Forest Soil Organic Carbon Quantification

This Module provides the requirements and procedures for the quantification of net carbon dioxide equivalent (CO₂e) removal from the atmosphere via improvements to soil organic carbon (SOC) stocks in forested systems. The eligibility of this carbon pool and is set by the governing protocol under which the project is crediting.

Soils represent the largest terrestrial carbon pool on Earth, storing an estimated 3,000 Pg of organic carbon.¹ It is estimated that forest soils store upwards of 40% of this terrestrial organic carbon despite occupying a smaller share of land cover.^2,3 Deforestation and forest degradation drive substantial losses from the forest soil organic carbon pool⁴. Reforestation, agroforestry, and natural regeneration may increase soil organic carbon stocks⁵. This increase is particularly strong for projects operating on previously degraded land.

In addition to climate mitigation, improvements to SOC in forested systems may provide environmental and social co-benefits, including enhanced soil water retention and drought resilience, reduced dependency on synthetic fertilizers, mitigation of erosion and nutrient runoff into waterways, and support for soil biodiversity^6,7,8.

Project Proponents must meet all the requirements set out in the relevant Protocols and Modules, as well as the requirements set out in this Module. Where this Module contains requirements that duplicate or conflict with those in other Modules, this Module takes precedence.

Throughout this Module, the use of "must" indicates a requirement, "should" indicates a recommendation, and "may" indicates an option or permission.

This Module was developed based on the current state of the art and publicly available science regarding forest soil organic carbon dynamics. This Module aims to be scientifically stringent and robust. We recognize that some requirements may exceed the status quo in the voluntary carbon market and that there are numerous opportunities to improve the rigor of this Module as new approaches and techniques emerge.

Additionally, this Module will be reviewed when there is an update to published scientific literature, government policies, or legal requirements which would affect net CO₂e removal quantification or the monitoring guidelines outlined in this Module, or at a minimum of every 2 years.

Isometric will evaluate alternative counterfactual approaches for the SOC pool, including time-dependent SOC response functions for detected land-cover transitions, against measured SOC data as they become available.

Isometric will evaluate, by simulation, the coverage of the uncertainty procedure in Section 5.0 against its nominal 30th-percentile target across the sample sizes and conditions permitted by this Module, and will revise the Module where coverage departs materially from nominal.

The following requirements apply to all projects certifying under this Module:

• The length of the Crediting Period of the soil organic carbon pool must be the same as the Crediting Period of the aboveground woody biomass carbon pool, as established in the governing protocol.
• The length of the Reporting Period of the soil organic carbon pool may differ from the Reporting Period of the aboveground woody biomass carbon pool. The length of the Reporting Period for the soil organic carbon pool must not exceed 5 years. Project Proponents are permitted to certify the aboveground woody biomass carbon pool on a shorter interval.

Prior land use, tree species, and other site conditions will influence SOC accumulation in the project area relative to the baseline trajectory. Certificates will only be issued for SOC accumulation above what would have happened in the baseline scenario in that project area. See Section 4.2 for more information. While this Module will not set applicability criteria for land use, species, or site conditions, Project Proponents are strongly encouraged to assess their site for suitability of additional CDR compared to the counterfactual scenario.

The overall net soil organic carbon removal is assessed as the difference between the increase in soil organic carbon storage in the project area and the estimate of the counterfactual soil organic carbon storage increase that would have happened in absence of the project intervention. A distinct counterfactual is assessed for soil organic carbon as described in Section 4.2. This applies specifically to the soil organic carbon pool, and the counterfactual otherwise assessed for other carbon pools under the governing Protocol is not applied to the SOC pool. Assessed on a cumulative basis since project initiation this is:

$$CO_2e_{Removal,\ SOC,\ cum,\ n} = CO_2e_{Stored,\ SOC,\ cum,\ n} - CO_2e_{Counterfactual,\ SOC,\ cum,\ n}$$

(Equation 1)

Where:

• $CO_2e_{Removal, SOC, cum, n}$ is the cumulative net soil organic carbon removal from $t$ = 0 to the end of the most recent Reporting Period ($n$), before application of uncertainty and conservativeness discounts, in tonnes CO₂e
• $CO_2e_{Stored, SOC, cum, n}$ is the cumulative change in carbon removed from the atmosphere and stored within the project as soil organic carbon from $t$ = 0 to the end of the most recent Reporting Period, calculated from the measurements described in Section 4.1, in tonnes CO₂e.
• $CO_2e_{Counterfactual, SOC, cum, n}$ is the cumulative change in counterfactual carbon that would have been stored as soil organic carbon within the project area in the absence of project activities from $t$ = 0 to the end of the most recent Reporting Period, calculated in accordance with Section 4.2, in tonnes CO₂e.

The cumulative change in carbon storage in the project area is calculated as the change in stock since project initiation. The Project-level total carbon stock at any time $t$ is expressed as total carbon mass of soil organic carbon across all strata:

$$CO_2e_{stored,t} = \sum_{j=1}^J(SOC_{j,t} \times A_j) \times \frac{44}{12}$$

(Equation 2)

Where:

• $CO_2e_{stored,t}$ is the project-level carbon stock at time $t$ in tonnes CO₂e
• $SOC_{j,t}$ is the SOC stock in stratum $j$ at time $t$ in tonnes C ha^-1
• $A_j$ is the area of stratum $j$ in ha
• $J$ is the total number of strata
• $\frac{44}{12}$ is the mass ratio for converting carbon to CO₂e

The SOC stock in each stratum is calculated from the measurements in Section 4.1.

At validation, the VVB must confirm that the sampling plan: (a) uses a design permitted under Section 4.1.2.2 and justified for The Project; (b) defines quantification units and strata in accordance with Sections 4.1.2.1 and 4.1.2.3; (c) meets the sample-size floors in Section 4.1.3; (d) specifies design-unbiased estimators or, for model-assisted estimation, design-consistent estimators; and (e) contains each element of the statistical analysis plan listed above.

Sampling must be designed to produce an unbiased, statistically defensible estimate of SOC stocks and stock changes at The Project level, with a transparent and reproducible link between sampling locations and the population they represent. The choice of design is determined by The Project Proponent and justified at validation against The Project's quantification approach, the heterogeneity of The Project area, and the expected precision of The Project-level estimate. The Module specifies a default design but does not mandate sub-field stratification or any particular set of stratification factors where a simpler design can be justified to deliver equivalent or better project-level precision.

Where stratified random sampling is used in a paired-difference design (i.e., the same locations are resampled across Reporting Periods), stratification factors should be selected for their expected influence on the rate of SOC change under project management, not on absolute baseline SOC levels. Within-location baseline absolute SOC largely cancels out in the paired difference; residual within-stratum variance is dominated by heterogeneity in management practice intensity, climate, soil texture, and initial SOC saturation. Where The Project area is homogeneous in these factors, a coarser sampling unit may deliver equivalent project-level precision to a finely stratified design.

Project Proponents must use the sample design set at project initiation for sampling during subsequent Reporting Periods. Sampling locations may be substituted over the course of The Project Commitment Period only when there are documented barriers, including:

• Loss of contractual access (e.g., disenrollment of a property)
• Active hazards that prevent access to sampling site (e.g., natural disaster)

In such a scenario, the sampling location must be replaced with another location in the same stratum selected using the same probability sampling rule that was applied at project initiation. The substitution must be clearly documented in the Monitoring Report for review as part of the subsequent Verification. Uncertainty associated with the substitution also must be accounted for following the requirements in Section 5.0. This substitute sampling location must then be used for the remainder of the Reporting Period.

Project Proponents must track all substitutions over the entire Project Commitment Period. If the number of substitutions within a single stratum exceeds 15% of sampling locations within that stratum within a single Reporting Period, or cumulatively exceeds 25% of the sampling locations within that stratum over The Project Commitment Period, the stratum must be re-evaluated in accordance with Section 4.1.2.5.

If the sampling location is only temporarily inaccessible (e.g., temporary flooding) or data collection was missed because of a documented operational issue (e.g., unforeseen capacity issues that did not allow sampling in the temporal window), the sampling location will be considered missing for the given Reporting Period. These locations may be excluded from the stratum-level paired-difference calculation for that Reporting Period and uncertainty appropriately handled. These missing sampling locations must be clearly documented at the relevant Verification. If data are missing for a sampling location during a second consecutive Reporting Period, the sampling location must be substituted.

This mechanism applies equally where a timing miss affects a whole campaign or a large share of a stratum's sampling locations; in such cases, the out-of-window provision in Section 4.1.1 should be used in preference to exclusion. Where sampling locations treated as missing make up more than 25% of a stratum's sampling locations in a Reporting Period, the Project Proponent must demonstrate that the retained locations are representative of the stratum (e.g., by comparing baseline SOC stocks and stratification covariates between missing and retained locations). Where this cannot be demonstrated, the missing locations must be sampled (within or outside the window in accordance with Section 4.1.1) before the Reporting Period is submitted for Verification. Samples whose integrity is compromised after collection (e.g., through a failure to meet the sample handling and storage requirements of Section 4.1.6) should be re-collected, within or outside the window in accordance with Section 4.1.1, or otherwise treated as missing.

Strata must be defined to support direct comparison of SOC stocks across Reporting Periods. Project Proponents may re-aggregate, split, or otherwise revise strata at a Reporting Period where this improves project-level precision, where field divergence under management has rendered the original stratification non-homogeneous, or where additional data have become available. Any change must:

• Preserve a documented mapping between the previous and revised stratification, so that prior measurements can be reconciled to the new design;
• Where the revision changes the membership of any stratum, recalculate from the retained location-level data, for each revised stratum and for all sampling events from $t_0$ onwards, the stratum-mean mineral-mass profile and reference mineral mass (Equation 6), and re-evaluate all location-level ESM-corrected SOC stocks at the revised reference mineral mass (Section 4.1.10). Where a revised stratum contains sampling locations selected at different sampling intensities under the previous design, stratum means must weight each location in proportion to the area it represented under the previous design;
• Repeat the rarefaction analysis (Section 4.1.3) and update any power analysis (Appendix A) for the revised strata at the event at which the revision takes effect;
• Demonstrate that the revised design does not selectively exclude areas of expected SOC loss, including by reporting the cumulative SOC stock change at the event at which the revision takes effect under both the previous and the revised stratification; and
• Be reported in the Monitoring Report and approved at verification.

Certificates issued for Reporting Periods before the revision are not recalculated or reissued. Consistent with the cumulative accounting approach of this Module (Equation 1), any difference arising from the revision is reflected in the quantity issued for the current Reporting Period, and a net decrease is addressed under the reversal and Buffer Pool provisions of the governing protocol.

