River and Ocean Losses

1.0 Introduction

This module outlines the requirements for quantifying loss of alkalinity and/or CO₂ to the atmosphere due to natural processes occurring in rivers and oceans, for Carbon Dioxide Removal (CDR)pathways that enhance alkalinity in the natural Earth system. Alkalinity represents the capacity of water to neutralize acids, dominated by bicarbonate (HCO₃^-) and carbonate (CO₃^2-) ions in natural waters. The efficacy of carbon dioxide removal (CDR) methods that rely on alkalinity enhancement in the Earth system is dependent on the transport of that alkalinity through river networks to the ocean. As alkalinity-rich water traverses from rivers to the ocean, stored carbon can be lost from the system through two chemically distinct classes of processes: (i) reductions in alkalinity itself, primarily through removal of HCO₃⁻ and CO₃²⁻ as CaCO₃ in stoichiometric balance with a cation; and (ii) reductions in DIC at conserved alkalinity, primarily CO₂ outgassing during re-equilibration of the carbonate system. The specific relevant processes are:

• Carbonate mineral precipitation (inorganic or biologically mediated)
  • Inorganic: in rivers and estuaries, the change of pH and carbonate saturation state may lead to inorganic carbonate precipitation^1,2,3,4. This process consumes HCO₃^- and CO₃^2- ions, reducing alkalinity.
  • Biologically mediated: calcifying organisms (biota that make their shells from carbonate minerals) in estuaries and oceans consume alkalinity through CaCO₃ formation.⁵
• CO₂ outgassing
  • When CO₂ degasses, for example from turbulent water flows or photosynthesis-driven low pH conditions, the equilibrium of the carbonate system shifts, and HCO₃^- and CO₃^2- can convert to CO₂. Because H⁺ is consumed in equal stoichiometry, alkalinity is conserved, but DIC is reduced as CO₂ is released to the atmosphere.
• Changes in natural alkalinity fluxes
  • Additional alkalinity from a CDR Project can suppress natural alkalinity release from sediments (normally driven by CaCO₃ dissolution), reducing the net gain of alkalinity in riverine and coastal systems.⁶

This Module standardizes the quantification of these loss processes across CDR pathways that enhance alkalinity in aquatic and hydrologic systems (groundwater, rivers, and the ocean), ensuring a consistently rigorous standard in how river and ocean losses are quantified and reported. This Module will be adapted as science evolves and will be reviewed regularly following the cadence set out in the Isometric Standard.

Throughout this Module, use of the word "must" indicates a requirement, whereas "should" indicates a recommendation.

2.0 Applicability

This Module applies to Projects that enhance alkalinity in the Earth system, such as through one of the following Protocols and/or Modules:

• Enhanced Weathering in Agriculture Protocol
• Open System Ex-situ Mineralization Protocol
• River Alkalinity Enhancement Protocol
• Wastewater Alkalinity Enhancement Protocol
• Electrolytic Seawater Mineralization Protocol
• Ocean Alkalinity Enhancement from Coastal Outfalls Protocol
• Direct Ocean Capture and Storage Protocol
• Enhanced Weathering in Closed Engineered Systems Module

All GHG accounting and quantification of net carbon removal that occurs upstream and downstream of river and ocean losses must be carried out according to one of the Protocols and/or Modules listed above.

2.1 Eligibility Criteria for River Transport

This Module employs simplified assumptions for river transport and biogeochemistry to quantify losses in river transport. The eligibility criteria below define when these simplifications may be applied and when more detailed modeling is required.

Eligibility criteria applicable to all projects:

• Desert basins, closed lake systems, and ephemeral rivers that sink into karst or alluvial fans before reaching the coast are ineligible. These systems lack a continuous hydrologic pathway to the ocean, and durable storage of dissolved inorganic carbon cannot be assured.
• Dosing at locations with downstream wastewater treatment facilities discharging directly into rivers is eligible subject to Isometric and VVB approval.

For diffuse-input pathways:

For diffuse-input pathways (Enhanced Weathering in Agriculture, Open-System Ex-situ Mineralization), a single-mixing-point calculation using the default Isometric river loss model (Section 4.1.5) is permitted regardless of transit time, provided the mixed solution represents conditions at the point of entry of dissolved weathering products into the river network. Loss processes in soils and groundwater prior to river entry are quantified under the respective Protocol. Project Proponents using diffuse-input pathways are recommended to assess whether conditions along the river reach change substantially and to use a longitudinal assessment where this is the case.

The river transit time for losses is determined from where removal quantification ends in the respective Protocol to the river mouth.

• For example, in WAE (Wastewater Alkalinity Enhancement) or Enhanced Weathering in Closed Engineered System Projects, this is from the discharge point to the river mouth, as removal quantification is calculated within the closed system prior to discharge.
• RAE (River Alkalinity Enhancement) Projects are required to directly measure river conditions downstream of initial mixing, so river losses and river transit time for losses apply from the last monitoring station for quantification to the river mouth.

Projects that do not meet the default model validity conditions must instead use a longitudinal river loss assessment, such as a reactive transport model, sequential multi-point equilibrium calculation, or equivalent approach that represents loss processes at locations along the flow path where water chemistry changes significantly. The longitudinal assessment must meet the requirements in Section 4.1.6 (Alternative River Transport Model Requirements).

River eligibility must be demonstrated based on evidence. Examples of accepted evidence include:

• Hydrologic gauge records or regional discharge models
• Publicly available surface-water storage volume datasets
• Established hydraulic routing or residence-time calculations
• Direct tracer studies are accepted as supporting evidence but are not required

If a Protocol has its own river eligibility criteria, the Protocol overrides this Module’s eligibility criteria.

3.0 Relevant Loss Processes

[Image: Figure 1]

Figure 1 Flow chart for a Project to determine which subset of losses are required to be considered.

3.1 Coastal Discharge

The treatment of losses from Projects with coastal discharge will differ based on whether the effluent has equilibrated with the atmosphere or not prior to release into the ocean. This distinction determines which loss processes are applicable, and how the losses are applied during quantification of gross CDR.

3.1.1 Point-Source Coastal Discharge with Subsequent Air-Sea CO₂ Uptake

In Projects where the effluent is not equilibrated with the atmosphere prior to discharge, CO₂ removal occurs after discharge in the ocean through air-sea gas exchange. This scenario applies to pathways such as Ocean Alkalinity Enhancement (OAE) and Direct Ocean Capture and Storage (DOCS). For these Projects, losses of alkalinity and/or DIC upon discharge will impact the air-sea CO₂ drawdown potential, and must be quantified or demonstrated to be negligible prior to using the Air-Sea CO₂ Uptake Module.

These Projects must include the following ocean loss processes:

• Inorganic carbonate precipitation (Section 4.2.2)
• Natural alkalinity flux reduction (Section 4.2.3)
• Changes to biotic calcification (Section 4.2.4)

3.1.2 Point-Source Coastal Discharge Without Subsequent Air-Sea CO₂ Uptake

In Projects where the effluent is equilibrated with the atmosphere prior to discharge, CO₂ is removed and quantified upstream of discharge. This scenario is relevant for pathways such as Electrolytic Seawater Mineralization (ESM), Enhanced Weathering in Closed Engineered Systems with ocean outfalls, and Wastewater Alkalinity Enhancement (WAE) with ocean outfalls. Subsequent losses upon entering the ocean must be quantified and deducted from gross carbon removal or robustly justified as negligible.

These Projects must include the following ocean loss processes:

• Re-equilibration of the carbonate system upon entering the ocean (Section 4.2.1)
• Inorganic carbonate precipitation (Section 4.2.2)
• Natural alkalinity flux reduction (Section 4.2.3)
• Changes to biotic calcification (Section 4.2.4)

3.2 Terrestrial Discharge

Projects with terrestrial discharge include pathways such as Enhanced Weathering in Agriculture (EW), Open-System Ex-situ Mineralization (OSEM), and River Alkalinity Enhancement (RAE) or other Projects (such as Enhanced Weathering in Closed Engineered Systems and Wastewater Alkalinity Enhancement) that discharge directly into rivers. These pathways include removing and storing CO₂ as Dissolved Inorganic Carbon (DIC) in porewater and/or receiving ground and surface waters which are eventually transported to the ocean for long term storage. Losses of CO₂ may occur along the entire transport pathway from groundwater to rivers to the ocean. Accordingly, potential losses must be evaluated at each stage: within the soil profile to the water table, during groundwater transport, during riverine transport, and upon entering the ocean.

3.2.1 Diffuse Runoff

CO₂ removed from pathways such as Enhanced Weathering in Agriculture (EW) or Open-System Ex-situ Mineralization (OSEM) is transported to rivers through runoff such as soil flow, surface runoff, lateral flow, and groundwater baseflow. This can collectively be represented as a diffuse discharge into rivers. This Module focuses on losses that occur in rivers and oceans only. Please see the relevant Protocols for details on quantifying losses in soils and groundwater (Enhanced Weathering in Agriculture Protocol).

