remain highly uncertain^42–44 (see methods). Field or pot experiments generally provide lower estimates than laboratory experiments⁴⁵, suggesting that the weathering rate depends on complex interplay of soil pH, temperature,hydrological conditions, and biological activity ^46,47. This is therefore a critical source of uncertainty. As shown in Fig. 6, the lower the weathering rate, the less basalt is applied and carbon captured. For weathering rates below 1% per year, EW can become a viable cost-effective option only in the 1.5°C with high OS scenario. The higher the weathering rate is, the higher the cost-effective deployment levels of EW over croplands and forests areas are.

We showed that the CDR potentials of EW under cost-effective mitigation pathways can be larger than previously thought by additionally considering the potentials associated with the phosphorus fertilisation, or ‘biotic’ effect of EW. EW neither accelerates climate change mitigation nor reduces temperature overshoot in our cost-effectiveness analysis, yet its potential for lowering peak temperatures to mitigate near-term climate damage could be assessed through cost-benefit analyses. Deploying EW in addition to BECCS reduces the willingness to pay for biomass and could thereby lower the pressure on land conversion as well as on food prices, although the reliance on bioenergy remains significant.

Besides, potential impacts of EW on health or ecosystems ^48,49, which were not considered in this study, may limit the sustainability and effectiveness of basalt soil amendment. Basalt extraction in the 1.5°C with high OS case reaches 46 Gt/year (Fig. S1), half of the current global material footprint and 10 times the global cement production, potentially having significant ecological impacts, as could the application of in forests altering soils geochemistry for centuries. More field experiments are required to reduce the uncertainty on weathering rates, but also to explore possible negative side-effects of enhanced weathering, particularly as rock material, once added to the soil, is almost impossible to extract.

We further demonstrated that under mitigation pathways, in particular, for the 1.5°C warming target, the use of EW reduces the total mitigation cost, lowers the peak carbon price, and replaces a larger amount of BECCS when the ‘biotic’ effect is included, even if we account for the high costs for EW application over forest areas by aeroplanes. These findings are robust under a range of uncertainties considered. Such benefits of EW were found to be more pronounced under pathways with high temperature overshoot than those with low or no overshoot. Nevertheless, in high overshoot pathways, EW is used to compensate for higher emissions for the upcoming decades, which is a risky strategy, given the increased likelihood of climate disasters at high overshoot levels, which is not considered in our analysis. Furthermore, even if we explored uncertainties as comprehensively as possible, the true uncertainties cannot be wholly captured inherently and certain classes of uncertainties cannot be assessed via quantitative means, indicating a need for careful interpretation and dissemination of our results for stakeholders.

Modelling framework

We developed an energy-economy-climate model by hard-linking GET7.1 with the reduced-complexity carbon-cycle, atmospheric chemistry and climate model ACC2. GET7.0 is a bottom-up, cost-minimising energy system model, with a focus on energy supply and transformation. GET7.1 derives from GET7.0 with updated techno-economic parameters, and a price-responsive energy demand, that follows the SSP2 baseline⁵⁰. The GET-ACC2 approach allows to assess least-cost emission pathways directly considering the temperature target (and not a carbon budget target) with a detailed representation of the energy system. Such a feature is important for an analysis under overshoot pathways involving several different greenhouse gases and EW as a CDR option, where the carbon budget approach may not necessarily work.

The coupled model produces internally consistent social-surplus maximising pathways to meet a reference energy demand in five end-use sectors (transportation, electricity, heat for industrial processes, space heat and industrial feedstocks), with perfect foresight, while respecting a given climate target as well as resource constraint for a range of primary energy source (oil, gas, coal, uranium, wind power, solar power, biomass, hydropower). Figure 1 shows the structure of the model. Primary energy is transformed into secondary and then final energy through investments and operations in order to satisfy a demand-supply equilibrium. CCS can abate emissions from fossil fuel power plants, or directly remove CO₂ from the atmosphere if combined with bioenergy (BECCS). The maximum achievable carbon capture by BECCS is limited by the deployment of carbon storage infrastructures, and bioenergy supply, as BECCS are competing with other bioenergy uses. GET-ACC2 does not explicitly model land-use: the primary bioenergy supply is exogenously limited to 50 EJ in 2020 and to 260 EJ per year in 2100 following a supply curve (see SI.3). The growth rates of energy conversion technologies and CO₂ storage are limited under assumed upper bounds. There is no constraint on emission levels reduction rate as long as the energy demand is met. Since energy demand is price-responsive, stringent climate targets are achievable in an optimization model sense. The energy module has a 10-year timestep, while ACC2 has an annual resolution.

