Model and Measurement Based Quantification of Enhanced Weathering

The Enhanced Weathering (EW) in Agriculture Protocol requires quantification of feedstock dissolution and alkalinity export across the project area. Model-based approaches can provide a scalable path to quantifying carbon removal from spatially limited measurements, and models are expected to play an increasing role in EW Measurement, Reporting, and Verification (MRV) as the sector matures and scales. This Module outlines the requirements for measurement-and-model-based quantification approaches for EW projects. This Module includes requirements for model development, validation against direct measurements, reporting, and transparency, as well as requirements for model evaluation during the verification process. Note that significant direct measurements are still required for baselining and stratification, as well as training, calibrating, and validating models. Measurement requirements for this Module are described in Section 9. 

Within this Module, a model is defined as a computational tool used to estimate feedstock weathering and alkalinity export over a given area. This includes:

1. Process-based models, which represent the underlying geochemical, physical, and biological mechanisms governing weathering and alkalinity generation;
2. Data-driven models, which use statistical or machine learning approaches to predict weathering rates based on environmental and site variables;
3. Hybrid models that combine both approaches.

The application of models as a quantification tool for EW is nascent, and technical understanding of model performance and data requirements continues to evolve. This Module is designed to support the responsible implementation of models within current technical constraints, establishing requirements based on current scientific understanding while providing a framework that can be updated as the field matures. The goal is for the Module to set a high bar to guide the development of projects and models, recognizing that it may be difficult for any existing model today to meet the bar set out. This Module will be updated as the scientific basis for model-based EW quantification evolves. See the Companion Document in Appendix X for more information on the considerations behind this Module. 

To build community trust in models and encourage knowledge sharing across the field, this Module requires public disclosure of the following, regardless of model type:

• all data from the monitoring sites in the project area  
• all data used for model validation
• a plain-language model description
• summary validation statistics
• model outputs used for Project validation and verification
• model training and calibration code regardless of model type.

This Module strongly recommends the use of open-source models supported by peer-reviewed publications. Where proprietary models are used, this Module requires additional independent review by an Expert Panel of qualified third parties. The specific transparency, disclosure, and review requirements are set out in Section 10.3.

Note that throughout this Module, the term “model calibration” or “training” refers to the process by which model parameters are adjusted so that the output matches the measured data. This Module uses “calibration” in the context of tuning process-based model parameters, while “training” is used in the context of data-driven models. The term "model validation" refers to the process by which a model's predictive performance is tested against independent data, and is distinct from the validation and verification process for credit issuance. Throughout this Module, use of the word "must" indicates a requirement, whereas "should" indicates a recommendation.

This Module applies to Projects operating under the Enhanced Weathering in Agriculture Protocol using model-based approaches to quantify feedstock weathering in the near-field zone (NFZ). Alkalinity export through the deeper subsurface and far field zone (FFZ) is discussed in the Protocol and is not covered by this Module. 

Any type of model (e.g. process-based, data-driven, hybrid) can be used to quantify alkalinity export, provided that the relevant data, validation and performance requirements in this Module are met. 

Models must be developed and validated using data representing the full range of operational conditions experienced in the project area during the Reporting Period. Particularly, the relationship between meteorological forcing or soil conditions and weathering rates is nonlinear, and feedstock dissolution responds differently under varying seasons and year-to-year variability (e.g. average vs extreme conditions). For these reasons, models must be initially validated on at least 12 consecutive months of data to capture the complete annual cycle of seasonal variation. Additionally, models must be validated using the latest available Reporting Period data. 

Project Proponents are permitted to perform temporal translation under the following conditions:

• The extremes of required meteorological parameters (temperature and precipitation) experienced in the Reporting Period must be within the validation envelope.
• The length of the Reporting Period must be less than the length of the time period represented in the training data.
• The model must be re-validated every Reporting Period, using data collected within the past twelve months.

Project Proponents must define the validated envelope of the data used for model development and validation. The meteorological envelope must be based on temperature and precipitation. The soil envelope must be based on contextual agronomic conditions and practices including soil pH and soil amendments.

Where forcing conditions during a Reporting Period exceed the validated envelope, The Project Proponent must either: (a) provide a documented, process-based justification that model performance is not materially affected; or (b) exclude the affected period from crediting.

• (a) This justification must include a sensitivity analysis demonstrating that the model's CDR prediction under the observed forcing conditions does not differ from the prediction under the nearest in-envelope conditions by more than the model's validated uncertainty bounds.
• (b) If a period is excluded from crediting, the model must be re-initialized using field measurements collected at or after the end of the excluded period before it can be applied to subsequent periods. Model state variables that may have changed during the excluded period (e.g., remaining feedstock mass, particle size distribution, soil cation inventory, base saturation) must be updated based on direct measurements. The model must then be re-validated in accordance with Section 7 before crediting can resume.

This Module does not apply to:

• Modeling subsurface losses below the NFZ. Losses occurring in the deeper subsurface and during transport to durable storage are governed by the Protocol and the River and Ocean Losses Module (link). Isometric recognizes that model-based approaches to quantifying these losses, including system-level accounting frameworks that integrate across the full transport path from soil to durable storage, are an active area of scientific development. Guidance on model-based approaches to subsurface and downstream loss quantification will be addressed in future updates as the science matures.
• Supplementary model use. Models may be used for other purposes in the EW in Agriculture Protocol, such as uncertainty estimation, sensitivity analysis, or in support of a direct-measurement approach. This Module does not apply to other types of models that are not primarily used for the determination of near-field zone weathering quantification.

This Module follows the quantification framework outlined Section 8 of the EW Protocol 1.2. The Module provides an alternative approach to quantifying the $CO_2e_{Stored, RP}$ term in the EW Protocol, which represents the total amount of CO₂ stored from an EW project. $CO_2e_{export, RP}$ is given by:

$CO_2e_{Stored, RP} = CO_2e_{export, RP} \times \eta_{RiverOcean}$

Equation 1

Where:

• $CO_2e_{export, RP}$ is the amount of CO₂ that is removed and exported from the base of the near-field zone (NFZ), in tonnes CO₂
• $\eta_{RiverOcean}$ is the total retention factor for all relevant processes in rivers and the ocean that lead to a reduction of CO₂ that ends up durably stored in the ocean. This factor is dimensionless with values between 0 and 1. See the River and Ocean Losses Module for quantification of this term.

The NFZ represents the portion of the upper soil column in which the weathering reaction and subsequent processes (e.g. soil and biomass uptake, secondary mineral formation) must be directly tracked and, for practical purposes, is defined as the depth of deepest soil sampling or the depth of porewater sampling.

$CO_2e_{export, RP}$ encompasses all processes occurring in the NFZ, and may be quantified as individual components and calculated as:

$CO_2e_{export, RP} = CO_2e_{Weathering, RP} - CO_2e_{BiomassLoss, RP} - CO_2e_{NetNewCarbonate, RP} - CO_2e_{NetNewSilicate, RP} - CO_2e_{NetSorption, RP} - CO_2e_{NonCarbonicNeut,RP}$

Equation 2

Where:

• $CO_2e_{Weathering, RP}$ is the CO₂ removed from the release of base cations from feedstock dissolution over the Reporting Period
• $CO_2e_{BiomassLoss, RP}$ is the amount of $CO_2e_{Weathering, RP}$ that is undone by the uptake of base cations in harvested plant biomass during the RP. 
• $CO_2e_{NetNewCarbonate, RP}$ is the amount of $CO_2e_{Weathering, RP}$ that is undone from the net formation of new carbonate minerals in the soil column during the RP. This will typically lead to a ~50% decrease in the removal efficiency for silicate (100% for carbonate) feedstocks over aqueous phase export.
• $CO_2e_{NetNewSilicate, RP}$ is the amount of $CO_2e_{Weathering, RP}$ that is undone from the formation of net new silicate minerals (e.g. clays) in the soil column during the RP. This term is included for completeness and is not required to be quantified at this time. 
• $CO_2e_{NetSorption, RP}$ is the amount of $CO_2e_{Weathering, RP}$ that is undone from the net sorption of base cations to cation exchange sites in the NFZ. In some instances, this value may be negative, indicating a net release of cations that had accumulated in previous Reporting Periods.
• $CO_2e_{NonCarbonicNeut, RP}$ is the amount of $CO_2e_{Weathering, RP}$ that is undone from neutralization of acids other than carbonic acid for the RP.

All terms have units of tonne CO₂e. 

Models under this Module may quantify $CO_2e_{export, RP}$ in one of two ways:

A model may predict $CO_2e_{export, RP}$ directly as an integrated output, without independently resolving each component term. 

In this scenario, The Project Proponent must demonstrate that the model accounts for all the terms in Equation 2 (excluding $CO_2e_{NetNewSilicate, RP}$), either explicitly in a process-based model, or implicitly through the training data used for data-driven models. 

1. The model must meet the relevant validation requirements described below in this Module.

Alternatively, separate models or model components may be used to predict the individual terms in Equation 2, which are then combined to calculate $CO_2e_{export, RP}$.

1. If separate models are used to quantify individual terms, each model must individually meet the relevant validation requirements described for the models used during quantification under this Module.
2. Project Proponents may also elect to individually model some terms and empirically quantify others through direct measurement, following the requirement for that term outlined in the relevant section of the Enhanced Weathering in Agriculture Protocol.

This Module supports the following approaches for calculating $CO_2e_{export, RP}$ and/or its constituent terms: 

1. Process-based models, which simulate the geochemical, physical, and biological mechanisms governing weathering and alkalinity generation through explicit representation of processes such as mineral dissolution kinetics, solute transport, and soil chemistry. See Section 4 for requirements.
2. Data-driven models, which use statistical methods to establish empirical relationships between environmental variables and measured weathering or alkalinity export outcomes, including spatial extrapolation from monitoring areas to the wider deployment area using agronomic measurements. See Section 5 for requirements.
3. Hybrid models, which combine process-based and data-driven components, for example, using a geochemical model to simulate relevant processes and a statistical model to extrapolate outputs spatially. See Section 6 for requirements.

Process-based models are a class of computational models that simulate the physical, chemical and biological laws that govern a system of interest. In the case of EW, this includes mass balance equations, thermodynamic equilibria, mineral dissolution kinetics and fluid dynamics. Process-based geochemical models play a central role in chemical weathering science, enabling research to move beyond intensive field-based measurements to and toward advanced algorithms that combine descriptions of fluid flow, transport processes and biogeochemical reactions in order to calculate changes in solutes, minerals and even microbial communities over space and time¹, ². These models have a history in the geochemical weathering community, from the theoretical foundation of supergene enrichment of copper (³), to kinetic and transport coupling (⁴), and to weathering studies (²). Process-based models can be viewed as a “glass-box” modeling framework where the underlying mechanisms and relationships are transparent and interpretable.

In the context of EW and adjacent geochemical fields, process-based models derive their core value from encoding thermodynamic and kinetic laws governing mineral dissolution, secondary mineral precipitation, ion exchange, and fluid transport. Process-based models can take the form of multicomponent reactive transport models (RTMs), coupled ecohydrological-geochemical models, box models, and other formulations that explicitly represent the geochemical and physical processes governing weathering. These models divide the subsurface into discrete spatial grids, calculating the advection, dispersion, and diffusion of aqueous species coupled with mineral dissolution, ion exchange, surface complexation, and secondary mineral precipitation at each defined time step. By explicitly defining the governing partial differential equations for fluid flow and chemical reactions, these models provide a mechanism for scaling CDR estimates across varied climatic and agronomic domains. The scientific literature surrounding EW relies on several foundational reactive transport codes, which have recently been adapted or coupled with ecohydrological models to serve the specific needs of quantifying carbon cycling in agricultural systems.

