The model parameters for CO₂ sorption on soil amendments were based on sorption isotherms fitted to dry sorption data collected under soil-relevant gas conditions without the presence of soil (Ringsby et al., 2024) (Figure 1 and Supplementary Table S1). Dry sorption experiments with sorbent were chosen because the presence of water and soil hinders comparability between studies and makes generalization difficult. However, it should be noted that water (Davidson et al., 2013) and soil (Kwon and Pignatello, 2005) can reduce the specific sorption capacity.

The sorbents were either not pre-treated before the sorption experiment (“as received”) or they were outgassed at 150°C before the sorption experiment (“outgassed”). This is an important distinction because pre-treatment has been identified as a major source of uncertainty (Figini-Albisetti et al., 2010). No outgassing or an outgassing temperature that is too low will likely underestimate sorption capacity while elevated temperatures applied to temperature-sensitive materials might irreversibly alter the sorbent behavior (Figini-Albisetti et al., 2010). However, the authors also noted that the outgassing temperature must be consistent with final application. During the large-scale application process of sorbents as soil amendment, elevated temperatures are not expected. Therefore, sorption isotherms “as received,” were assumed to be best in line with the intended application. The sorbent with the highest “as received” sorption capacity was Biochar 3 and was chosen for simulations, while the outgassed isotherm for Biochar 3 indicates the upper bounds likely for biochar sorbents (Ringsby et al., 2024).

A sorption isotherm model that is often used to describe experimental observations such as those above is the Langmuir model (Equations 1–3). The single site Langmuir model makes following assumptions: (1) there is a limited sorption capacity, (2) all sorption sites are equal, (3) one site sorbs one molecule of sorbent, and (4) all sites are energetically independent of the number of sorbed molecules (Limousin et al., 2007). The assumed reaction is: (1) q m − q + p C O 2 ↔ q

Where q is the surface complex, q m is the maximum sorption capacity, q m − q indicates free sites, and pCO₂ is partial pressure of CO₂. The conditional stability constant can be written as: (2) K = q q m − q p C O 2

Where K is the Langmuir constant. The equation can be rearranged to the typical Langmuir isotherm: (3) q = q m K p C O 2 1 + K p C O 2

In many cases an improved description of experimental data can be achieved with a multisite Langmuir model (Equation 4): (4) q = ∑ i = 1 p q m , i K i p C O 2 1 + K i p C O 2

Where K i and q m , i are Langmuir constant pairs p for multiple sorption sites.

For inclusion in the reactive transport model, a multisite competitive Langmuir sorption model was adapted (Limousin et al., 2007). A reaction for a strong and a weak sorption site was implemented (Equations 5, 6): (5) > S strong 0 + C O 2 g ↔ > S strong C O 2 0 (6) > S weak 0 + C O 2 g ↔ > S weak C O 2 0

Where >S_strong⁰ refers to a strong sorption site and > S_weak⁰ refers to a weak sorption site. The Langmuir constants K 1 and K 2 were implemented as the equilibrium constants for the two reactions. The maximum adsorption capacities q m , 1 and q m , 2 can be directly entered in the RTM. Physical properties necessary to simulate the sorbent mass were from the same published study (Supplementary Table S2). The Biochar 3 sample was obtained from Atlas Olive Oils, which produces biochar from olive tree byproducts, including pulp, pits, and branches. The chemical properties that were provided by the supplier are listed in Supplementary Table S3.

Simulations were conducted with the multi-component reactive transport code, CrunchFlow (Steefel et al., 2015). CrunchFlow allows simulation of variably saturated conditions at steady state, including gas diffusion as well as sorption of gas species. Gas diffusion was simulated via Fick’s law assuming a tortuosity correction via Millington (1958). A surface complexation model (SCM) capability in CrunchFlow simulates sorption. The SCM provides flexibility to simulate sorption mechanisms or empirical sorption reactions, e.g., via the Langmuir sorption model. Equilibrium between the gas and aqueous phase is governed by Henry’s law, and gas concentrations are simulated via the ideal gas law.