These Projects must include the following loss processes:

River Losses

• Transport river losses
  • Re-equilibration of the carbonate system (Section 4.1.1)
    • This may be omitted if pH > 6 is maintained from the point of discharge into the river to the ocean.
  • Inorganic carbonate precipitation (Section 4.1.2)

Ocean Losses

• Re-equilibration of the carbonate system upon entering the ocean (Section 4.2.1)

3.2.2 Point-Source River Discharge

Pathways with direct river discharge may include River Alkalinity Enhancement (RAE), Wastewater Alkalinity Enhancement (WAE) Projects and Enhanced Weathering in Closed Engineered Systems Projects.

These Projects must include the following losses:

River Losses

• Re-equilibration of the carbonate system (Section 4.1.1)
  • This may be omitted if pH [math: \gt] 6 is maintained from the point of discharge to the river to the ocean.
• Inorganic carbonate precipitation (Section 4.1.2)
• Natural alkalinity flux reduction (Section 4.1.3)
• For RAE projects only: Additional (bio)geochemical sinks of alkalinity (Section 4.1.4)

Ocean Losses

• Re-equilibration of the carbonate system upon entering the ocean (Section 4.2.1)

4.0 Quantification of Losses

Sections 4.1 and 4.2 below outline the specific requirements and recommendations for each of the different loss processes in rivers and oceans. Much of the existing research in these losses have been motivated by research in Enhanced Weathering, River Liming, and Ocean Alkalinity Enhancement, which may not exactly simulate the carbonate chemistry state of the effluent from the different project types that this Module is applicable to. It is recommended that Project Proponents conduct additional site-specific studies to optimize loss estimates and research on the relevant carbonate chemistry parameters for their particular process conditions.

The total retention factor is the product of the retention factors associated with each loss process:

[math: \eta_{\text{Total}} = \eta_{\text{River}} \cdot \eta_{\text{Ocean}}]

(Equation 1)

Where:

• [math: \eta_{\text{Total}}] is the total retention factor for all relevant river and ocean loss processes. This factor is dimensionless with values between 0 and 1, and is applied to the gross CO₂ removed.
• [math: \eta_{\text{River}}] is the overall river retention factor, representing the fraction of CO₂ retained after considering all relevant loss processes that occur in the river. This factor is dimensionless with values between 0 and 1.
• [math: \eta_{\text{Ocean}}] is the overall ocean retention factor, representing the fraction of CO₂ retained after considering all relevant loss processes in the ocean. This factor is dimensionless with values between 0 and 1.
• A retention of 1 means 100% of the CO₂ is retained (i.e. no losses), and a retention of 0 means none of the CO₂ is retained for durable storage (i.e. all lost).

If the Project does not transit through any rivers, then the [math: \eta_{\text{River}}] term is ignored and Equation 1 is [math: \eta_{\text{Total}} = \eta_{\text{Ocean}}].

Marginal definition of retention factors

All retention factors in this Module are defined on a marginal (project-attributable) basis. Each [math: \eta_i] represents the fraction of the project-added DIC retained for durable storage, relative to what would have occurred in the absence of the Project. In general, net CDR is conceptually quantified as [math: CDR_{Net} = ΔCDR_{gross} × η_{Total},] where [math: ΔCDR_{gross}] is the project-attributable gross removal ([math: CDR_{gross,\ project} − CDR_{gross,\ counterfactual}]). See the relevant Protocol for the specific formulations of the net CDR calculations. 

There are two permissible approaches to computing a marginal [math: \eta_i]:

• Baseline-chemistry approach ([math: \eta_{baseline}]): [math: \eta_{baseline}] is computed from the sensitivity of the loss process to a small perturbation evaluated at baseline river or ocean chemistry (for example, ∂DIC/∂Alk at baseline ocean state). This is valid in the infinite-dilution limit, where the project signal is rapidly diluted and does not materially alter local chemistry. Because the sensitivity is evaluated at baseline, it is inherently marginal and captures only project-attributable loss. This regime applies to diffuse-input pathways (EW, OSEM) and to ocean re-equilibration across all pathways.
• Dual-run marginal approach ([math: \eta_{marginal}]): For point-source discharge into rivers where the project may materially alter local chemistry (e.g., RAE, WAE, Enhanced Weathering in Closed Engineered Systems with river outfalls), near-field chemistry can cross kinetic thresholds for carbonate precipitation or CO₂ outgassing that are not captured by baseline-chemistry methods. In these cases, [math: \eta_{marginal}] must be computed by running the loss model twice — once on the counterfactual scenario, once on the project scenario — and taking the difference. See Section 4.1.5 and Appendix 1 for more details. 

Note that [math: \eta_{marginal}] converges to [math: \eta_{baseline}] in the limit of infinite dilution. 

4.1 Riverine Losses

This section includes an overview of riverine loss processes and how to quantify them.

[math: \eta_{\text{River,\ RP}} = \prod_{i=1}^N \eta_i]

(Equation 2)

Where:

• [math: \eta_{\text{River,\ RP}}] represents the total fraction of CO₂ removal retained upon reaching the river mouth before entering the ocean, dimensionless value between 0 and 1
• [math: \eta_i] is the fraction of CO₂ removal that is retained after a given loss process, [math: i], dimensionless value between 0 and 1
• [math: N] is the total number of loss processes

Note that for RAE Projects, [math: \eta_{\text{River}}] represents the losses from the last carbonate chemistry monitoring station to the river mouth. For all other Projects, [math: \eta_{\text{River}}] represents the losses occurring upon entering the river and during transport to the river mouth.

This section covers the following riverine loss processes:

1. Re-equilibration of the carbonate system
2. Inorganic carbonate precipitation
3. Natural alkalinity flux reduction
4. Additional (bio)geochemical sinks of alkalinity

Note that not every process above is applicable to every Project. See Section 3 to determine the list of relevant processes for a specific Project.

Background

In rivers, total alkalinity (TA), which represents the acid-neutralizing capacity of the water, is dominated by bicarbonate and carbonate ions: TA [math: \approx] HCO₃^- + 2CO₃^2-. The addition of alkalinity from CDR Projects with terrestrial discharge may shift these equilibria, consuming protons (H⁺) and increasing the pH. This, in turn, shifts the speciation of DIC away from dissolved CO₂ and towards bicarbonate HCO₃^- and carbonate CO₃^2-, increasing the water's capacity to hold inorganic carbon. This increased "buffer capacity" is the central mechanism of alkalinity-based CDR.

Natural river systems are rarely in equilibrium with the atmosphere. Due to the influx of CO₂-rich groundwater and the respiration of organic matter within the river channel and its floodplain, many of the world's rivers are naturally supersaturated with respect to atmospheric CO₂^7,8. This means the partial pressure of CO₂ (pCO₂) in many rivers is higher than that of the atmosphere, making them natural sources of CO₂ outgassing to the atmosphere^9,10. Equilibrium assumptions should be applied conservatively when used to simplify the dynamics of gas exchange and mineral precipitation.

4.1.1 Re-Equilibration of the Carbonate System

Concept

Equilibrium speciation of DIC is primarily dependent on pH, and to a lesser extent temperature, salinity and pressure as shown in Equation 3.

[math: \text{CO}_2 + \text{H}_2\text{O} \leftrightarrow \text{H}_2\text{CO}_3 \leftrightarrow \text{H}^+ + \text{HCO}_3^- \leftrightarrow 2\text{H}^+ + \text{CO}_3^{2-}]

(Equation 3)

The release of CO₂ due to re-equilibration of DIC may occur due to mixing of fluids with different pH. This may occur upon initial dosing of alkalinity into a river, when groundwater enters a river, and at river confluences. The extent and rate of re-equilibration are highly site and project specific, depending on local water chemistry, hydrodynamic conditions, and effluent characteristics. If river gas transfer velocity is high, re-equilibration can be rapid. Conversely, in deep, slow-flowing, large rivers, the gas transfer velocity is much lower, and the water may travel for hundreds of kilometers without fully equilibrating with the atmosphere. Hydrology and pH are therefore both key variables controlling the potential for degassing losses.

Quantification

• For freshwater with pH ≥ 6, the carbon-capture retention factor based on enhanced alkalinity, defined as [math: d[DIC]/d[Alk]], is approximately equivalent to or higher than that of the ocean (Figure 2 adapted from Bertagni and Porporato (2022)¹¹). In these cases, only losses of DIC due to inorganic carbonate precipitation will reduce carbon storage below the final ocean retention factor.
• However, for freshwater pH [math: \lt] 6, [math: d[DIC]/d[Alk]] is less than the final ocean values (Figure 2). Outgassing during freshwater transport must be quantified in this scenario as it would not be captured by using the final ocean efficiencies alone.

Therefore, the pH [math: \lt] 6 threshold serves as a safeguard against over-crediting carbon removal.