Over the past years, a growing body of EW-specific process-based models have emerged in the peer-reviewed literature. Below are some examples:

• PHREEQC-based RTMs (Kelland et al., 2020 ⁵; Lewis et al., 2021 ⁶; Vienne et al., 2022 ⁷)
• Geochemist's Workbench ⁸
• SMEW - Soil Model for Enhanced Weathering (Bertagni et al., 2025 ⁹; Anand et al. (2026) ¹⁰)
• T&C-SMEW - Tethys & Chloris coupled with SMEW (Zhang et al., 2025 ¹¹)
• ARTEMIS v1.0 (Taylor et al., 2026 ¹²)
• MIN3P-HPC (Su et al., 2021 ¹³)
• TOUGHREACT (Xu et al., 2006 ¹⁴, Deng et al. (2023) ¹⁵)
• Beerling model (Beerling et al. (2020) ¹⁶; Beerling et al. (2025) ¹⁷)
• SCEPTER (Kanzaki et al. (2022) ¹⁸; Kanzaki et al. (2024) ¹⁹)

The application of process-based models for quantifying CDR from EW is nascent. The literatures are actively evolving, field-scale calibration datasets remain sparse, and there is a need for more community consensus on which processes must be explicitly resolved in models versus aggregated or parameterized. 

This Module sets out the requirements that a process-based model must meet under current scientific understanding, recognizing that no model in practice may yet meet the full bar at the time of Module certification. Two structural challenges are acknowledged: parameter underdetermination, where the number of free parameters in a process-based model exceeds the number of independent observations available to constrain them; and structural uncertainty, where multiple defensible model formulations may produce divergent predictions for the same field site. 

This Module addresses underdetermination through requirements on parameter classification, sensitivity analysis, and ensemble treatment of highly sensitive parameters that cannot be independently constrained. Structural uncertainty²⁰ is not expected to be fully resolved at the level of a single project and is acknowledged here as a field-wide limitation that will be addressed through multi-model comparison work as the EW literature matures, see Section 8.1 for more details. 

Process-based models used under this Module must be constrained by and validated against empirical measurements collected from the project area; their use as a crediting tool is conditional on demonstrated field-scale validation, not on theoretical completeness of process representation.

This section defines the boundaries for a process based model to be used under this Module. To accurately represent the systems and the dynamic fluxes that are consistent with thermodynamic principles and satisfy mass balance principles, process-based models must explicitly define boundaries and distinguish between zones that reflect the governing processes within that zone. 

The NFZ is characterized by strong geochemical gradients in moisture, pH, pCO₂, cation concentration, and alkalinity, which drive the weathering reaction and loss processes. Models representing this zone must resolve these gradients at sufficient spatial and temporal resolution to capture their non-linear feedback. Evidence to demonstrate such resolution requirements are met include but are not limited to:

1. a spatial discretization at a depth increment appropriate to capture vertical gradients within the NFZ, supported either by a grid convergence test or by reference to published literature demonstrating adequacy for the soil and feedstock type; 
2. a temporal resolution appropriate to capture seasonal and event-scale variability in porewater chemistry and soil moisture, supported either by a timestep sensitivity test or by equivalent justification.

The primary output of the NFZ should be geochemical parameters that accurately reflect changes in this zone, including demonstration that the principal non-linear feedbacks are represented, including (but not limited to) dissolution rate dependence on pH and temperature, and sensitivity of predicted CDR to seasonal variation in rainfall and temperature. The processes that must be explicitly represented are defined in Section 4.3.

To be more specific, the NFZ is the zone over which the gross CDR signal ($CO_2e_{Weathering, RP}$) and the primary soil-column loss terms ($CO_2e_{BiomassLoss, RP}$, $CO_2e_{NetNewCarbonate, RP}$, $CO_2e_{NetNewSilicate, RP}$, $CO_2e_{NetSorption, RP}$, $CO_2e_{NonCarbonicNeut, RP}$) are determined, consistent with Equation 2. Where a single integrated process-based model is used, the quantification approach must demonstrably account for all terms in Equation 2. Where individual terms are quantified separately, each must be determined using a distinct process-based model or model component. In addition, all models used must be validated against measurements as described in Section 7. 

A process-based model used under this Module must represent the first-order controls on EW efficiency and is identified as either required (“must”) or recommended (“should”). This section distinguishes between required and recommended processes.

A process is required (“must”) in a process-based model when:

1. The process is well understood and can be represented accurately in current process-based modelling frameworks.
2. Sufficient data exist to constrain and parameterize the process at The Project scale.

A process is recommended (“should”) in a process-based model when:

1. The process is known to influence EW efficiency, but current process representations in models are uncertain, simplified, or under active scientific development.
2. The data needed to constrain and parameterize the process are not yet routinely available, or are only available for a subset of project conditions.
3. The process is material to CDR for some project configurations but not others, such that universal representation would impose disproportionate burden.

Required processes must be explicitly represented in the model. Recommended processes should be represented where the supporting data and parameterization allow. Non-Carbonic Acid Weathering, Net sorption, and Plant Cation Uptake must be included in the net CDR equation, but are not required to be modeled. These terms may instead be accounted for through direct measurements from the Monitoring Area, in accordance with the relevant section of the Enhanced Weathering in Agriculture Protocol.

The model must be capable of predicting the time-integrated evolution of porewater geochemistry and alkalinity export from the soil column as a function of site-specific inputs, such as feedstock and baseline soil mineralogy, particle size distribution, meteorological and hydrological inputs (i.e., temperature, precipitation and Evapotranspiration), soil properties (i.e., soil moisture), and land management. Where a Project Proponent represents additional processes beyond those listed as required, the corresponding data needed to constrain and validate those processes must be collected and reported alongside the standard monitoring requirements.

Hydrological State and Solute Transport

The hydrological state of the soil column is a primary control on mineral dissolution rate, secondary mineral precipitation, and the timing of alkalinity export. Water flux governs the contact time between porewater and feedstock, the concentration of dissolved species, and the breakthrough of base cations from the NFZ to the deeper subsurface. The following hydrological processes and parameters calculation/representation must be included:

• Evapotranspiration (ET): The model must couple soil moisture dynamics with plant transpiration and soil evaporation to compute actual evapotranspiration (ETa), using a physical formulation such as FAO-56 Penman-Monteith downscaled by a crop coefficient (Kc) and a soil water stress coefficient (Ks). A satellite-derived ETa product (e.g., MODIS MOD16, ECOSTRESS, OpenET) appropriate for the spatial and temporal resolution of The Project Area may be used with clear justification. Reference or potential ET must not be substituted for actual ET, as this overestimates water loss in water-limited systems. ETa removes water from the soil profile, concentrating solutes in the remaining porewater. During dry periods, this can drive secondary mineral saturation and precipitation, which can suppress further weathering under some conditions, for example, surface passivization and/or porewater approaches equilibrium with the dissolving phase, or when elevated common-ion activities inhibit dissolution kinetics. Conversely, rainfall events dilute porewater solute concentrations, relieving saturation and promoting dissolution. Failure to represent these ET-driven dynamics may result in systematic underestimation or overestimation of dissolution rates and CDR.
  • Water budget closure: The model must produce a water budget for the project area that is consistent with the water budget required for CDR quantification under the Section 10.5.1.1.1 of the Enhanced Weathering in Agriculture Protocol, including rainfall, irrigation, ET, and drainage flux terms.
• Advection-Dispersion: The vertical transport of dissolved ions (Mg²⁺, Ca²⁺, HCO3^-) must be modelled via appropriate advection-dispersion equations. In most process-based models (including PHREEQC-based RTMs), the standard ADE (Advection-Dispersion-Equation) formulation covers advection and dispersion, with diffusion either included explicitly or treated as part of the hydrodynamic dispersion coefficient. Specific implementation of this process in process-based model could look like:
  • Project Proponents specify the ADE (Advection-Dispersion-Equation) formulation used (multicomponent (fully coupled) or species-by-species(decoupled)), and whether reactions are coupled via operator splitting (sequential non-iterative or sequential iterative) or globally implicit. Most PHREEQC-based RTMs (e.g., PHAST, PHT3D, IPhreeqc-coupled codes) use operator splitting.
  • Clearly define transport parameters including but not limited to: porewater velocity (derived from the water balance), effective porosity, longitudinal dispersivity (α_L). Dispersivity values must be justified using either site-specific tracer test data or peer-reviewed scale-dependent compilations appropriate to the modelled depth interval.
  • Clear definition of boundary conditions of the transport condition of surface boundary consistent with the water balance and applied feedstock flux, and a lower boundary condition (free drainage, specified flux, or specified concentration) at the base of the modelled domain.
  • Numerical stability constraints for the advection-dispersion solver must be satisfied at the chosen Δz and Δt, and the resulting stability constraints must be reported.

Soil Carbonate Chemistry and Gas Exchange

The production of carbonic acid (H₂CO₃), formed when soil CO₂ dissolves in porewater, is frequently the rate-limiting step for silicate weathering in agricultural soils. Thus, soil pCO₂ is a primary control on carbonic acid availability, and therefore on dissolution rates. Soil CO₂ exchange is controlled by root respiration, microbial decomposition, and gas diffusion and is typically one to two orders of magnitude higher than atmospheric pCO₂, providing the proton supply that drives dissolution. Models that fail to capture this dynamic will underestimate proton availability and may result in underestimation or overestimation of dissolution rates and CDR. The following are specific processes and parameters that should be included:

• Soil pCO₂: Process-based models should account for CO₂ entering the soil system from multiple sources: dissolved in rainwater, dissolved in irrigation water, and produced by root respiration or microbial respiration of organic matter within the soil profile. Elevated soil pCO₂ lowers porewater pH, which accelerates silicate dissolution and shifts carbonate equilibrium towards increased bicarbonate alkalinity, both of which drive CDR. Because soil respiration rates vary with temperature, moisture, and organic matter availability, soil pCO₂ is dynamic rather than fixed, and the model should accordingly represent this term as dynamic. This coupling between respiration and dissolution kinetics is a key reason field-scale weathering rates diverge from laboratory measurements.
• Open system dynamics: Process-based models should represent the soil column as an open system in which carbonic acid consumed by weathering is continuously replenished from biological sources and atmospheric diffusion. In scenarios where gas diffusion is restricted (e.g., waterlogged soils, high clay content), the model should also capture the potential for pCO₂ depletion and the transition to closed system behaviour, which limits the rate of carbonic acid weathering.

Mineral Dissolution  - Quantification of $CO_2e_{Weathering, RP}$

Mineral dissolution drives CO₂ removal in EW projects. It is the process by which silicate feedstock reacts with carbonic and other acids in soil porewater, releasing base cations (Ca²⁺, Mg²⁺, K⁺, Na⁺) and generating alkalinity. All other processes in the system are downstream consequences of this primary reaction; errors in its representation propagate directly into the gross CDR estimate.