Under baseline conditions with no sorbent present, simulated pCO₂ increased with depth and was higher in scenarios with higher CO₂ production (Figure 3A). The model adequately reproduced observed CO₂ trends for low, medium, and high CO₂ production where concentrations often rapidly increase to concentrations between 5,000 and 30,000 ppm over the first 50 cm (Cerling, 1984; Amundson et al., 1998; Davidson et al., 2006; Wang et al., 2013; Chirinda et al., 2014; Winnick et al., 2020). CO₂ gradients over depth (dCO₂/dz) were positive, meaning an efflux from the soil was simulated (Figure 3B). Simulated DIC increased, pH decreased and Ca²⁺ increased with depth and pCO₂ (Figures 3C–E). Depletion of the calcite mineral volume fraction was higher with higher pCO₂ (Figure 3F). As noted in the methods section, the calcite distribution over depth was simplified for model interpretation and will typically vary as a function of depth depending on climate (Pfeiffer et al., 2023).

Sorption of CO₂ affected soil pCO₂ and soil CO₂ efflux (Figure 4). The simulated sorption capacity (sorbed CO₂/g sorbent) aligned with observed data that had been used to derive sorption isotherms (Figure 4A). Sorption increases with pCO₂, which in the simulations increased with depth and CO₂ production. The scenario with the highest CO₂ production reached almost 0.015 bar within the application depth of 25 cm, under which the sorption capacity was almost three times higher than at atmospheric pCO₂. Over the simulation time, the addition of the sorbent to the soil is visible in a decline of pCO₂ (Figure 4B). At a depth of 20.5 cm, the simulated pCO₂ was initially around 2,000 ppm for a scenario with low CO₂ production. At day 400 of the simulation, sorbent was added and pCO₂ decreased to almost 0 ppm. After several days the pCO₂ rose again and then slowly returned to steady state after around 50 days. The return to steady state was faster with higher CO₂ production. Sorption behavior was transient over depth because gas diffusion and production are not instantaneous (Figure 4C). Immediately after application, sorbed CO₂ over depth followed a u-shape with high sorption at the atmosphere-soil and the shallow-deep soil interface. The shape indicates that gas from the deeper soil and the atmosphere was diffusing in (Figure 4D). The sorption temporarily reduced CO₂ efflux and even caused CO₂ influx from the atmosphere (Figure 4B). The effect on efflux lasted longer when CO₂ production was lower.

Total maximum sorption was higher with higher CO₂ production and higher total sorbent mass (Figure 5). Total sorption can be related to mean steady state pCO₂ over application depth (Supplementary Figure S3). A temporary reduction in efflux was related to CO₂ production and sorbent mass, as was expected (Figure 5B).

Transport occurred in simulations only via diffusion, which is slow compared to advection and results in a notably delayed breakthrough and broadened breakthrough curve (Figure 6) compared with sorption studies that pump gas into columns (Kaur et al., 2019; Pal et al., 2019; Al Mesfer et al., 2020).

Depth profiles show that changes in pCO₂ through sorption affected all simulated parameters (Figure 7). Changes are particularly visible immediately after application and where sorbent had been applied (in the top 25 cm). Immediately after sorbent application, the pCO₂ reached almost zero over the application depth. The CO₂ gradients changed from positive to negative at the atmosphere-soil interface, indicating that there was CO₂ influx to the soil instead of efflux. The CO₂ gradients strongly increased where sorbent amended soil meets the unamended soil. Over the application depth, simulated DIC was reduced by over 90%, and pH increased from 7.5 to 8. The pH was increased because sorption of CO₂ that is in equilibrium with the aqueous phase removes bicarbonate ions and protons from solution via: (12) C O 2 a q + H 2 O ↔ H C O 3 - + H +

The simulated Ca²⁺ was around 50% lower and the calcite mineral volume fraction was slightly increased due to precipitation. The precipitation was temporary, and calcite redissolved. The transient change in calcite mineral volume fraction was larger with higher total sorption. Transient conditions lasted longer when CO₂ production was lower. Transient conditions lasted for 30–50 days when only sorption and no increased CO₂ production was simulated.