When quantification is required (pH [math: \lt] 6), there are two contexts in which outgassing may occur:

1. Initial mixing zone outgassing: Upon initial mixing of effluent with the receiving water body, rapid changes in water chemistry can drive CO₂ outgassing. The recommended quantification approach is to use a two-endmember mixing model to estimate the DIC of the effluent and ambient water mixture. The difference between the measured DIC of the effluent and the calculated DIC of the mixture represents the the loss from CO₂ outgassing, with additional loss occurring from carbonate precipitation. Isometric provides a default river loss model to quantify this, see Section 4.1.5.
2. Outgassing during transport: Equilibrium models provide a conservative and generally acceptable framework for representing riverine CO₂ outgassing because they treat rivers as a series of batch reactors during downstream transport (see Section 4.1.6 for requirements for river transport models). However, in some river systems—particularly those with long residence times, shallow depths, or turbulent flow conditions, outgassing can occur as water travels toward the ocean. This is particularly relevant where the gas transfer velocity is high relative to travel time because these are conditions under which equilibrium assumptions may oversimplify CO₂ losses. In such cases, inclusion of kinetic processes, such as gas transfer velocity, flow regime, and transport time between discharge and ocean delivery, can provide a more accurate assessment of DIC loss via CO₂ evasion¹².

Alternative quantification approaches may be used if they can be demonstrated to accurately capture the carbon losses under site-specific conditions.

[Image: ACE]

Figure 2 Alkalinization Carbon-capture Efficiency (ACE), defined as [math: d[DIC]/d[Alk]], as a function of pH for natural waters. Figure is adapted from Bertagni and Porporato (2022)¹¹ Figure 1. For seawater of 15[math: \degree]C and an average ocean pH of 8.1, [math: d[DIC]/d[Alk]] is approximately 0.84, which is equal to the freshwater ACE at pH 6.

4.1.2 Inorganic Carbonate Precipitation

Concept

Secondary precipitation of carbonate minerals is a pathway for carbon loss. Typically secondary precipitation of calcium/magnesium carbonate, such as calcite (CaCO₃), magnesite (MgCO₃), and dolomite (CaMg(CO₃)₂) could cause CO₂ outgassing by the following reaction as shown in Equation 4:

[math: \text{Ca}^{2+} + 2\text{HCO}_3^- \rightarrow \text{CaCO}_3 + \text{CO}_2 + \text{H}_2\text{O}]

(Equation 4)

Calcium carbonate precipitation may result in a reduction in carbon loss up to 50% for non-carbonate feedstocks or up to 100% for carbonate feedstocks. This is because for every mole of calcite precipitated, two moles of alkalinity are consumed, and one mole of CO₂ is released. The thermodynamic potential for this reaction to occur is described by the calcite saturation index (SIc) as shown in Equation 5 and Equation 6:

[math: SI_c = \log_{10} \frac{\alpha_{Ca^{2+}} \times \alpha_{CO_3^{2-}}}{K_{sp(calcite)}}]

(Equation 5)

With:

[math: K_{sp(calcite)} = \alpha_{sat,\ Ca^{2+}} \times \alpha_{sat,\ CO_3^{2-}}]

(Equation 6)

Where:

• [math: \alpha] is the measured solution activities of those ions
• [math: \alpha_{sat}] is the ion activity at saturation

When [math: SIc \geq0] the effluent is supersaturated and precipitation is thermodynamically favorable. However, a crucial distinction must be made between thermodynamic favorability and kinetic reality. The precipitation of calcite from solution is often kinetically inhibited, meaning it does not occur instantaneously even in supersaturated waters. Many natural river systems maintain a state of supersaturation [math: SIc \geq1]^13,14,15 without significant precipitation occurring. Some studies suggest that extensive, rapid precipitation may only be triggered at a much higher kinetic threshold, such as when the saturation state (Ω) exceeds a value of approximately 10, or higher in some instances^16,17. Relying solely on the thermodynamic threshold ([math: SIc \geq0]) to predict loss could therefore lead to a significant overestimation of carbonate precipitation. Kinetics and the presence of other elements can inhibit precipitation even at higher saturation states. Laboratory experiments simulating local water conditions can be used to bolster predictions of precipitation risk during river transport.

The kinetics of precipitation are also strongly influenced by the availability of nucleation sites. In rivers and coastal areas, higher suspended particulates may increase nucleation. Early research suggests there is a relationship between increased alkalinity loss with higher TSS (Total Suspended Solids) in the receiving water body¹⁸. Thus, the risk of secondary precipitation is most pronounced in the near-field zone near the discharge site, where the carbonate chemistry and TSS perturbation are largest. Limiting pH and the saturation state has been shown to be effective at avoiding this result, and laboratory research to characterize the critical thresholds that trigger precipitation under close-to-natural conditions are ongoing^{19,20,21,22,23}. Furthermore, precipitation dynamics occur on a timescale between minutes to hours^19,21, which suggests that dilution could be an effective risk mitigation strategy²⁴.

Quantification

An example recommended quantification strategy is to employ a simple two-endmember mixing simulation using PHREEQC to quantify the risk of losses. River water chemistry data (pH, temperature, Ca²⁺, Mg²⁺, Na⁺, K⁺, SO₄^2-, Cl^-, NO₃^-, PO₄^3-) collected at nearfield monitoring stations are mixed with the Project's effluent to calculate carbonate speciation and calcite saturation state. The model simulates the mixing of these two waters at various ratios to predict the resulting chemistry of the plume. While PHREEQC can model both equilibrium and kinetic precipitation, the default approach assumes instantaneous equilibrium for carbonate mineral precipitation as a conservative estimate of maximum potential loss. Alternatively, Projects may use kinetic rate laws for calcite precipitation (based on saturation state, surface area, and temperature) to more accurately represent precipitation dynamics in flowing river systems where residence time may limit precipitation. Ultimately, the model should focus on potential calcite precipitation and changes in total inorganic carbon (TIC). This allows Projects to determine if the mixed solution will exceed critical thresholds for pH or the calcite saturation ([math: SIc] > ~1, or site, flow and kinetic specific value), thereby quantifying losses. See Isometric’s default river loss model in Section 4.1.5.

By default, this Module assume that precipitation occurs when the saturation index [math: SIc] = 0 (thermodynamic saturation). This default is conservative and it treats the system as precipitating at the onset of thermodynamic favorability, neglecting kinetic inhibition and is universally applicable without site-specific calibration. Projects accepting this default face no additional modeling or justification burden. The Isometric default river loss model in Section 4.1.5 implements this default threshold.

However, Project Proponents may adopt a higher precipitation threshold where kinetic inhibition of precipitation is expected under the Project's site conditions. Critical Ω values reported in the literature span a wide range (~1 in Ringham et al. 2024; ~1.2 in Moras et al. 2022; ~1.5 in Suitner et al. 2024), and these are lab-scale observations whose translation to specific river systems depends on site-specific factors, TSS and nucleation site availability, inhibitor concentrations (Mg²⁺, DOC, phosphate), temperature, residence time, and flow regime.

Projects may adopt the modeling/quantification approach most appropriate to capture the precipitation dynamics of their specific system. This include but not limited to:

• Equilibrium-based quantification (Isometric default model, Section 4.1.5);
• Kinetic rate-law-based modeling;
• Avoidance-based approaches where Projects design operating conditions (pH, TA, [math: SIc]) to keep precipitation risk negligible, demonstrated through monitoring.

4.1.3 Natural Alkalinity Flux Reduction

Concept

A Project that artificially increases the alkalinity and [math: SIc] of the water column can potentially reduce or reverse the natural alkalinity flux from marine or river sediments²⁵. Furthermore, if the overlying water becomes supersaturated, precipitation could occur on the sediment surface. This suppression of a natural alkalinity source in the river system reduces the additionality of the CDR Project and constitutes an effective alkalinity loss that must be considered.

This risk may be exacerbated by Projects with settling particles that result in local alkalinity enrichment in marine or river sediments, and the potential impacts on the net removal calculation is uncertain at this time. This loss term applies only to point-source discharge Projects. Diffuse runoff Projects are exempt because distributed delivery of alkalinity through baseflow and runoff precludes the localized near-field sediment conditions that drive reductions in natural alkalinity flux. However, more research in this area is needed and the Module will be updated with future advancements.