Where strata were derived from covariates over part of the project area (e.g., from a pilot or a conditioned Latin hypercube analysis), they may be applied to the remainder of the project area only where the covariates are available across the whole area, all of the project area is assigned to a stratum, and the remainder lies within the covariate range used to define the strata. Areas with conditions outside that range must be assigned to new strata under this Section, with sampling locations selected under the validated probability sampling rule and $t_0$ sampling completed before the area contributes to quantification (Section 4.1.2.6). Re-running a covariate-based stratification over the whole project area at a Reporting Period is permitted as a stratum revision under this Section.

Project-specific strata, their areas, the sampling locations within each, and any revisions across Reporting Periods must be reported as an annex to project documentation at every verification.

Where the governing protocol permits new planting areas or grouped-project instances to be added to The Project after validation, each added area must:

• be stratified using the stratification factors and rules validated in the PDD. Where an added area contains conditions not represented by existing strata (e.g., covariate values outside the range used to define strata), new strata must be defined in accordance with Section 4.1.2.5;
• have sampling locations selected using the probability sampling rule and design sampling intensity validated in the PDD, subject to the sample-size floors in Section 4.1.3;
• complete baseline ($t_0$) sampling no later than its own project initiation date. An added area does not contribute to quantification until its $t_0$ campaign is complete; and
• be documented in the Monitoring Report for the Reporting Period in which it is added, with an updated boundary file, strata map and sampling-location list, for review at Verification.

Areas added after validation that follow the validated design rules do not require re-validation of the sampling plan.

Areas sharing a project initiation date form a cohort. For each cohort, cumulative stored and counterfactual SOC (Equations 1, 2 and 9, or Equation 11 where Section 4.2.4 applies) are calculated from that cohort's $t_0$, with $D$ and $d_i$ in Equation 10 measured from the cohort's project initiation. Cumulative net removal for a primary quantification unit is the sum across the cohorts it contains. Within each Monte Carlo iteration (Section 5.1), all cohorts are sampled jointly, with shared event-level errors applied to all cohorts analyzed in the same campaign, and the cohort totals are summed within each iteration to give the SOC net removal for each primary quantification unit in that iteration. This per-iteration SOC total is the quantity carried into the governing protocol’s joint simulation; the 30th percentile is applied once, to the combined across-pool distribution at the project level, not to the SOC total alone. A cohort that has not yet been re-sampled contributes zero stock change.

The requirements of this Section govern the design of the sampling campaign and, specifically, whether the campaign supports reliable estimation of the change in SOC stocks within each stratum. They do not determine the size of the uncertainty discount applied to issued Certificates, which is set separately under Section 5.0. Project Proponents should conduct a formal power analysis to set the number of samples at design stage; a recommended minimum-detectable-difference (MDD) power-analysis procedure is set out in Appendix A. This procedure can help ensure a well-powered design that can decrease the associated uncertainty.

Beginning at the first re-sampling event ($t_1$), Project Proponents must conduct a rarefaction analysis to demonstrate empirically that each stratum's sample count supports stable estimates of the mean SOC stock change. The rarefaction procedure is:

1. For each stratum, compute the bootstrap mean of the location-level paired SOC stock difference $\Delta SOC_{loc} = SOC_{loc,t_n} - SOC_{loc,t_0}$ using progressively larger random subsets of the available sampling locations, starting from a minimum subset of 5 locations and increasing in increments of 1 (or 5, where the stratum contains > 50 locations) up to the full sample set.
2. Repeat each subsample size at least 200 times to generate a distribution of bootstrap means at each subsample size.
3. For each subsample size $m$ tested, compute the width $W(m)$ of the 70% interval of the bootstrap means. Identify the smallest tested size $n^*_j$ such that, for every larger size $m$ tested up to and including $n_j$, $|W(m) - W(n^*_j)|$ is less than 5% of the range (maximum minus minimum) of the location-level paired differences $\Delta SOC_{loc}$ observed in the stratum. $n_j$ itself cannot be $n^*_j$, because no larger size is tested. The stratum passes where such an $n^*_j$ exists and $n^*_j < n_j$. The stratum's design sample size for subsequent Reporting Periods must equal or exceed $n^*_j$.

Where a stratum fails the rarefaction criterion (no $n^*_j < n_j$ exists, or the stratum has fewer than six sampling locations) and is not pooled under the pooling rule above, location resampling under Section 5.1.1 (Step 1) is not permitted for that stratum at that event, and the parametric fallback in Section 5.1.1 applies. The Project Proponent must increase the design sample size for the next Reporting Period to at least $n^*_j$ or, where $n^*_j$ could not be identified, to the number of sampling locations allocated to the stratum by the power analysis in Appendix A, using the observed standard deviation of location-level paired differences.

Additional sampling locations required under this Section must be selected within the stratum using the same probability sampling rule that was applied at project initiation (Sections 4.1.2.2 and 4.1.2.4): for example, further random draws under the documented random-seed procedure for stratified random sampling, or the next points in the ordered reserve sample for a spatially balanced design. They must avoid any exclusion zones defined under Section 4.1.1, and are retained as permanent sampling locations for the remainder of the Project Commitment Period. Until an additional location has been measured at two sampling events, it contributes to the stratum estimate as an unpaired observation, with the unpaired component of variance propagated separately as set out in Section 5.2 for substituted locations. Project Proponents should generate and document, at project initiation, an ordered reserve list of candidate locations for each stratum, for use in both substitution and augmentation.

At sampling events after project initiation, an individual sampling location may require an extension increment of up to 10 cm below the common reporting depth so that the location's measured column reaches the reference mineral mass defined in Section 4.1.10 (Equation 6). An extension is required at a sampling location in the circumstances set out in Section 4.1.10, and Project Proponents may elect to collect an extension increment at all sampling locations at every re-sampling event (recommended where soil mineral mass is expected to decline). The actual depth of collection must be recorded and reported. The extension increment is used only to evaluate the location's SOC stock at the reference mineral mass by interpolation under Equation 7 (as increment $b$); it does not extend the certified profile, and it is excluded from the stratum-mean profile totals used to define the reference mineral mass in Equation 6. The extension is limited to 10 cm. Where the extended column does not reach the reference mineral mass, the location's SOC stock is evaluated at its own measured profile total in accordance with Section 4.1.10 and documented as such; no further increase in sampling depth is required at subsequent sampling events. Locations at which a documented physical barrier prevents sampling to the common depth are exempt from the extension requirement and are evaluated under the location reference mineral mass rule in Section 4.1.10. Project Proponents may also collect an extension increment at baseline.

For ESM purposes, baseline ($t_0$) increments do not need to be subdivided into finer layers than those used at later sampling events, and each increment may be measured as a single sample at baseline. Baseline sampling must use the same depth increments as all later sampling events.

The certified cumulative SOC stock change must be calculated on this basis.

The SOP must be version-controlled. Any change made after validation must be documented and justified before the revised procedure is used, and reported at the next Verification. Some changes affect the comparability of measurements between sampling events, including changes to core dimensions, compositing design, depth increments, laboratory or analytical method. These changes are permitted only as provided in Sections 4.1.4 to 4.1.9.

The following requirements apply:

• Both the intended and actual sampling point locations must be recorded and georeferenced.
• Compositing of cores at a sampling location is optional. A sampling location may be represented by a single core or by a composite; either counts as one sampling location towards the floors in Section 4.1.3. The compositing design (the number and layout of cores, N in Equation 3) must be documented and held constant across sampling events.
• SOC content, oven-dry fine soil mass, and sample volume must be obtained from the same sample or from adjacent samples taken during the same sampling event, if the sample size is insufficient. Where multiple cores are combined into a single sample, all cores must be taken from the same depth and fully homogenized prior to subsampling for the different measurements and this must be disclosed in the documentation of the sampling procedures.
• Soil cores must be collected using equipment of documented cross-sectional area. Core dimensions and corer type must be held constant across all sampling events within a project, including between baseline and all subsequent remeasurement campaigns, except as set out below, because they affect the fine soil mass recovered per unit area independently of Equation 3 (e.g., through compaction during insertion, loss from the core base, edge effects, and the exclusion of coarse fragments and roots). The auger or core diameter and cross-sectional area used at each sampling event must be recorded and reported at each Verification event. A change in core dimensions or corer type is permitted where justified by soil conditions (e.g., stoniness, hardness or dryness that prevents full recovery with the original equipment) or by the unavailability of the original equipment, subject to the following: (a) within a sampling event, the same core dimensions and corer type must be used at all sampling locations within a stratum, except where conditions at a specific location require otherwise, in which case the exception must be documented for that location; (b) before or during the first sampling event at which the new equipment is used, The Project Proponent must conduct a paired comparison in which co-located cores are collected with both the previous and the new equipment at a representative subset of sampling locations (at least 10% of the sampling locations in each affected stratum, and not fewer than ten sampling locations in total), and test for a difference in fine soil mass per unit area (Equation 3) and SOC concentration; (c) where a mean difference is statistically significant at the 10% level (two-sided), a documented correction derived from the paired comparison must be applied to measurements made with the new equipment; and (d) the uncertainty of the comparison, and of any correction, must be propagated as an event-level error under Section 4.1.7 (Step 4) through the ESM correction and the Section 5.1 Monte Carlo simulation. The change, its justification and the paired comparison must be reported at the next Verification.

All organic material (e.g. living plants, leaf litter) must be cleared from the soil surface prior to sampling. This must be documented via a photograph taken after sample removal.

• SOC stocks within each stratum must be calculated on an equivalent soil mineral mass (ESM) basis. Use of soil mineral mass, rather than fine soil mass, ensures that the reference quantity against which SOC stocks are normalized is itself insensitive to changes in soil organic matter content driven by project activities. Sampling events are denoted $t_n$, where $t_0$ is the baseline measurement at project initiation and $t_1$, $t_2$, ... are subsequent resampling events.

Fine soil mass per unit area. For each depth increment $d$ in stratum $j$ at sampling event $t_n$, the oven-dry fine soil mass per unit area is:

$$M_{fine,j,d,t_n} = \frac{m_{fine,j,d,t_n}}{\pi \left(\dfrac{\phi}{2}\right)^{2} \times N} \times 1000$$

(Equation 3)

Where:

• $M_{fine,j,d,t_n}$ is the oven-dry fine soil mass per unit area in depth increment $D$ of stratum $j$ at sampling event $t_n$ (kg m⁻²);
• $m_{fine,j,d,t_n}$ is the oven-dry mass of the fine (< 2 mm) soil recovered for that increment ($g$), after exclusion of coarse material retained on the 2 mm sieve;
• $\phi$ is the internal diameter of the auger or corer (mm);
• $N$ is the number of cores composited into the sample, such that $π(ϕ/2)2×N$ is the total cross-sectional area sampled (mm²);
• The factor 1000 converts g m⁻² to kg m⁻².