Assuming an increased CO₂ production after amendment application resulted in deviation of soil geochemical parameters after 20 days (Figure 7): higher pCO₂, higher dCO₂/dz, higher DIC, lower pH, higher Ca²⁺, and lower calcite volume fraction. This indicates that changes in CO₂ production – an empirical representation of soil respiration – have the potential to persistently change soil geochemistry.

A high retardation factor of R f = 37.5 was calculated in a simplified simulation scenario with either sorbent or unreactive quartz. The delay in diffusion due to sorption is clearly visible in pCO₂ heatmaps (Figure 7). In the column with quartz, pCO₂ increases rapidly in <1 day and is then at steady state. With sorbent, there is a slow increase over 30 days, after which steady state is reached.

Figure 8 shows how carbonate alkalinity and Ca²⁺ concentrations are related to carbonate dissolution via acids in addition to other processes, e.g., degassing and sorption. The 1:1 line in Figure 8 indicates carbonate dissolution through carbonic acids (Semhi et al., 2000; Perrin et al., 2008): (13) CaCO 3 + C O 2 + H 2 O ↔ 2 H C O 3 - + C a 2 +

And a possible reaction for the 2:1 line is (Zamanian et al., 2018): (14) CaCO 3 + N H 3 + H 2 O + 2 O 2 → H C O 3 - + C a 2 + + NO 3 - + 2 H 2 O

Equation 14 describes calcite dissolution after N fertilizer application. Acidification leads to increased calcite dissolution rates and cations are balanced by nitrate anions, as opposed to only bicarbonate (Zamanian et al., 2018). This reaction has been identified as a CO₂ source in agricultural areas that are either limed or where carbonates naturally occur (Semhi et al., 2000; Perrin et al., 2008; Zamanian et al., 2018). Transient conditions above the 2:1 line occurred in the simulations due only to sorption and degassing—contributing to lower bicarbonate concentrations but no cations. Some calcite precipitation occurred simultaneously resulting in a slight drop in cation concentrations.

Transient conditions in drylands are often driven by wetting events, which cause a complex biogeochemical soil response (Jarvis et al., 2007) including increased soil respiration, desorption (Sánchez-García et al., 2020), and dissolution and reprecipitation of carbonate minerals (Angert et al., 2015; Gallagher and Breecker, 2020). A short-term increase in CO₂ efflux is known as “Birch effect” and is mostly attributed to increased soil respiration although immediate release of CO₂ has been associated with desorption (Kemper et al., 1985; Sánchez-García et al., 2020) which strongly depends on OM content in soils (De Jonge and Mittelmeijer-Hazeleger, 1996). Carbonate dissolution increases with elevated pCO₂, which dampens the soil CO₂ efflux after wetting events and has been associated with underestimation of soil respiration rates when carbonates are present (Angert et al., 2015; Gallagher and Breecker, 2020). A second important source of transient conditions in drylands are daily, seasonal, and annual temperature changes. Increased temperature generally leads to increased soil respiration and desorption although concomitant changes in moisture can either amplify or reduce this response (Tang et al., 2003; Shen et al., 2009; Darrouzet-Nardi et al., 2015; Sagi et al., 2021).

Transient conditions lasted for varying time scales in the simulations, which has implications for monitoring (Figure 9). Increased calcite precipitation lasted only a few hours while the soil CO₂ efflux was affected over more than 10 days. Comparison to field observations shows similar variations in time scales. The Birch effect, which occurs on dryland soils, is most pronounced for a few hours or days after a wetting event (Jarvis et al., 2007; Unger et al., 2010). Seasonal variations in wet-dry cycles will lead to prolonged variation in carbonate dissolution and precipitation (Breecker et al., 2009; Gallagher and Breecker, 2020; Domínguez-villar et al., 2022).

Transient conditions are also important to for managing carbon cycling in drylands. In 5 h laboratory experiments, the peak after wetting composed almost 80% of the total CO₂ efflux (Sánchez-García et al., 2020). Transient conditions due to drying and rewetting—even when short-lived—were found to result in higher soil CO₂ emissions than constantly moist soils and gain relevance because of the spatial extent of drylands (Jarvis et al., 2007; Shen et al., 2009).