Models must use mineral abundances taken directly as characterized under the Rock and Mineral Feedstock Characterization Module and implement kinetic rate laws and calculate dissolution rate as a function of mineral saturation state in porewater. Where feedstocks contain multiple reactive mineral phases, each phase must be represented with its own rate law, surface area evolution, and dissolution stoichiometry. Treating a polyphase feedstock as a single-phase proxy mineral is not permissible. Project-specific laboratory experiments may be used in lieu of, or in combination with, peer-reviewed literature values for feedstocks that are not well-represented as a combination of individual mineral phases (e.g., feedstocks with high amorphous content or alkaline industrial wastes such as steel slag and fly ash). Where experiments are used, the experimental design must characterize pH dependence across the relevant field pH range, reactive surface area and its evolution during dissolution, and surface passivation effects, and the experimental Protocol, data, QAQC and derived parameters must be documented in the PDD. Models must be initialized with site-specific baseline soil mineralogical conditions because baseline soil mineralogy controls the initial porewater chemistry and the baseline saturation state of the system, particularly the SI of calcite, dolomite, and secondary silicates 

To implement kinetic rate laws for mineral dissolution, Project Proponents must incorporate pH and temperature dependence:

• pH dependence: The dissolution rate law must incorporate pH dependence through explicit acid, neutral, and base mechanism terms, consistent with the transition state theory (TST) rate law formulation, R = A · (k_acid · [H⁺]^n_acid + k_neutral + k_base · [OH⁻]^n_base), where k_acid, k_neutral, and k_base are the temperature-dependent rate constants for each mechanism, n_acid and n_base are the empirical reaction orders, and A is the instantaneous reactive surface area. Rate constants and reaction orders must be parameterized from peer-reviewed laboratory data for the relevant mineral phases.
• Temperature dependence: The dissolution rate law must incorporate temperature dependence of the rate constants k_acid, k_neutral, and k_base, typically through an Arrhenius formulation, k(T) = k_ref · exp[−(E_a/R) · (1/T − 1/T_ref)], where E_a is the activation energy for the relevant mechanism, R is the universal gas constant, T is the soil temperature, and T_ref is the reference temperature at which k_ref is reported. Activation energies must be parameterized from peer-reviewed laboratory data for the relevant mineral phases.

The following additional terms are not required to be quantified but are highly recommended for completeness in implementing kinetic rate laws for mineral dissolution. 

• Surface area evolution: Feedstocks may be widely dispersed in particle size, with fines dissolving rapidly while coarse grains persist. Where this process is represented, the model should employ a framework (e.g., shrinking core) that explicitly tracks changes in radius and surface area of multiple particle size bins over time, rather than assuming constant surface area for the entire modelling period.
• Surface passivation: The formation of leached layers or secondary coatings (e.g., amorphous silica) can progressively inhibit dissolution. Where this process is represented, the model should include terms describing its onset, rate, and effect on the active reactive surface area.

Ion Exchange  - Quantification of $CO_2e_{NetSorption, RP}$

The soil solid phase, i.e. clay minerals and organic matter, and Fe/Al oxide coatings, acts as a capacitive buffer for base cations and acidic cations, complicating the relationship between mineral dissolution and alkalinity export. Models should include an ion exchange process that partitions cations between the porewater and the soil exchange complex. Where ion exchange is represented in the model, the following processes are required:

• Exchanger composition: The exchanger composition must represent both base cations (Ca²⁺, Mg²⁺, Na⁺, K⁺, or a subset used for quantification) and exchangeable acidity (Al³⁺ and H⁺), such that the sum of exchanger-bound species equals the measured effective cation exchange capacity (CEC).
• Selectivity coefficients: Selectivity coefficients governing the partitioning between competing cations, including acidic cations, must be parameterized from site-specific baseline measurements of CEC, base saturation, and exchangeable acidity, consistent with the measurements required under the EW Protocol.
• Method consistency: The extraction method used to characterize the exchange complex must be consistent with the operational definition of CEC used in the model. 
• CEC evolution: Total CEC should be allowed to evolve over the crediting period where the contribution of variable-charge surfaces, secondary clay formation, or changes in soil organic matter are material to the CEC pool. 
• Land management effects: Where The Project results in changes to land management practices that influence base saturation (e.g., fertilizer or lime application), these effects must be represented in the exchanger composition over time.
• Depth resolution. The cation exchange model must be resolved through the full depth of the NFZ.

Secondary Mineral Precipitation - Quantification of $CO_2e_{NetNewCarbonate, RP}$

Secondary mineral formation has competing effects on CDR efficacy. In particular, secondary carbonate precipitation directly reverses CDR by consuming dissolved base cations and alkalinity and must be represented in the Model. Secondary silicate and oxide formation, however, can both reduce CDR (where Ca/Mg-bearing phases consume base cations, or where surface coatings passivate feedstock grains) or enhance CDR (by consuming Si and Al released during weathering, keeping the porewater undersaturated with respect to primary minerals, and sustaining higher dissolution rates through the affinity term in the rate law). The following are processes in this category.

• Formation of secondary carbonates: In porewaters, dissolved Ca²⁺ and HCO₃^- may reach supersaturation and precipitate as calcite. This reaction releases CO₂, effectively reversing carbon removal. Models must track saturation indices (SIs) for minerals including calcite, aragonite, dolomite, siderite, and magnesite and implement precipitation when supersaturation thresholds are exceeded. Where SI exceeds the thermodynamic saturation threshold, precipitation must be represented using precipitation kinetics, equilibrium-only approaches, or a combination. Project Proponents must demonstrate that the threshold for precipitation is appropriately calibrated against site-specific or literature-based kinetic data.
• Formation of secondary silicates and oxides: the quantification of this process is not required under this Module but is highly recommended for completeness of the Model. Secondary silicate and oxides include but not limited to: secondary clay minerals (e.g., kaolinite, smectite); amorphous silica phases; Al/Fe oxides (e.g., gibbsite, ferrihydrite) that consumes Si, Al, and in some cases base cations released during feedstock weathering. Where this process is represented in the model, it could be represented through mass-balance, monitoring of saturation indices, equilibrium-based approaches (precipitation proceeds to thermodynamic saturation), kinetic approaches (precipitation rate governed by a rate law with affinity and rate constant terms), or a combination, provided the selected approach is justified against site-specific or literature-based evidence for the relevant phases and conditions. The model must ensure that solutes consumed by secondary phase precipitation are removed from the porewater inventory and that the resulting changes in solute concentration are fed back into the primary mineral dissolution rate calculation.

Non-Carbonic Acid Weathering -  Quantification of $CO_2e_{NonCarbonicNeut, RP}$

In agricultural soils, mineral weathering is driven not only by carbonic acid but also by strong acids. Where the model does not dynamically simulate strong acid production, non-carbonic acid weathering must be quantified empirically using direct measurements following the EW Protocol and deducted from the gross CDR estimate. Where non-carbonic acid weathering is represented in the model, the following processes are required: 

• Nitrification: Nitrogen fertilizers (urea, ammonium) undergo nitrification, releasing protons and nitrate (NH₄⁺ + 2O₂ → NO₃^- + 2H⁺ +H₂O). Weathering driven by nitric acid does not contribute to CO₂ removal and needs to be accounted for in the Model.
• Stoichiometric charge balance: Models must track the source of protons. This includes protons released from the pre-existing exchangeable acidity pool on soil mineral and organic surfaces (e.g., exchangeable H⁺ and Al³⁺) during displacement by weathering-derived base cations. The representation of this process is addressed under the ion exchange requirements above. The Module requires that the fraction of weathering attributable to strong acids (nitric, sulfuric) be deducted from the gross CDR. Sulfide oxidation (e.g., of pyrite or pyrrhotite) in applied feedstock can generate sulfuric acid in situ. While most basalts and ultramafic rocks have relatively low sulfide content, even trace amounts can become reactive once crushed and exposed to oxic soil conditions. Upon confirming the presence of non-carbonic acid, the model must include minimum representation of non-carbonic acid input, kinetics, so that residual proton loading to the soil from strong acid sources can be calculated explicitly.

Plant-Soil Interactions -  Quantification of $CO_2e_{BiomassLoss, RP}$

Root uptake of base cations represents a direct loss term for CDR (CO₂e_BiomassLoss in the Protocol). Root respiration is the primary driver of elevated soil pCO₂. The following processes should be represented in the model: 

• Plant base cation uptake: Models may represent the uptake of base cations (Ca²⁺, Mg²⁺, K⁺ at minimum) by the crop as a function of biomass growth rate. This uptake must then be scaled by the harvested yield reported during that Reporting Period. Plant uptake in harvested biomass constitutes a permanent loss of CDR potential and should be explicitly quantified as a model output mappable to the CO₂e_BiomassLoss term in Equation 2. Alternatively, Project Proponents may elect to pursue a measurement based approach for biomass uptake following the requirements in Section 10.4.5.6 in the Enhanced Weathering in Agriculture Protocol.
• Biotic CO₂ production and root respiration: Models should simulate CO₂ production from root respiration and microbial activity as the primary driver of soil pCO₂.

Where the model does not dynamically simulate plant-soil interaction, it must be quantified with measurements or a default soil pCO₂ value from peer-reviewed literature appropriate for the climate, soil type, and cropping system of the Project Area. Furthermore, the Project Proponent must demonstrate through the model validation requirements (Section 7) that omission of this process does not introduce a systematic bias in the CDR estimate (e.g., omitting plant cation uptake may lead to overestimation of alkalinity export). 

Several routinely-measured soil parameters used as model inputs are method-dependent proxies for the underlying state variables that govern weathering and ion exchange in the model. For example, soil pH, as commonly measured in a 1:1 or 1:2.5 soil-to-water or soil-to-0.01 M CaCl2 suspension, is not equivalent to the in-situ porewater pH that controls mineral dissolution kinetics. Cation exchange capacity and base saturation, as measured by ammonium acetate, BaCl2, or similar extraction methods, are operational estimates of the exchangeable cation pool that depend on the extractant, pH, and ionic strength used. Because these proxy-to-state-variable gaps can introduce systematic bias if treated as direct measurements, Project Proponents using a process-based model must:

• State explicitly, in the PDD, which measured parameters are used as model inputs and which model state variables they are intended to represent (e.g., "measured soil pH (1:1 water) → porewater pH" or "ammonium acetate CEC at pH 7 → modelled exchangeable cation pool").
• For each proxy-to-state-variable mapping, justify the appropriateness of the conversion for the specific soil conditions of the project area, with reference to peer-reviewed literature, site-specific characterisation data, or paired direct measurements of the state variable in question (e.g., porewater extraction or in-situ pH measurement at a representative subset of monitoring locations).
• Where a model implements an explicit conversion, describe the conversion, its assumptions, and its parameter values in the model description.
• Where a model relies on calibration to absorb the proxy-to-state-variable gap, this must be flagged in the sensitivity analysis required under Section 4.5, and the parameter(s) absorbing the gap must be reported with their calibrated values and the range explored.

Process-based models contain parameters that may vary depending on project-specific characteristics including feedstock type and project location.  Calibration is the process by which model parameters are adjusted so that the model reproduces observed field behavior. The Project Proponent must classify all model parameters as either fixed or calibrated parameters, and document this classification with a justification in the PDD. See below for examples of parameters that are typically prescribed or calibrated. Note that these lists are for illustrative purposes and are not exhaustive.

