Air-Sea CO₂ Uptake

Several marine Carbon Dioxide Removal (CDR) approaches rely on altering the surface ocean chemistry to enable additional ocean uptake and storage of CO₂ from the atmosphere or to reduce natural oceanic CO₂ outgassing. For these pathways, quantifying the air-sea gas exchange process is crucial for demonstrating net atmospheric CO₂ removal. This Module describes how CDR from air-sea gas exchange should be quantified.

This Module is applicable to CDR approaches that induce a pCO₂ deficit in the surface ocean compared to the natural ocean baseline, and relies on the subsequent re-equilibration with the atmosphere to remove CO₂. This can include enhancing the ocean’s uptake of CO₂ from the atmosphere, or reducing the ocean’s natural outgassing of CO₂. Examples of applicable CDR approaches with certified Isometric protocols at this time include:

• mineral ocean alkalinity enhancement (OAE)
• electrochemical OAE

This Module will be updated in future iterations to be compatible with other marine CDR pathways.

This Module does not apply to approaches where the seawater being returned to the ocean is already pre-equilibrated with the atmosphere, as there is no additional CDR through air-sea gas exchange.

The transfer of CO₂ across the air-sea interface occurs when there is a thermodynamic disequilibrium between the ocean and atmosphere, and gas is exchanged between the two fluids to restore equilibrium. The rate of exchange is known as the air-sea CO₂ flux $\Phi$, which is calculated through the bulk formula¹:

$$\Phi = k*sol*(pCO_{2\,ocean} - pCO_{2\,atmosphere}) * (1 - ice)$$

Equation 1

Where:

• $k$ is the gas transfer velocity (cm h^-1)
• $sol$ is the solubility of CO₂ in seawater (mol m^-3 μatm^-1)
• $pCO_{2\,ocean}$ is the the partial pressure of CO₂ in the surface ocean (μatm)
• $pCO_{2\,atmosphere}$ is the partial pressure of CO₂ in the atmosphere (μatm)
• $ice$ represents the fraction of ice coverage (ranging from 0 to 1, dimensionless)

Note that if pCO_{2 atmosphere} is larger than pCO_{2 ocean}, then the flux in Equation 1 is negative, representing carbon flowing from the atmosphere into the ocean. On the other hand, if pCO_{2 ocean} is larger than pCO_{2 atmosphere}, then the flux is positive representing CO₂ outgassing from the ocean into the atmosphere. Ocean pCO₂ exhibits significant spatial and temporal variability, and naturally there are regions of the ocean where the air-sea CO₂ flux is predominantly positive or negative. Globally averaged, there is net ocean uptake of CO₂ from the atmosphere, due to excess CO₂ being placed in the atmosphere by human activity.

In water depths greater than 10 m, the gas transfer velocity $k$ is typically well-parameterized as a function of U₁₀ (m s^-1), the wind speed at 10 meters above the sea surface,² and the dimensionless Schmidt number Sc, which represents the ratio of kinematic viscosity of water to molecular diffusivity of gas. There are multiple possible approaches to parameterizing $k$.³ For example, a common formulation for $k$ is to use quadratic dependence on the wind speed^4,5:

$$k = 0.251 \langle {U_{10}}^2 \rangle (Sc/660)^{-0.5}$$

Equation 2

Where $\langle {U_{10}}^2 \rangle$ represents an average squared wind speed at 10 meters above the sea surface in (m/s)², and Sc is the dimensionless Schmidt number. The convention is that the gas transfer velocity $k$ has units of (cm/hr), so the coefficient 0.251 has units of (cm/hr)(m/s)^-2.⁵

It is important to consider and disclose the uncertainty and conditions for which a particular parameterization is valid. For example, the parameterization in Equation 2 has an uncertainty of 20%, and is meant for temperature ranges of -2 to 40 °C and wind speeds in the range of 3-15 m/s.⁵ Furthermore, Equation 2 may not accurately represent the gas exchange velocity in shallow coastal regions, where wind is not necessarily the only dominant source of turbulence impacting gas exchange. For example, in a shallow tidal estuary where bottom turbulence can impact gas exchange, a more appropriate parameterization of $k$ includes the current velocity in addition to the wind speed.⁶ There is no universal parameterization for shallow coastal settings yet, so the larger uncertainties in those settings should be taken into account.