The CH₄, N₂O and net energy-related CO₂ emissions calculated from GET7.1 are transferred to ACC2 for temperature calculations. The temperature calculations also use exogenous non-energy and other greenhouse gases and pollutants emissions, which are assumed to follow SSP1-1.9 and SSP1-2.6 for the 1.5°C and 2°C target cases, respectively. In ACC2, a box model represents oceanic and terrestrial carbon cycles. The ocean CO₂ uptake is represented by a four-layer box model, the uppermost representing the atmosphere and ocean mixed layer and the others the ocean’s inorganic carbon storage capacity, and the land CO₂ uptake model consists of four reservoirs connected with the atmosphere. The atmospheric concentrations of greenhouse gases respond dynamically to their emissions and removals e.g. chemical sinks. The resulting radiative forcing is an input to a heat diffusion model, which further calculates the global temperature. The temperature change in turn affects the carbon cycle through soil respiration and ocean-atmosphere carbon flux. ACC2 is comprehensively described in ref²⁷.

Enhanced weathering module: Basalt supply

The enhanced weathering module has two main components: the basalt dust supply and the biogeochemical module calculating the removal rate of CO₂. The costs and energy requirements of basalt supply are integrated in GET. We followed ref.¹⁴ for the parameterisation of the extraction, grinding and tractor application costs. The electricity for grinding basalt is 0.2 EJ/Gt (central value) and ranges from 0.02 to 0.6 EJ/Gt in the uncertainty analysis. Tractors used to spread basalt in agricultural fields and mining machinery were assumed to use petroleum products ⁴⁹. The energy requirements of transport from mines to application areas are based on ref.⁹ and increase the energy demand in each transport subsector (road, train or water freight). Transport modes are substitutable but an assumed minimum share (70–90%) must be transported on the road. The transport distance for basalt applied on croplands follows ref.¹⁴, the mean distance for the basalt applied on forest areas ranges from 350 to 550 km. It was estimated by comparing a map of basalt resources⁵², airports and suitable application sites (see SI.1). A share of the basalt spread on forests is assumed to be applied with aircrafts (70%-90%), since 80% of the global surface is more than 1 km away from the nearest road⁵³. This share can be expected to decline in the future, with the expansion of new roads⁵³. On the other hand, applying basalt on forests by means of land transport can be challenging, even when a road is available. This share depends on the development of roads and on the share of forests that tractors can penetrate. Aerial application is likely to be more expensive and energy intensive than land-based alternatives. If the share of aircraft use were lower, the energy consumption would also be lower, and basalt application could become higher in a cost-optimisation model. Assuming a large part of aerial spraying is therefore pessimistic as far as costs are concerned.

Enhanced weathering module: Airborne basalt application

We considered that small agricultural aeroplanes such as the AirTractor 802 (AT802), which can be equipped with a dust spreader, could be used to spread basalt dust. This kind of aircraft is commonly used to spread limestone^54–56 although issues with rock discharge have been reported, due to the wide range of the particle size distribution⁵⁴. Details of rock dust discharge are beyond the scope of this analysis, and more research would be needed on how to spread large quantities of basalt dust by air. An AT802 burns 330 litres of kerosene per hour, flies at 306 km/h, can carry 4.3t of rocks (we assume that rock dust can be spread without mixing it with water) and costs USD 1.8 million. Using an open-source map of airports, we estimate that the mean distance per flight ranges between 160 and 240 km. If one adds 10 minutes for spreading and landing operations, the average flight should last between 41 and 57 minutes. This represents an energy use of 1.8 to 2.5GJ/t_rock. Assuming 20 minutes of ground operations per flight, 10 hours of use per day, five days out of seven, the capacity cost for spreading one ton per year is 170–214$. We do not consider the non-CO₂ climate effect of aerial application⁵⁷, nor those of diesel combustion⁵⁸.

