The soil samples used in the study by te Pas et al. (2023) originated from the topsoil of a sandy grassland (pH-H₂O = 5.16) in Wageningen, the Netherlands (51°59′39.3″N 5°40′05.9″E). Based on the location, the soil was classified as Gleyic Phaeozem according to the FAO World Reference Base system. Crushed olivine minerals were supplied by the Åheim Gusdal Mine located in Steinsvik, Norway. Crushed wollastonite minerals were retrieved from a mine located at Saint Lawrence Wollastonite Deposit, Ontario, Canada. Albite was obtained from a mine at Bancroft, Ontario, Canada, and was crushed using a jaw crusher. Table 1 shows the major elemental composition and specific surface area (SSA) of the baseline soil and the three minerals used for the soil column experiment. For further details on the soil and minerals, we refer to te Pas et al. (2023).

The experimental set-up was described in te Pas et al. (2023). In brief, a down-flow soil column experiment was conducted for 64 days in a conditioned room of 20 ± 2°C. Soil columns (180 mL, Ø 5 cm) were connected via a funnel to a closed container, in which the leachate was collected. Columns were filled with 150 g soil and 100 mL de-mineralized water using a five-step wet packing procedure (Gilbert et al., 2014; ISO, 2019), followed by 2 days of pre-incubation in which redundant water leached from the columns. On day 1 of the experiment, 18.75 g (125 g kg⁻¹ soil) of olivine, wollastonite, and albite were applied to different columns as a layer on top of the soil. Each treatment was studied in duplicate, and one control soil without silicate amendment was used. Here, we present additional analyses for one of the duplicates, which were referred to in te Pas et al. (2023) as Olivine 1 (Ol1), Wollastonite 2 (Wo2), and Albite 1 (Al1). Every 2 to 4 days, 40 mL de-mineralized water was applied to the top of the soil columns. Afterward, leachate was collected in the containers below the soil columns and sampled at 9 time points between 1 and 64 days for analyses of base cation concentrations (Ca²⁺, Mg²⁺, K⁺, Na⁺) using inductively coupled plasma optical emission spectrometry (ICP-OES), and at 21 time points for pH measurements and titrations with 0.02 M HCl to determine TA, with a decreasing frequency over time. Upon termination of the experiment, the thin layer of applied minerals on top of the soil was removed based on visual observations, producing two separate samples of the post-treatment soil and the layer of applied minerals for each treatment. Although separated, the layer of applied minerals very likely contained some soil particles and vice versa. The samples were separately dried at 40°C, sieved over 2 mm, and homogenized.

The baseline soil, the three mineral feedstocks (olivine, wollastonite, and albite), the post-treatment soils, and the separated layers of applied minerals were collected at the end of the experiment (10 samples in total) and used for further analysis using total fusion ICP-OES. Total fusion was conducted by mixing samples with a flux of lithium metaborate and lithium tetraborate to induce a fused sample within an induction furnace. The resultant molten melt was poured into a 5% nitric acid solution until completely dissolved prior to analysis. The final processed samples were then analyzed using ICP-OES.

We present three methods to calculate CDR associated with EW (Table 2). Method 1 (M1) is a soil-based mass balance approach using base cation concentrations measured in the thin layer of applied minerals and mineral feedstock, determined by total fusion ICP-OES. Since olivine, wollastonite, and albite amendments were applied to the soil surface, the characterization of elements in the separated layer of applied minerals was used to calculate weathering rates. Method 2 (M2) was based on the elemental mass balance (EMB) method presented in te Pas et al. (2023), which is derived from the base cations measured in the leachate and in a strong acid (0.43 M HNO₃) extract of the soil, analyzed using ICP-OES. Mass balances (M1 and M2) were constructed using the major base cation present in the mineral feedstock, being Mg for olivine, calcium (Ca) for wollastonite, and sodium (Na) for albite (Table 1). Finally, method 3 (M3) involved TA titrations of the leachates.