Quantification

A recommended avoidance strategy is to limit accumulation of alkalinity on the river or seabed through careful design of discharge rates and benthic monitoring to confirm feedstock does not accumulate. Examples of monitoring include analyzing sediment cores against a baseline for changes in metals, carbonate content, grain-size distributions; underwater imagery compared to pre-dosing or an immediately upstream location. If this risk cannot be avoided, monitoring plans are needed to confirm that avoidance strategies are working, so if alkalinity accumulation or precipitation is detected, then quantification methods must be applied. Potential approaches that should be adopted by Project Proponent include:

• Conduct early consultation with relevant regulatory authorities to establish acceptable monitoring and assessment approaches
• Implement quantitative assessment through one or more of the following methods:
  • Numerical modeling of particle transport and alkalinity distribution in receiving waters
  • Regular sediment sampling and chemical analysis at discharge points and reference sites
  • Direct measurement of benthic alkalinity fluxes using chamber or eddy correlation techniques

4.1.4 Additional (Bio)geochemical Sinks of Alkalinity

Context

This section applies to RAE Projects only. For other point-source pathways (WAE, Enhanced Weathering in Closed Engineered Systems), feedstock reactions occur upstream of discharge in engineered systems, and any acid generation, metal precipitation, or other reactive-species losses are captured in the effluent chemistry measured at the outfall under the respective Protocol.

Additional (bio)geochemical sinks of alkalinity may be operative in river systems. This may include pH-mediated precipitation of soluble metals, sorption of cations to surfaces or suspended solids or the biological uptake of cations. Some river systems may also have biogeochemical transformations that are not otherwise addressed in this Module, and alternative quantification approaches may be described in the PDD and is allowable subject to approval from Isometric. The Project Proponent is recommended to identify any material site-specific sinks of alkalinity in the river reach and take appropriate action to quantify or mitigate the risk of alkalinity loss due to these site-specific sinks.

It is important to note that some feedstocks may contain acid generating constituents like sulfide minerals, which when weathered can decrease a Project’s net carbon removal. Some silicate rocks, for example, may contain trace amounts of sulfide minerals (e.g., pyrite, FeS₂). The oxidative weathering of these minerals is a potent source of acidity as shown in Equation 7:

[math: 4\text{FeS}_2(\text{s}) + 15\text{O}_2(\text{g}) + 14\text{H}_2\text{O} \rightarrow 4\text{Fe}(\text{OH})_3(\text{s}) + 8\text{H}_2\text{SO}_4(\text{aq})]

(Equation 7)

This sulfuric acid will neutralize alkalinity, directly negating the CDR benefit.

Quantification

4.1.5 Isometric Default River Loss Model for Near Field Mixing

To facilitate and standardize the approach for quantifying riverine loss across applicable pathways, Isometric provides a default model for calculating near-field riverine losses. The Isometric default model is PHREEQC-based geochemical model that quantifies dissolved inorganic carbon (DIC) loss from carbonate precipitation when effluent or alkalinity enhanced groundwater mixes with local river water and re-equilibrates with the river's original pCO₂. This model allows users to input Project specific solution chemistry for both the effluent/groundwater source and receiving river water. The model simulates mixing at various ratios (0-50% effluent) followed by river pCO₂ re-equilibration and carbonate mineral precipitation.

Key assumptions include:

1. Re-equilibration with site-specific river pCO₂ occurs after mixing. Projects must adapt measured or modeled river pCO₂ values representative of their discharge location and seasonal conditions. In the absence of site-specific data, Projects may use spatially-resolved river pCO₂ estimates from Liu et al. (2022)²⁶ or equivalent peer-reviewed datasets. River pCO₂ typically ranges from ~1,000 to >10,000 ppm depending on watershed characteristics, river size, seasonality, and climate⁹
2. The system reaches thermodynamic equilibrium
3. For enhanced weathering (EW) applications, feedstock dissolution is parameterized using a dissolution fraction ([math: F_d]) and application rate

Depending on the pH of mixture from effluent and receiving river waters, the model will either only quantify carbonate mineral precipitation (calcite), or will include CO₂ degassing following Section 4.1.1. The model outputs retention factors across different mixing scenarios and water chemistry conditions.

This model serves as a standardized default approach for Projects and provides a third-party verification tool for cross-checking. Detailed description of the model, code, table of parameters, and sensitivity analysis can be found in Appendix 1 of this Module.

4.1.6 Alternative River Transport Model Requirements

The Isometric default river model in Section 4.1.5 focuses on quantifying the mixing of effluent or groundwater when it first comes in contact with river water, because this is the zone where the risk of losses is expected to be greatest. However, losses may occur heterogeneously as effluent alkalinity is transported through rivers and eventually to the oceans. Risks of losses may be more pronounced at areas with water inputs with different chemical properties, such as industrial, municipal or groundwater discharge, surface runoff, tributaries or confluences along the river network. Additionally, river water which does not get discharged to the ocean, such as through water withdrawal, losing rivers, or flow diversions, are considered direct losses of alkalinized river water.

Natural river systems exhibit considerably greater complexity than represented in this default model, including spatially and temporally variable mixing zones, heterogeneous flow patterns, biological processes, and fluctuating biogeochemical conditions. The simplifying assumptions in the model are deliberate methodological choices designed to balance two critical objectives: (1) providing a scalable, standardized approach applicable across diverse Project contexts, and (2) maintaining conservative estimates. As scientific understanding advances and field validation expands, future versions will incorporate additional complexity and site-specific refinements.

Project Proponents are strongly encouraged to identify if there are significant changes in river conditions during transport. If there are, it is highly recommended that Project Proponents estimate and quantify a loss discount for both re-equilibration and precipitation along the entire river transport path, as opposed to using the Isometric default river model in Section 4.1.5 only.

Recent publications have outlined modeling approaches that combine baseline river geochemical data, equilibrium modeling of water chemistry and scenarios of terrestrially exported DIC, which may serve as useful references^16,27.

The minimum requirements for river transport loss models are:

• Domain:
  • The spatial domain of the model must encompass the full river network through which bicarbonate and carbonate ions will be transported. This defines the extent over which loss processes must be represented; it does not require model of fluid transport. Projects may represent chemical state along this domain.
• Inputs:
  • River characteristics:
    • Baseline calcite saturation index ([math: SIc])
    • pH
    • pCO₂
    • Alkalinity
    • Temperature
    • Salinity
    • Major cation concentration (e.g., Ca²⁺)
  • Effluent characteristics:
    • Discharge rate
    • Alkalinity fluxes
    • Cation fluxes
• Outputs:
  • [math: SIc] along river
  • pH along river
  • [math: \eta_i] for re-equilibration of DIC during river transport
  • [math: \eta_i] for carbonate precipitation during river transport
  • [math: \eta_i] for direct losses of alkalinized water during river transport, if applicable to the Project

Project Proponents are required to submit a detailed description of their modeling approach, including the model used, the river/watershed data used in model construction and the source of that data. See Appendix 2 for more details on model reporting requirements. Alternate approaches may be considered on a case by case basis.

4.2 Ocean Losses

This section includes an overview of loss processes occurring in the marine environment, with requirements and recommendations for how to mitigate and quantify them.

[math: \eta_{\text{Ocean,\ RP}} = \prod_{i=1}^N \eta_i]

(Equation 8)

Where:

• [math: \eta_{\text{Ocean,\ RP}}] is the overall ocean retention factor, accounting for all loss processes occurring upon entering the marine environment. This term is dimensionless and represents the total fraction of removed CO₂ retained upon reaching the ocean
• [math: \eta_i] is the fraction of removed CO₂ that is retained after a given loss process, [math: i]
• [math: N] is the total number of loss processes, dimensionless

This Module covers the following ocean loss processes:

1. Re-equilibration of the carbonate system upon entering the ocean
2. Inorganic carbonate precipitation
3. Changes to natural alkalinity fluxes
4. Changes to biotic calcification

Note that not every process above is applicable to every Project. See Section 3 to determine the list of relevant processes for a specific Project.

4.2.1 Re-Equilibration of the Carbonate System

Concept

Equilibrium speciation of DIC is primarily dependent on pH, and to a lesser extent temperature, salinity and pressure:

[math: \text{CO}_2 + \text{H}_2\text{O} \leftrightarrow \text{H}_2\text{CO}_3 \leftrightarrow \text{H}^+ + \text{HCO}_3^- \leftrightarrow 2\text{H}^+ + \text{CO}_3^{2-}]

(Equation 9)

The extent and rate of re-equilibration are highly site and Project specific, depending on local water chemistry, hydrodynamic conditions, and effluent characteristics. The release of CO₂ due to re-equilibration of DIC may occur due to mixing of fluids, such as when rivers discharge to the ocean.

Once alkalinity reaches the ocean, changes in pH, temperature or salinity can shift the carbonate system and result in a re-equilibration of DIC. Estimates from peer-reviewed studies suggest that marine losses of terrestrially exported DIC could amount to 10-30% loss of carbon, depending on temperature, salinity, pCO₂, and ocean circulation^28,29,30. Typically, the ocean has a higher pH than rivers, which shifts the carbonate equilibrium towards a higher proportion of CO₃²⁻ in oceans. As a result, the amount of DIC stored per unit of alkalinity decreases between inland waters and the ocean.