Coarse material must be prevented from passing through the 2 mm sieve. Deriving the fine soil mass per unit area directly from sample mass and corer cross-sectional area in this way eliminates the need for independent bulk-density sampling and the imprecision associated with it (Wendt & Hauser 2013)¹⁰. This is the reason core dimensions ($\phi$) and the compositing design (N) must be documented at every sampling event and held constant across sampling events, except as permitted under the core-dimension requirements above.

Soil mineral mass per unit area. The soil mineral mass per unit area for each depth increment is derived from the fine soil mass per unit area, adjusted to exclude the mass of soil organic matter:

$$M_{min,j,d,t_n} = M_{fine,j,d,t_n} \times \left(1 - 1.724 \times C_{j,d,t_n} \times 10^{-3}\right)$$

(Equation 4)

Where:

• $M_{fine,j,d,tn}$ is the oven-dry fine soil mass per unit area as derived in Equation 3 (kg m⁻²);
• $C_{j,d,t_n}$ is the SOC concentration in that increment determined in accordance with Sections 4.1.8 and 4.1.8.1 (g C kg⁻¹ fine soil). Total carbon must not be used for samples that require treatment under Section 4.1.8.1; and
• G-SRHX-01.724 is the van Bemmelen conversion factor from organic carbon mass to organic matter mass. Where Project Proponents have project-area-specific data on the carbon fraction of soil organic matter, that value may be substituted for 1.724 with justification at validation. This Module is only scoped to mineral soils. For mineral soils with SOC concentrations below about 30 g C kg⁻¹, the choice between 1.724 and 2.0 changes soil mineral mass by less than 1%, and because the same factor is applied at all sampling events its effect on the stock change largely cancels.

Sampled volume, where required, is the product of the cross-sectional area sampled and the increment depth. Fine-earth bulk density, where reported, is a derived quantity calculated as the oven-dry fine soil mass divided by the sampled volume; it is used only for reporting and diagnostic purposes. Neither bulk density nor sampled volume is used as a direct input for the quantification calculations.

Drying and sieving procedures must follow laboratory-specific standard operating procedures (SOPs) and must be applied consistently across all samples throughout The Project lifetime, including where there is a change in analytical laboratory. Sample processing procedures must be reported in detail, explicitly describing sieving and grinding procedures.

Samples for SOC analysis and for archiving (Section 4.1.6.1) must be air-dried, or oven-dried at a temperature not exceeding 40 °C, before sieving (consistent with ISO 11464). The oven-dry fine soil mass used in Equations 3 to 5 is the mass after drying at 105 °C to constant mass (consistent with ISO 11465). It may be determined by drying a separate subsample at 105 °C to derive a moisture-correction factor that is applied to the mass of the fine soil dried at no more than 40 °C, so that the analytical and archive subsamples are not heated above 40 °C. SOC concentrations must be expressed on the same 105 °C oven-dry basis.

"Composite" in this Section refers to the physical homogenization of multiple cores collected at a single sampling location, prior to laboratory analysis. The composite is the analytical sample; the sampling location is the statistical unit. Pairwise SOC stock differences computed at the sampling-location level (the difference between the composite measurement at $t_n$ and at $t_0$) are the basis for stratum-level variance estimation in Section 4.1.3. Project Proponents are not required to physically pool samples across sampling locations or across strata at any point.

Composite sample (composite). A single analytical sample formed by physically combining and fully homogenizing two or more soil cores collected at the same sampling location and from the same depth increment, prior to laboratory analysis or subsampling. The composite sample is the analytical unit, the specimen on which SOC concentration and soil mass are measured, whereas the sampling location is the statistical unit at which SOC stocks are estimated and at which paired ($t_0$ vs $t_n$) stock differences are computed for variance estimation under Section 4.1.3.

Compositing is a physical operation and is distinct from statistical pooling. Cores must not be combined across different sampling locations, across different depth increments, or across strata. Where cores are composited, all constituent cores must derive from the same sampling location and the same depth increment and must be fully homogenized before any subsampling for separate measurements; soil mass data must be recorded separately for each depth increment even where SOC content is determined on a single composite per increment (Section 4.1.4).

Following sampling, samples may be temporarily stored on-site in a location protected from sunlight, humidity, and precipitation, with different soil materials kept separate. Soil samples must be shipped within five days, or stably stored (e.g., dried or refrigerated, but not frozen) in a way that will be maintained until analysis. Once shipped, samples must be stored under environmentally controlled conditions that minimize biological activity (e.g., dried or refrigerated, but not frozen) until analysis. The duration of refrigerated storage prior to analysis must not exceed three months.

Project Proponents must retain archived subsamples to enable future cross-calibration and audit. A dried, sieved (< 2 mm) archive subsample, with sufficient mass for at least one full dry-combustion re-analysis, must be retained from: (a) at least 25% of baseline ($t_0$) sampling locations in each stratum, and not fewer than five sampling locations per stratum (or all sampling locations where a stratum has five or fewer), selected by stratified random selection documented before analytical results are available and spanning the soil types and SOC range of the project area; and (b) at least 5% of sampling locations in each subsequent campaign, including, where practicable, sampling locations archived at baseline. Project Proponents are encouraged to archive all baseline sampling locations where storage allows.

Archived samples must be stored air-dried or oven-dried at a drying temperature not exceeding 40 °C (Section 4.1.5; the 105 °C oven-dry determination is made on a separate subsample and does not apply to archived samples), in sealed, labeled, inert containers, under cool, dry, dark conditions protected from moisture, contamination, and pests, and retained for the duration of the Project Commitment Period.

Archived samples stored under these conditions are assumed to be stable, and periodic re-analysis of the archive is not required. The Project Proponent must maintain an inventory and a storage log recording storage conditions and an inspection of container integrity at least annually. A certified reference material or an in-house reference soil must be stored under the same conditions and analyzed alongside archived samples whenever they are re-analyzed. Where the co-stored reference indicates a material change, the affected archived results must not be used without a documented correction, with additional uncertainty propagated through the Monte Carlo simulation.

Where archived samples are unavailable, including for project years predating this requirement, cross-calibration on a laboratory transition must instead be performed using certified reference materials and shared independent reference soils spanning the project's soil types and SOC range, with a conservative additional analytical uncertainty applied and propagated through the Monte Carlo simulation.

All samples collected throughout The Project lifetime should be analyzed by the same laboratory wherever practicable. A transition to a different laboratory is permitted, including in cases where the incumbent laboratory is no longer able or willing to process project samples, provided that:

• The change is justified in writing and documented for review at the subsequent verification;
• The replacement laboratory satisfies the accreditation requirements set out above; and
• A documented cross-calibration procedure is completed prior to the new laboratory's results being used for quantification. The cross-calibration must involve parallel analysis of a representative set of samples (including, where available, archived samples and certified reference materials) by both laboratories. The cross-calibration passes where, across the parallel-analyzed set, the mean relative bias between laboratories is within ±5% (or within the certification uncertainty of the certified reference materials used, whichever is greater) and the precision, expressed as the relative standard deviation of paired results, is within 10%. Where either threshold is exceeded, the systematic offset must be addressed through method alignment or a documented correction before the new laboratory's results are used, and any residual uncertainty propagated through the Monte Carlo simulation as an event-level error (Step 4 below). The cross-calibration report must be submitted as part of project documentation.
  • Where any project samples require treatment under Section 4.1.8.1, the parallel-analyzed set must include such samples, analyzed by both laboratories using the same treatment method.

Quantification of analytical uncertainty. For each batch of project samples, analytical uncertainty must be characterized as follows:

1. Systematic bias correction. Identify any systematic bias in the analytical run against the certified reference material(s), expressed as the mean signed difference between measured and certified SOC values. Where systematic bias exceeds the CRM's certification uncertainty, project sample measurements must be corrected for the bias and the residual uncertainty (after correction) documented in the Monitoring Report.
2. Random error characterization. The random analytical error must be characterized as the greater of:
   • the relative standard deviation (RSD) of laboratory duplicate analyses on project samples within the same analytical batch, expressed as a fraction of the measured value; or
   • the relative error derived from CRM recovery, i.e., the standard deviation of CRM measurements within the batch divided by the certified value.
3. Use in the Monte Carlo simulation. Random analytical error at individual locations is contained in the observed between-location variation of paired differences and is propagated through location resampling under Section 5.1.1 (Step 1); it must not be applied as a separate per-location perturbation. The random error characterized in Step 2 must be reported at each Verification and assessed against the laboratory's defined error thresholds.
4. Shared (event-level) error. The Project Proponent must characterize, for each sampling event, the uncertainty of errors common to all samples in that event that are not captured by location resampling, including: residual bias after CRM correction (Step 1); any laboratory or method transition offset (cross-calibration); any correction for a change in corer or core dimensions (Section 4.1.5); the uncertainty of the 105 °C moisture correction applied to fine-soil mass; any proximal-sensing calibration offset correction (Section 4.1.9); any shared bias in inorganic-carbon determination (Section 4.1.8.1); and any correction applied to archived results (Section 4.1.6.1). These errors are propagated under Section 5.1.1 (Step 2) as a single draw per sampling event per iteration. The distribution may be assumed Gaussian where the supporting data support this assumption; where it is materially non-Gaussian, the empirical distribution must be used directly via inverse-transform sampling or a documented alternative.

A minimum of 5% of project samples within each analytical batch must be analyzed as laboratory duplicates. Where the batch size is small (< 20 samples), a minimum of three duplicates must be analyzed regardless of percentage.

The Project Proponent must retain run-level analytical data for all project samples, including individual measurement results, replicate analyses, calibration records, reference material results, and associated QC flags, and ensure data is available for audit by Isometric or a VVB. Quality control documentation, together with any cross-calibration reports, must be submitted as an annex to project documentation at each verification.

Where a Project Proponent utilizes an accredited laboratory The Project Proponent must provide raw data files to Isometric and the VVB, if requested.