The concentrations of soil exchangeable base cations (Ca²⁺, Mg²⁺, K⁺, Na⁺) were determined using a 0.1 M BaCl₂ extraction followed by ICP-OES measurements (ISO, 2018). Soil carbonate content was determined using Scheibler calcimetry (Allison, 1960; ISO, 1995). Both soil pools were corrected for the concentrations measured in the baseline soil and compared to the results obtained by total fusion ICP-OES analysis, with the aim of retrieving the fate of weathering products in the retarded fraction. We then defined an unknown soil pool by subtracting the weathering products traced in the leachate, the exchangeable pool and precipitated as carbonate minerals from the weathered fraction defined by total fusion ICP-OES analysis. This unknown soil pool represents the weathering products that were retarded in the soil column but not in the exchangeable fraction or as carbonate minerals.

The CDR calculated using three methods for the three different minerals is shown in Figure 1A. For the olivine treatment, 15.5 g CO₂ kg⁻¹ soil was calculated using M1, which involved a mass balance using the major base cation present (Mg) based on total fusion ICP-OES analyses of the layer of applied minerals. M2 involved a mass balance using the Mg concentrations measured in the leachate and the soil extracted with 0.43 M HNO₃, indicating 1.39 g CO₂ kg⁻¹ soil. M3, i.e., TA titrations of leachate samples, resulted in the lowest estimates of 0.21 g CO₂ kg⁻¹ soil. For the wollastonite treatment, the highest CDR estimate was also found for M1, namely, 12.0 g CO₂ kg⁻¹ soil. Lower CDR estimates were found for M2, 1.44 g CO₂ kg⁻¹ soil, and M3, 0.12 g CO₂ kg⁻¹ soil. M1 also produced the highest CDR estimates for the albite treatment, 3.67 g CO₂ kg⁻¹ soil, followed by 0.36, and 0.14 g CO₂ kg⁻¹ soil using M2 and M3, respectively. Figure 1B shows the carbon that was actually leached during the experiment, producing values that were all at least an order of magnitude lower compared to the calculated CDR, except for M3 where calculated CDR equals leached C. Furthermore, the difference in estimated leached C between the four methods was <0.2 g CO₂ kg⁻¹ soil for all treatments, showing values of 0.21–0.26, 0.12–0.22, and 0.14–0.27 g CO₂ leached kg⁻¹ soil for the olivine, wollastonite, and albite treatments, respectively.

Using M1, the fraction of retarded weathering products was quantified (Table 3). For the olivine treatment, 98.3% of the weathered Mg was calculated to be retained within the soil profile during the experiment. Of the Ca weathered from the wollastonite amendment, 98.2% was retained in the soil column. For the albite treatment, a retarded fraction of 92.7% was calculated for Na. Additional analyses were conducted to gain insights into the fate of base cations in the retarded fraction (Supplementary Table S2). A comparison of the base cation concentrations extracted with 0.1 M BaCl₂ to the concentrations measured with total fusion ICP-OES showed that 1.47% (albite), 6.48% (olivine), and 12.3% (wollastonite) of the weathered cations measured with total fusion ICP-OES could be traced in 0.1 M BaCl₂ extractions (not corrected for the baseline soil). While albite produced a soil CaCO₃ content below that of the baseline soil (56.4 mg per 150 g soil), soil CaCO₃ content increased to 149 mg for olivine and 190 mg for wollastonite per 150 g soil in the column (Supplementary Table S2).

We showed that the CDR associated with EW quantified by soil-based mass balance approaches was one or two orders of magnitude higher than leachate-based TA measurements (Figure 1A). The calculated fractions of retarded weathering products were all nearing 100% (Table 3), indicating that the vast majority was retained within the soil profile. When correcting for this retarded fraction, the calculated leached C (M1 and M2) closely overlapped with the measured leachate-based TA (M3) (Figure 1B; Table 3). Hence, soil-based mass balance approaches are only able to fully quantify CDR, involving both the capture of CO₂ and its durable storage (see definition in Section 1), over a given time and depth interval (here 2 months and 6 centimeters of soil) when accounting for the retarded fraction. Our conclusions are consistent with those of Reershemius et al. (2023). In addition, our study allows a quantitative assessment of the importance of the fraction of retarded weathering products and we provide calculations for a range of elements and mineral feedstocks.