Quantification

1. Using a conservative upper limit based on thermodynamic equilibrium between the ocean and atmosphere. This will be the default option and Isometric will independently calculate and report this for each Project. See Section 4.2.1.1 for more details.
2. Using a 3D Earth Systems Model or ocean physical-biogeochemical model to explicitly simulate ocean circulation and air-sea CO₂ fluxes³⁰. See Section 4.2.1.2 for more details.
3. Alternate approaches may be considered on a case by case basis, provided it is sufficiently described and justified in the PDD.

This Module assumes that the Project intervention signal in the ocean will be diluted to undetectable levels either by the time riverine transport reaches the ocean, or within a few hundred meters of a direct coastal discharge point.

4.2.1.1 Option 1 [Default]: Isometric Calculated

Given the latitude and longitude coordinates of the Project's coastal discharge or the relevant river mouth, Isometric will carry out the following standardized workflow:

1. Isometric will use oceanographic conditions from the publicly available OceanSODA-ETHZ dataset. This is a global dataset of monthly ocean surface carbonate system parameters on a 1-degree grid, from 1982-2022. Isometric will use climatology values by averaging over the last 30 years of the dataset (i.e. from January 1993 to December 2022), to avoid biases resulting from interannual and decadal variability. The dataset will be updated to use the most recent version when available.
2. Isometric will identify the nearest N grid cells to the provided lat-long coordinate of the coastal discharge location. The following parameters from the OceanSODA-ETHZ dataset will be averaged across the N grid cells: Alkalinity, DIC, temperature, and salinity.
3. Isometric will calculate the ocean retention factor [math: \partial \text{DIC} / \partial \text{Alk}] using pyCO2sys, a python package for solving the marine carbonate system³¹. Inputs used are time and space averaged Alk, DIC, temperature, and salinity. pyCO2sys calculates the isocapnic quotient³², defined as [math: \partial \text{TA} / \partial \text{DIC}]. The ocean retention factor we are interested in is the inverse of the isocapnic quotient.
4. Isometric will conduct a sensitivity analysis to assess the range of values of the retention factor when using n=1 grid point nearest to the lat-long coordinate, the nearest 2 grid cells, etc., up to averaging over the nearest N grid cells. N will be determined based on the smallest value at which the retention factor starts to plateau. This number will vary by region, and may be on the order of 100 grid cells.
5. The median value will be used for [math: \eta_{OceanOutgas}] and the standard deviation will be reported as the uncertainty.
6. There may be some edge cases where a Project discharges into a region where environmental conditions are not representative of typical oceanographic conditions. For example, the Baltic sea has lower salinity, pH and alkalinity compared to the North Sea and North Atlantic, and using the nearest coastal grid cells may underestimate the expected outgassing. These situations can be identified from the sensitivity analysis as there will be a large standard deviation in the results. In these cases, Isometric will evaluate which grid cells are most representative for estimating outgassing loss, based on the residence time of the discharge region.

Isometric will share the input data source and code with the VVB to enable reproducibility of results during verification.

[math: \eta_{\text{OceanOutgas}}] is in units of mol C/mol alkalinity and must be converted to a dimensionless retention factor [math: \eta_i], representing the fraction of CO₂ retained upon discharge to the ocean.

If a non-carbonate feedstock is used, then [math: \eta_{\text{OceanOutgas}}] can be converted by assuming that 1 mol CO₂ is removed per 1 mol alkalinity generated. However if a carbonate feedstock is used, then dissolution of the feedstock itself contributes to an increase in ocean DIC, and 1 mol of CO₂ is removed per 2 mol alkalinity generated. Isometric will use the following equation, which is derived from Equation 6 in Bach (2024)²⁵, to determine the fraction of CO₂ retained upon ocean discharge:

[math: \eta_i = f(2 \eta_{OceanOutgas}-1) + (1-f) \eta_{OceanOutgas}]

(Equation 10)

Where:

• [math: \eta_{\text{OceanOutgas}}] is the output of the pyCO2Sys calculation, in units of mol C/mol alkalinity
• [math: f] is the fraction of alkalinity from carbonate feedstock sources, between 0 and 1

If 0% carbonate feedstocks are used, then [math: f=0] and Equation 10 simplifies to [math: \eta_i = \eta_{\text{OceanOutgas}}]. If 100% carbonate feedstocks are used, then [math: f = 1] and Equation 10 becomes [math: \eta_i = 2 \eta_{\text{OceanOutgas}} - 1].

If a feedstock of mixed mineralogy is used, Isometric will make conservative assumptions in quantifying CDR and determining [math: f]. For example, if a feedstock contains MgO and MgCO₃, [math: f] represents the fraction of alkalinity from MgCO₃ dissolution. Isometric will assume that the phase with the lowest conversion potential dissolves first, e.g. if a feedstock is 90% MgO and 10% MgCO₃ by mass, the first 10% of dissolved weathering products by mass are assumed to come from MgCO₃. In this scenario, if 50% of the total feedstock dissolved, then [math: f=0.2] since 20% of the total dissolved weathering products is attributed to MgCO₃.

See Appendix 3 for an example.

4.2.1.2 Option 2: Project Proponent Modeling

The Isometric default option in Section 4.2.1.1 provides a conservative estimate of the ocean outgassing loss. However, a more realistic estimate of the loss can be obtained by considering the 3D ocean circulation and not assuming immediate equilibrium with the atmosphere upon entering the ocean. This may lead to a higher retention factor in certain regions where the exported DIC is subducted out of atmospheric contact for long periods of time prior to complete air-sea equilibration.

An alternative approach to quantifying ocean losses is to use a 3D Earth Systems Model or ocean physical-biogeochemical model to explicitly simulate ocean transport and air-sea CO₂ fluxes. For example, Kanzaki et al., 2023 used an Earth system model to estimate the ocean leakage of CO₂ from terrestrial enhanced weathering projects³⁰. Similar model-based approaches may be used, provided that simulations of ocean losses specific to the Project site. A globally averaged loss factor may not be used at this time since it may not be conservative, given the large variability that exists in different regions of the ocean.

• Model used and domain
• Inputs and forcing data, including atmospheric forcing and initial conditions
  • The duration of model simulations must be long enough so that an equilibrium is reached, i.e. the retention factor plateaus and no longer changes with time. It is recommended to demonstrate this with at least one simulation that is 1,000 years long to capture all outgassing that would occur over the claimed durability of the Removal. If it is proven that equilibrium is reached after a shorter amount of time (e.g. a few hundred years), then simulations for the ensemble may be shorter.
• Carbonate system representation and parameterization of air-sea CO₂ fluxes
• Representation of the CDR Project, e.g. as represented through an additional flux of DIC and alkalinity into the ocean at a particular river mouth
• Baseline simulations
• Description of how uncertainty is quantified. At a minimum, Project Proponents must:
  • Disclose a list of known limitations and biases of the model (e.g. coarse resolution, simplified parameterizations, biases in the physics or carbonate system, etc.), and discuss how those uncertainties are expected to impact the computed retention factor. This may be informed by literature and data-model comparisons.
  • Identify a list of parameters that are expected to lead to the largest uncertainties in the retention factor for their particular simulations (e.g. gas transfer velocity, vertical mixing, atmospheric forcing, etc.), and discuss expected impacts on the retention factor.
  • Quantify an uncertainty in the retention factor using an ensemble with a minimum of [math: n \geq 5] members, varying at least one of the key parameters identified above. For each parameter varied:
    • The range of variation must represent the full plausible uncertainty in the parameter, not an arbitrary fraction of its central value. The range must be justified against a creditable, objective sources (e.g., published literature, model intercomparison studies, measured site data, or established parameterization ranges);
    • The Project Proponent must also prepare a justification documentation details (i) the range used for each parameter, (ii) the source(s) justifying that range, and (iii) why that range is considered representative of the parameter's plausible uncertainty for the Project's specific site, model, and conditions.

Furthermore, the model must be well-validated and skillful for the purpose that it is used for. Proof of model validation can be achieved through either:

1. A track record of use in science, industry, or government applications, which is demonstrated through multiple peer-reviewed papers, or proof of usage in a number of previous applications.
2. Newly developed models without a track record of usage must be validated against reputable data sources, which include quality-controlled in situ measurements and public datasets adhering to FAIR (Findable, Accessible, Interoperable and Reusable) principles³³. Sufficient model validation data must be provided with the PDD.

4.2.2 Inorganic Carbonate Precipitation

Concept

Secondary precipitation of calcium carbonate could cause CO₂ outgassing by the following reaction:

[math: \text{Ca}^{2+} + 2\text{HCO}_3^- \rightarrow \text{CaCO}_3 + \text{CO}_2 + \text{H}_2\text{O}]

(Equation 11)

Calcium carbonate precipitation may result in a reduction in carbon loss up to 50% for non-carbonate feedstocks or up to 100% for carbonate feedstocks, due to short-term CO₂ degassing associated with alkalinity loss. While carbonate weathering largely recycles inorganic carbon, silicate weathering drives the ultimate fate of inorganic carbon sequestration through carbonate mineral formation and burial.