The climatological mean of air-sea gas equilibration timescales is 4.4 +/- 3.4 months.⁷ Note that this is an e-folding timescale, so that near-complete equilibration will take about triple the amount of time (e.g. 4.4 months x 3 or approximately 13 months to reach 95% of equilibrium concentration). However, this is a globally averaged value, and there is significant regional variability. Some places can have much faster complete equilibration that takes less than 1 year, while other regions may take over a decade to equilibrate. Equilibration time scales also vary seasonally and are affected by atmospheric conditions, storms or episodic events.

For many relevant CDR approaches, it is expected that the initial induced pCO₂ deficit in seawater will occur locally at a near-point source at the project site (e.g. at an ocean outfall). Due to turbulent mixing, the pCO₂-depleted seawater will diffuse and spread vertically and horizontally. The rate and areal extent of spreading will depend on the local ocean conditions of each project site. Consequently, the air-sea equilibration process will likely occur over a much larger area than the initial project activity site. Detectability of the diluted pCO₂ signal above the background noise will depend on the rate of dilution, detection limits of existing instruments and magnitude of the induced pCO₂ deficit.^{8, 9}

Furthermore, depending on the location and season of a CDR activity, the pCO₂-depleted seawater may be transported out of contact with the atmosphere due to subduction or vertical mixing prior to air-sea equilibration. Previously subducted pCO₂-depleted seawater may also upwell and come back into contact with the surface ocean at a later time and different location.¹⁰ The impacts of the physical ocean transport is important to account for when assessing the gross CO₂ removal from the atmosphere and the timeline of removal.

As a result, observations at the spatial and temporal scales necessary for quantifying CDR-related air-sea gas exchange are challenging to obtain, and are likely not operationally feasible for Project Proponents at this time.¹¹ It can also be difficult to separate baseline conditions from the Project Activity using direct measurements, particularly in locations with significant natural ocean variability. As of this writing, direct measurements of CO₂ uptake as a result of an induced pCO₂ deficit in seawater have not yet been demonstrated, although experimental efforts are underway.¹² Given this, the approach taken in this Module to robustly quantify the additional CO₂ removed through air-sea gas exchange is to use ocean models that have been extensively validated against measurements.⁸

The requirements in this Module follow current best practices established by the scientific community and will be updated as needed to stay up to date with the latest research.¹³

A 3D physical-biogeochemical ocean model must be used to calculate the net CO₂e removed and obtain a timeline of removal via air-sea gas exchange. At this time, explicit simulation with a 3D model is required to account for losses of pCO₂ deficit seawater out of the surface ocean due to subduction.

The ocean model model must be well-validated, demonstrated through one of the following:

• a track record of use in science, industry, government or other applications
• for a newly developed model, thorough model validation must first be performed and reported in the Project Design Document (PDD)

See Section Section 4.1 for more information on proof of model validation.

It is recommended that the model domain be large enough to encompass the area over which the majority of air-sea equilibration will occur. Any net CO₂e uptake that is not resolved in the model (e.g. it happens outside the model domain) cannot be credited. The CO₂ uptake can be quantified in either a more localized regional domain, a larger open ocean domain, or both if the domains are nested. It is also highly recommended that the domain has realistic bathymetry to ensure accurate representation of ocean circulation, boundary-enhanced turbulence and wave propagation. The model domain and justification for why it was chosen must be described in the PDD.

At minimum, the representation of the following must also be described and justified in the PDD. It is highly recommended that the following are represented as realistically as possible:

• parameterization of air-sea CO₂ flux
• representation of subduction/downwelling pathways
• horizontal and vertical grid resolution
• parameterization of sub grid-scale physics (e.g. horizontal and vertical mixing schemes)
• atmospheric forcing (e.g. wind, solar radiation, pCO₂)
• lateral boundary conditions

There is a wide range of biogeochemical model complexity,¹⁴ and the optimal choice may be site-specific. However, the biogeochemical model at minimum must explicitly simulate DIC and TA, with pH, pCO₂, and $\Omega_{CaCO3}$ calculated as diagnostic variables. In addition, representation of a limiting macronutrient (e.g. NO₃^-) and phytoplankton biomass is required for a minimum representation of the ocean carbon cycle. The model must be well-validated against observations.

The variables above are typically represented as tracers in the physical-biogeochemical model, and each tracer is governed by an equation that describes the time rate of change of the tracer concentration. The processes that affect the tracer concentration include advection by currents, diffusion, and sources and sinks of the tracer.