If the results of the third party validation show significant discrepancies with the overall dataset, an audit will be conducted by Isometric and the VVB. As part of this audit, Isometric or the VVB may request that additional samples are sent for third party validation. In this instance, Isometric or the VVB will select the samples for validation. Other materials that may be requested in an audit include:

• Run logs of analytical instruments within the academic or non-accredited facility;
• Information on sample preparation, such as laboratory notebooks and SOPs;
• Chain of custody of the samples analyzed;
• Raw, uncorrected data files for each sample analyzed.

Once a sampling location and depth increment requires treatment, it must be treated at every later sampling event, including where a later screen is negative.

Where treatment is first required after $t_0$, Project Proponents may re-analyze archived $t_0$ subsamples (Section 4.1.6.1) using the same method, subject to Section 4.1.7. Where they do:

• this must be done for every archived $t_0$ subsample in the stratum to which the requirement applies; and
• the re-analyzed values must replace the original $t_0$ results, whatever their direction.

Methods. Inorganic carbon must be addressed by either:

• (i) acid pre-treatment of the analytical subsample before dry combustion (e.g., acid fumigation or in-capsule acidification), with organic carbon measured directly; or
• (ii) a separate determination of inorganic carbon on a subsample of the same homogenized sample, with SOC calculated as total carbon minus inorganic carbon (consistent with ISO 10694). Suitable methods include volumetric calcimetry consistent with ISO 10693 and temperature-ramped combustion consistent with DIN 19539.

The method must remove or quantify dolomitic as well as calcitic carbonate. Results must be expressed per unit mass of untreated fine soil, on the 105 °C oven-dry basis of Section 4.1.5.

Each analytical batch must include a certified reference material or in-house reference soil of known organic and inorganic carbon content. It is used to verify complete carbonate removal under method (i), or inorganic-carbon recovery under method (ii).

Archived subsamples (Section 4.1.6.1) must not be acid-treated.

The method used for each sampling location must be documented in the sample analysis plan and held constant at every sampling event. A change of method must be treated as a laboratory transition and cross-calibrated in accordance with Section 4.1.7.

Uncertainty. The analytical uncertainty of SOC determined under this Section must be characterized in accordance with Section 4.1.7 and propagated through the Monte Carlo simulation (Section 5.1). Under method (i), duplicates and reference materials must be acid-treated in the same way as project samples. Under method (ii), the uncertainties of both the total-carbon and the inorganic-carbon determinations must be characterized and propagated. Random components at individual locations are captured through location resampling under Section 5.1.1 (Step 1) and must not be added again; shared components are propagated as event-level errors under Section 4.1.7 (Step 4).

Reporting. For each stratum and sampling event, the Monitoring Report must state:

• the screening results;
• which samples were treated, and on which basis ((a), (b) or (c), or election to treat all samples);
• the method used; and
• under method (ii), the measured inorganic-carbon concentrations.

The Project Proponent demonstrates, through published, peer-reviewed evidence, that the technique achieves accuracy and reliability comparable to dry combustion for the soil types, moisture conditions, and SOC content ranges present in the project area. Under this pathway, instruments and calibration models must be calibrated against project-area reference samples measured by dry combustion, following methods described in peer-reviewed literature and repeated at defined intervals over the project lifetime, and validated against independent reference samples not used in model development, with acceptance thresholds consistent with those reported in peer-reviewed literature.

The Project Proponent demonstrates accuracy on the project's own soils, validated against a representative set of the project's samples measured by dry combustion, without reliance on published equivalence. Under this pathway:

• Commercial or library-based calibration models may be used; per-instrument recalibration against project samples is not required.
• A representative reference set of project samples, spanning the soil types, moisture conditions, and SOC content ranges of the project area, must be measured by dry combustion.
• Before use for crediting, the technique's predictions must be checked against this reference set and must meet accuracy and bias targets that are pre-registered for the project's conditions and reviewed by the VVB. The check rests on the project's own data and need not cite published studies.
  • The reference set may be collected, and the validation analysis performed, by The Project Proponent, provided that the reference samples are measured by dry combustion at a laboratory meeting the requirements of Section 4.1.7, the accuracy and bias targets are pre-registered before the check is run, and the full validation dataset (including instrument outputs, model predictions and dry-combustion results) is available for audit by the VVB and Isometric. Data from outside the project area may be used to develop the calibration model but do not substitute for the project reference set.
• Any systematic offset identified must be corrected to the dry-combustion values before the predictions are used.
• Samples falling outside the range that the calibration model can reliably predict must be measured by dry combustion.

• Uncertainty. The measurement uncertainty of the technique must be fully quantified and propagated through the entire SOC removal calculation in accordance with Section 5.0. Where proximal sensing uncertainty exceeds that achievable through laboratory dry combustion, the more conservative estimate must be used for certificate issuance; a less precise method is not excluded, but yields fewer Certificates. Random measurement error at individual locations is captured through location resampling under Section 5.1.1 (Step 1) and must not be added again; calibration offsets and other errors shared across a campaign are propagated as event-level errors under Section 4.1.7 (Step 4).
• Ongoing verification and re-validation. A subset of samples measured by proximal sensing must be independently verified by laboratory dry combustion at each Reporting Period. The fit-for-purpose demonstration under Pathway A or Pathway B must be repeated at each measurement campaign and whenever the instrument, calibration model, or laboratory changes, with a portion of samples re-confirmed by dry combustion.
• Inorganic carbon. LIBS and INS measure elemental (total) carbon. They must not be used for samples that require treatment under Section 4.1.8.1 unless inorganic carbon is determined separately under that Section. For spectroscopic techniques, dry-combustion reference values must be SOC determined in accordance with Section 4.1.8.1. The calibration and validation sets must include carbonate-positive samples wherever such samples occur in the project area. Carbonate screening applies whether or not proximal sensing is used.

The ESM-corrected SOC stock density is obtained by expressing cumulative SOC mass as a function of cumulative soil mineral mass and evaluating it, by linear interpolation between measured increments, at a reference mineral mass common to all sampling events compared in a given calculation (Equation 6). This is the reduced cumulative-mass formulation common to the methods of Gifford & Roderick¹¹ and Ellert & Bettany¹² as set out in Wendt & Hauser¹⁰. A single method is prescribed and conservatism is applied at the certification step (the 30th-percentile estimate under Section 5.0).

Increment quantities. For each depth increment $d$ in stratum $j$ at sampling event $t_n$, and at each sampling location, compute the soil mineral mass per unit area $M_{min,j,d,t_n}$ (Equation 4) and the SOC mass per unit area:

$$M_{C,j,d,t_n} = C_{j,d,t_n} \times M_{fine,j,d,t_n}$$

(Equation 5)

Where:

• $C_{j,d,t_n}$ is the SOC concentration determined in accordance with Sections 4.1.8 and 4.1.8.1 (g C kg⁻¹ fine soil); total carbon must not be used for samples that require treatment under Section 4.1.8.1,
• $M_{fine,j,d,t_n}$ is the fine soil mass per unit area (Equation 3, kg m⁻²), and
• $M_{C,j,d,t_n}$ is the SOC mass per unit area for the increment (g C m⁻²).

Cumulative profiles. At each sampling location, accumulate mineral mass and SOC mass from the soil surface to the bottom of each increment $d$:

$$\text{cumulative mineral mass to } d = \sum_{k=1}^{d} M_{min,j,k,t_n} \qquad \text{cumulative SOC mass to } d = \sum_{k=1}^{d} M_{C,j,k,t_n}$$

Reference mineral mass. Define the reference soil mineral mass for stratum $j$ as the minimum, across all sampling events, of the total cumulative soil mineral mass of the stratum-mean profile:

$$M_{\min,\mathrm{ref},j} = \min_{t_n} \left( \sum_{k=1}^{D} \bar{M}_{\min,j,k,t_n} \right)$$

(Equation 6)

where $D$ is the total number of depth increments sampled to the common reporting depth (common to all sampling locations not limited by a documented physical barrier and all sampling events, and excluding any extension increment collected under Section 4.1.4) and $\bar{M}_{min,j,k,t_n}$ is the mean, across all sampling locations in stratum $j$, of the increment-$k$ mineral mass at event $t_n$. Taking the across-event minimum guarantees that the reference mass lies within the sampled stratum-mean column at every event, so no extrapolation beyond the measured profile is required¹². At the sampling event that yields the minimum, the reference mass equals the stratum-mean profile total and the ESM correction ratio for the stratum-mean profile is unity.

The minimum in Equation 6 is taken over $t_0$ and all sampling events up to and including the current event, so the reference mineral mass can decrease at a later event. At each sampling event, the ESM-corrected SOC stocks at $t_0$, and at any other earlier event used in the calculation, must be re-evaluated from the retained location-level data at the current reference mineral mass, so that the cumulative stock change from $t_0$ is always calculated on a common mineral-mass basis. This restatement applies only to the calculation of the current cumulative stock change. Consistent with the cumulative accounting approach of this Module (Equation 1), Certificates issued for prior Reporting Periods are not recalculated or reissued, and any difference arising from an updated reference mineral mass is reflected in the quantity issued for the current Reporting Period. Where the reference mineral mass changes, the Monitoring Report must report the previous and updated values and the effect of the change on the cumulative stock change.

Increments at a sampling location that lie below, or are truncated by, a documented physical barrier (Section 4.1.4) are excluded from the stratum mean for those increments in Equation 6; they are not entered as zero mass. Barrier-limited locations therefore contribute to the stratum mean only for common increments lying wholly above the barrier, and are evaluated under the location reference mineral mass rule below.

ESM-corrected stock density. Let $a$ be the deepest increment whose cumulative mineral mass does not exceed the reference mass, and let $b = a + 1$ be the increment within which the reference mass falls:

$$a = \max \left\{ d : \sum_{k=1}^{d} M_{\min,j,k,t_n} \leq M_{\min,\mathrm{ref},j} \right\}, \quad b = a + 1$$

The ESM-corrected SOC stock density at a sampling location in stratum $j$ at sampling event $t_n$ is then:

$$\mathrm{SOC}_{j,t_n} = \left[ \sum_{k=1}^{a} M_{C,j,k,t_n} + \left( M_{\min,\mathrm{ref},j} - \sum_{k=1}^{a} M_{\min,j,k,t_n} \right) \frac{M_{C,j,b,t_n}}{M_{\min,j,b,t_n}} \right] \times \frac{1}{100}$$

(Equation 7) Where:

• $SOC_{j,t_n}$ is the ESM-corrected SOC stock density in stratum $j$ at sampling event $t_n$ (t C ha⁻¹);
• $\sum_{k=1}^{a} M_{C,j,k,t_n}$ is the cumulative SOC mass to the bottom of increment $a$ (g C m⁻²);
• $\sum_{k=1}^{a} M_{\min,j,k,t_n}$ is the cumulative soil mineral mass to the bottom of increment $a$ (kg m⁻²);
• $M_{C,j,b,t_n} / M_{\min,j,b,t_n}$ is the ratio of SOC mass to soil mineral mass within increment $b$, used as the interpolation slope across that increment (g C kg⁻¹ mineral soil). This is distinct from the measured SOC concentration $C_{j,d,t_n}$, which is expressed per fine soil;
• $M_{\min,\mathrm{ref},j}$ is the reference soil mineral mass (Equation 6, kg m⁻²);
• the factor $1/100$ converts g C m⁻² to t C ha⁻¹.