Fixed parameters are those that are determined by direct site measurement or by peer-reviewed laboratory data for the specific mineral phase, temperature range, and chemical conditions in the Removal Area. Note that each of these parameters might have a range of values based on measurements rather than a single value. Examples of fixed parameters include: 

• Thermodynamic equilibrium constants. Project Proponents must use values provided directly from an established, peer-reviewed thermodynamic database. Examples of acceptable databases include, but are not limited to: llnl.dat / thermo.com.V8.R6, phreeqc.dat, wateq4f.dat, minteq.v4.dat, CEMDATA. Custom or in-house databases must be justified, include documentation of any modification from a published database, and is recommended to be peer-reviewed. The following serve as recommendations for database selection:
  • The selected database must be appropriate for system chemistry, the database must include reliable log K values for all primary and secondary mineral phases, aqueous species, and surface complexes represented in the model, at the relevant temperature, pressure, and ionic strength range.
  • Internal consistency between thermodynamic and kinetic databases: Where mineral dissolution kinetics are represented using a published rate database (e.g., Palandri & Kharaka 2004 ²¹; Marty et al. 2015 ²²), Project Proponents must demonstrate that the kinetic and thermodynamic databases are internally consistent. This means: (i) the affinity term in the rate law must be evaluated using log K values consistent with the conditions and conventions under which the rate constants were originally measured or compiled; and (ii) where database mixing is unavoidable, any inconsistencies in log K values for relevant mineral phases must be quantified, reported, and incorporated into the uncertainty quantification for the model.
  • Project Proponents must report the specific database(s) used, including version or release date, any modifications applied, and a justification for the chosen database in the context of the system chemistry.
  • Where thermodynamic data for a relevant mineral phase are not available in an existing database, Project Proponents may use values derived from project-specific laboratory experiments or peer-reviewed experimental measurements. Project-specific experimental values must be determined using standard analytical methods, with the experimental conditions, methodology, and associated uncertainties documented and submitted as part of the model description. These values must be included in the sensitivity analysis and uncertainty propagation.
• Site parameters that are directly measured, including CEC, bulk density, initial base saturation, feedstock particle size distribution, and feedstock mineral type and abundance. 
• Mineral dissolution rate constants and reaction orders. Project Proponents must use published literature and laboratory values or project-specific experiments determined values for the relevant mineral phases. A field-to-lab rate scaling factor may be applied during calibration to account for the well-documented discrepancy between laboratory and field dissolution rates.
• Cation exchange selectivity coefficients, where site-specific measurements are available
• Crop functional type or cropping system

Parameters that must be prescribed or calibrated are those that cannot be directly constrained by laboratory experiments or field scale measurements. The variation range of which parameters are calibrated must be pre-defined by The Project and limited to physical ranges, and must be documented in the PDD. Examples of parameters to calibrate include: 

• Reactive surface area evolution terms.
• Water flux accounting, excluding parameters such as precipitation, runoff, and drainage that are directly measurable or strongly constrained. Examples of terms that are uncertain and can be calibrated include but are not limited to: the partitioning of infiltrated water between matrix flow, preferential flow, and lateral subsurface flow within the NFZ; effective porosity and the fraction of pore space that transmits water, vertical flux profile within the soil column which cannot be directly measured.
• Soil pCO₂ variation with temperature, moisture content and crop type.
• Field-roughness factor (scaling lab rates to field rates), an empirical multiplier applied to laboratory-derived mineral dissolution rate constants to account for the well-documented discrepancy between rates measured in controlled laboratory experiments and rates observed in field weathering systems ²³²⁴, which arises from mineral surface area evolution. 
• Effective hydrological connectivity, the physical property of the soil/porous medium that quantifies how easily water flows through it under a hydraulic gradient.

Uncertainty in all model parameters must be propagated into the final CDR estimate. Project Proponents must address this through one of the following approaches for each parameter:

• Inclusion in Monte Carlo uncertainty propagation (see Section 8) with a justified distribution representing the parameter's measurement, literature, or calibration uncertainty;
• Substitution with a conservative value at the end of the parameter's physically defensible range that produces a lower CDR estimate.

The following are examples of data sources that could be used for calibration (see Section 9 for more details on monitoring requirements):

• Direct measurements from monitoring areas collected within the calibration period, including but not limited to: climate condition and evolution, feedstock mineral type and abundance, soil geochemistry, soil moisture, CEC, etc. 
• Baseline measurements collected prior to feedstock application, which may be used to initialize the model and constrain background geochemical conditions

Models must undergo cross-validation, where repeated splits of the full dataset into a calibration set and a validation set are performed, so that there is held-out data that can be used for independent model validation. See Section 7.1 for further details.  

Calibration Approaches

The number of calibrated parameters should be kept to the minimum needed to achieve adequate validation performance. The Project Proponent must report the ratio of calibrated parameters to independent calibration observations in the PDD. 

The following calibration approaches are permissible under this Module:

• Manual iterative calibration, in which parameters are adjusted individually and sequentially based on residuals between modeled and observed values for one or more independent calibration observation types (e.g., porewater pH, major cation concentrations, alkalinity, dissolved Si, exchangeable cation pools, solute export fluxes). Each parameter adjustment must be logged with the observation type, the residual that motivated the change, and the data that guided the new value.
• Automated parameter estimation using algorithms such as gradient-based optimization frameworks.

Where multiple parameters are calibrated simultaneously, The Project Proponent is recommended to adopt a multi-parameter optimization approach in which all calibrated parameters are adjusted jointly against the full set of independent calibration observations, rather than tuning parameters one at a time. Multi-parameter optimization reduces the risk that sequential adjustment masks parameter interactions and compensating errors, and provides a more honest characterization of the parameter covariance structure underlying the calibrated solution. Where adopted, the optimization objective function, the parameter covariance matrix (or equivalent), and any identifiability or correlation diagnostics must be reported in the PDD.

In addition, models may be calibrated against primary geochemical observables (e.g., porewater cation concentrations, pH, alkalinity) rather than directly against derived CDR estimates. Calibrating against primary measurements is acceptable and preferable where the CDR signal is noisy or not yet statistically significant. In this case, the CDR estimate should be treated as an emergent validation metric that is tested at the validation stage against independent data, rather than used as a calibration target.

Regardless of calibration strategy, all parameters within the process-based component must remain within physically defensible ranges after calibration. 

Calibration Record Requirements

The following must be submitted as part of the calibration documentation:

• The complete calibration record, including the full parameter trajectory. For automated methods, this includes the parameter estimation log. For manual methods this may include a log of each adjustment step with the motivating observation is acceptable.
• Pre-calibration and post-calibration values for all calibrated parameters, with units and the data source used to bound each parameter.
• A narrative description of any model adjustments made during calibration, with justification. Adjustments to model structure (as opposed to parameter values) must be clearly distinguished from parameter calibration and require additional justification.
• Where a specific value or range has been chosen for a parameter, a justification must be provided, including the scientific basis for the range and, where a fixed value is used rather than a range, the rationale for treating that parameter as invariant under project conditions

Models calibrated against one variable should reproduce other independently measured variables at monitoring areas without further tuning to demonstrate cross-variable consistency. For example, a model calibrated against porewater Ca²⁺ should be able to reproduce porewater Mg²⁺, pH, and alkalinity within acceptable performance bounds using the same parameter set (i.e., multi-parameter optimization). Achieving a good fit to one variable at the expense of other variables that have direct correlation is not acceptable and indicates gaps in process representation that should be resolved before proceeding to model validation. 

A sensitivity analysis must be performed across the full list of fixed and calibrated parameters, varying each with its physically defensible range to characterize the influence of each parameter on the modeled CDR output. Parameters in the model must correspond to physically meaningful entities (e.g., rate constants, transport coefficients, mineral abundances) and cannot be decomposed into sub-components for the purpose of sensitivity classification. 

Project Proponents must conduct a global sensitivity analysis to identify the parameters that most influence the CDR estimate and to account for interactions between parameters ²⁵. Suitable methods include variance-based (Sobol) sensitivity analysis, which decomposes output variance into first-order and total-order indices, and Morris screening, which ranks parameters by influence and identifies interaction effects at lower computational cost. One-at-a-time (OAT) approaches, where each parameter is varied independently while all others are held fixed, are not sufficient, as they do not capture parameter interactions. The chosen method, its results, and the parameters identified as most influential must be reported in the PDD.

Table 1 Summary of required and recommended processes to be included in a process-based model.  Asterisk (*) marks where processes are recommended, they should be represented where supporting data and parameterisation allow, and may otherwise be omitted from the model or quantified through direct measurement.

The transparency of process-based models is a foundational requirement for their use in CDR quantification. Because each term in the CDR calculation involves distinct physical, chemical, and biological mechanisms operating across different spatial and temporal scales, a process-based model must demonstrate not only that its aggregate CDR output matches observations, but that the individual mechanisms driving each term are represented and calibrated. This requirement is the basis for the minimum process representation standards set out in Section 4.3. 

The following input and output files are required to be submitted for calibration and validation of process-based models. Additional requirements for all models are further found in Sections 7 (Model validation), 8 (Uncertainty), and 9 (Monitoring). See Section 10 for more information on what data must be made publicly available.  

• Theory Manual: A detailed document describing every equation used in the model, the source of every parameter (literature citations or site data), and the justification for all assumptions (e.g., reason for excluding a certain secondary mineral).   
• Code Availability: For credit issuance, the model code and input and output files must be made available to Isometric and the VVB.
• Data used for calibration: Project Proponents may use a designated subset of field data (e.g., from the first year of monitoring) to adjust unconstrained parameters. The calibration data subset, including the temporal window, spatial monitoring locations, observation types, and any data quality screening criteria,  must be defined and documented in the PDD. 
• Model updates: It is recommended to update and recalibrate the model with each additional Reporting Period. If the model's predictive performance improves, the uncertainty discount can be reduced for future credit issuances. Project Proponents must provide a model update plan.
• Documentation of assumptions: All assumptions embedded in the model must be explicitly stated, justified, and traceable. This includes assumptions behind including and excluding each process. Assumptions that cannot be justified by published literature or direct site measurement must be flagged as unconstrained and will be subject to an explicit sensitivity analysis demonstrating their impact on the final CDR estimate.

Data-driven models are trained on observational datasets to learn relationships between observed inputs and outputs. An example is establishing an empirical relationship between directly measured weathering rates (e.g. via cation mass balance) and agronomic soil measurements (e.g., soil pH, buffer pH, base saturation) within a subset of the project area. The empirical relationship can then be applied to data collected across the full deployment area to determine weathering rates over the full deployment area. 

With sufficiently representative datasets and appropriate model structure and training, data-driven models may be able to learn the necessary empirical relationships for CDR quantification without needing to explicitly describe all the relevant processes and interactions in a system. However, depending on the model structure complexity, the model outputs may not always be readily interpretable. Models trained on data from one project or region may be highly specific to those conditions, limiting their generalizability. This section sets out requirements for model training, validation, and spatial applicability that ensure data-driven models used in EW quantification produce estimates that are robust, transparent, and bound to the conditions under which they were developed.

For data-driven models, the model boundary defines what input features the model is trained on, what outputs it predicts, and the range of conditions over which predictions are considered valid (the Area of Applicability). The model boundary must be clearly defined, covering spatial domain (including which constitutive zones are represented and the lateral extent of extrapolation), the temporal domain (start date, maximum prediction horizon, and internal timestep), and the complete set of input variables and output variables including the Protocol quantification term each output maps to. Boundary condition descriptions should not be revised after training begins. Any change to the model domain constitutes a structural revision that requires a full restart of the training or validation procedure and must be documented in the model update report submitted at the next verification.

Data-driven models must be trained on high-quality, representative data. The full dataset used for training and model validation must meet the following requirements:

1. The dataset must include direct measurements from the project area of parameters relevant to enhanced weathering and CO₂ removal calculation, at minimum spanning the following required measurements (see Section 9 for more details):

• Concentrations of immobile tracers and mobile cations in the soil for calculating CO₂ removal. 
• Parameters relevant to weathering: soil pH, soil texture, CEC, base saturation, soil moisture/water content

2. Any data used for training and validation must be from reputable sources and transparently disclosed:

• Data collected by The Project Proponent must follow the sampling and reporting requirements of the Section 9.
• Data not collected by The Project Proponent must be from reputable and well-documented sources, including peer-reviewed published studies, or documented field trials with known and reported experimental designs. 
• Where additional external database values are used, the databases must adhere to the FAIR (Findable, Accessible, Interoperable, and Reusable)²⁶ principles.
• Any data pre-processing, including QA/QC, outlier detection, feature engineering, must be described and code provided so that the final dataset used for training/testing/validation is reproducible from the raw data

3. The dataset must be representative of the full project area and range of conditions over which CDR is being quantified. These represented conditions must include:

• Soil pH
• Soil type
• Crop type
• Feedstock mineralogy
• Particle size distribution
• Application rate 
• Season of feedstock spreading
• Hydrology
• Climate
• Field management practices:
  • irrigation
  • strong acid fertilizer inputs
  • tillage
• The distribution of training data across key input variables must be documented and compared to the conditions at the deployment area. Deployment points that fall outside the model’s Area of Applicability (AoA), which defines the threshold for which predictions are within the model's domain of applicability, are ineligible for crediting. The model may still be used for the remainder of the deployment area where conditions are within the AoA. See Section 9.2 for further details.