In rivers and coastal areas, higher suspended particulates may increase nucleation. Early research suggests there is a relationship between increased alkalinity loss with higher TSS (Total Suspended Solids) in the receiving water body¹⁸. Thus, the risk of secondary precipitation is most pronounced in the mixing zone of the outfall, where the carbonate chemistry and TSS perturbation are largest. In addition, changes in salinity and saturation state upon reaching the ocean, as well as mixing-induced calcite undersaturation that occurs when waters in carbonate equilibrium are combined, can lead to calcium carbonate precipitation or dissolution³⁴.

Limiting pH and the saturation state ([math: SIc]) has been shown to be effective at avoiding this result, and laboratory research to characterize the critical thresholds that trigger precipitation under close-to-natural conditions are ongoing^19,20,21,22. Furthermore, precipitation dynamics occur on a timescale between minutes to hours ^19,21, which suggests that dilution could be an effective risk mitigation strategy²⁴.

Quantification

An example avoidance strategy is setting a threshold on TA and saturation state ([math: SIc]), with consideration of environmental conditions including carbonate chemistry variables, TSS and dilution at the site³⁵. Continuous monitoring of carbonate chemistry variables and TSS is recommended to ensure that conditions for secondary precipitation are avoided. In some cases, secondary precipitation can be identified by an observed increase in turbidity. Monitoring of turbidity is recommended, however it may be difficult to isolate a signal from secondary precipitation over natural fluctuations.

4.2.3 Natural Alkalinity Flux Reduction

Concept

Increased alkalinity in reactor effluent can potentially reduce the natural alkalinity flux from marine or river sediments²⁵. This risk may be exacerbated by Projects with settling particles that result in local alkalinity enrichment in marine or river sediments, and the potential impacts on the net removal calculation is uncertain at this time. More research in this area is needed and the Module will be updated with future advancements.

Quantification

A recommended avoidance strategy is to limit accumulation of alkalinity on the river bed or sea bed through careful design of discharge rates. If this risk cannot be avoided, potential approaches should be adopted by Project Proponent include:

1. Conduct early consultation with relevant regulatory authorities to establish acceptable monitoring and assessment approaches.
2. Implement quantitative assessment through one or more of the following methods:

• Numerical modeling of particle transport and alkalinity distribution in receiving waters
• Regular sediment sampling and chemical analysis at discharge points and reference sites
• Direct measurement of benthic alkalinity fluxes using chamber or eddy correlation techniques

3. Develop monitoring plans that demonstrate compliance with applicable water quality standards and environmental regulations.

4.2.4 Changes in Biotic Calcification

Concept

For coastal discharges, increases in marine biotic calcification can cause CO₂ outgassing. The carbonate chemistry conditions promoted by coastal discharge of alkalinity-enhanced wastewater could promote calcification due to the elevated pH or increased carbonate saturation state^36,37,38. Alkaline feedstock dissolution may release trace metals which has the potential to fertilize blooms of calcifiers³⁹.

Early stage research manipulating total alkalinity with the aim of simulating OAE has found no significant increase in biologically produced calcium carbonate at elevated alkalinity in the ocean⁴⁰. However, the Black Sea, a naturally elevated alkaline environment, harbors extensive blooms of the coccolithophores⁴¹, a major group of calcifying plankton. This is thought to be due to the favorable carbonate chemistry promoted by the elevated alkalinity regime³⁸.

This is still an area where more research is needed, particularly through mesocosm and field trials, albeit there is a rich body of literature on lab and mesocosm scale species-specific responses to changing seawater carbonate chemistry^42,43. The risk of outgassing due to biotic calcification may be Project and location specific. Recently published meta-analyses synthesizing data from ocean acidification studies for OAE supports this claim that species and functional group specificity is likely⁴⁴. Coastal areas with significant benthic calcification of CaCO₃ sediments may be especially susceptible to this feedback.

Quantification

A recommended avoidance strategy is setting thresholds on pH and TA based on what has been shown in previous studies to have no significant increase in biologically produced CaCO₃⁴⁰, or as determined for the specific deployment site, and monitoring for changes in ocean biota.

5.0 Required Records and Documentation

The following needs to be reported for Project verification and each credit issuance:

• If avoidance strategies are used, monitoring data to demonstrate adherence to conditions to avoid certain losses
• The following must be reported to ensure the loss factors from models are reproducible:
  • All model files and code needed to reproduce the model results
  • All model outputs and analysis code used to calculate the loss factors
• Results from model sensitivity tests and assessment of uncertainty

6.0 Acknowledgments

Isometric would like to thank the following reviewers of this Module:

• Shuang Zhang, PhD. (Texas A&M University)
• Mengqi Jia, PhD. (Institute for Sustainability, Energy, and Environment, University of Illinois Urbana‐Champaign)

7.0 Definitions and Acronyms

Independent components of Isometric Certified Protocols which are transferable between and applicable to different Protocols.

for open systems, biogeochemical and/or physical interactions which occur during the removal process that decrease the CO₂ removal .

Activities that remove carbon dioxide (CO₂) from the atmosphere and store it in products or geological, terrestrial, and oceanic Reservoirs. CDR includes the enhancement of biological or geochemical sinks and direct air capture (DAC) and storage, but excludes natural CO₂ uptake not directly caused by human intervention.

A collection of Removal or Reduction processes that have mechanisms in common.

The term used to represent the CO₂ taken out of the atmosphere as a result of a CDR process.

The stretch of tidally influenced river where the river and ocean meet. In this protocol, this region is bounded by the head of tide and the seaward limit of estuarine influence in the ocean.

An activity or process or group of activities or processes that alter the condition of a Baseline and leads to Removals or Reductions.

A document that describes how to quantitatively assess the net amount of CO₂ removed by a process. To Isometric, a Protocol is specific to a Project Proponent's process and comprised of Modules representing the Carbon Fluxes involved in the CDR process. A Protocol measures the full carbon impact of a process against the Baseline of it not occurring.

Those gaseous constituents of the atmosphere, both natural and anthropogenic (human-caused), that absorb and emit radiation at specific wavelengths within the spectrum of terrestrial radiation emitted by the Earth’s surface, by the atmosphere itself, and by clouds. This property causes the greenhouse effect, whereby heat is trapped in Earth’s atmosphere (CDR Primer, 2022).

The organization that develops and/or has overall legal ownership or control of a Removal or Reduction Project.

A carbon removal pathway that captures and durably stores carbon from seawater, which induces additional uptake of atmospheric carbon dioxide in the ocean.

The concentration of inorganic carbon dissolved in a fluid.

A carbon removal pathway in which a feedstock is added to the secondary treatment step of a wastewater treatment plant to capture biogenic carbon dioxide produced from the breakdown of organic material.

A carbon removal pathway that accelerates the natural chemical weathering process of alkaline rocks or minerals by pre-processing such as crushing or grinding.

Any process, activity, or mechanism that removes a greenhouse gas, a precursor to a greenhouse gas, or an aerosol from the atmosphere.

The document that clearly outlines how a Project will generate rigorously quantifiable Additional high-quality Removals or Reductions.

Purposefully erring on the side of caution under conditions of Uncertainty by choosing input parameter values that will result in a lower net CO₂ Removal or GHG Reduction than if using the median input values. This is done to increase the likelihood that a given Removal or Reduction calculation is an underestimation rather than an overestimation.

A database that holds information on Verified Removals and Reductions, and reviewed EACs, based on Protocols. Registries Issue Certificates, and track their ownership and Retirement.

A publicly visible uniquely identifiable Credit Certificate Issued by a Registry that gives the owner of the Credit the right to account for one net metric tonne of Verified CO₂e Removal or Reduction. In the case of this Standard, the net tonne of CO₂e Removal or Reduction comes from a Project Validated against a Certified Protocol.

Certificates are issued to the Certificate Account of a Project Proponent with whom Isometric has a Validated Protocol after an Order for Verification and Certificate Issuance services from a Buyer and once a Verified Removal or Reduction has taken place.

The location where the river meets the ocean. In this protocol, the river mouth is defined as the head of tide, where tidal effects begin to influence the river’s flow.

Defined as an excess of proton acceptors over proton donors, which functionally describes the ability of a solution to neutralize acids to the CO₂ equivalence point.

Any process or activity that releases a greenhouse gas, an aerosol, or a precursor of a greenhouse gas into the atmosphere.

A regulatory concept describing the spatial area surrounding the discharge infrastructure where water quality criteria can be exceeded.

A calculation, series of calculations or simulations that use input variables in order to generate values for variables of interest that are not directly measured.

Raw material which is used for CO₂ Removal or GHG Reduction.

Soil Inorganic Carbon

Total Inorganic Carbon.

An evaluation of the likelihood that an intervention—for example, a CDR Project—causes a climate benefit above and beyond what would have happened in a no-intervention Baseline scenario.