When $a = D$ the reference mass equals or exceeds the location's full profile mineral mass, increment $b$ does not exist, and the interpolation term is set to zero; Equation 7 reduces to the location's full-profile SOC mass divided by 100.

Where the profile is sampled as a single depth increment ($D=1$), set $a=0$ with both cumulative sums equal to zero; Equation 7 then reduces to the single-layer ESM correction:

$$\mathrm{SOC}_{j,t_n} = M_{\min,\mathrm{ref},j} \times \frac{M_{C,j,1,t_n}}{M_{\min,j,1,t_n}} \times \frac{1}{100}$$

(Equation 8)

The same equation therefore serves both single-layer and multiple-layer assessments. (Under Section 4.1.4 a minimum of two depth increments is required at all project sampling events. The $D=1$ reduction applies only to legacy measurements used under Section 6.1 (Tier 1) and to sampling locations where refusal occurs within 10 cm of the surface (Section 4.1.4). Where a single-increment legacy $t_0$ is paired with multi-increment re-sampling, the stratum reference mineral mass is the lower of Equation 6 and the stratum-mean $t_0$ single-increment mineral mass, and later events are evaluated at that mass using Equation 7.)

Estimation and aggregation across locations. The reference soil mineral mass $M_{min,ref,j}$ (Equation 6) is a stratum-level constant defined on the stratum-mean mineral profile. Equation 7 must be evaluated at each sampling location, using that location's own cumulative SOC and mineral masses against the common stratum reference $M_{min,ref,j}$ (or against the location reference mineral mass where the rules below apply). The stratum-level stock $SOC_{j,t_n}$ carried into Equation 2 is the mean of the location-level values across all sampling locations in the stratum. Evaluating Equation 7 at the location level is required so that the location-level paired stock differences $\Delta SOC_{loc} = SOC_{loc,t_n} - SOC_{loc,t_0}$ used in the rarefaction analysis (Section 4.1.3) and the hierarchical bootstrap (Section 5.1.1) are defined consistently with the certification point estimate.

Because the reference mineral mass is defined on the stratum-mean profile, an individual sampling location's measured column may not reach it. The following rules apply:

• Location reference mineral mass for barrier-limited locations. For a sampling location whose measured column is limited by a documented physical barrier (Section 4.1.4) at any sampling event, the location reference mineral mass is the lower of $M_{min,ref,j}$ and the minimum, across $t_0$ and all sampling events to date, of that location's total measured mineral mass. The location's SOC stock at every sampling event must be evaluated at its location reference mineral mass using Equation 7. Where this mass decreases at a later event, SOC stocks at earlier events are re-evaluated at the new value for the calculation of cumulative stock change; Certificates already issued are not restated, and any difference is reflected in the current Reporting Period.
• Truncation after baseline. For other locations, where a location's total measured mineral mass at a sampling event after $t_0$ (including any extension increment under Section 4.1.4) is less than $M_{min,ref,j}$, that location's cumulative SOC mass at that event must be evaluated at its own measured profile total (that is, $a$ is set to the location's deepest measured increment and the interpolation term is zero) rather than extrapolated beyond the measured column. This truncation omits SOC between the location's profile total and the reference mass and is conservative for certification.
• Truncation at baseline. For locations not limited by a documented physical barrier, where a location's total measured mineral mass at $t_0$ (including any extension increment) is less than $M_{min,ref,j}$, evaluating the location at its $t_0$ profile total and at the full reference mass at later events would overstate its paired stock change. For such a location, the location reference mineral mass is its $t_0$ profile total, and its SOC stock at every sampling event must be evaluated at that mass (or, where lower, at its measured profile total at that event under the previous rule), so that its paired difference is calculated on a common mineral mass.
• Extension where truncation recurs. Each occurrence of truncation must be documented at Verification. Where truncation after baseline occurs at the same location at two consecutive sampling events, that location must be sampled with an extension increment of up to 10 cm below the common reporting depth under Section 4.1.4 at the next and all subsequent sampling events, unless the location is limited by a documented physical barrier. Where the extended column still does not reach the reference mineral mass, the location continues to be evaluated at its own measured profile total under the truncation-after-baseline rule, and no further increase in sampling depth is required.

Truncation is an expected consequence of a stratum-mean reference: at the sampling event that sets the reference, a substantial proportion of locations (up to about half) may fall below it. Project Proponents are therefore recommended to collect an extension increment at all sampling locations at every re-sampling event, which avoids truncation at nearly all locations and the associated conservative reduction in the certified stock change.

Linear interpolation yields an approximately unbiased point estimate of the ESM-corrected stock provided increments are thin enough that the SOC–mineral-mass relationship is close to linear within each increment; the point estimate must be incorporated into the Monte Carlo simulation (Section 5.1) to account for uncertainty.

Linear interpolation assumes SOC concentration is uniform within each increment. Where increments are thick and the SOC–mineral-mass relationship is strongly curved (for example across buried or spodic horizons), this introduces interpolation error. That error propagates as increased uncertainty in the Section 5.1 Monte Carlo simulation and, through the conservative lower bound, into the certified quantity. Project Proponents expecting a non-linear SOC distribution with depth should sample thinner increments across the affected depth intervals to reduce it.

Baseline event. At the baseline event, before any resampling event exists, the minimization in Equation 6 is taken over a single event and therefore returns that event's own stratum-mean profile total; the ESM correction ratio is unity at baseline by construction. The correction takes full effect from the first resampling event $t_1$ onwards, once the cross-event minimum is defined over more than one event, and the reference mineral mass is re-evaluated at each subsequent event as set out under Reference mineral mass above.

The variance terms used in Section 5.0 must reflect the sample size at each depth increment across all sampling locations.

Aggregation to total carbon stock. Equation 7 produces an SOC stock density for a single stratum at a single event. These densities are aggregated to The Project level, area-weighted across strata and converted to CO₂e, by Equation 2; no separate aggregation is defined here. Under this Module the stored-carbon pool is SOC only, so The Project total carbon stock is the SOC stock delivered by Equation 2.

Instead of exclusively using the field sampling data to estimate stratum-level SOC stock ($SOC_{j,\ t}$) in a design-based approach, Projects may elect to use a model-assisted estimator approach. In this approach, a model relating SOC to auxiliary variables known across the project area is developed and combined with the probability sample of measured SOC data from each Reporting Period to generate an estimate of SOC stock across the project area. Critically, the estimate from a model-assisted procedure remains anchored to the field-measured probability sample, ensuring that the model cannot generate a relatively biased estimate and the outcome remains conservative¹³. Where a well-performing model can be developed, this approach has the potential to increase precision and decrease uncertainty in estimates as compared to a purely design-based estimate from the same set of field measurements.

This process is distinct from model-based quantification. In model-assisted quantification, the model is always applied to a set of field samples and enables better spatial interpolation between the sampling locations. The model output is then corrected back to the carbon actually measured in the field, to ensure no possible bias relative to the design-based estimate. This is different from model-based estimation where field samples may be used for model calibration and validation, but the model can be applied independently in time and space from any field sampling. Purely model-based estimation of SOC is not permitted under this Module.

A parallel design-based estimate from the same sample data must be supplied at every Verification and compared to the model-assisted estimates. Projects must use the design-based estimates in scenarios where:

• A valid variance estimate for the model-assisted estimate is not produced;
• The estimated variance of the model-assisted estimate of SOC stock change for the stratum is not lower than the variance of the design-based estimate from the same sample; or
• The spatially blocked cross-validated performance metric reported under Section 4.1.11.1 for that Verification falls below the threshold pre-registered in the PDD at validation.

The counterfactual ($CO_2e_{Counterfactual,\ SOC,\ cum,\ n}$) represents the cumulative soil organic carbon storage that would have occurred within the project area in absence of the project interventions. This is used to assess the additionality of the project's soil organic carbon removal. This counterfactual is specific to the soil organic carbon pool, and the soil organic pool is not included in the counterfactual for other carbon pools in the governing protocol.

The counterfactual is determined using one of two approaches: monitoring of matched control pixels, as set out in Sections 4.2.1 to 4.2.3, which is the default; or direct measurement of control plots, as set out in Section 4.2.4, where elected by The Project Proponent at validation. Under either approach, SOC losses in the counterfactual are not credited, so that additionality is assessed for removals only.

Where the counterfactual is determined under Sections 4.2.1 to 4.2.3, it must use the matched control pixels for the project area selected by Isometric via the matching algorithm in the governing protocol. Details of this procedure are included in the governing protocol, and this Module only addresses procedures for subsequent analyses following the matching procedure.

The Project Proponent may propose the variables it considers important for matching in the project's context (for example, pre-project land use or land cover, vegetation type, management regime, soil or climate), with supporting evidence, at validation and before each Verification. Isometric will take these proposals into account, but the choice of matching variables and the selection of control pixels rest with Isometric. In selecting control pixels for the SOC counterfactual, Isometric will take account of pre-project land use and land cover where data allow, and may exclude or replace control pixels that are not representative of the pre-project land use of the project area. Any exclusion or replacement is documented at Verification.

Where the counterfactual is determined under Sections 4.2.1 to 4.2.3, it is determined independently by Isometric and is conservative by design. At each Verification, Isometric will provide to The Project Proponent and the VVB the control pixel set, the indicator products and years used, the per-pixel index time series, the Pre-project Baseline and Current Levels, the reference dispersion and the value of $k$, the classification and $d_i$ of each control pixel, the resulting $f_{weighted,\ t}$, and code or a documented procedure sufficient to reproduce these results.

The counterfactual must be conservatively estimated via monitoring of dynamics in the matched control pixels. Given the challenges in remote monitoring of SOC stocks directly, the counterfactual instead focuses on monitoring changes in land use and land cover, particularly transitions that are anticipated to result in an increase in soil organic carbon. This is most likely to occur when there is the establishment or recovery of woody vegetation, or the establishment or recovery of herbaceous (grassland) vegetation.¹⁴ Where no change in land use or land cover occurs, it is assumed that the SOC stock remains unchanged. Where a transition occurs which is anticipated to decrease SOC stock, the counterfactual for that control pixel is considered to be zero. Under this Module, SOC losses in the counterfactual are not credited under either approach (see also Section 4.2.4), so that additionality is assessed for removals only.