Shown as comparison to the simulated soil CO₂ efflux is the range of carbonate alkalinity fluxes in rivers in carbonate-dominated catchments (Zhang S. et al., 2022) (Figure 9). Carbonate alkalinity export to rivers derived from calcite correlates with hydrological conditions and carbonate precipitation under dry conditions leads to increased CO₂ soil efflux (Wen et al., 2022). Therein lies a potential benefit of increased gas sorption within carbonate containing soils. Sorption is reversible and desorption of CO₂ that occurs when water is present could aid export of carbonate alkalinity to rivers. How much of the desorbed CO₂ escapes to the atmosphere or is trapped in pore space depends on a myriad of environmental factors, such as water amount and soil properties (Sánchez-García et al., 2020).

The simulated dynamics indicate both potential co-benefits and disadvantages for co-application of various soil amendments. Application of soil amendments that cause positive priming might be suitable to be combined with EW, because the increased production of CO₂ could drive mineral dissolution. However, soil amendments that induce negative priming associated with reduced CO₂ production could hinder EW. Biochar can cause positive or negative priming, but the underlying drivers are still poorly understood (El-Naggar et al., 2019). Thus, sites-specific evaluation of the response to biochar may be required.

The simulations have further implications for monitoring established or promising soil CDR methods. CDR via biochar currently only considers C that is contained in biochar, but biochar also affects native soil C. This is why recommendations for monitoring would be relevant for biochar if native soil C is regulated in the future. This is especially important because fragile drylands soils are more vulnerable to climate change (Lal, 2019). Key drivers for carbon cycling, such as temperature and precipitation, are currently changing at a regional scale, while the local response of SOC and SIC pools in drylands is uncertain (Shen et al., 2009; Wang et al., 2022). Depending on specific climatic and soil conditions in drylands, monitoring campaigns need to adequately capture transient conditions over different time scales. If degassing, (de)sorption, and soil gas displacement are expected to play a major role and should be investigated (Sánchez-García et al., 2020), monitoring needs to capture transient conditions that might last only a few hours or days. On the other hand, climates dominated by seasonal variations need to capture these variations over longer time scales and to avoid under-or overestimation of carbon fluxes.

Various monitoring methods need to be applied to distinguish different processes within the carbon cycle. There are a range of parameters that can help to monitor CDR by distinguishing between organic and inorganic carbon cycling. Carbon mass balance over depths, pCO₂ depth profiles, O₂ concentrations or depth profiles, and carbon isotope composition can help to distinguish biotic and abiotic process (Angert et al., 2015; Gallagher and Breecker, 2020). Monitoring major cations and anions is helpful to resolve if carbonate and silicate weathering consumes CO₂ or is driven by other acids (Perrin et al., 2008; Zamanian et al., 2018).

Simulated carbon dynamics are specifically relevant for monitoring of EW. Monitoring of all parameters that are affected by CDR methods like EW can be expensive, which is why monitoring schemes that provide reliable CDR estimates based on as little monitoring as possible are under development and there is no consensus yet on what constitutes a reliable method. Fuhr et al. (2023) also points out that highly dynamic natural background conditions need to be accounted to monitor EW fluxes reliably. Various methods to monitor or predict EW have been presented in the literature: (1) carbonate alkalinity and cation concentrations either in rivers (Knapp and Tipper, 2022; Zhang S. et al., 2022) or in soils (Holzer et al., 2023), (2) Ca, Mg and nitrate ions and rare earth elements (Kantola et al., 2023) (3) total alkalinity (Fuhr et al., 2023), (4) electrical conductivity (Rieder et al., 2023), and (5) simulations of varying complexity and spatial scale (Beerling et al., 2020; Cipolla et al., 2021; Kanzaki et al., 2023). An important process that was highlighted by simulations here and should be considered when monitoring EW is degassing, which resulted in additional removal of DIC from solution as well as short-lived calcite precipitation. Most streams are oversaturated with respect to CO₂ and degassing is prevalent (Stets et al., 2017). Estimates suggest up to 60% of CO₂ emissions from streams originate from DIC (Duvert et al., 2019; Winnick and Saccardi, 2024), and 30% of CO₂ originate from DOC (Khadka et al., 2014). Spatial and temporal patterns of pCO₂, degassing and sources of degassing depend on flow regimes, respiration, alkalinity, and groundwater inputs (Khadka et al., 2014; Winnick and Saccardi, 2024). A positive correlation between the pool of DIC and the contribution of DIC to degassing fluxes has been found (Winnick and Saccardi, 2024). In the simulations, degassing and removal of DIC also led to calcite precipitation. However many rivers are supersaturated with respect to calcite potentially due to inhibition (Knapp and Tipper, 2022).