A systematic and independent process for evaluating the reasonableness of the assumptions, limitations and methods that support a Project and assessing whether the Project conforms to the criteria set forth in the Isometric Standard and the Protocol by which the Project is governed. Validation must be completed by an Isometric approved third-party (VVB).

A set of data describing pre-intervention or control conditions to be used as a reference scenario for comparison.

A lack of knowledge of the exact greenhouse gas impact (removal, reduction, or avoidance) associated with a particular process or Environmental Attribute. Uncertainty may be quantified using probability distributions, confidence intervals, or variance estimates.

The increase in GHG emissions outside the geographic or temporal boundary of a project that results from that project's activities.

Reactive Transport Model

8.0 Appendix 1: Default Riverine Loss Quantification Model

8.1 Model Description

A PHREEQC-based thermodynamic equilibrium geochemical model is developed to assess riverine loss of various Projects. The model uses PHREEQC (via IPhreeqcPy) to simulate dissolved inorganic carbon (DIC) lost when Project effluent (i.e., groundwater with dissolved feedstock) mixes with river water and equilibrates with the atmosphere. The primary output is the percentage of dissolved inorganic carbon (DIC) lost through carbonate precipitation and CO₂ degassing, which represents a reduction in carbon dioxide removal (CDR) efficiency for Projects that enhance alkalinity in the Earth system.

The model have two variants depending on the input data availability:

Variant 1: Riverine Loss Model via porewater data

Variant 2: Riverine Loss Model via groundwater data

Variant 1: For Projects with porewater measurements available (e.g., Enhanced Weathering)
This model takes timestamped porewater measurements (Treatment + Control) as input. Project Proponents provide porewater chemistry data measured at from beginning to the end of reporting period. The model computes cumulative weathering changes across time points for each sample, then averages across all samples to derive the representative effluent chemistry used as input for the PHREEQC simulation.

Note: the median of timestamped porewater measurements (e.g., pH, alkalinity, cation concentration) will be calculated and used as input for the model.

Variant 2: For all other Projects (e.g., Open System Ex-situ Mineralization, Wastewater Alkalinity Enhancement, Enhanced Weathering in Closed Engineered Systems), the model uses a forward modeling approach where the alkalinity-enhanced effluent is generated by simulating groundwater dissolution of feedstock minerals (parameterized by mineral type, abundance, and fraction dissolved). Water chemistry (pH, alkalinity, major cations, and temperature) of the alkalinity enhanced effluent (i.e., groundwater, waste water, aqueous phase where CO₂ stored as DIC) is required. The model assesses the stability of DIC by simulating the mixing of alkalinity enhanced effluent with river water across various volumetric fractions, the model quantifies potential carbon losses driven by re-equilibration of the carbonate system and secondary mineral precipitation. The same pH-dependent logic to determine whether CO₂ is primarily lost through atmospheric degassing or solid carbonate formation applies.

Overall, both variants follow a three or four-step PHREEQC simulation workflow:
Step 1: Define alkalinity enhanced effluent chemistry (pH, alkalinity, pCO₂, major cation concentration, temperature)
↓
Step 2: Define river water chemistry (pH, alkalinity, pCO₂, major cation concentration, temperature)
↓
Step 3: Mix solutions at specified fractions; allow carbonate precipitation (precipitate_only)
↓
If Mixed solution pH > 6
Step 4: Equilibrate with river pCO₂ values representative of their discharge location and seasonal conditions; quantifying CO₂ degassing during re-equilibrium

Riverine Loss Calculation

Two simulations must be run to compute a marginal, project-attributable loss:

• Baseline run: river water alone or river water + groundwater (with no mineral dissolution), equilibrated with river pCO₂, with carbonate precipitation allowed if thermodynamically favorable.
• Project run: river water mixed with project effluent at the specified mixing fraction f, equilibrated with river pCO₂, with carbonate precipitation allowed.

The project-attributable loss fraction is the difference between the two runs, normalized by the DIC contributed by the project effluent:

[math: Loss\ fraction = (Loss_{project} − Loss_{counterfactual}) / Δ DIC_{added}]

The retention factor for this loss process is:

[math: η_i = 1 − Loss\ fraction]

The model applies a pH-dependent calculation framework as discussed in details in Section 4.1.1. In summary:

When [math: pH_{mixed}] ≥ 6.0: DIC speciation is dominated by bicarbonate (HCO₃^-), and CO₂ degassing is minimal. Loss is calculated as:

[math: Loss = \frac{(CarbonatePrecipitation_{project} - CarbonatePrecipitation_{baseline})} {DIC_{added}}]

where carbonate precipitation (Calcite) is tracked via PHREEQC's [math: d_{Calcite}] output.

When [math: pH_{mixed}] 6.0: At lower pH, dissolved CO₂ (H₂CO₃) dominates, and significant degassing occurs during river equilibration. Loss is calculated as:

[math: Loss = \frac{(net DIC decrease + Carbonate Precipitation)_{project} - (net DIC decrease + Carbonate Precipitation_{baseline})} {DIC_{added}}]

This captures both CO₂ outgassing and secondary carbonate mineral precipitation losses.

The pH threshold determines whether carbon is primarily lost through solid carbonate formation (high pH) or a combination of atmospheric CO₂ degassing and carbonate precipitation (low pH).

8.2 Table of Input Parameters

Note: Annual average is encouraged for both river and groundwater parameters input; single measurements are acceptable with the recommended sensitivity analysis ranges specified in Section 8.3.

8.3 Sensitivity Analysis

The model provides sensitivity information through:

1. Mixing Ratio Variation: By running 4 different mixing scenarios (0%, 15%, 25%, 50%), the model shows how DIC loss varies with alkalinity enhanced effluent dilution.
2. Baseline vs. CDR Comparison: The net CDR benefit calculation (CDR - Baseline) shows the sensitivity to feedstock addition.

To fully characterize model behavior, the following sensitivity analyses are recommended:

1. [math: F_d] (Dissolution Fraction): Vary from 0.1 to 0.5

• Rationale: Dependent on fraction dissolved in EW applications

2. Application Rate: Vary from 0.001 to 0.1 kg/kg

• Rationale: Dependent on EW supplier Project set up

3. Influent Cation concentration and Alkalinity: Vary ±10%

• Rationale: Primary control on calcite precipitation

4. River Alkalinity: Vary ±10%

• Rationale: Affects buffer capacity and carbonate chemistry

5. Temperature: Vary ±5°C

• Rationale: Affects solubility and equilibrium constants

6. Atmospheric pCO₂: Vary from 400 to 600 ppm

• Rationale: Historical and future scenarios, vary by geographic locations

7. Volumetric Mixing Fraction: Vary 0 to 50% by different resolution (e.g., ±1% or ±5% or ±10% interval)

• Rationale: Affect model output results, depend on discharge amount, Project size and river size

8. River pCO₂: Vary from -3.5 to -2.5 (log scale)

• Rationale: Seasonal and diurnal variation

8.4 Uncertainty Quantification

The following sources of uncertainty have been identified for the model and should be considered when optimizing.

• Measurement uncertainty from water chemistry: ±5-10%, feedstock composition: ±2-5% (qXRD, XRF) and temperature: ±0.5°C
• Model uncertainty from thermodynamic database accuracy, equilibrium assumption validity, lack of kinetic constraints, simplified mixing model
• Parameter uncertainty from [math: F_d]: ±10-50%, application rate: ±20-50%, seasonal water chemistry variation: ±20-50%

9.0 Appendix 2: Guidelines for Riverine Loss Models

9.1 Types of Models

Geochemical models are important tools for quantifying the complex chemical interactions that govern riverine losses through (e.g., re-equilibrium, degassing and carbonate precipitation). Below is a list of example models that could be adapted.

For speciation / batch reaction (with some 1-D transport)

• PHREEQC - USGS tool for speciation, batch reactions, inverse modeling, and 1-D transport; public-domain. USGS
• iPHREEQC / PhreeqcRM - PHREEQC libraries for embedding/coupling into other simulators and doing parallel reactive transport.
• PyCO2SYS - the Python implementation of CO2SYS for solving the marine (and estuarine/freshwater) carbonate system.
• Seacarb - R package for calculating parameters of the seawater carbonate system (including pH, pCO₂, DIC, alkalinity, and saturation states).
• Geochemist’s Workbench - Aqueous speciation, reaction path, reactive transport (X1t/X2t).
• University of Hamburg Modeling Tools for Geochemistry - interactive calculators for carbonate chemistry, charge-balance checking, and mineral-oxide conversions.