Enhanced weathering module: ORCHIDEE emulator

The biogeochemical module is an emulator of the response of net primary productivity (NPP) to phosphorus fertilisation induced by the dissolution of phosphorus-rich basalt dust, as simulated by the land surface model ORCHIDEE-CNP model. Tailored simulations in which basalt dust is applied on all ice-free non-agricultural land in the year 2018 were used for the calibration. Once applied to soils, basalt is assumed to have a constant dissolution rate, referred to in this study as the weathering rate. This simplistic approach reflects current understanding and data availability to parameterize weathering rates, and does not account for certain phenomena, such as the reduction of reactive surface over time, as well as the soils, plants and hydrological processes that can potentially influence weathering. More detailed models that account for some of these processes have been proposed ^12,59; however, many processes are not yet well quantified, and consequently the weathering rates ^45,48.

Here, the stock of basalt in soils B [Gt] increases with the supply ${S}_{B}$[Gt]. The dissolution of basalt follows a law of decay, parameterized with the weathering rate ${w}_{r}$ [year^− 1] (E.1).

$$\frac{dB}{dt}=-{w}_{r}B+{S}_{B}$$

E.1

As we assume that the grain size is 20µm, a range of 1%-25% per year is assumed for ${w}_{r}$. The high end is the global average weathering rate used in ORCHIDEE-CNP, where the pixel-level values are based on ref¹⁴ and on temperatures at a given model pixel. The low end follows ref⁴³, which assumes similar grain size, temperature and pH as in ref¹⁴, but a lower dissolution rate per unit of specific surface area, and a lower specific surface area than in ref¹⁴. However, this uncertainty range is small compared to the 5–95% range in ref¹⁴, which varies the weathering rate by a factor of a thousand, and is solely based on rates estimated in idealised lab incubation experiments which might differ from the ones in actual soil environments

Geochemical CO₂ capture happens when basalt dissolves: the released base cations (calcium potassium, natrium, and magnesium) are transferred to surface waters, where they are charge-balanced by the formation of bicarbonate ions²⁰. The capture rate p_B depends on the assumed concentration of these elements in rock material, and ranges between 0.24 and 0.37 t_CO2 /t_rock. In GET-ACC2, the geochemical capture G_CO2 is assumed to be instantaneous and controlled by equation (E.2), but it should be noted that these values are not necessarily reached before minerals are leached to the ocean, and that the actual rate of in situ capture depends on local freshwater pH and alkalinity⁶⁰.

$${G}_{C{O}_{2}}={p}_{B}{w}_{r}B$$

E.2

Land carbon cycle

The land carbon cycle component of ACC2 interacts with the enhanced weathering module. It consists of four carbon pools ${C}_{i}$ [Gt], with different turnover rates, which exchange carbon with the atmosphere. The inflow is the net primary production of the terrestrial biosphere: its magnitude is assumed to depend on the atmospheric CO₂ concentration and (to a lesser extent) on the global temperature change $\varDelta T$. The outflow is the heterotrophic respiration (HR) (E.3b): it is proportional to the quantity of carbon in each pool and to their turnover rate $\frac{1}{{\tau }_{i}\left(\varDelta T\right)}$ [year^− 1], which increases with land surface temperature. The apparent NPP is thus the sum of the temperature-dependent NPP (NPP^climate), plus the CO₂ fertilisation effect F^CO2 (E.3a). The net land sink is thus the difference between the NPP and the heterotrophic respiration, and is zero at equilibrium (E.3c) (i.e. a quasi-steady state assumption at preindustrial). Note that land use CO₂ emissions are treated separately and do not directly influence the land biomass as typically assumed in many simple climate and carbon cycle models.

$${\varSigma }_{i\in pools}{{NPP}_{i}}^{climate}\left(\varDelta T\right)+{{F}_{i}}^{C{O}_{2}}=NP{P}^{climate}\left(\varDelta T\right)+{F}^{C{O}_{2}}\left(\varDelta C{O}_{2}\right)$$

E.3a

$$H{R}_{i}\left(t\right)=\frac{{C}_{i}\left(t\right)}{{\tau }_{i}\left(\varDelta T\right)}$$