In practice, the counterfactual is assessed at each verification by (i) classifying whether each control pixel is or is not on a trajectory consistent with an increase in SOC using two complementary indicators capturing woody and herbaceous vegetation changes; (ii) aggregating these classifications across the ensemble of control pixels; and (iii) scaling the measured SOC change in the project area by the fraction of control pixels on an increasing-SOC trajectory and the time on which they have been for this trajectory.

The method assumes that a control pixel classified as on an increasing-SOC trajectory accrues SOC at the rate measured in the project area over the same period. This is intended as a conservative upper bound on SOC accrual in transitioned control pixels; the method does not estimate SOC change in control pixels directly. Project Proponents may instead elect to measure the counterfactual directly in control plots under Section 4.2.4.

At each verification, Isometric will determine whether each control pixel is on a trajectory where increases in SOC are expected. This is done across two pathways, with one focused on assessing if there is an increase in woody biomass occurring (e.g., regeneration, forest recovery, or reforestation) and the other focused on assessing if there is an increase in herbaceous vegetation (e.g., establishment or recovery of a grassland). If neither is indicated, the pixel is considered to not be increasing its SOC stock.

The woody biomass proxy set in the governing protocol should be used as the indicator for the woody increase. Unlike the protocol-level dynamic baseline process, this applies the binary detection method described below to the data.

The herbaceous indicator is selected at validation by Isometric, working with The Project Proponent, to give a robust detector of sustained increases in herbaceous cover in the project's vegetation type and climate. The selection covers the index or data product (for example, NDVI, EVI, SAVI or MSAVI, or a fractional-cover product), the averaging window used for the Current Level and the Pre-project Baseline Level (five years by default), and the treatment of inter-annual noise, including the margin coefficient $k$ (Section 4.2.2.2). In drylands and other systems where productivity is driven by rainfall, the detector must account for rainfall-driven variation, for example by adjusting the index for growing-season precipitation (e.g., residual trend analysis, RESTREND¹⁵) or by using a longer averaging window. The selection must be supported by evidence, from peer-reviewed literature or from the pre-project record of the control pixels, that the detector separates sustained increases in herbaceous cover from inter-annual variation with an adequate signal-to-noise ratio. The final choice rests with Isometric. The detector is fixed at validation, documented, and applied identically to all control pixels. The same binary detection method is used for this indicator.

The binary detection method determines if there has been an SOC-relevant transition or condition change in the control pixel; it does not estimate the impact on SOC stock. Here a transition is considered to be a sustained increase in the level of the index relative to a pre-project reference level. This is done to support like-for-like comparison over different time windows, and to ensure short-term noise is not inaccurately characterized as a transition.

The detection method is applied to both the woody indicator and the herbaceous indicator. For each pixel and each indicator, two values are calculated from the annual values of the index within the pixel:

• Current Level: This is defined as the mean of the index over the most recent five years from the end of the current Reporting Period. This is recalculated for each Verification. Where fewer than five years have elapsed since project initiation, the window includes pre-project years.
• Pre-project Baseline Level: This is defined as the mean of the index over the five year period prior to project initiation.

Five-year windows apply to the woody indicator and are the default for the herbaceous indicator. Where a different averaging window is selected for the herbaceous indicator under Section 4.2.2, that window is used for both levels of that indicator.

A control pixel is considered to be on an increasing-SOC trajectory when the current level becomes elevated above the pre-project baseline level of the index by at least $k$ reference dispersion units (see Section 4.2.2.2). This captures scenarios where either the control continues on a SOC-increasing trajectory or begins on such a trajectory during the Project Commitment Period. This condition is triggered when there is an increase in at least one of the woody or herbaceous indices as a binary classification of an increasing SOC trajectory. When triggered, the classification applies from the later of the first year of the five-year window used to calculate the Current Level and the project initiation date. Where a pixel remains classified as on an increasing-SOC trajectory at consecutive Verifications, its classification start date is carried forward from the earliest of those consecutive classifications. The classification must be determined for each control pixel for each Reporting Period and is not fixed for the duration of the project.

If a control pixel classified as on an increasing-SOC trajectory at one Verification falls below the threshold at a later Verification, it is reclassified as not increasing and its $d_i$ is set to zero in Equation 10. Because the counterfactual is assessed cumulatively from $t_0$ at each Verification, this reduces $CO_2e_{Counterfactual,\ SOC,\ cum,\ n}$, and the resulting increase in cumulative net removal is reflected in the quantity issued for the current Reporting Period. Certificates issued in earlier Reporting Periods are not restated.

Because some amount of inter-annual variation can be expected in the indices due to noise in the data and short-term climate fluctuations, a reference dispersion is defined for assessing whether the control pixel has meaningfully departed from its pre-project state. The reference dispersion is defined as the pooled within-pixel standard deviation of the pre-project period for the population of control pixels. The reference dispersion is thus expressed in the same units as the index to which it applies.

The margin coefficient $k$ is set so that, for a control pixel with no underlying change and independent annual variation, the probability of a trigger on either indicator at a Verification is no more than 5%. Under these assumptions, with five-year windows, this corresponds to $k$ = 1.24. Where a different averaging window or detector is selected for the herbaceous indicator, Isometric sets $k$ for that indicator from the pre-project noise of the selected detector so that the same false-positive rate is met. Isometric will increase $k$ where the trigger rate among control pixels with no change in land-cover class over the assessment period (from the land cover data used in the governing protocol) exceeds this rate, or where index values show serial correlation (e.g., multi-year rainfall anomalies) that inflates the false-positive rate. The value of $k$, the basis for it and the trigger rate observed in unchanged pixels must be reported at each Verification. Due to the cumulative nature of the accounting, an increase and then reversal of SOC storage in a control pixel equates to a zero baseline.

At each verification, the cumulative counterfactual SOC storage up to time $t$ is calculated as The Project's cumulative measured SOC storage at time $t$, scaled by a time-weighted proportion of the matched control ensemble classified as being on an increased-SOC trajectory at time $t$. Each transitioned control pixel at time $t$ is weighted by the duration of the elapsed project commitment period it has been classified as transitioned. As such, pixels that transitioned earlier contribute more than ones which only transitioned recently.

$$CO_2e_{Counterfactual,\ SOC,\ cum,\ t} = f_{weighted,\ t} \times \sum_{j=1}^{J} \max\left(0,\ CO_2e_{Stored,\ SOC,\ cum,\ t,\ j}\right)$$

(Equation 9)

Where $CO_2e_{Stored,\ SOC,\ cum,\ t,\ j}$ is the cumulative stored SOC in stratum $j$. The zero floor is applied for each stratum within each Monte Carlo iteration, so that a decline in stored SOC does not produce a negative counterfactual.

Where the time-weighted transitioned fraction $f_{weighted,\ t}$ ranges from 0 to 1 and is defined as:

$$f_{weighted,\ t} = \frac{1}{N}\sum_{i=1}^{N}\frac{d_i}{D}$$

(Equation 10)

Where:

• $N$ is the total number of control pixels.
• $d_i$ is the duration of time, in years, over which control pixel $i$ has been classified as being on an increased-SOC trajectory as of time $t$. For a pixel not currently classified as being on an increased SOC trajectory, this value is 0. $d_i$ must not exceed $D$.
• $D$ is total elapsed time since project initiation, in years, as of time $t$.

In words, the time-weighted transitioned fraction is the mean, across all $N$ control pixels, of the proportion of the time elapsed since project initiation for which each pixel has been classified as on an increasing-SOC trajectory. For areas added after validation, $D$ and $d_i$ are measured from the project initiation of each cohort (Section 4.1.2.6).

Within each Monte Carlo iteration (Section 5.1), Equation 9 is evaluated using that iteration's draws of stratum-level cumulative stored SOC and that iteration's value of $f_{weighted,\ t}$, recomputed from control pixels resampled with replacement.

Worked example. A project has 100 control pixels. At the first Verification ($D$ = 8 years), 10 pixels are triggered, with the classification applying from the first year of the five-year window, so each has $d_i$ = 5 years and $f_{weighted,\ t}$ = (10 × 5 / 8) / 100 = 0.0625. At the second Verification ($D$ = 13 years), 4 of those pixels have fallen below the threshold and are reclassified with $d_i$ = 0, while the remaining 6 are still classified and their start date is carried forward, so each has $d_i$ = 10 years and $f_{weighted,\ t}$ = (6 × 10 / 13) / 100 ≈ 0.046. Had no pixels reverted, $f_{weighted,\ t}$ would have been (10 × 10 / 13) / 100 ≈ 0.077. The lower cumulative counterfactual is reflected in the quantity issued for the second Reporting Period.

Where a control plot becomes unavailable for reasons outside The Project Proponent's reasonable control (e.g., sale or change of land manager), a replacement must be drawn from the candidate set within the same stratum under the same procedure and baselined at the next sampling event, with the discontinuity documented and its uncertainty propagated under Section 5.0. Replacement for reasons within The Project Proponent's control is not permitted. Areas added after validation (Section 4.1.2.6) must have control plots selected under this Section before they contribute to quantification.

Control plots must be sampled at $t_0$ and at every re-sampling event, following all requirements of Section 4.1 for sampling design, sample collection, analysis, ESM correction and reporting, using the same procedures as the project area. Where a control plot adjoins planted areas, sampling locations must be at least 10 m from the boundary, or a greater distance justified by the expected rooting and litterfall extent of the planted species.

The counterfactual SOC stock at time $t$ is calculated as:

$$CO_2e_{Counterfactual,\ SOC,\ t} = \frac{44}{12} \sum_{j=1}^{J} \left( SOC_{CP,j,t} \times A_j \right)$$

(Equation 11)

Where:

• $CO_2e_{Counterfactual,\ SOC,\ t}$ is the counterfactual SOC stock at time $t$, in tonnes CO₂e;
• $SOC_{CP,j,t}$ is the mean ESM-corrected SOC stock density of the control plots corresponding to stratum $j$ (or its control-plot group) at time $t$, calculated under Section 4.1.10, in t C ha^-1; and
• $A_j$ is the area of stratum $j$ in the project area, in ha.