The equations and parameters used for each biogeochemical variable must be reported and described in the PDD. For example, the following sources and sinks should be considered for DIC and TA:¹³

• DIC: air-sea CO₂ exchange, freshwater flux, biological uptake and respiration, sinking of calcium carbonate and re-dissolution at depth, sinking of particulate organic matter and remineralization at depth
• TA: riverine input, biogenic calcium carbonate formation and dissolution, nutrient cycling

At minimum, two simulations must be run: a baseline simulation and a CDR intervention simulation that represents the Project Activity. The exact numerical experimental setup and how the Project Activity is represented in the model will depend on the CDR approach and specific project design (e.g. continuously operating or operating over discrete periods). See the relevant Protocol for guidance. Descriptions of the numerical experiments carried out must be described and justified in the PDD.

The following model output is needed from both the baseline and intervention simulations for quantification:

• 2D maps of the air-sea CO₂ flux, at a minimum output frequency corresponding to the frequency of credit issuance (e.g. monthly), where results must be the cumulative flux in time since the beginning of the simulation
• 3D output of DIC, at a minimum output frequency corresponding to the frequency of credit issuance (e.g. monthly), where results must be averaged in time for each output period

The net CO₂e removal due to air-sea gas exchange at a given time t, $\Delta CO_{2, AirSeaFlux}(t)$, is determined as:

$$\Delta CO_{2, AirSeaFlux}(t)=(44/12)*(DIC_{intervention}(t) -DIC_{baseline}(t))$$

Equation 3

Where $DIC_{intervention}(t)$ and $DIC_{baseline}(t)$ are the total amounts of DIC in the ocean domain at time t with and without the CDR intervention, respectively. The units of $DIC_{intervention}(t)$ and $DIC_{baseline}(t)$ are tonnes of carbon, so a factor of (44/12) is used to convert from tonnes of carbon to tonnes CO₂.

The removal over a Reporting Period, RP, spanning the time period from $t_1$ to $t_2$ is $\Delta CO_{2, AirSeaFlux, RP} = \Delta CO_{2, AirSeaFlux}(t_2) - \Delta CO_{2, AirSeaFlux}(t_1)$. Note that $\Delta$ is used to represent a difference between the CDR intervention and baseline scenario.

The terms on the right-hand side of Equation 3 can be calculated with two methods described below. To ensure this calculation is correct, we recommend computing $\Delta CO_{2, AirSeaFlux}(t)$ using both approaches to make sure the same answer is obtained.

Method 1: Surface integral of CO₂ fluxes

Integrating the air-sea gas CO₂ flux over the model domain, in both the intervention and baseline simulations yields:

$$DIC_{intervention}(t) = \int \,dx \int \,dy ~ \Phi_{intervention} \,(x,y,t)$$

$$DIC_{baseline}(t) = \int \,dx \int \,dy ~ \Phi_{basline} \,(x,y,t)$$

Equation 4

In Equation 4, $\Phi$ is the cumulative CO₂ flux in time since the start of the simulation, with units of mass of carbon per area. Here, $x, y$ represent horizontal coordinates. After integrating in space and time, the result of the above integral represents the total amount of carbon that entered or remained in the ocean between time 0 (start of the simulation) and time $t$. Subtracting the baseline from the intervention yields the additional amount of carbon removed due to the project activity.

Method 2: Volume integral of DIC

The second approach calculates the total amount of DIC at time $t$ for each simulation, and subtracting the baseline simulation from the intervention simulation yields how much additional DIC is stored in the ocean at time $t$ as a result of the Project Activity.

$$DIC_{intervention}(t) = \int \,dx \int \,dy \int \,dz \,~ DIC_{intervention} (x,y,z,t)$$

$$DIC_{baseline}(t) = \int \,dx \int \,dy \int \,dz \,~ DIC_{baseline} (x,y,z,t)$$

Equation 5

In Equation 5, Here, $x, y$ represent horizontal coordinates and $z$ represents vertical coordinates.

Sense check

As a sense check to ensure the above calculations are reasonable, $\Delta CO_{2, AirSeaFlux}(t)$ should always be > 0, representing a net increase in DIC in the ocean through either an increase of CO₂ entering the ocean or a decrease of CO₂ outgassing.