This section sets out requirements for model training, validation, and ongoing re-validation. 

Model Architecture and Objective Function

Project Proponents are recommended to train and report results for at least three model architectures drawn from distinct model families (e.g. at least one linear or additive model, one tree-based model, and one neural or kernel-based model), to explore different model structures and identify the best fit for the functional relationship they are trying to fit. The architecture chosen must be documented and justified in the PDD. If a single model architecture is explored and used, Project Proponents must provide justification for why other model architectures are unsuitable. 

Project Proponents must document the objective function that the model is optimized for during training, and this selection must be justified in the PDD. Determination of crediting outcomes in EW is a regression problem. Project Proponents are therefore recommended to use mean squared error (MSE), mean absolute error (MAE), or mean average percent error (MAPE) in their regression algorithm. 

See Section 7 for further model validation requirements. 

The following are reporting requirements specific to data-driven models. Additional requirements for all models are further found in Sections 7 (Model validation), 8 (Uncertainty), and 9 (Monitoring). See Section 10 for more information on what data must be made publicly available.  

• Data used for training and model validation:
  • Overview of the full dataset used for training and validation, including location of monitoring areas, and distributions of parameters. In the scenario of a pretrained model, the pretraining and fine-tuning set must be specified. 
  • The measurement methodology for each training observation must be documented, including measurement type (e.g., soil mass balance, porewater alkalinity), sampling depth, temporal resolution, and analytical techniques used
  • Description of data pre-processing and code
• A description and justification of the model structure, including: 
  • Model architecture
  • Inputs
  • Outputs
  • Time over which the model is applied
• Overview of model development, including:
  • the objective function, with a justification for why that was chosen 
  • An overview of the optimization algorithm 
  • How hyperparameters are tuned
  • Description of how data was split for training
  • Code used in the training such that the trained model can be reproduced
  • Validation metrics (e.g. MAPE, RMSE) on both the training dataset and the test dataset for each model trained, to evaluate model performance and overfitting. See Section 7 for further requirements on model validation.

Process-based and data-driven models each have their strengths and weaknesses. For example, process-based models may incompletely represent all relevant processes or rely on uncertain parameterizations, while data-driven models may have data biases, ignorance of confounding factors and lack generalizability beyond training conditions. Hybrid models are models that integrate components of process-based and data-driven models. The motivation for hybrid approaches stems from the potential to combine the strengths of process-based models, including physical consistency, confidence in extrapolation, and mechanistic interpretability, with the computational efficiency, flexibility, and empirical accuracy of data-driven models. However, we note that performance advantages of hybrid models over single-framework models have not yet been broadly demonstrated in Earth system science or EW quantification, and this remains an area of active research (Reichstein et al., 2019 ²⁷; Razavi et al., 2022 ²⁸). 

The combination of process-based and data-driven models may take shape in many forms. Examples include but are not limited to:

1. Sequential frameworks, where process-based and data-driven models operate in sequence. A process-based model is used to represent the system and capture known process dynamics, while a data-driven model is applied to quantify residual uncertainty, correct systematic biases, or characterize errors in the process-based model output.
2. Modular frameworks, where data-driven and process-based components are used interchangeably within a coupled model structure, with explicit justification for which processes are represented by each model type and how the data-driven Modules relate to the process-based Modules.
3. Embedded frameworks, where mechanistic formulations grounded in physical, biological, or chemical laws are incorporated directly into the architecture or training of a data-driven model. The process-based knowledge serves to constrain the model and fill gaps in process understanding, while preserving the flexibility and extrapolation capacity of the data-driven framework.

These categories are not mutually exclusive, and a single hybrid model may incorporate multiple integration strategies. This Module does not prescribe a specific hybridization framework. This Module allows any defensible combination of process-based and data-driven models, provided the individual model components satisfy the requirements set out in Sections 4 (Process-based model requirements) and Section 5 (Data-driven model requirements). Specifically, process-based components of a hybrid model must meet the requirements for process-based models with respect to process coverage, parameterization traceability and model calibration, while data-driven components must meet the requirements for data-driven models with respect to training data requirements, model architecture, and model development. Furthermore, hybrid models cannot be used outside the Area of Applicability for the data-driven components, see Section 9.2 for details. The hybrid model must meet the same validation, uncertainty, and reporting requirements for all models. 

The development process of hybrid models go beyond standalone development of process-based or data-driven models, because the interactions of the components can introduce errors, order-dependent outcomes, and loss of physical representativeness and consistency if not carefully managed. 

The following are additional requirements for hybrid models:

1. Project Proponents must describe each model development step, as well as clearly stating whether the process-based and data-driven components are calibrated/trained against observations independently, sequentially, or jointly. The chosen strategy must be justified in the PDD.
2. Where model components are developed independently or sequentially, Project Proponents must demonstrate that the components produce physically consistent outputs when joined (e.g. consistent units, conservation of mass), and that the final output is not sensitive to the order in which components were calibrated or trained. Where ordering sensitivity exists, the chosen sequence must be justified and its effect on the final output and uncertainty quantification must be characterized and documented.
3. Project Proponents must document how observational data are partitioned across model development and validation for each component of the hybrid model. Where the same observational dataset is used to calibrate the process-based component and to train the data-driven component, Project Proponents must provide justification that this does not introduce data leakage or lead to overfitting, for example by showing that the data-driven component's performance on held-out data does not degrade when trained on process-based model residuals versus independent observations. Data leakage occurs when there is unintended exposure of validation data to the model during training or calibration, such that the model learns to reproduce validation outcomes rather than generalize to unseen conditions. In sequential frameworks where the data-driven model learns residuals of the process-based model, the use of independent datasets for the calibration and training steps is strongly recommended.

Given that hybrid models introduce coupling between process-based and data-driven components, The Project Proponent must provide detailed end-to-end pipeline documentation. The purpose of this documentation is to demonstrate that the hybrid model, taken as a whole, produces physically meaningful and internally consistent outputs, and that no artefacts are introduced at the interface between model components. 

The following are a list of components that must be included in this document:

• Model architecture: Projects must provide a complete description of the model architecture, including:
  • All model components and sub-components, each clearly identified as either process-based or data-driven, with scientific justification for the approach selected. 
  • The interfaces between components, documenting the variables exchanged, any data transformations applied, and confirmation that units, coordinate systems, and temporal and spatial resolutions are consistent across all component boundaries.
• End-to-end model development and validation: Project Proponents must clearly document the calibration metrics for the process-based components as prescribed in Section 4 and satisfy the requirements of Section 5 for the data-driven components. The end-to-end development and validation must be documented and reported.
• Uncertainty quantification: Project Proponents must document an uncertainty quantification framework for the hybrid model that accounts for the distinct sources, types, and propagation pathways of uncertainty across both process-based and data-driven components. See Section 8 for further details on uncertainty requirements for all models and specific process-based and data-driven components.

All models used under this Module must demonstrate predictive performance on field data collected from the project area that was not used in model calibration or training. Any model that involves empirical fitting with observations, whether process-based, data-driven, or hybrid, is susceptible to overfitting to the data used for calibration or training. Thus, the results of all models must be validated against unseen data. Specifically:

1. Project Proponents must demonstrate that the calibrated or trained model reproduces measured porewater chemistry, soil geochemistry, and other relevant monitoring observations from the project area, on a held-out subset of the monitoring data, to within the validation performance bounds.
2. Where the model is used to predict more than one CDR term (e.g., CO₂e_Weathering, CO₂e_NetSorption, and CO₂e_NetNewCarbonate from a single coupled model), validation must be demonstrated for each predicted term individually. A model that performs well on one term while failing on another is ineligible for crediting on the failing term.

Model validation is the process by which a model's predictive performance is tested against independent, withheld data. It is distinct from model verification, which confirms that the model has been correctly implemented (e.g. that code, databases, and numerical solvers are functioning as intended). The goals of validation are to confirm that:

• For process-based models: the model captures the relevant geochemical and physical processes and produces predictions consistent with observed data under project-relevant conditions
• For data-driven models: the model generalizes to unseen data and produces predictions within the performance thresholds defined in Section 7.3
• For all models: predictions are physically plausible and the estimated uncertainty bounds are consistent with observed prediction errors

Moreover, the validation requirements in this Module are designed to detect overfitting through three checks: 

• Cross-validation across spatial units tests whether the model generalizes beyond the specific data used to train it
• Re-validation at each Reporting Period tests the model against data that did not exist during model development. 
• Deployment area validation tests performance on a broader set of conditions

A model that has overfit to its training data is expected to fail one or more of these checks.

Specific validation requirements and metrics are described in the sections below.

Any component of any model whose parameters are tuned, calibrated, or learned from data must be validated against data that was not used during calibration or training. The subset of data used for calibration or training will be referred to as the training set and the subset of data held-out for validation will be referred to as the validation set. The training set must comprise between 50% and 90% of the available data, with the remainder reserved for the validation set. This split must be repeated across multiple folds to perform cross-validation, ensuring that validation performance is not an artefact of a single favourable split. The splits in each fold must be determined based on baseline measurements only. Cross-validation must be performed, and the following method is recommended:

1. The monitoring area is partitioned into spatial units, such that there are at least three units. Where the monitoring area comprises multiple monitoring sites, each site is a unit. Where the monitoring area comprises one or two monitoring sites, or where sites are spatially extensive, the site(s) must be partitioned into spatial blocks. Block size must be at least equal to the spatial autocorrelation range determined from the empirical variogram of the modelling residuals.
2. Cross-validation is conducted by leave-p-out: in each fold, p units are held out as the validation set, with the remaining units forming the training set. The value of p must be chosen such that p/n ≥ 10%, where n is the total number of units. The number of folds is k_folds = n/p, with each unit appearing in exactly one fold's validation set.
3. Geochemical representativeness of cross-validation folds must be assessed. It is recommended to use the multivariate Mahalanobis distance defined in Equation 10 of the EW Protocol on the fingerprint variables defined in Section 9.2 below. The covariance matrix used in the Mahalanobis distance computation should be estimated from the full set of units across the monitoring area. For each fold, the following checks should be performed:
4. Per-unit envelope check: for each held-out unit i in the validation set, the Mahalanobis distance to the nearest training unit, denoted $D(i, train_{nearest})$, where $D(i, train_{nearest})$ should satisfy $D(i, train_{nearest}) ≤ k · D̄(within, train)$, where $D̄(within, train)$ is the mean pairwise Mahalanobis distance between training units in the fold, and k is the coverage factor specified in Section 10.1.2.3 of the parent EW Protocol (k = 2 by default). Held-out units exceeding this threshold are interpreted as testing model extrapolation rather than interpolation, and should be flagged in the PDD.
5. Distributional representativeness check: where p > 1, the multivariate distribution of fingerprint variables across the held-out units must be statistically representative of the distribution across the training units. The mean Mahalanobis distance from held-out units to their nearest training units, $D̄(held-out, train_{nearest})$, should satisfy $D̄(held-out, train_{nearest}) ≤ k · D̄(within, train)$. Where this distributional check fails, fold composition must be reconstructed through stratified random sampling on the fingerprint variables until the condition is met.