The cumulative counterfactual, $CO_2e_{Counterfactual,\ SOC,\ cum,\ n}$, is the sum across strata (or control-plot groups) of the change in Equation 11 between $t_0$ and the end of the most recent Reporting Period, with the change for each stratum set to zero where it is negative, and is used in Equation 1. A decline in SOC in the control plots is not credited: this Module certifies removals only, and SOC losses that would have occurred in the absence of The Project are not recognized as removals.

Uncertainty in the counterfactual must be characterized using the same procedures as for the project area (Section 5.1), with control-plot sampling locations resampled within each iteration alongside the project area, and shared event-level errors applied to both where analyzed in the same campaign. The zero floor for each stratum is applied within each iteration.

Where a project is crediting the SOC pool under this Module, the uncertainty in the SOC quantification must be characterized and included in the broader uncertainty treatment under the governing protocol through joint propagation with the woody biomass pools in the Monte Carlo treatment. In this section, particular considerations for SOC uncertainty within the broader uncertainty treatment are detailed.

Uncertainty in the SOC pool must be characterized by propagating all material sources of uncertainty through a Monte Carlo simulation, in accordance with the below requirements, the governing Protocol, and the corresponding Section of the Isometric Standard. Monte Carlo simulation is required for the following reasons:

• It does not require the assumption that measurement or model errors are uncorrelated beyond the location level, making it appropriate for the structured spatial and temporal error patterns present in SOC measurement campaigns and in model-assisted estimation of SOC stocks.
• It can directly estimate the correlation of errors across years, avoiding the underestimation of uncertainty over shorter time horizons where annual errors may be positively correlated.
• Where implemented as a hierarchical bootstrap, it requires minimal assumptions about the shape of the underlying data distributions, which is important for paired SOC stock differences that are typically non-normal.

The Monte Carlo simulation must be implemented as follows:

• An appropriate number of iterations must be performed, and not fewer than 10,000. Project Proponents must demonstrate that the Monte Carlo standard error of the 30th-percentile estimate is no more than 2% of the standard deviation of the simulated distribution of net SOC removal, estimated from the empirical density at the 30th percentile or from independent replicate runs, and must report the achieved standard error at each Verification.
• Each iteration must be independent of other iterations. Within a given iteration, the sources of uncertainty contributing to the SOC estimates must be sampled jointly, with correlations between sources preserved in accordance with the correlation requirements below. The requirement of inter-iteration independence does not imply that sources sampled within an iteration are independent of one another.
• Within each iteration, $CO_2e_{Counterfactual,\ SOC,\ cum,\ n}$ must be calculated from the same iteration's draw of $CO_2e_{Stored,\ SOC,\ cum,\ n}$ (Equation 9) or from the same iteration's resampled control plots (Equation 11), and net removal calculated using Equation 1, so that the stored and counterfactual terms are correlated as they are in the underlying calculation.
• Input probability distributions must be justified with reference to empirical data or published literature and must not be assumed normal without justification. Where distributions are non-normal, appropriate alternative distributions must be used.
• Correlations between uncertain inputs must be explicitly assessed and, where material, accounted for through appropriate joint sampling procedures rather than assuming independence.
• The correlation structure of errors across time periods must be characterized and incorporated into the simulation, to avoid underestimation of cumulative uncertainty over multi-year Reporting Periods.
• Where the SOC and woody biomass pools share sampling locations, each iteration’s SOC draw must be generated from the same resampled sampling units as the corresponding woody biomass draw, so that cross-pool correlation is preserved within the iteration rather than across separate simulations.

For propagating sampling and analytical uncertainty, a hierarchical bootstrap Monte Carlo procedure is recommended since it makes minimal assumptions about the shape of the underlying data distributions and naturally captures within-stratum and between-stratum variability. The procedure has three steps:

Step 1: Location resampling within strata. Within each stratum $j$, resample sampling locations with replacement, drawing $n_j$ locations where $n_j$ is the number of sampling locations in stratum $j$. Resampling is performed on locations (not on individual cores or depth increments), so that the paired structure ($t_0$ and $t_n$ measurements at the same location) is preserved within each bootstrap iteration. Before resampling, location-level paired differences in stratum $j$ must be rescaled about the stratum mean by $\sqrt{n_j/(n_j-1)}$ to correct the downward bias of the bootstrap variance in small samples. Location resampling at stratum $j$ may only be applied where the rarefaction analysis in Section 4.1.3 demonstrates that $n_j$ supports stable estimates; otherwise the parametric fallback below applies. The skewness of location-level paired differences must be reported for each stratum. Where the absolute skewness exceeds 1 in a stratum with fewer than 20 sampling locations, the parametric fallback must be used for that stratum with a distribution that preserves the observed shape.

Step 2: Event-level error. For each sampling event, draw once per iteration from the distribution of shared errors characterized under Section 4.1.7 (Step 4) and apply the draw to all locations analyzed in that event, for SOC concentration and soil mineral mass. Random measurement error at individual locations is contained in the observed between-location variation resampled in Step 1 and must not be added again.

Step 3: Stratum and project aggregation. Compute the stratum-level mean SOC stock change from the resampled locations. Compute The Project-level mean as the area-weighted average of stratum-level means. Repeat steps 1–3 across iterations until the convergence criterion in Section 5.1 is met.

Parametric fallback. Where a stratum has fewer than six sampling locations with paired measurements, or fails the rarefaction analysis (Section 4.1.3), or meets the skewness condition in Step 1, and is not pooled under the pooling rule in Section 4.1.3, a parametric Monte Carlo simulation must be used for that stratum. In each iteration, the stratum-level mean paired change is drawn from a Student-t distribution with $n_j - 1$ degrees of freedom, centered on the observed stratum mean, with scale $k_j \, s_{\Delta,j} / \sqrt{n_j}$, where $s_{\Delta,j}$ is the observed standard deviation of location-level paired differences and $k_j$ is the conservative uncertainty penalty:

$$k_j = \sqrt{\frac{n_j - 1}{\chi^2_{0.30,\,n_j - 1}}}$$

where $\chi^2_{0.30,\,n_j-1}$ is the 30th percentile of the chi-squared distribution with $n_j - 1$ degrees of freedom. $k_j$ is the one-sided 70% upper confidence bound on the ratio of the true to the observed standard deviation, consistent with the 30th-percentile issuance criterion. It depends only on $n_j$ and can be calculated at design stage (for example, $k_j$ = 1.67, 1.45, 1.35, 1.29, 1.19 and 1.11 for $n_j$ = 3, 4, 5, 6, 10 and 20). Where the observed distribution of paired differences is materially skewed or heavy-tailed, a distribution preserving that shape, scaled by the same $k_j$, must be used in place of the Student-t distribution, with justification. Event-level errors are propagated for the stratum as under Step 2. The use of the fallback and the value of $k_j$ must be reported in the Monitoring Report; no other additional uncertainty penalty applies.

Combination with bootstrap strata. In each iteration, the Project-level mean is the area-weighted average (Step 3) of the resampled means of strata that pass the rarefaction analysis and the parametric draws for fallback strata. The penalty $k_j$ applies only to the sampling variance of fallback stratum $j$. Its effect on the Project-level variance is therefore bounded by that stratum's squared area weight (a contribution of $w_j^2 k_j^2 s_{\Delta,j}^2 / n_j$, where $w_j = A_j / \sum_j A_j$), and it does not alter the treatment of any other stratum.

At minimum, the following uncertain inputs for the SOC pool must be characterized and each propagated once in the Monte Carlo simulation. Random measurement error at individual locations is propagated through location resampling (Section 5.1.1, Step 1) as part of sampling uncertainty, and must not be added again as a separate input:

• Sampling uncertainty: the uncertainty in each stratum-mean paired SOC stock change arising from estimation from a finite sample of sampling locations. Under design-based estimation it is propagated once, by location resampling under Step 1 or the parametric fallback in Section 5.1.1, and includes random measurement error at individual locations. Where model-assisted estimation is used, it is propagated using the variance estimator under Section 4.1.11.2 in place of Step 1.
• Shared (event-level) analytical and soil-mass errors characterized under Section 4.1.7 (Step 4), drawn once per sampling event per iteration.
• Counterfactual uncertainty, characterized by resampling control pixels with replacement within each iteration and recomputing $f_{weighted,\ t}$ (Equation 10) from the resampled set, applied to the same iteration's draw of $CO_2e_{Stored,\ SOC,\ cum,\ n}$ (Equation 9), or, where control plots are used, as set out in Section 4.2.4.
• In the event that any sampling locations are substituted or added during a given Reporting Period (see Sections 4.1.2.4 and 4.1.3), the unpaired component of variance for these locations must be propagated separately from the paired component, with the two components using sample-count weighting. The procedure for this must be clearly documented.
• Where the project-level SOC stock is estimated using a model-assisted approach, The Project Proponent must supply a design-consistent variance estimator appropriate to the estimator used, or a resampling-based estimator demonstrated to achieve nominal confidence-interval coverage at the sample sizes used. A parallel design-based estimate must be computed from the same probability sample and reported alongside the model-assisted estimate, so that the uncertainty attributed to the model-assisted estimator can be assessed rather than assumed.

In addition to any reporting requirements within the governing Protocol and Isometric Standard, the uncertainty reporting for the SOC pool at each Verification must include, at minimum:

• The input distributions used and their justification

• The correlation structure assumed among SOC uncertainty sources

• The skewness of location-level paired differences by stratum

• Where model-assisted estimation is used, the estimator's reported explanatory power and the parallel design-based estimate

• Evidence of convergence of the Monte Carlo results, including the achieved Monte Carlo standard error of the 30th-percentile estimate

• Any use of the parametric fallback, with the value of $k_j$ for each fallback stratum, must be disclosed and justified

• A decomposition, for the SOC pool, of the difference between the central estimate of net SOC removal and the SOC pool's own 30th-percentile estimate, showing the contribution of each uncertainty source listed in Section 5.2 (estimated by re-running the simulation with that source omitted and all others unchanged) and, separately, the counterfactual deduction (Equation 9 or Equation 11) and any parametric-fallback penalty ($k_j$)

• The SOC sampling locations that are shared with, or spatially proximate to, the woody biomass sampling network, so that the preservation of cross-pool correlation in the governing protocol’s joint simulation can be verified

Projects that can demonstrate this may then apply a data hierarchy for estimating missing measurements (Section 6.1) for the Reporting Period. This issuance is then subject to a later correction that is determined from subsequent module-aligned measurements (Section 4.1). Alternatively, Projects that meet the requirements of Section 6.3 may elect to set $t_0$ at their first module-aligned sampling campaign and forgo crediting the earlier period.