Models are never a perfect representation of the real world and all models will have limitations due to simplifying assumptions. At this time, more research is needed to better understand and constrain the impacts of model uncertainties on the carbon removal quantification. Types of uncertainties that can arise in the calculation of $\Delta CO_{2, AirSeaFlux}(t)$ include:

1. Uncertainty in the representation of a CDR intervention in the model. This can be due to uncertainty in the measurements and models used to quantify the turbulent mixing and local dynamics in the vicinity of the CDR intervention. For example, there may be some variability in the depth-distribution of the pCO₂ deficit water, which can lead to uncertainty in how the CDR intervention is represented in the ocean model.
2. Uncertainty in the model’s representation of the real world. This is because models must make simplifying assumptions for the sake of computational tractability. Examples of these assumptions include parameterizing dynamics smaller than the model grid size, or simplifying the representation of diverse phytoplankton species into a single pool of primary producers. Furthermore, the inputs, boundary conditions and forcings applied to models are based on imperfect and incomplete observations, which leads to additional uncertainty.

Uncertainty in the representation of a CDR intervention can be assessed by quantifying the expected variability and uncertainty of the CDR forcing that is applied to the model. This is specified by the relevant protocols for each CDR approach. Then, multiple simulations can be run across various inputs that span the uncertainty in CDR forcing, generating a spread of $\Delta CO_{2, AirSeaFlux}(t)$ from which an uncertainty discount can be determined.

Uncertainty in the representation of the real world can be assessed in multiple ways, such as:

• Within a single model, there are many choices of model parameters that can be varied which may lead to a spread of $\Delta CO_{2, AirSeaFlux}(t)$ results, e.g. the gas transfer velocity, or the eddy diffusivity and viscosity. Ensemble simulations where these parameters are varied based on their uncertainties can be used to assess their impact on $\Delta CO_{2, AirSeaFlux}(t)$
• Also within a single model, the intrinsic chaotic variability of the ocean or atmospheric forcing can be assessed with ensemble simulations where the initial ocean state and/or atmospheric forcing is slightly perturbed.
• There is also a wide range of ocean physical-biogeochemical models with different parameterizations, numerical solvers, representations of biogeochemistry, etc., and simulating the same CDR intervention with different models will likely never produce the exact same results. Multi-model comparisons can be used to identify and decrease uncertainties due to model biases.
• Data-model comparisons, which are already done as part of model validation, provide valuable insight into model skill. However, note that mismatch between observations and models can be due to uncertainty in both the model, as well as uncertainty in the observations as the ocean is relatively sparsely sampled, and sampling can be biased towards certain regions and seasons.

It is not expected that a Project Proponent quantifies all potential uncertainties, as there will always be unknown unknowns, and a thorough assessment of the all known uncertainties is beyond the capabilities of a single project. Furthermore, the dominant sources of uncertainty will vary for each site and project. At this time, it is encouraged for Project Proponents to contribute to advancing scientific knowledge by assessing and quantifying different sources of uncertainties and sharing their results. At a minimum, Project Proponents are required to:

• Disclose known limitations of the model(s) used based on the literature and data-model comparisons in the PDD, and discuss how those uncertainties are expected to impact the net CDR calculation.
• Identify the largest expected sources of uncertainty for their particular CDR approach and discuss expected impacts on the net CDR calculation.
• Quantify an uncertainty in $\Delta CO_{2, AirSeaFlux}(t)$ for at least one of the largest sources of uncertainty identified, based on one of the example types of ensemble simulations described above, or through another approach that is thoroughly described and justified in the PDD.
• Use the distribution of $\Delta CO_{2, AirSeaFlux}(t)$ obtained through the uncertainty analysis to quantify the overall uncertainty in the net CDR removal equation for a given Protocol, for example by taking a conservative estimate of$\Delta CO_{2, AirSeaFlux}(t)$ as 1 standard deviation below the mean.
• For other identified large sources of uncertainty that are not explicitly quantified, Project Proponents must estimate a conservative discount effect on $\Delta CO_{2, AirSeaFlux}(t)$, with a plan to reduce this uncertainty over time through quantification.

The treatment of uncertainty will be updated with learnings from initial marine CDR projects and scientific studies.

Model validation requirements are based on the intended usage, and models need to be accurate to the degree that is necessary to quantify carbon uptake. As the requirements for carbon removal quantification evolve in the future, model requirements and validation will also be updated accordingly. As of this writing, there is a lack of datasets available for validating and calibrating specific representations of CDR interventions in ocean models, so model validation is performed by comparing baseline simulations to historical observations. For accurate representation of CO₂ uptake through air-sea gas exchange, it is necessary for the model to have a high fidelity representation of the physical flow field as well as the carbonate system. This can be demonstrated either through using a previously validated model, or conducting an in-depth validation of a newly developed model.