Where temporal autocorrelation is present in the data, the cross-validation approach must also account for this to avoid information leakage between training and validation sets. Project Proponents must document the cross-validation strategy in full, along with the proposed tests for geochemical representativeness. Per-unit validation metrics must be reported alongside aggregate metrics across all folds and aggregate metrics within each fold.

For hybrid models, model validation must be conducted at both the component-level (e.g. the process-based component of the model, and the data-driven portion of the model), and the system-level (i.e. the full hybrid model output). The hybrid model's performance must be reported alongside the performance of its individual components operating as standalone models, to confirm that the hybrid configuration does not degrade performance relative to its components.

1. For component-level validation, each tuned component of the hybrid model is validated individually against its own target variables–e.g. the process-based model and data-driven model components must be individually validated. This is necessary to establish a performance baseline for each component and make sure any degradation or improvement in performance of the model is traceable to whether it is from the individual components or the integration of them.
2. For system-level validation, the model is validated at the level of the final integrated output. Component-level validation alone is not sufficient because individually well-performing components may produce degraded or physically inconsistent results when joined. System-level validation assesses whether the end-to-end pipeline reproduces observed system behaviour across the range of conditions for which the model will be applied.

Project Proponents must report validation metrics on the CDR estimate and any required calibration target variables computed using the held-out validation data. The metrics should be aggregated across all the cross-validation folds. The choice of metrics must be justified and must include, at the minimum, the following:

• Root mean squared error (RMSE)
• Mean bias (mean signed error across all held-out predictions)
• Mean absolute percentage error (MAPE), with documentation of how near-zero observations are handled
• A 1:1 scatterplot of model predictions against observations, with the line of perfect agreement shown

Project Proponents must demonstrate that the model of choice and its performance is adequate for the purpose of CDR quantification for The Project, which must include the following checks:

1. The bias must be less than the pooled measurement uncertainty of the validation observations, defined as the median measurement uncertainty estimated from replicate variability within each site and pooled across sites. Where mean bias exceeds pooled measurement uncertainty, the model must be recalibrated or simplified, or the excess bias must be applied as an additional uncertainty deduction as described in Section 8.
2. The predicted 90% confidence interval, produced from the Monte Carlo iterations described in Section 8, must contain at least 90% of the held-out observations, demonstrating that the estimated uncertainty bounds are consistent with observed prediction errors.

The model must be initially validated on at least 12 consecutive months of data to capture the complete annual cycle of seasonal variation. Models must then be re-validated at each Reporting Period, using updated data collected since the previous Reporting Period. This is to check that the model is still applicable, or whether any project changes, such as changes in site conditions (e.g., feedstock composition, soil properties, climate regime), should trigger a model update. For re-validation, it is sufficient to report the model validation metrics against newly collected data (that has not been used for model development). If the model fails the validation checks, then the model must be re-calibrated and re-trained with the updated data. Project Proponents must document the process by which recalibration is carried out and validated. If the model still fails the validation check, then it is ineligible for use for further crediting. 

A model that has been validated for a given Reporting Period may be used for all claims within that Reporting Period without requiring re-calibration, provided deployment conditions remain within the model's Area of Applicability.

Deployment area validation is a separate and independent check from the cross-validation conducted on monitoring area data. Deployment area validation confirms that the similarity matching process functions as intended, that conditions at deployment areas are genuinely represented by their matched monitoring areas. The goal is not to independently quantify CDR at every deployment location, but to verify that the matching and extrapolation methodology is robust. This must be done at least as part of the first Reporting Period as a safeguard against where the similarity measure might fail to capture meaningful differences between monitoring and deployment areas.

Requirements:

1. Model predictions must be compared against independent field measurements collected from a subset of the deployment area, as defined in Section 9.1.2. These measurements must be derived from concentrations of immobile tracers and mobile cations collected from the deployment area and must not have been used in model training.
2. This must include a minimum of 10% of deployment sites that are withheld entirely from model training so that they can serve as independent validation points. The subset of sampling locations used for model validation will be chosen by Isometric after project and removal area registration.
3. The comparison must include the same validation metrics specified in Section 7, reported for the deployment area subset.
4. Where model performance on the deployment area is consistent with the cross-validation performance (i.e. bias and RMSE are within the ranges observed across cross-validation folds), the deployment area validation is considered to have passed and does not need to be repeated in subsequent Reporting Periods, provided the model version and deployment conditions remain unchanged.
5. Where there is a significant discrepancy between model predictions and deployment area measurements–defined as RMSE exceeding 2 times the cross-validation RMSE–the model must be reassessed and retrained as this indicates that the model performance is significantly degraded in the deployment area and may not be suitable for use. In this scenario the model must be successfully revalidated before used to credit that deployment area.

Uncertainty in the models and measurement-based quantification approach outlined in this Module stems from a number of sources, such as model structural uncertainty and uncertainty in the observations and data used. While exhaustive quantification of all possible sources of model uncertainty is not feasible, this Module requires safeguards including rigorous model validation against field data, transparent reporting, Monte Carlo uncertainty propagation, and conservative crediting to ensure results are robust. 

Uncertainty in process-based model components arises from incomplete knowledge of the system being modeled, imperfect representation of governing processes, and limitations in the data used to parameterize and force the model. 

Process-based models are simplified representations of natural systems and necessarily omit or approximate certain processes. Incomplete knowledge of the system being modeled arises when the model's governing equations do not fully capture the relevant physics, chemistry, or biology. Model structural uncertainty can be assessed in multiple ways, such as:

• Varying parameters within a single model to generate a range of results
• Multi-model comparisons, where the same numerical experiments are run using different core model codes to identify spread and model biases
• Data-model comparisons, which are required as part of model validation in Section 7.

Project Proponents must account for structural uncertainty within a single model in the Monte Carlo uncertainty propagation, by varying model choices such as the thermodynamic database, kinetic rate formulation, and treatment of secondary mineral formation. The structural choices made for each ensemble member must be documented in the PDD and model uncertainty must be accounted for in line with Section 10.1.4.5 of the EW Protocol.

Furthermore, process-based models rely on input data such as meteorological forcing, soil properties, mineral type and composition, and application rates, all of which are subject to analytical and sampling uncertainty. Process-based models also rely on parameters that represent specific properties of a system (e.g., mineral dissolution rate constants, soil hydraulic conductivity, reactive surface area). These parameters are often derived from laboratory measurements, literature values, or site-specific calibration, each of which carries its own uncertainty. Project Proponents must account for analytical, sampling and parameter uncertainty inline with the requirements in Section 10.1.4 of the EW Protocol.  

Uncertainty in data-driven models and model components arises from both observational uncertainty and structural uncertainty in the model itself. 

Observational uncertainty arises from imperfect measurements of the real world, which are used to train models and used as inputs into models for determining CO₂ removal. 

• Training data uncertainty: The CDR or weathering rate observations used to train the model are themselves subject to measurement and sampling uncertainty. Because the model is trained to reproduce these observations, uncertainty in the training outputs is partially absorbed into the model's learned parameters, and partially manifests as increased scatter in predictions relative to held-out observations.
• Input measurement uncertainty: The data used as input into the model at deployment areas (e.g. soil pH, application rate, temperature) are subject to measurement uncertainty. Uncertainty in these inputs propagates through the model into uncertainty in the CDR prediction.

Model structural uncertainty arises because models must make simplifying assumptions for the sake of computational tractability, and represents a model's limitations in representing the true underlying geochemical system.

• Cross-validation parameter uncertainty: Models trained on different subsets of the training dataset will have slightly different learned parameters and may generate different predictions on the same unseen data. This is assessed through the ensemble of models trained during spatial cross-validation (Section 7). 
• Model structural uncertainty: A model may fail to capture the true functional relationship between inputs and CDR, for example, a linear model applied to a non-linear system, or a model omitting a key input variable. Since held-out validation can confirm a model is wrong but cannot rule out misspecification when validation and training data share the same blind spots, this uncertainty is best addressed by exploring an ensemble of structurally distinct model architectures during training. See Section 5.4 for more details.

Uncertainty in CDR predictions for all models must be quantified through Monte Carlo (MC) simulation. The MC simulation must propagate through the model structural uncertainty by randomly selecting a model from the ensemble of models at each MC iteration. This propagates uncertainty arising from the choice of model architecture and its effect on the CDR estimate. Analytical, parameter, and sampling uncertainty must be accounted for in line with Section 10.1.4 of the EW Protocol. It is recommended to use the uncertainty quantification algorithm outlined in Section 10.1.4.4. The MC simulation must be repeated until the resulting CDR estimate and any required calibration target variables vary by less than 1%  (in line with the materiality threshold outlined in the Isometric Standard).

Each model parameter must be either (i) included in the Monte Carlo with a distribution that represents the parameter's full physically defensible range or (ii) substituted with a conservative value at the end of its physically defensible range that produces a lower CDR estimate. All input parameter distributions to the MC must be reported and justified. If the exact distribution is unknown for a parameter, a uniform distribution must be used across the full possible parameter range for conservativeness.

The credited CDR value must be taken from a conservative percentile of the final MC distribution. The 16th percentile must be used as a conservative estimate. Furthermore, the credited CDR value must not exceed the 50th percentile calculated from measurements in the matched Treatment plots, following the quantification approach outlined in the EW 1.2 Protocol. Where mean model bias, as estimated from spatial cross-validation, is positive (the model tends to overpredict CDR), the bias must be subtracted from the final credited value:

CDR_credited = min[p16(MC distribution) − max(bias, 0),  p50(measured treatment)]. 

Project Proponents must report the results of the uncertainty quantification and ensure they are transparent and reproducible. At minimum, the following must be reported:

1. Full probability distribution: Project Proponents must report the full probability distribution of the CDR estimate (e.g., as a histogram or cumulative distribution function), not just a point estimate.
2. Sensitivity analysis results: Project Proponents must report the results of the sensitivity analysis identifying which parameters, inputs, or model components have the greatest influence on the CDR estimate. The sensitivity analysis must cover the full range of conditions under which the model is applied, not only a single reference scenario.
3. Assumptions and distributional choices: Project Proponents must document and justify the probability distribution assigned to each uncertain parameter or input variable in line with Section 10.1.4 of the EW Protocol.
4. Known limitations and unquantified uncertainties: Project Proponents must disclose any sources of uncertainty that are known to exist but could not be formally quantified within the uncertainty framework. This includes model structural uncertainty for example, if only a single model formulation was available and/or processes known to be relevant but excluded from the model, and conditions outside the applicability domain that may be encountered during the crediting period. Project Proponents should assess this impact on the final CDR estimate and take appropriate measures to discount it from the total Credits.

This section outlines the in-field monitoring approach that Project Proponents must take. Project Proponents must quantify the amount of rock spread and carbon dioxide removed using direct measurements of soil geochemistry in a small subset of the project area. These measurements must be used in model training, calibration and validation, and to determine project area heterogeneity.

Project Proponents must maintain two types of sites in their project design:

1. A monitoring area, which represents a small fraction of the total project area in which rock application and carbon dioxide removal will be directly measured and quantified. The monitoring area is densely sampled and analyzed for geochemical and agronomic parameters throughout The Project lifetime. These measurements must be used for model development and validation.
2. A deployment area, which represents the majority of the project area. The deployment area is less densely sampled and monitored for agronomic parameters throughout The Project lifetime and a subset of geochemical parameters at baseline and in the first Reporting Period. These measurements must be used for assessing model applicability and model validation.