Estimation of $T_{n-1}$ SOC stocks must be done using the following data hierarchy. The hierarchy reflects the preference for empirical, spatially and temporally resolved data. Prior to implementation of the hierarchy, The Project must complete the required stratification process for quantification (see Section 4.1.2) and identify the pre-project land use in each strata. Here, the pre-project land use is considered to be the primary land-use in the three year period prior to project initiation, with determination supported by evidence used in the Protocol's pre-project productivity analyses. Given spatial-specificity is embedded within the hierarchy, the hierarchy must not be applied to the aggregate project area. Projects should apply the hierarchy to strata, or may elect to group strata together when they share IPCC climate zones and soil classes¹⁶ and prior land use. Any grouping used for this purpose must be clearly disclosed. For each portion of the project area, a lower tier may only be used where the Project Proponent demonstrates, with documented evidence, that no qualifying source exists in any higher tier.

The tiers are as follows:

• Tier 1 - Measurements which were taken within the project area, but did not follow the exact module requirements
• Tier 2 - Empirical regional data representative of the projects conditions at $T_{n-1}$
• Tier 3 - Regional estimates of the land-cover transition occurring with the project intervention
• Tier 4 - IPCC default values

Further details for each Tier are described below. All estimates must also be appropriately treated within the broader uncertainty analysis for The Project. Each estimate must be assigned the uncertainty reported by its source and propagated through the Monte Carlo simulation in Section 5.1. Where the source does not report uncertainty in a form that can be propagated, the following minimum uncertainties, expressed as a coefficient of variation of the estimated $T_{n-1}$ SOC stock, must be used: Tier 2, 20%; Tier 3, 30%; Tier 4, the uncertainty given in IPCC (2019)¹⁶ for the default value used, and not less than 30%. Tier 1 uncertainty must be derived from the data.

Tier 1 comprises direct sampling and measurement of SOC within the project area at $T_{n-1}$ (or within one year of project initiation where $T_{n-1}$ corresponds to project initiation) which did not fully comply with this Module's requirements for sampling design, depth, or analytical method. This only applies when there are pre-existing data available, as data cannot be retroactively collected.

Where measurements exist, Project Proponents must clearly describe the procedures used and apply appropriate calculations to yield estimates of SOC stock. Justification must be provided that it yields a defensible stock estimate, and this is subject to review by the VVB and Isometric.

To demonstrate the lack of availability of Tier 1 data, Project Proponents must provide an affidavit attesting to the lack of data, and provide any relevant supporting documentation (e.g., management logs).

Tier 2 comprises measured SOC data from literature or databases that is representative of the project area's conditions at $T_{n-1}$.

To be considered comparable and relevant, a Tier 2 source, at minimum, must provide an estimate of SOC stock from a location which shares the IPCC climate zone and soil class, and is under the same land use/management as the pre-project land use.

To demonstrate a lack of availability of Tier 2 data, Project Proponents must provide a list of search terms used (reflecting above requirements) and a list of databases which were consulted (e.g., Google Scholar, Web of Science, etc) which yielded no viable candidates, including any details, as relevant, if particular data sources were considered but determined to be insufficient.

Where $T_{n-1}$ does not correspond to project initiation and therefore represents an actively increasing SOC stock, Projects should proceed to Tier 3.

Tier 3 comprises published estimates of the rate or magnitude of SOC change associated with the land cover change or management transition that is occurring within the project (e.g., Poeplau et al., 2011). Compared to Tier 4, these estimates offer the advantage of being temporally resolved, capturing the potentially non-linear trajectory of SOC change rather than temporally averaged estimates.

As Tier 3 estimates are rates or stock changes, they should be anchored to the $T_n$ estimate, and $T_{n-1}$ back-calculated from $T_n$based on the Tier 3 data. Tier 3 estimates are considered relevant when the data are derived from the same broad IPCC climate and soil class, and represent the type and direction of land cover transition.

To demonstrate a lack of availability of Tier 3 data, Project Proponents must provide a list of search terms used (reflecting above requirements) and a list of databases which were consulted (e.g., Google Scholar, Web of Science, etc) which yielded no viable candidates, including any details, as relevant, if particular data sources were considered but determined to be insufficient.

Tier 4 comprises the IPCC default SOC values from the 2019 Refinement, Volume 4, Chapter 2¹⁶. As these are generalized estimates which have applicability across the globe, these represent the lowest tier and should apply to any scenario where Tiers 1-3 are not available.

All project measurements following Certification of this Module must follow the requirements for measurements and quantification of SOC in the project area. All module-aligned measurements occurring in the 5 years starting from the first Verification for The Project under this Module must be used to generate an estimate of SOC accrual within the project area. The assessment requires at least two module-aligned sampling events. Where only two are available, the rate is the paired stock change between them divided by the elapsed time. Where three or more are available, the rate is estimated by linear regression through all events in the period. Where fewer than two module-aligned sampling events occur within the five-year period, the period is extended to the next module-aligned sampling event. The rate must be computed for each stratum or, where strata were grouped under Section 6.1, for each group of strata. Uncertainty must be characterized in this assessment using the Monte Carlo simulation in Section 5.1, and the 30th percentile of the estimated rate used.

The 30th-percentile measured rate must then be compared with the 30th-percentile estimate of the pre-Certification stored-SOC rate, before the counterfactual deduction. Where the estimated pre-Certification rate is greater, the corresponding shortfall must be applied as a correction to subsequent certification events for the Project. Where the estimate for the pre-Certification period was based on a documented non-linear trajectory (e.g., a Tier 3 response function), the comparison must use the rate expected from that trajectory over the measurement period rather than a linear extrapolation. Where the measured rate is equal to or greater than the estimated rate, no correction is applied. This reflects the conservative nature of this Module, the fact that the pre-Certification period cannot be remeasured, as well as the potential for non-linear or accelerating rates of SOC accrual, under which a higher measured rate does not demonstrate that the pre-Certification rate was underestimated.

Where a correction is indicated, it is applied as an evenly amortized deduction to issuances for the ten year period starting from the year in which the correction is calculated. The amortized correction for each Reporting Period must be deducted from the net removals calculated for the Project over the Reporting Period. If a given Reporting Period certificate volume is insufficient to absorb the correction for that period, the remaining balance is carried forward and added to the next amortized volume for the subsequent period. Any remaining correction volume which has not been accounted for by the end of the 10 year period will be compensated as an avoidable reversal from the Buffer Pool. Projects are then responsible for replacement of these certificates within the Buffer Pool.

Areas that do not meet these conditions may be credited for the pre-Certification period only under Sections 6.1 and 6.2, where the requirements of this Section 6.0 are met. For the purposes of Section 4.2, the Pre-project Baseline Level remains the five years before the original project initiation, and $D$ and $d_i$ in Equation 10 are measured from the elected $t_0$. The election must be made in the PDD and cannot be reversed.

The power analysis applies at the primary quantification unit level, not stratum-by-stratum. Where a stratified design is used, the total number of samples should be allocated across strata to meet The Project-level MDD using optimal (Neyman) allocation based on stratum area and within-stratum variance, or an equivalent allocation rule documented in the Project Monitoring Plan.

Where ancillary variables (e.g., remote-sensed indices, terrain attributes, digital soil maps) are used either to inform the design or to support a regression or model-assisted estimator at The Project level, the sample size calculation may incorporate the variance reduction expected from those covariates, provided the correlation has been quantified using project-area or comparable regional data and is reported transparently.

The MDD-based power analysis below uses the SD of location-level paired SOC stock changes (the differences between $t\_0$ and the most recent sampling event at each location), because this directly reflects the noise in what The Project is trying to detect. Cross-sectional SD in absolute SOC stocks is not used and is generally a poor predictor of paired-difference variance.

The minimum number of samples needed to detect a given MDD at The Project level is calculated as:

$$MDD = \frac{S}{\sqrt{n}} \times (t_{\alpha,\upsilon} + t_{\beta,\upsilon})$$

(Equation A1)

$$n \geq \left(\frac{S \times (t_{\alpha} + t_{\beta})}{MDD}\right)^2$$

(Equation A2)

Where:

• $MDD$ is the minimum detectable difference in SOC stocks (t C ha$^{-1}$);
• $S$ is the standard deviation of the SOC stock change at fixed sampling locations, i.e., the location-level differences $\Delta SOC_{loc} = SOC_{loc,t_n} - SOC_{loc,t_0}$ computed at each sampling location, combined across strata as $S = \sum_j W_j S_j$ under optimal (Neyman) allocation, or $S = \sqrt{\sum_j W_j S_j^2}$ under proportional allocation, where $W_j$ is the proportion of the primary quantification unit's area in stratum $j$ and $S_j$ is the standard deviation of location-level paired changes in stratum $j$ (t C ha$^{-1}$). "Combined" here refers to the statistical aggregation of within-stratum SDs into a project-level SD for the purposes of this power analysis, and does not imply any physical pooling of samples.
• $n$ is the minimum number of samples required;
• $\upsilon = n - 1$ is the degrees of freedom;
• $t_{\alpha}$ is the two-sided critical value of the t-distribution at significance level $\alpha$. $\alpha$ should not exceed 0.05, meaning the sampling design should control the probability of falsely concluding a SOC change has occurred when none has, to no more than 5%.
• $t_{\beta}$ is the one-sided quantile of the t-distribution corresponding to the probability of a Type II error $\beta$. $\beta$ should not exceed 0.10, meaning the sampling design should achieve at least 90% statistical power to detect a true SOC change of magnitude $MDD$ when one is present.

Where database- or literature-derived variance is the only design-stage source available, The Project Proponent should conduct a pilot pre-sampling round of at least 10 sampling locations per stratum, drawn under the same probabilistic design as will be used for the full sampling campaign, prior to finalizing the sample size and committing to the first sampling campaign. The variance observed in the pilot replaces the database- or literature-derived estimate in the power analysis. The pilot samples are not certificate-relevant and may be drawn at reduced analytical cost (e.g., proximal sensing where validated under Section 4.1.9, or single-increment composited samples).

The initial power analysis remains provisional and should be updated at each subsequent re-sampling event using observed within-stratum variance from the preceding Reporting Period. Where the observed variance is materially higher than was assumed at the design stage, the consequences for certificate precision are absorbed through the uncertainty discount at certificate issuance under Section 5.0; where the observed variance is materially higher than the design-stage power analysis can support at the proponent's chosen MDD, the sample size should be increased for the next Reporting Period.

Isometric would like to thank the following external contributors to this Module:

• Lindsay Todman PhD (Cyclops MRV Inc.)

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