Large differences in quantified CDR were also observed among the different soil-based mass balance approaches, where M2 yielded substantially lower Fw and CDR than M1 (Figure 1A; Table 3). M2 was based on base cations measured in the leachate and extracted from soils, excluding the thin layer of applied minerals that besides the applied mineral also contained some soil particles. Other soil column and mesocosm studies found the dissolved base cation concentrations in the bottom layer to be about an order of magnitude lower than in the top layer (Amann et al., 2020; Buckingham et al., 2022). As a result of the limited mobility of weathering products in our experiment, as confirmed by the quantified retarded fraction, it is likely that weathered base cations were primarily retained in the upper part of the soil profile, directly below the layer of applied minerals. Since the fraction of weathering products retained in this thin upper layer was not considered in M2, we conclude that M2 underestimates Fw and CDR. However, M1 is based on the assumption that base cations are truly mobile (Clarkson et al., 2024), while our quantified retarded fractions suggest otherwise. Methods such as those used by Reershemius et al. (2023) incorporate pre-treatment steps that leach out labile forms of cations bound to reactive soil surfaces, thereby removing part of the cations in the retarded fraction. We did not deploy such methods and instead extracted total concentrations through total fusion, hence allowing for the quantification of both the full retarded and leached fractions of weathering products. Our approach allows for a continued improvement of our understanding of cation behavior within soil and supports the development of soil-based mass balance methods for CDR quantification.

Uncertainties in mass balance approaches mainly arise from three primary factors. First, analytical errors may propagate through the largest term in the mass balance, i.e., the soil (Pogge von Strandmann et al., 2021). Second, error is introduced by analyzing a small sub-sample of a larger mass of soil, as discussed in Reershemius et al. (2023). Third, uncertainty was introduced by using the replicates of te Pas et al. (2023) for which the columns experienced reduced through-flow of water over time and (likely temporarily) anoxic soil conditions. These specific conditions were observed in all three treatments presented here and, while not invalidating the method, may have impacted cation mobility and the fate of cations within the soil. Further research should therefore include replicates to provide insights in the uncertainty and variability of the presented methods to quantify the retarded fraction.

Recent EW studies indicated that weathering signals measured in soil may not be reflected in significant changes in leachate alkalinity (Kelland et al., 2020; Vienne et al., 2024). This phenomenon can be explained by the retarded fraction of weathering products. Using the results for M1-olivine as an example (similar values were observed for wollastonite and albite), we observed a Fw of 13.1% over the course of the experiment, while the retarded fraction represented 98.3% of the weathered amount of Mg. The latter means that of the weathered Mg, only 1.71% could be traced in the leachate. Hence, the actual CDR is lower than the potential CDR. The C that is leached from soil (as measured by leachate-based TA titrations (Equation 8) or calculated by Equations 5, 7) is what we define as the actual CDR realized over a given time and depth interval (here 2 months and 6 centimeters of soil; Figure 1B). The potential CDR equals the CDR calculated based on Fw over a given time and depth interval (Figure 1A) and represents the CDR that could be achieved once the weathering products are fully leached from the soil column (assuming all weathering is driven by carbonic acid). Referring to the definition of CDR (see Section 1 and Smith et al., 2024), the actual CDR involves both the capture and durable storage of CO₂ in soils or oceans, while the potential CDR involves the capture of CO₂ through mineral weathering which is for a large part not (yet) followed by durable storage (i.e., C leaching). The 98.3% of Mg that originated from weathered olivine (M1) and was retarded within the soil profile in the initial stage of weathering can thus result in actual CDR once leached from the soil. We must consider that the potential CDR may involve base cations lost through plant uptake followed by harvest, retention in less-easily exchangeable pools by strong binding to reactive soil surfaces, and/or mineral precipitation. Whether weathered base cations in those pools are truly lost without further contribution to CDR depends on their fate, i.e., decomposition of crop residues, cation desorption, and mineral redissolution may (partly) return those base cations to soil. The relevance of adsorption and precipitation mechanisms in our experiment will be discussed in Section 4.3. Plant uptake was not possible in our soil column experiment but was found to have a minor impact under mesocosm and field conditions (Beerling et al., 2024; Kelland et al., 2020). Note that potential CDR should not be confused with CDR_pot, which is the maximum theoretical CO₂ removal potential of a mineral feedstock (g CO₂ g⁻¹ mineral weathered) based on its elemental composition (see Section 2.4.1 and Reershemius et al., 2023). In summary, soil-based mass balance approaches can be used to quantify the Fw and potential CDR but are unable to quantify the actual CDR over a given time and depth interval without correcting for the retarded fraction, while leachate-based TA concentrations can only indicate the actual CDR over a given time and depth interval but provide no indication of the Fw.