Each deployment area must be matched to at least one monitoring area using the similarity framework outlined in Section 9.2. Deployment areas with no sufficiently similar monitoring areas, according to the justified similarity threshold, must be excluded from crediting. Deployment areas should be within a 50 km radius of the monitoring areas to which they are matched to ensure consistency in climate conditions. Project Proponents hosting deployment areas outside of this radius from the matched monitoring area must demonstrate consistency in climatic conditions over their project area. In this case, Project Proponents must identify the climate variables identified for similarity matching and perform statistical similarity measures.

A sampling round must be collected at baseline, prior to rock spreading. Additional sampling rounds must be conducted at the end of the Reporting Period. Project Proponents may perform additional, intermediary sampling rounds during the Reporting Period at their discretion. The minimum required monitored parameters and sampling frequency for each site type are given below in Tables X and Y.

Samples must be taken to the depth of the NFZ as defined in the model.

Project Proponents must maintain at least one monitoring area and are strongly recommended to maintain multiple monitoring areas to better capture the field heterogeneity observed in the deployment areas and because redundancy will increase confidence in the modeled result. Project Proponents may be required to maintain more than one monitoring area per project if the similarity framework outlined in Section 9.2 indicates that the range of field conditions in the deployment area are sufficiently different from what the monitoring area can reasonably cover.

There is no minimum sampling density within the monitoring area. Project Proponents must demonstrate sufficient spatial coverage of the monitoring area through the similarity framework (see Section 9.2). Project Proponents must also demonstrate how a sufficient sampling density was chosen within the monitoring area, including statistical tests used to inform the sampling density. 

The monitoring area must be further subdivided into two plot types: a treatment plot, where feedstock is applied, and a control plot. In each treatment and control plot, the number of independent samples collected at each sampling event must demonstrate adequate statistical power for quantifying uncertainty. It is recommended to determine this using the power and rarefaction analyses described in Section 10.1.2.2 of the EW Protocol, after accounting for spatial autocorrelation as described in Section 10.1.4.3.1. 

In all projects, the area of control and treatment plots in the monitoring area should each total at least a minimum percentage of the total Project area. The project area is the sum of the monitoring and deployment area. The minimum percentages, p, are as follows:

$p = \begin{cases} 2.5\%, & A \le \text{1000 ha} \\ 2.5\% - 1.5\% \times \log_{10}\!\left(\frac{A}{1000}\right), & \text{1000 ha} \lt A \lt \text{10,000 ha} \\ 1\%, & A \ge \text{10,000 ha} \end{cases}$

Equation 3

Where:

• p is the minimum percentage of the project area that must be allocated to each of control and treatment plots within the monitoring area
• A is the total Project area (sum of all Removal Areas), in hectares

Treatment plot

The purpose of the treatment plot is to quantify carbon dioxide removal and gather measurements that will be used in models. Application of feedstock to the treatment area must be uniform. Project Proponents may subdivide the treatment plot of a monitoring area to test multiple application rates. In this scenario, Project Proponents must clearly demarcate boundaries between different application rates, collect a number of samples that demonstrates adequate statistical power to quantify uncertainty, and perform the minimum monitoring requirements listed in Table 2 in each application rate area.

Project Proponents must determine the alkalinity application rate over the treatment area from both operational logs and direct measurement, in accordance with Section 10.4.4 of the Enhanced Weathering in Agriculture Protocol.

Control plot

The purpose of a control plot is to quantify the removal that would have otherwise occurred without the application of rock or mineral feedstock.

Project Proponents may maintain an unamended or business as usual control plot, and state their selection and reasoning in the PDD.

In a business as usual control plot, farmers or Project Proponents must continue to deploy all soil amendments to the project area at the same application rate and frequency that they deployed to their farmland prior to project activities. These soil amendments include pesticides and fertilizers as well as pH amendments such as agricultural lime. In this scenario, any CO₂ removal attributable to agricultural liming can be directly measured in a BAU control plot. In a BAU control plot, carbon dioxide removal must be quantified in the same manner in which it is quantified in the treatment plot, and any CDR from agricultural lime must be subtracted from the net CDR value for The Project. All loss terms are accounted for in counterfactual removals, see Section 8.4.1 of the Enhanced Weathering in Agriculture Protocol for further discussion.

In some project areas it may be operationally infeasible to maintain a business as usual control plot within the project area because the monitoring area control plot is a small fraction relative to the entire project. In this scenario, Project Proponents may instead maintain an unamended control plot, where farmers or Project Proponents do not deploy any soil pH amendments such as agricultural lime. It is not possible to directly quantify counterfactual CDR from lime application in an unamended control plot. Therefore Project Proponents must collect liming records from the past 10 years and assume that the liming rate from the 10 years prior would have continued as the average liming application rate and frequency during The Project lifetime. Project Proponents must then assume either (a) a 100% efficient CO₂ removal processes (i.e., all lime is exported in the aqueous phase as bicarbonate with no losses) or (b) that the loss terms measured in the treatment area also apply to the liming counterfactual. Where option (b) is selected, The Project Proponent must demonstrate that applying treatment-area loss terms does not underestimate counterfactual CDR from liming. Where The Project Proponent cannot demonstrate that applying treatment-area loss terms produces a counterfactual CDR estimate equal to or greater than would be expected under liming conditions, then option (a) must be used. 

Project Proponents must perform a control plot correction in accordance with Section 8.4.1 of the Enhanced Weathering in Agriculture Protocol.

The entirety of the deployment area is treated with feedstock. Application of feedstock to the deployment area must be uniform unless otherwise stated (see Section 10.1.1.6.1 of the Enhanced Weathering in Agriculture Protocol for further guidance on variable application rates).  Soil samples must be collected from the deployment area at a minimum sampling density of 1 sample per 10 hectares. 

The deployment area must be monitored for key agricultural parameters, as defined in Table 3, throughout The Project lifetime. These results may be used as an input to the model. Collection of this data has two additional benefits: (i) to continue to assess that the monitoring area is sufficiently representative of the deployment area at each Reporting Period and (ii) to build an evidence base for using agronomic parameters as an indicator of weathering without direct measurements of feedstock dissolution. Monitoring area representativeness must be assessed at each Reporting Period by re-running the similarity matching framework to determine that it is still valid to extrapolate results from the monitoring area to the deployment area. 

In the first Reporting Period there is an additional set of required parameters, given in Table 4 below, used to satisfy the matching criteria check. These parameters will be used to quantify CDR empirically within a small portion of each deployment area. Project Proponents may choose the location within the deployment area, the total spatial coverage, and the sampling density. The number of independent samples collected at each sampling event from the deployment area must hold adequate statistical power for quantifying uncertainty. It is recommended to determine the number of independent samples using the power and rarefaction analyses described in Section 10.1.2.2 of the EW Protocol, after accounting for spatial autocorrelation as described in Section 10.1.4.3.1 of the EW Protocol. These measurements will be used to quantify gross CDR in the deployment area as a mechanism to confirm that the monitoring area adequately represents the deployment area (see Section 7.5) and to inform future modeling improvements. The median of the measured CDR distribution in the deployment plot must be greater than or equal to P16 of the modeled result determined. Once the matching criteria check is passed, Project Proponents will not be required to analyze deployment area samples for geochemical parameters in subsequent Reporting Periods.

Models can only be applied to deployment areas that are sufficiently represented by the monitoring data used to train or calibrate the model. Representativeness is assessed through two mechanisms: matching of categorical parameters and a quantitative similarity assessment of continuous parameters using the Area of Applicability framework. Each deployment area must be matched to at least one monitoring area in order to be credited using a model based quantification framework. Matching must consider the following parameters, which are described in detail below:

Matching Requirements

The following parameters must be matched between monitoring plots and deployment areas, or demonstrated that they don’t need to be matched because they are: (1) explicitly simulated by a process-based model, (2) explicitly represented as a model input, or (3) homogeneous across the entire project region. Homogeneity can be demonstrated by data showing that the parameter does not vary beyond the measurement uncertainty across the project area, documented in the PDD. Note that there may be additional matching requirements for data-driven models compared to process-based models–this is because process-based models can explicitly simulate processes such as crop growth and particle size evolution, while data-driven models require closer parameter alignment to ensure the trained models are applicable. 

Categorical parameters to match:

• Feedstock type. The feedstock applied at monitoring and deployment areas must have the same mineral type and composition, as this directly controls dissolution rates. Where feedstock is sourced from different batches, The Project Proponent must demonstrate compositional equivalence.
• Mean annual temperature and mean annual precipitation, or seasonal equivalents (e.g., growing-season means) where the model operates at sub-annual resolution. These variables capture the climatic conditions that drive seasonal variation in weathering rates and alkalinity export.
• Cropping system. Models must be trained and applied within the same crop functional type, as crop physiology and rooting behaviour influence soil chemistry and weathering conditions.

Models trained on monitoring data from one category cannot be applied to deployment areas in a different category. 

Similarity-Based Assessment: Area of Applicability

For continuous soil and environmental parameters, representativeness must be assessed quantitatively using a Dissimilarity Index (DI), following the Area of Applicability framework (Meyer & Pebesma, 2021 ²⁹), or similar framework. 

Each monitoring plot and deployment area is characterized by a vector of continuous parameters. This vector should include the following pre-application soil properties:

• Soil pH
• Soil texture 
• Cation exchange capacity (CEC)
• Base saturation
• Application rate, if not explicitly simulated. This is required for data-driven models.

Other non-discrete variables that must be considered in the similarity based assessment include:

• Farm management practices. Tillage regime, irrigation practice, and fertilizer application should be consistent between monitoring and deployment areas, as these affect soil moisture, pH, and mineral–soil contact.
• Feedstock grain class size. The feedstock applied should be within the same Wentworth grain size classification. Grain size is a continuous spectrum, so the Wentworth classification should serve as guidance to establish similarity, but exact matching is not required.

Any additional parameters used as inputs to the model must be considered for inclusion in the similarity assessment.

Project Proponents must document and provide justification for:

• The exact set of variables used to define the vector and how they are scaled
• The distance metric selected to compute similarity
• Any inclusion or exclusion thresholds

The AoA framework, including the choice of variables, distance metric, weights, and threshold, must be provided for review at project validation. At each subsequent verification, the AoA must be reassessed where new monitoring data have been added to the training set or where new deployment areas are claimed for crediting. Deployment areas for which conditions have materially changed since the previous verification (e.g., change in management practice) must also be reassessed.

Recommended approach

The Dissimilarity Index for a deployment point p is defined as the weighted Euclidean distance to the nearest training point in the normalised input space (Meyer & Pebesma, 2021):

DI(p) = min_i √( Σⱼ wⱼ · (xₚ,ⱼ − xᵢ,ⱼ)2 / σⱼ2 )

where xₚ,ⱼ is the value of parameter j at deployment point p, xᵢ,ⱼ is the value at training point i, σⱼ is the standard deviation of parameter j across the training data (used for normalisation), and wⱼ is the weight assigned to parameter j.

Weights may be derived from the feature importances of the trained model, such that parameters with greater influence on model predictions contribute more to the similarity assessment. Where feature importances are not available (e.g., for transparent models without built-in importance measures), equal weights must be used.

The AoA threshold defines the maximum allowable DI for a deployment prediction to be considered within the model's domain of applicability. The threshold is determined empirically from the training data as follows:

• Following a modified version of the approach outlined in Meyer and Pebesma 2021, for each training point, compute the average DI to its nearest 3 neighboring training points not in the same fold (using the same distance metric and weights). Note that this has been modified to use the average DI to the nearest 3 training points as opposed to nearest single point, to reduce the risk impact of an outlier point. 
• The AoA threshold should be set as the 75th percentile + 1.5 x IQR (inter-quartile range) of the training point DI values, following the method of Meyer and Pebesma 2021.