A previously validated model must have a track record of use in science, industry, government, or other applications. This can be demonstrated through multiple peer-reviewed papers, or proof of usage in a number of previous applications. These models can be used for OAE if one of the following cases is true:

• the model was specifically formulated for studying a marine CDR intervention similar to the Project Activity (e.g. the model is fit-for-purpose for marine CDR)
• the model formulation and original use case is general enough that it can be reasonably used for OAE applications. For example, an acceptable model might be developed to generally accurately represent the ocean physics and biogeochemistry of a region and has been used to study many different applications.

An unacceptable model is one that was specifically developed to investigate a non-marine CDR process because certain assumptions may have been made to that specific case.

Models without a track record of use must be validated against reputable data sources, which include quality-controlled in situ measurements and public datasets adhering to FAIR principles.^{15, 16} Note that mismatch between observations and model results can be due to uncertainty in both the model, as well as uncertainty in the observations as the ocean is relatively sparsely sampled (and sampling can be biased towards certain regions and seasons).

It is highly recommended that as part of model validation, the Project Proponent report multiple metrics such as: root mean square error (RMSE), bias, correlation coefficient, z scores, and model skill.^{14, 17} If applicable, the accuracy of representing important regional processes (e.g. sea ice) is also needed. An example of model validation that uses a combination of multiple metrics as well as qualitative comparisons of sea ice representation is shown in Kearney et al. (2020).¹⁸ Examples and recommendations of ways to demonstrate accurate representation of the physical flow field and carbonate system are discussed below.

Validation of physical flow field

Accurate representation of physical transport (advection, mixing, subduction) can be assessed through evaluating the mean distributions, seasonal variability and time-dependent evolution of:

• 3D temperature and salinity (e.g. from Argo data, ship tracks, moorings, gliders)
  • Sea surface temperature (from satellites)
  • Mixed layer depth
• Surface currents (e.g., large scale geostrophic currents from satellite altimetry)
• Eddy kinetic energy (e.g., from current meters or inferred from satellite)

Validation of carbonate system

Accurate representation of the baseline carbonate system can be assessed through comparing the mean 3D distributions, seasonal variability and time-dependent evolution (if possible) of the following modeled parameters against observational data:

• Carbonate system: DIC, alkalinity, pH, pCO₂, 𝞨CaCO₃
• Biogeochemical parameters: oxygen, nutrients (NO3-), chlorophyll-a, phytoplankton biomass (if possible)

Note that for DIC and alkalinity, datasets from direct bottle samples as well as derived from other measurements can both be used. Direct measurements from bottle samples are the most accurate but are much more limited since they are expensive and difficult to collect. On the other hand, datasets where DIC and alkalinity are derived using algorithms with more easily measured parameters (e.g. biogeochemical Argo floats¹⁹) may have larger uncertainties, but wider spatial and temporal coverage, which is useful for assessing relative variability.

The model results that inform credit issuance must be reproducible. Thus, the following needs to be reported in the PDD for verification:

• Written description and justification of model choices
• Proof of model validation, including description and results of validation if necessary
• All model files and code needed to repeat the simulation, including:
  • Initial conditions
  • Model grid file
  • Boundary conditions
  • Atmospheric forcing files
• All model output analyzed to calculate CO₂ removal
• Results from model sensitivity tests and assessment of uncertainty

Project Proponents must specify a Crediting timeline in the PDD, which describes the frequency at which Credits will be issued based on the progression of air-sea gas exchange. For example, one option could be that Credits will only be issued once, after (near) complete air-sea equilibration has occurred. In this case, the Project Proponents should pick a time t in Equations 3 to 5 that represents the timescale of near-complete air-sea gas exchange. Another option is to issue Credits incrementally, for example monthly, based on the amount of net CO₂e removal that has occurred since the previous issuance of Credits.¹¹

1. Garbe, C. S., Rutgersson, A., Boutin, J. et al. (2014). Transfer Across the Air-Sea Interface. Ocean-Atmosphere Interactions of Gases and Particles. https://doi.org/10.1007/978-3-642-25643-1_2 ↩

2. Ho, David T., De Carlo, Eric H., Schlosser, Peter (2018). Air-sea Gas Exchange and CO2 Fluxes in a Tropica Coral Reef Lagoon. Journal of Geophysical Research: Oceans, 123, 8701-8713. https://doi.org/10.1029/2018JC014423 ↩