For reactive transport (1-D / 2-D / 3-D simulators with geochemistry)

• PFLOTRAN - Massively parallel subsurface flow + reactive transport (LGPL); widely used and actively maintained.
• PHAST (USGS) - 3-D groundwater flow + multicomponent reactive transport using PhreeqcRM.
• CrunchFlow / CrunchTope - Reactive transport (equilibrium + kinetic) widely used for water–rock interaction.
• TOUGHREACT - numerical simulation program for modeling coupled thermal-hydrological-chemical (THC) processes in multiphase fluid flow through porous and fractured media, widely used for applications including CO₂ geological storage, geothermal systems, and reactive transport in subsurface environments.
• MIN3P (incl. MIN3P-HPC) - General purpose subsurface flow and multicomponent reactive transport code for variably saturated porous media.

9.2 Equilibrium and Speciation Models (e.g., PHREEQC): Capabilities and Limitations

PHREEQC is a versatile computer program designed to perform a wide range of aqueous geochemical calculations. Its core function is to solve for the equilibrium speciation of a solution based on its measured chemical composition. PHREEQC can also simulate a variety of geochemical reactions, including the mixing of different solutions, the addition of reactants, and equilibration with mineral phases or gas phases. Within the context of this Module, PHREEQC is particularly well-suited for several specific tasks that align with its core capabilities.

First, PHREEQC is the ideal tool for near-field mixing zone analysis. As mentioned earlier, a simple two-endmember mixing simulation can be performed.

Second, PHREEQC is good for scenario testing and developing avoidance strategies. Project Proponent can use PHREEQC to answer critical "what-if" questions before deployment. For example: "What is the maximum alkalinity concentration our effluent can have before the [math: SIc] in the mixing zone exceeds a conservative kinetic threshold of 1?" or "How does the risk of precipitation change with seasonal variations in river temperature and baseline chemistry?"

Third, PHREEQC can be used to construct a simple, conservative, upper-bound estimate of the degassing loss, which can be used as a default discount factor in cases where more complex kinetic modeling is not feasible.

The primary strength of PHREEQC is its basis in thermodynamic equilibrium. At the same time, this is also its most significant limitation which: the absence of kinetic controls. Another major limitation is the lack of integrated transport dynamics. Regardless, these limitations clarify the appropriate role for equilibrium models like PHREEQC to be adopted for riverloss quantification. Isometric developed an internal PHREEQC model that could be used for river loss quantification, particularly for EW Projects. Project Proponents who do not have the capacity to conduct specific modeling studies for river loss could choose to use this model by providing relevant information on feedstock and water chemistry data and take the output from this model as the loss discount from gross CO₂ removal.

9.3 Reactive Transport Models (RTM): Capabilities and Limitations

To overcome the limitations of equilibrium-only models, a more advanced class of tools known as Reactive Transport Models (RTMs) is recommended. These models mechanistically couple the physical processes of water flow and solute transport with the full suite of geochemical reactions. The principle of RTM is that they solve a set of coupled partial differential equations that describe the conservation of mass for water and each chemical component in the system. The fundamental equation for the transport of a dissolved species combines terms for advection (transport with the bulk flow of water), hydrodynamic dispersion (spreading due to velocity variations and molecular diffusion), and a source/sink term (R) that accounts for all chemical reactions.

This framework allows RTMs to simulate non-equilibrium conditions explicitly. RTMs can simulate dynamic carbonate precipitation via a kinetic rate law (e.g., a transition state theory-based expression) to calculate the actual rate of precipitation as a function of the degree of supersaturation and other factors like temperature and the presence of inhibitors. Similarly, gas exchange can be modeled as a rate-limited flux dependent on the pCO₂ gradient and a physically-based gas transfer velocity.

A number of sophisticated RTM codes capable of these simulations are available, including MIN3P^45,46, as well as TOUGHREACT, CrunchFlow, and PFLOTRAN. MIN3P and CrunchFlow are typically used for process-based simulations of mineral-fluid reactions in porous media. TOUGHREACT is well-suited for systems involving multi-phase flow and geochemistry (such as geothermal or CO₂ storage settings). PFLOTRAN is designed for high-performance computing environments so is best suited to watershed or regional scale reactive transport simulations.
Within the context of this Module, some advantages that RTM may bring include:

• First, RTMs are the primary tools for simulating the soil column and characterizing the source term.
• Second, RTMs can perform detailed simulations of in-stream processes to directly quantify transport losses.

These make RTMs much more useful for solving geochemical problems through their use of coupled transport-reaction equations.

The limitations of RTMs are its data intensity and computational demands. A credible RTM simulation requires a substantial amount of site-specific data for parameterization and calibration. This means RTMs may not be suited as a tool for routine, network-wide application, but as a high-fidelity instrument for detailed process investigation. However, they can serve as a "virtual laboratory" to test understanding of the controlling mechanisms in critical zones, such as the near-field mixing plume or a confluence known to be a hotspot for biogeochemical activity. The use of RTMs for river loss quantification is recommended for targeted, high-resolution studies and will be evaluated on a case-by-case basis.

9.4 Framework for Validation and Calibration of Models

The credibility of any model-based quantification of riverine carbon loss relies on a robust framework for validation & calibration. Currently, various modeling approaches of different types (e.g., thermodynamic equilibrium model, reactive transport model, dynamic river network (DRN) models) have been suggested in the literature^{17,47,48,30,29}. However, no scientific consensus exists on the best approach to quantify riverine loss as there are too many different scenarios and project set ups. As different models can vary significantly with respect to the data required, inputs, outputs, and process definitions, it is important that an established criteria is used for evaluation. This section of the Module identifies a set of criteria for high-quality models, including the need for a peer-reviewed scientific basis, transparent documentation, and capabilities for sensitivity and uncertainty analysis. Although it is unlikely that a given model would explicitly include every single criteria, an adequate modeling approach should comply with several of the criteria listed in Table A.1 below.

Table A.1 Guidance & Evaluation Criteria of Riverine Loss Models

9.5 Data Requirements

Data Type Inputs for Riverine Loss Models

• Hydrological Data (e.g., discharge rate, flow rate, channel geometry etc.) This is essential for both equilibrium model and RTM.
• Water Chemistry Data (required): pH, temperature, Total Alkalinity (TA), major cations, Salinity, pCO₂, temperature and Dissolved Inorganic Carbon (DIC).
  • A minimum of two carbonate chemistry parameters must be measured in order to constrain the carbonate system. All others may be calculated using an appropriate tool e.g. PyCO2sys.
• Atmospheric and Climatic Data (required): local atmospheric pCO₂, annual average precipitation, annual average temperature, wind speed.
• Soil or rock mineralogy and composition: particle size distribution and surface area, porosity, permeability, and moisture content.

9.5.1 Acceptable Data Source

• Direct measurements
• Public scientific databases (e.g., USGS, BGS, ThermoData, GRDC)
• Published literature values (peer-reviewed studies)
• Sensor or monitoring equipment data
• Regional average

9.5.2 Data QA/QC Requirements

• Calibration and traceability of instruments
• Frequency and representativeness of sampling
• Documented uncertainty for each data point
• Data validation protocols (e.g., outlier checks, range checks)
• QA/QC procedures before data entry (cross-checks, duplicates)
• Documentation for critical samples, missing data, gaps
• Regular update or review of code base and methods

9.5.3 Data Format

• Standardized digital formats (e.g., CSV, JSON)
• Metadata included (units, method, timestamp, location)
• Consistent units and naming conventions

9.6 Guideline for Communication of Modeling Results

The results from modeling should consist of detailed reporting rather than simple numerical outputs. Project Proponents must provide the following to ensure transparent communication and high scientific rigor:

• Detailed methods, annotated code, and full datasets in accessible formats
• Model version control and tracking documentation
• Model calibration and parameterization details
• Discussion of uncertainties, validation approaches, and planned updates
• Comparison to observed or measured data where available
• Documentation of all assumptions, sensitivity tests, uncertainty calculations, model limitations, and potential future changes
• Evidence of peer review or external validation where applicable

The reporting should include best- and worst-case scenarios to fully communicate the range of plausible outcomes. Upon changes to modeling results or updates, Project Proponents must:

• Explain all changes to input and output data
• Describe how results affect crediting and reporting
• Update version control documentation accordingly

10.0 Appendix 3: Default Ocean Loss Model & Example

This is the Isometric default ocean loss model.

This is an example of how Isometric will go through the workflow outlined in Section 4.2.1.1 to calculate a default ocean re-equilibration loss for Projects. For this example, a hypothetical Project is discharging into the Hudson river in New York, and wants to know what the ocean loss would be upon entering the Atlantic. The coordinates of the river mouth provided are 40.603, -74.048.

From the sensitivity analysis, we determine N by the point at which adding another grid cell changes the retention factor by < 0.1% for 10 consecutive additional grid cells. This gives N = 68. The retention factor ranges from 0.828-0.857, with the median being 0.836 and the standard deviation being 0.007. The median value is used for quantification.

[Image: Figure 3]

Figure 3 Sensitivity of the ocean retention factor to the number of pixels of data averaged (left), and location of nearest pixels that were used (right).

11.0 Relevant Works