A deployment point with DI exceeding this threshold falls outside the Area of Applicability. Models may not be used for crediting at deployment points outside the AoA. 

The AoA threshold should be computed at project validation using the initial training dataset, and this threshold value is fixed for the duration of The Project unless the model undergoes substantial revision (e.g., retraining with a materially different dataset or change in model structure). When new monitoring sites are added to the training dataset, deployment points are reassessed against the fixed threshold using updated DI values, which may bring additional areas within the AoA as new nearby training points reduce their DI, but the threshold itself does not change. This ensures that deployment areas previously within the AoA cannot retrospectively lose eligibility as the monitoring network expands.

Climatic and Hydrological Representativeness

Climatic variables, such as temperature and precipitation, are strong controls of both feedstock reaction kinetics and the rate of alkalinity export. Where climatic parameters (mean annual temperature, mean annual precipitation) and hydrological characteristics (slope, drainage class) are not included as model inputs, these must be assessed qualitatively for consistency between monitoring and deployment areas. It is recommended that humidity, windspeed, and solar radiation be included in this assessment. The Project Proponent must demonstrate that monitoring and deployment areas are within the same climate zone and have comparable hydrological conditions.

Acceptable climatic and hydrologic data sources include sensors deployed directly in the project site or obtained from the geographically nearest weather station.

To account for in-field heterogeneity, soil samples should consist of multiple soil cores or subsamples. It is strongly recommended that soil samples be composed of 10-20 composited soil cores or subsamples randomly or arbitrarily distributed about a sample coordinate. The overall compositing procedure must be reported and justified in the PDD.

The following parameters must be analyzed at each sampling point in the monitoring area. The sampling density and monitoring frequency should be the same in the control and treated plots of the monitoring area. Deviations in monitoring frequency and sampling density between control and treated plots may be employed on a case by case basis, in consultation with Isometric.

Porewater measurements are not required but are strongly recommended as input parameters for process based models and training data for data driven models to improve quantification accuracy and validate the soil phase method.

Any additional measured parameters used as inputs to the model must also be measured in the monitoring area.

Table 2. Summary of required parameters to be analyzed at each sampling point in the monitoring area.

Deployment area

Table 3. Summary of parameters that must be analyzed at each sampling point in the deployment area. All samples from deployment areas must be taken at a minimum sampling density of 1 sample per 10 ha.

Table 4. Summary of parameters that must be analyzed over a subset of the deployment areas. The number of independent samples collected must demonstrate adequate statistical power for quantifying uncertainty as described above.

This section sets out the documentation, reporting, transparency, public disclosure, and independent review requirements under this Module. These requirements apply to process-based, data-driven, and hybrid models, and to all model components used to quantify CDR terms in Equation 2. Requirements on documentation and reporting are organised by submission stage: project validation (in the PDD), and project verification. In addition, public disclosure requirements are listed separately. 

The purpose of Project Validation is to ensure that The Project design and plan are sufficient to meet the Module requirements. The following must be included in the PDD and provided to Isometric and the VVB as part of Project Validation:

1. Description of Model and Measurements

• A detailed description of the model type (process-based, data-driven, or hybrid) and its scientific basis, including references to peer-reviewed literature on which the model design relies
• The model version or release used, including version numbers for any software, thermodynamic databases, or external libraries on which the model depends
• Source code, including all model configuration files and data necessary to reproduce model calibration/training and validation  
• Description of the model development process, including model boundary description, overview of data used and description of data pre-processing
  • For process-based models or model components, see Section 4
  • For data-driven models or model components, see Section 5
  • For hybrid models, see Section 6
• Description of model simulation setup and quantification approach, including initial conditions.
• Description of the model validation approach, see Section 7 for more details
• Description of the uncertainty quantification approach, including the method used to propagate parameter uncertainty into the final CDR estimate, see Section 8 for more details
• Description of monitoring plan, see Section 9 for more details
• Data collection and storage approach, description of how data is transmitted, collected, stored, archived, and backed up.

2. Model development and re-validation plan

• A model re-validation and update plan must be provided describing how the model will be maintained over the crediting period. Note that re-validation is required at every Reporting Period, see Section 7.4 for more details.  
• The model update plan must describe anticipated directions for model development, such as planned improvements to process representation, incorporation of additional data sources, or changes to calibration approach. While this description does not need to represent a formal commitment, Project Proponents are encouraged to communicate planned changes to Isometric as early as possible to facilitate review. Any changes to the model that affect CDR quantification must be documented and re-validated.

The following must be reported to Isometric and the VVB as part of Project Verification: 

1. Model validation results

• The results of model-data comparisons must be provided, including the data sets used for validation as well as model results. 
• Intermediate model results must be provided to enable verification of component-level validation. See Section 7 for more details.

2. CDR Quantification and model results

• The final CDR estimate for the Reporting Period, including uncertainty propagation
• Source code, including all model configuration files and inputs necessary to reproduce the CDR estimate as well as the uncertainty propagation

3. Model update (if applicable)

• Where the model has been recalibrated or structurally revised since the previous verification, a model update report must document the changes made, the new validation results, and the scientific justification for the revision.

Model transparency spans several dimensions including the accessibility of source code and documentation, the interpretability of model outputs, the disclosure of underlying data and assumptions to the public, and the choice of model type used for quantification. Open-source models are strongly recommended. An open-source model publicly provides the source code, configuration files, parameter values, and dependencies under a license that permits independent review and replication. Proprietary models do not publicly provide the information needed for independent review and replication. Proprietary models are permitted under this Module but will require an additional independent expert panel review to ensure the model can be fully interrogated.

The full model description in the PDD will be made publicly available through Isometric and is subject to the same public consultation period required for all PDDs prior to Project Validation. 

The following subset of information submitted for Project Validation and Verification must be made publicly available and hosted by Isometric. At minimum, this must include:

• A Plain-Language Model Description
• All training, calibration, and validation datasets, or, where data sharing is restricted by third-party agreements, documented procedures for accessing the data
• Model inputs and outputs, including the model outputs and the full probability distribution from the Monte Carlo uncertainty propagation used for credit issuance
• Summary validation statistics, including the metrics specified in Section 7.3 (Model validation requirements): RMSE, mean bias, MAPE, and a 1:1 scatterplot of model predictions against held-out observations

Additional disclosure may be required where the Independent Expert Panel determines that the publicly available information is insufficient to assess scientific defensibility, or where Isometric determines that disclosure is necessary to maintain transparency.

To facilitate accessibility, transparency and interoperability of research relevant data, data collected from projects used to train and validate models must adhere to FAIR (Findable, Accessible, Interoperable, and Reusable) ²⁶principles.

An Independent Expert Panel may be involved during the review of proprietary models as part of project validation and at the first verification. Subsequent verifications require Expert Panel review only where the model has undergone structural revision since the most recent panel review. 

Panel Composition

Isometric will select the members of the expert panel for each project requiring an Independent Expert Panel. Panel composition must include at least one expert in the modeling approach used (process-based, data-driven, or hybrid) and at least one expert in ERW field science. 

The Project Proponent must, at the time of panel appointment, identify or suggest any member with whom they have a conflict of interest and request recusal. Conflicts of interest include but are not limited to direct financial relationships, prior employment, ongoing collaboration, or any other relationship that could reasonably impair independent judgment. 

Scope of Review

The Independent Expert Panel review must cover:

• The scientific basis of the model and its suitability for use in the deployment region
• The model description, including its accuracy, completeness, and clarity
• The full model code, calibration logs, parameter values, and training and validation datasets, provided under confidentiality
• The validation results and uncertainty quantification framework
• The Area of Applicability and matching framework

The Panel's review report and decisions will be incorporated into, and made publicly available as part of, the verification and validation report.

This document is a companion to v1.0 of the Model and Measurement based Quantification of Enhanced Weathering Module, providing supporting information around the development of  this module and the considerations behind it. This guidance document should be read in conjunction with the module. Should there be any discrepancy or inconsistency between this companion document and the module itself, the requirements of the module will prevail. 

There is broad agreement that models will play an important role in quantifying Enhanced Weathering (EW) as the pathway scales. Field measurements alone cannot, in the long run, support the spatial coverage and temporal density needed to verify CDR at the scale the carbon market requires. Models offer a path to bridging this gap. The development of such models, and the underlying data collection they depend on, is a multi-year process. This module has been created to give project developers the guidance they need now on how to design their deployments and data collection programs to support the development of rigorous models for EW quantification. 

There are methodologies already in use that permit models for EW quantification with only limited requirements on validation, transparency, or uncertainty quantification. To prevent premature and inappropriate model usage we must articulate what rigorous model-based quantification requires, so it is clear when a model does not meet that bar. Without a high standard to converge on, there is a risk that the field defaults to weaker existing guidance. 

This module sets a deliberately high bar as we believe it’s important for the EW ecosystem to coalesce around a rigorous target for the field.

This module sits under the EW Protocol and will add an alternative quantification option approach to the EW Protocol. Fundamentally, this module does not replace measurements with models. The module requires direct field measurements to constrain and continuously validate any model used for quantification. Projects using this module must maintain the same minimum area requirements for control and treatment plots as outlined under v1.2 of Isometric’s EW Protocol. This ensures parity with the measurement-based approach in the densely sampled monitoring area, provides sufficient data for model calibration and ground-truthing, and enables direct comparison between quantification approaches during the early stages of model adoption. It also provides a fallback: if a model fails validation, the measurement-based data from the treatment and control plots remains available for quantification.

Model development for EW is at an early stage, and no existing model–whether it be a process-based model (e.g., multicomponent reactive transport models) or data-driven model–may yet meet all module requirements. This module is intended to set a direction of travel for the field, and we expect it to evolve as the science advances and as we learn from early model submissions.

Our approach is to set stringent model validation requirements, based on demonstrated model performance against measured outcomes. All models must be initially validated against a minimum of one full year of field data to capture seasonal variation. Re-validation is then required at every subsequent reporting period using newly collected data, providing a continuous check on model performance as weathering and site conditions evolve over time. 

The module also requires cross-validation across spatial units to assess model generalization and prevent cherry-picking a favorable validation split. Furthermore, deployment area validation confirms the matching between treatment and deployment areas and that the model generalizes beyond the monitoring sites where it was developed. Models that do not meet this criteria are ineligible.

Model and data transparency are crucial for building trust and advancing the field. In alignment with the Isometric Standard, the module requires public disclosure of all model documentation, inputs, outputs, underlying data and assumptions, and validation results. We strongly recommend the use of open-source models supported by peer-reviewed publications. 

Where a project developer uses a proprietary model, the full model code and code used for calibration or training must be made available to Isometric, the Validation and Verification Body (VVB), and an independent expert panel for review. The expert panel provides a rigorous independent check while respecting commercial sensitivities around the development of proprietary models.

The module requires uncertainty quantification through Monte Carlo simulation, propagating analytical, parameter, and input data uncertainty simultaneously. The credited carbon dioxide removal (CDR) value is conservatively taken at the 16th percentile of the resulting distribution. 

As an additional safeguard, predictions are capped at the 50th percentile of the measured CDR from the treatment plot. This ensures that the model-based approach cannot exceed what the direct measurements support, anchoring predictions to observed measurements.

As with all Isometric protocols and modules, the Model and Measurement Based Quantification of Enhanced Weathering Module will be updated as the science advances. It does not attempt to address every open question, and there are many areas we are interested in exploring for future revisions, including: the development of external benchmarking frameworks for EW models, refining quantitative thresholds for model validation metrics, and considering system-level accounting approaches that look at the carbon balance beyond the near-field zone. 

The 30-day public consultation period is an opportunity for the ecosystem to stress-test this module, and we welcome your comments.

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