The simulations show that abiotic C-sinks such as CO₂ sorption gain importance as a C sink in soils when biological activity is low, which is the case in many dryland ecosystems (Warner et al., 2019; Sagi et al., 2021). The relative reduction in CO₂ efflux over relaxation time was higher with lower CO₂ production (Figure 5). Moreover, dryland soils with low organic matter content have the lowest sorption capacity of all naturally occurring soils and around 10 times lower sorption capacity than the simulated sorbents (De Jonge and Mittelmeijer-Hazeleger, 1996; Ravikovitch et al., 2005; Davidson et al., 2013). Although CDR through sorption is estimated to be relatively low for a single application (around 2% of total C for the simulated biochar as detailed in SI), soil amendments could be relevant for drylands due to the limitations of other methods and through provision of soil health benefits.

Soil amendments have the co-benefit of alleviating soil degradation, specifically salinization. Soil salinity is a worldwide concern, with drylands, irrigated lands, and agricultural lands most at risk (Dregne et al., 1991; Ivushkin et al., 2019). Mechanisms that have been implicated in salinity amelioration with biochar are: release of Ca²⁺ and Mg²⁺, adsorption of Na⁺, proton release that promotes Na⁺ uptake in certain plant species, increased salt leaching through increased porosity (Akhtar et al., 2015; Amini et al., 2016), reduced EC (Lashari et al., 2015), and changes in evaporation dynamics (Liang et al., 2021; Lee et al., 2022). However, depending on biochar characteristics biochar could release Na⁺ (Saifullah Dahlawi et al., 2018) and some biochar studies have been criticized because salt stress was induced with NaCl (Akhtar et al., 2015).

Challenges for soil amendment application are health risks, transport emission and albedo changes. Although biochar feedstock can contain heavy metals and organic contaminants, the fraction that is bioavailable after pyrolysis tends to be small (Godlewska et al., 2021). Sorbent materials generally immobilize contaminants if the sorbent is immobile (Godlewska et al., 2021) suggesting positive health effects. Soil amendments can lead to reduced wind erosion long-term, which could be an important benefit for drylands (Şeker and Manirakiza, 2020; Pi et al., 2021).

Emissions from implementation, e.g., material preparation and transport will reduce the CDR potential. Transport emissions are a particular concern, because there is typically little infrastructure in drylands. Sources for biochar are scarce in drylands due to relatively lower above ground biomass (Cook-Patton et al., 2020), however, most of the global irrigated lands are situated on drylands (Dregne et al., 1991; Siebert et al., 2015) and could provide biomass sources, as could other organic wastes.

Albedo refers to surface albedo, which varies by land cover type, color, wetness and surface irregularities (Zhang X. et al., 2022). Albedo is highest in deserts (0.2–0.45) and dry soils (0.15–0.36) while increased water content (0.06–0.19) and vegetation cover reduce albedo (grasses 0.2, savannah 0.15–0.2) (Garratt, 1993). Biochar application was found to lead to albedo reduction of 0.05 on agricultural soil, which lowered the predicted climate change mitigation benefit by 13–22% (Meyer et al., 2012). The changes in soil albedo are less of a concern for vegetated grasslands and shrublands, which make up around two thirds of global drylands. Future work should assess albedo changes in field trials.