The retardation of weathering products implies a time lag between potential and actual CDR, with implications for upscaling CDR and MRV associated with EW. Spatial upscaling seems feasible but is complicated by defining the boundaries of the system. Here, we used the entire soil column for CDR quantification, while in the field one may define the system based on the topsoil only (i.e., the mixing layer) or include also the subsoil where weathering products are (temporarily) retained. Temporal upscaling of CDR may be even more complicated due to the time lag introduced by the retarded fraction. Limited knowledge on the fate and thus residence time of this retarded fraction (see Section 4.3) and consequently when leaching of retarded cations will occur (i.e., when potential CDR will become actual CDR) challenge the temporal upscaling of CDR. These obstacles for spatial and temporal upscaling of CDR may hinder the development of cost-effective MRV and carbon credit systems for EW. However, our methods allow quantification of the retarded fraction in a way that is relatively straightforward without the need to use isotopes (Kelland et al., 2020; Larkin et al., 2022), which is important for the economical scaling of EW (Clarkson et al., 2024). The construction of lysimeter set-ups to properly monitor the migration of weathering products and leaching of C is a one-time costly and time-consuming step, but this will drastically improve our understanding of retarded weathering products and the time lag between actual and potential CDR. The duration of our experiment was limited to 64 days, as in te Pas et al. (2023) and similar to several other small-scale EW studies (e.g., Dietzen et al., 2018; Haque et al., 2019; Kelland et al., 2020). It is important to note that the retarded fraction is a function of time. As soil transport processes take place over time, this fraction is expected to change. Although our results may not be representative of long-term scenarios, the calculation methods that we present are relevant to apply in EW experiments of any duration.

Our final aim for this study was to provide insights on the fate of retarded weathering products and the potential binding and/or precipitation mechanisms responsible for the retarded fraction. A comparison of the results of total fusion ICP-OES to 0.1 M BaCl₂ extractions shows that of the major base cations in the retarded fraction 0% (albite), 9.07% (olivine), and 32.5% (wollastonite) could be traced in 0.1 M BaCl₂ extractions after correction for the baseline soil (Figure 2). Hence, only a small portion of the retarded base cations was adsorbed onto soil exchange sites, such as SOM and clay minerals (Weil and Brady, 2016), from which these base cations can be desorbed by exchange with 0.1 M Ba²⁺ ions. For albite, the limited contribution of soil CEC to the retarded fraction (Supplementary Table S2) may be explained by the low strength of adsorption of Na to reactive soil surfaces (Weil and Brady, 2016). However, the retarded fraction found for albite-Na (92.7%; Table 3) was substantially higher than expected based on the high mobility of Na. Given that incongruent albite weathering results in the formation of the non-Na-bearing kaolinite (Hartmann et al., 2013), we cannot yet provide an explanation for the nature of this apparently retained Na fraction. In addition, the quantified base saturation for the albite treatment is substantially lower than for the olivine and wollastonite treatments (Supplementary Table S2), despite fairly similar final pH values (7.30 for olivine, 7.93 for wollastonite, 7.42 for albite; te Pas et al., 2023) under which base saturation is expected to be approaching 100% (Magdoff and Bartlett, 1985). Together with the low contribution of Na to the overall CEC, this suggests that using 0.1 M BaCl₂ may not effectively extract the retained Na, as was earlier observed in a study comparing methods for quantifying exchangeable base cations (Jönsson et al., 2002). Although our analyses indicate that the contribution of soil CEC to the retarded fraction of cations is small (Supplementary Table S2), the application of EW also increases soil CEC through the increase in soil pH and potentially via secondary mineral formation resulting from incongruent weathering (te Pas et al., 2023). Despite the limited contribution of soil CEC to the retarded fraction on the short term, the binding of weathered base cations to soil exchange sites may enhance over time as soil CEC increases.