3. Ho, D.T. and Wanninkhof, R., 2016. Air–sea gas exchange in the North Atlantic: 3He/SF6 experiment during GasEx-98. Tellus B: Chemical and Physical Meteorology, 68(1), p.30198.DOI: https://doi.org/10.3402/tellusb.v68.30198 ↩

4. Ho, D. T., Law C. S., Smith, M. J., et. al. (2006). Measurements of air-sea gas exchange at high wind speeds in the Southern Ocean: Implications for global parameterizations, Geophysical Research Letters, 33, L16611, doi:10.1029/2006GL026817 ↩

5. Wanninkhof, R. (2014). Relationship between wind speed and gas exchange over the ocean revisited. Limnology and Oceanography Methods, 12. https://doi.org/10.4319/lom.2014.12.351 ↩ ↩² ↩³

6. Ho, D. T., N. Coffineau, B. Hickman, N. Chow, T. Koffman, and P. Schlosser (2016), Influence of current velocity and wind speed on air-water gas exchange in a mangrove estuary, Geophys. Res. Lett., 43, 3813–3821, https://doi.org/10.1002/2016GL068727 ↩

7. Jones, D., Ito, T. Takano, Y., et. al. et al. (2014) Spatial and seasonal variability of the air-sea equilibration timescale of carbon dioxide. Global Biogeochemical Cycles, 28, 1163–1178. https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2014GB004813 ↩

8. Ho, D. T., Bopp, L., Palter, J. B., et. al. (2023). Monitoring, reporting, and verification for ocean alkalinity enhancement. State of the Planet, 2-oae2023, 12, https://doi.org/10.5194/sp-2-oae2023-12-2023. ↩ ↩²

9. Mu et al. (2023) Considerations for hypothetical carbon dioxide removal via alkalinity addition in the Amazon River watershed, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2022-1505 ↩

10. Zhou, M., Tyka, M., Ho, D., Yankovsky, E., Bachman, S., Nicholas, T., ... & Long, M. (2024). Mapping the global variation in the efficiency of ocean alkalinity enhancement for carbon dioxide removal. ↩

11. Bach, L.T., Ho, D.T., Boyd, P.W. and Tyka, M.D. (2023). Towards a consensus framework to evaluate air-sea CO₂ equilibration for marine CO₂ removal. Limnology and Oceanography Letters, 8: 685-691. https://aslopubs.onlinelibrary.wiley.com/doi/full/10.1002/lol2.10330 ↩ ↩²

12. https://carbontosea.org/grantees/ ↩

13. Fennel, K., Long, M. C., Algar, C., et al. (2023) Modelling considerations for research on ocean alkalinity enhancement (OAE). State of the Planet 2-oae2023, 9, https://doi.org/10.5194/sp-2-oae2023-9-2023 ↩ ↩²

14. Fennel, K., Mattern, J.P., Doney, S.C. et al. (2022). Ocean biogeochemical modelling. Nature Review Methods Primers 2, 76. https://doi.org/10.1038/s43586-022-00154-2 ↩ ↩²

15. Wilkinson et al., 2016 The FAIR Guiding Principles for scientific data management and stewardship. Scientific Data https://www.nature.com/articles/sdata201618 ↩

16. Some examples of acceptable datasets can be found at: Copernicus Marine Environment Monitoring Service - Data store, Integrated Climate Data Center, OCADS ↩

17. Stow, C. A., Jolliff, J., McGillicuddy, D. J., Doney, S. C., Allen, J. I., Friedrichs, M. A. M., Rose, K. A., & Wallhead, P. (2009). Skill assessment for coupled biological/physical models of marine systems. Journal of Marine Systems, 76(1–2), 4–15. https://doi.org/10.1016/j.jmarsys.2008.03.011 ↩

18. Kearney, K., Hermann, A., Cheng, W., Ortiz, I., and Aydin, K. (2020). A coupled pelagic–benthic–sympagic biogeochemical model for the Bering Sea: documentation and validation of the BESTNPZ model (v2019.08.23) within a high-resolution regional ocean model, Geosci. Model Dev., 13, 597–650, https://doi.org/10.5194/gmd-13-597-2020. ↩

19. Williams et al. (2017). Calculating surface ocean p CO₂ from biogeochemical Argo floats equipped with pH: An uncertainty analysis. Global Biogeochemical Cycles. https://doi.org/10.1002/2016GB005541 ↩