E.3b

$$\frac{d{C}_{i}}{dt}=NP{P}_{i}\left(t\right)-H{R}_{i}\left(t\right)$$

E.3c

Increase of the land carbon sink

The dissolution of basalt releases phosphorus which is available for plant uptake, leading to an increase in the NPP by a fraction $\delta NPP\left(t\right)$. In the extreme case where 50 kg/m² of basalt dust are applied on all forests worldwide, global NPP over the next 40 years is 4.4 GtC/year higher on average than without basalt application, based on the results of ORCHIDEE-CNP (Daniel Goll, unpublished). The assumed phosphorus content in basalt is 0.161%-weight, thus 50 kg/m² on 41Mkm² would supply 70 times the current global use of phosphorus as a fertiliser.

Global NPP is higher in ACC2 than in ORCHIDEE. Therefore, in order to replicate the magnitude of the increase in NPP from ORCHIDEE, we scale the increase in NPP by the ratio of preindustrial NPP in ACC2 and the NPP in ORCHIDEE for the year 2018 (E.4). The CO₂ fertilisation term F^CO2 is not affected by phosphorus from basalt as it was calibrated based on predictions of models which omit nutrient constraints on the CO₂ fertilisation effect²⁷ and thus reflects an upper boundary of the stimulation of NPP by increasing CO₂⁶¹ which cannot be further enhanced by phosphorus additions. .

We limit basalt application to forest ecosystems, where the stimulation of NPP results in substantially more carbon sequestered for multiple decades compared to grasslands in simulations by ORCHIDEE-CNP.

$$NP{P}_{i}\left(t\right)=NP{{P}_{i}}^{climate}\left(\varDelta T\right)(1+\frac{NP{P}_{}^{ORCHIDEE-CNP}\left(2018\right)}{{\varSigma }_{i\in pools}NP{P}_{i}^{climate}} \delta NPP\left(t\right))+{{F}_{i}}^{C{O}_{2}}\left(t\right)$$

E.4

The increase in the NPP is followed by the increase of heterotrophic respiration, which releases a part of the sequestered carbon following the decay rate constant (E.3b). Our phosphorus cycle emulator quantifies $\delta NPP$, the fractional increase of NPP following basalt application: $\delta NPP=\frac{NP{P}_{EW}}{NP{P}_{Baseline}}-1$.

In the spatially explicit land surface model ORCHIDEE-CNP, the increase of NPP due to phosphorus release depends on the soil, biome and climate and saturates with increasing basalt additions. Since there is no spatial resolution in GET-ACC2, we express $\delta NPP$ as the function of two unidimensional variables: the area of basalt application a_B [Mkm^− 2], and the rock application rate c_B. The variable a_B is defined by ranking the application pixels according to their NPP stimulation from high to low. A multiplicative function of the area of application ${a}_{B}$ [Mkm²] and rock application rate ${c}_{B}$[Gt.Mkm^− 2] is used to fit the mean NPP response during the forty years that follow basalt application, $\stackrel{̄}{\delta NPP}$ (E.5, Fig. S5).

$$\stackrel{̄}{\delta NPP}={\stackrel{̄}{\delta NPP}}_{max}\left(1-{e}^{-\alpha {c}_{B}}\right)\left(1-{e}^{-\gamma {a}_{B}}\right)$$

E.5

This analytical form, which was chosen to fit the ORCHIDEE-CNP predictions for the forest biome, allows to minimise any cost function that would depend on the surface and rock concentration. Here, we assume that the first-order costs are proportional to ${B}_{0}={a}_{B}{\cdot c}_{B}$ [Gt] (the total mass of basalt applied). The emulator is based on the following assumptions: the increase in NPP responds to the increase ${\delta c}_{P}$ in soil phosphorus concentration [Gt.Mkm⁻²], which is proportional to the application rate of basalt, and decreases over time (E.6). For simplicity, the surface of basalt application on forest areas does not evolve with time, although this is not cost-optimal.

$$\delta NPP\left(t\right)=\delta NP{P}_{max}\left(1-{e}^{-\alpha {\delta c}_{P}\left(t\right)}\right)\left(1-{e}^{-\gamma {a}_{B}}\right)$$