Another potential mechanism removing base cations from soil is CaCO₃ formation, which is especially likely for wollastonite (Figure 2; Khalidy et al., 2023; te Pas et al., 2023). Based on Scheibler calcimetry, 34.0% of the retarded Ca was found to have precipitated as CaCO₃ in the wollastonite treatment corrected for the baseline soil. Given that another 32.5% of retarded Ca for this treatment was bound to exchange sites, a third of the retarded base cations was retained otherwise (Figure 2). For olivine and albite, CaCO₃ precipitation is more likely than the formation of MgCO₃ and Na₂CO₃ due to their high solubilities, despite Mg and Na being the major base cations of the applied minerals. While the exact carbonate mineral formed is unknown, it is likely that Ca co-precipitated with other cations to form carbonate minerals (Li et al., 2020; Molnár et al., 2021; Mucci and Morse, 1983). Therefore, we calculated both the formation of CaCO₃ and MgCO₃ (olivine) or Na₂CO₃ (albite) based on Scheibler calcimetry results, producing a range for the fractions of the major base cations retained as carbonate minerals and in the unknown soil pool (Figure 2). For olivine and albite, the unknown soil pool is even larger (83.6–92.7%) relative to wollastonite. Ca, but also Mg, may be bound to reactive groups on organic compounds in the soil (Tipping, 2002), while several studies have shown that 0.1 M BaCl₂ may not fully extract organically bound cations (Dauer and Perakis, 2013; Rosenstock et al., 2019). Other retention mechanisms not (fully) retrieved using a 0.1 M BaCl₂ extraction may include incorporation in microbial biomass, adsorption into the interlayers of clay minerals such as vermiculite (Weil and Brady, 2016), and ternary complex formation of phosphate and Ca or Mg when binding to iron oxides (Mendez and Hiemstra, 2020). Considering that these mechanisms can (substantially) delay or potentially even hinder actual CDR generation on a range of timescales depending on the specific mechanism, we recommend further research on defining the underlying mechanisms through geochemical modeling and high-resolution microscopic and spectroscopic analyses. In addition, sequential extractions, as deployed by Niron et al. (2024), can provide insights on the fraction of weathering products that is readily exchangeable and the fraction that is bound to SOM, carbonate minerals and oxide minerals.

The likely involvement of weathered base cations in strong adsorption and/or mineral precipitation reactions in soil has important implications for the quantification of actual CDR and MRV. In current literature, authors often assume that the retention of weathered base cations within the soil profile is temporary with no effect on actual CDR, and therefore, corrections for the retarded fraction are overlooked (Beerling et al., 2024; Kantola et al., 2023; Reershemius et al., 2023). However, we show that this assumption cannot be made before progressing our mechanistic understanding of the fate of the retarded fraction within the soil. In conclusion, soil-based mass balance approaches can be used to quantify weathering rates and potential CDR; however, a correction for retarded weathering products through additional calculations as those shown here, and/or leachate-based TA titrations, is needed to constrain actual CDR for a given time and depth interval.