E.6

The dynamic evolution of the soil phosphorus concentration ${\delta c}_{P}$ is designed to reproduce the results of ORCHIDEE-CNP. It is modelled with an auxiliary pool of phosphorus which is unavailable to plants, exchanges phosphorus with the soil concentration with a turnover time ${\tau }_{e}$, and is leached to inland waters with a time ${\tau }_{l}$.

$$\frac{d\delta {c}_{P}}{dt}=\frac{\lambda {w}_{r}B}{{a}_{B}}-\frac{{\delta c}_{P}}{{\tau }_{e}}+\frac{{\delta u}_{P}}{{\tau }_{e}}$$

E.7a

$$\frac{d{u}_{P}}{dt}=\frac{{\delta c}_{P}}{{\tau }_{e}}-\frac{\delta {r}_{P}}{{\tau }_{e}}-\frac{\delta {u}_{P}}{{\tau }_{l}}$$

E.7b

The comparison with ORCHIDEE-CNP data (Fig S.5, Fig S.7) shows that the stimulation of NPP by basalt addition is generally slightly underestimated by the emulator.

Uncertainty analysis

To assess the sensitivity of our results to the uncertainty of parameters, we apply a double uncertainty analysis.

Quasi Monte-Carlo

First, we use a quasi-Monte Carlo sampling method to derive the distribution of outputs from the distributions of parameters. A Quasi Monte Carlo method is similar to a Monte Carlo method but uses quasi-random sampling instead of random sampling to minimise errors. The Latin Hypercube Sampling method is used. On the supply side, we vary the costs and efficiency of new technologies, as well as their maximum diffusion speed and rates. The climate model uncertainty is also quantified by varying the equilibrium climate sensitivity³⁰. More details about the parameters assessed, as well as their distribution, are described in SI.2.

Morris method

Second, we apply the Morris screening method^40,41,62 to quantify the influence of each parameter on the outputs. Let $X=\{{x}_{1},\dots ,{x}_{m}\}$ be a vector of parameters which are normalised to [0,1], $Y=f\left(X\right)$ the output. A trajectory T is initiated by choosing an initial point${X}_{0}^{t}$ in ${\left[\frac{1}{2*N-1},\frac{2}{2*N-1}, ...,\frac{2N-1}{2\left(2N-1\right)}\right]}^{m}$, and then iteratively increasing each parameter i by $\frac{N}{\left(2N-1\right)}$ in a random order ${\{P}^{t}{\left(i\right)\}}_{i\in [1,p]}$ where ${P}^{t}$ is a permutation, to obtain T={${X}_{0}^{t}, {X}_{1}^{t}\dots {X}_{m}^{t}$}. Computing the output along this trajectory yields the elementary effects for each parameter i: ${d}_{i}^{t}=f({X}_{\sigma \left(i\right)}^{t}$)-$f\left({X}_{\sigma \left(i\right)-1}^{t}\right)=f\left({x}_{1},\dots {x}_{i}+\varDelta \dots {x}_{m}\right)-f({x}_{1},\dots {x}_{m})$. We produce N=20 trajectories. The means ${\mu }_{i}$ of the elementary effects, their standard deviation ${\sigma }_{i}$ and the mean of their absolute values ${\mu }_{i}^{*}$ give useful information about the influence of these parameters.

Initial points are sampled following a Latin Hypercube method, and trajectories are chosen to maximise their dispersion and thus their coverage of the parameters space, following ref.⁴¹, but we improve the sampling strategy by changing the dispersion measure: we maximise the sum over all parameters of the Euclidean pairwise distances of all the points used to compute elementary effects of this parameter. Additionally, we use a simulated-annealing algorithm instead of their brute force approach, which greatly reduces the computational burden (more details in SI.2).

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Leveraging ecosystems responses to enhanced rock weathering in mitigation scenarios

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Abstract

Figures

INTRODUCTION

RESULTS

Enhanced weathering deployment

Impact of enhanced weathering on mitigation scenarios

Policy costs

Reduction of BECCS

Impacts on energy use

Uncertainty analysis

DISCUSSION

METHODS

Modelling framework

Enhanced weathering module: Basalt supply

Enhanced weathering module: Airborne basalt application

Enhanced weathering module: ORCHIDEE emulator

Land carbon cycle

Increase of the land carbon sink

Uncertainty analysis

Quasi Monte-Carlo

Morris method

References

Additional Declarations

Supplementary Files

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