Substantial inter-model variation in OAE efficiency between the CESM2/MARBL and ECCO-Darwin ocean biogeochemistry models

Tyka, Michael Dominik; Zhou, Mengyang; Yankovsky, Elizabeth; Carroll, Dustin

doi:https://doi.org/10.5194/egusphere-2025-3713

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https://doi.org/10.5194/egusphere-2025-3713

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27 Aug 2025

| 27 Aug 2025

Substantial inter-model variation in OAE efficiency between the CESM2/MARBL and ECCO-Darwin ocean biogeochemistry models

Michael Dominik Tyka, Mengyang Zhou, Elizabeth Yankovsky, and Dustin Carroll

Abstract. Induction of a surface-ocean DIC (dissolved organic carbon) deficit through alkalinity-based or direct CO₂ removal methods has been recognized as a promising approach to meet the projected need for negative emissions. The difficulty of directly measuring the counter-factual CO₂ flux due to rapid spreading of the DIC-deficient plume has put ocean circulation models in the center of the Measurement, Reporting and Verification (MRV) challenge. Confidence in the results of such models is essential for the emerging industry to access carbon credit markets and grow at the required pace, to reach substantial negative emissions by 2050, as envisioned by the Intergovernmental Panel on Climate Change (IPCC).

The kinetics and equilibration time of such a DIC deficit have been shown to vary substantially depending on the location and season of the initial induction point. A major component of this variance is the vertical transport and mixing of the DIC-deficient plume; however, air-sea CO₂ gas exchange and carbonate chemistry are also important.

Currently, it is poorly understood how much the results of DIC-deficit pulse simulations depend on the models chosen. To help close this knowledge gap, we investigate two global circulation models, the CESM2/MARBL model (1°) and the data-assimilative ECCO-Darwin model (1/3°). We perform pulse injection simulations at twelve locations with both models, matched precisely in terms of injection patch geometry, release year and season. We analyze the differences in CO₂ uptake curves, vertical mixing, gas exchange and carbonate chemistry.

We show that in some locations, such as subtropical regions, substantial differences exist between these two models — well beyond the expected intrinsic variation of each model. Furthermore, we demonstrate that the majority of the differences are attributable to the representation of vertical transport, followed by the effect of wind parameterizations. A small amount of difference is attributable to carbonate chemistry parameterization. In some locations, there exists good agreement between the models. In most injection locations, the largest differences between models are found in the first 7 years post alkalinity injection, followed by slow convergence towards the expected theoretical maximums.

Received: 30 Jul 2025 – Discussion started: 27 Aug 2025

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Michael Dominik Tyka, Mengyang Zhou, Elizabeth Yankovsky, and Dustin Carroll

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-3713', Anonymous Referee #1, 16 Oct 2025
This work is innovative and highly relevant. It addresses the complex challenge of comparing models when plume trajectories and CO₂ equilibration both differ and are interlinked. The proposed methodology is elegant and offers a valuable approach for disentangling model parameterizations. This study could inspire future multi-model comparisons of OAE. Overall, it represents a strong and meaningful contribution to understanding OAE model uncertainties. It requires minor clarifications, figure adjustments, and additional context for full clarity.
Specific comments:
Line 110: Sea ice should be mentioned here, given that it is studied in your work. You could also consider mentioning thermal effects (e.g., changes in dDIC/dCO₂ affecting equilibration rate constants) and salinity.

Table 1: How the optimization method of ECCO-Darwin may influence the results?

Line 151: Please include the corresponding figure in the supplementary materials.

Line 188: Could you rephrase this sentence. It is unclear why this equilibration rate differs from Zeebe and Wolf-Gladrow (2001). Also, clarify that μ represents vertical dilution, not horizontal (if I understood correctly), and clarify z0.

Lines 200–230: Equations (3) and (4) are referenced but not explicitly defined. Please add their definitions.

Line 220: The weighting method appears to overestimate the plume extent since surface decay is not included. Will this plume attribution method remain valid in longer simulations with multiple OAE deployments? It seems that plumes extent could be overestimated, with accumulation in the ocean and mixing occurring without any corresponding effect on the carbon flux.

It is not entirely clear to me weighting with ΔDIC is problematic, shouldn’t the weights reflect both the trajectory and gas exchange history?

Please provide an explicit definition (equation) for the weights wᵢⱼ.

Lines 295–305: This section suggests that all locations converge after seven years. Please rephrase for clarity. The phrase “not observed in the North Atlantic” is confusing since Figure 1 indicates similar behavior is absent in the Western Sahara, Oman, and the U.S. East Coast. Even Although you discuss these differences later in the text, consider rewording this paragraph to introduce the subsequent sections.

Lines 310–320: A short discussion on how interannual variability influences nₘₐₓ, and why this differs between injection sites and models, would be valuable.

Line 325: Can convergence can really be concluded from Figure 2? It is only evident in panel 2a.

Figure 3: Please move the legend away from the curves for readability. Consider adding a zoom on the first few months.

Line 340: The reported correlation is not immediately evident. It may help to show this relationship explicitly in an additional panel or inset. There appears to be sufficient blank space in Figure 3 to include both plots clearly.

Line 340: The phrasing “the effect is much stronger” suggests subduction causes the n(t) difference in Norway, but this interpretation seems premature. The correlation is not clear, Alaska shows similar n(t) curves between models despite larger surface fraction differences.

Line 370: Did Xie et al. use coastal or offshore injection? Can this change their interpreatation?

Line 402: The sentence “This is consistent with a general understanding that ocean carbonate chemistry is well understood and therefore not a major contributor to the final efficacy of OAE” seems to be missing a word—perhaps “uncertainty” or “variability”?

Lines 410–420: Could you comment on the effect of wind on MLD?

Line 433: The discussion on biological influence is insightful. However, the cause–effect relationship in this sentence is unclear: “However, the shape of the OAE efficiency curves is, in principle, independent of the quantity added, so in that sense the efficiency curves appear to be indeed relatively independent of biological activity’. Consider rephrasing for clarity.

Line 451: It would help readers if you reiterated which parameters are being referred to here. Also, it is not clear how parameters vary in Figures 9–12 or the magnitude of these variations. This information could be added to the Methods section.

Line 462: Please specify the magnitude of the change in β.

Line 464: Please add a reference to a figure supporting this result.

Figures 9–11: Add x-axis labels and include the black line in the text legend.

Figure 9: Were ECCO-Darwin parameters also changed to CESM2 ones? Does the 3-hourly versus 6-hourly wind forcing matters?

Line 490: One might argue that the remaining challenge lies in accurately determining the location of the plume.

Line 502: Providing specific locations would make the statement clearer to readers.

Figure 13: You might consider moving this figure earlier in the manuscript.

Line 576: It may be worth reiterating that vertical DIC and alkalinity gradients need to be appropriately resolved, as this is highly dependent on the biological representation.

Limitations paragraph: Could you discuss limitations specific to ocean-only models? For instance, are internal variability and feedback processes a concern?

General :
Ensure consistent labeling of subplots : use i), ii), iii) in figure, referred to a) b) c) in the text legend.

Fig 11 & 12 : Should it be “ECCO minus CESM2” in figures inset legend?
Citation: https://doi.org/10.5194/egusphere-2025-3713-RC1
RC2: 'Comment on egusphere-2025-3713', Anonymous Referee #2, 21 Oct 2025

Review of “substantial inter-model variation in OAE efficiency between the CESM2/MARBL and ECCO-Darwin ocean biogeochemistry model”

This study presents a model intercomparison examining how ocean alkalinity enhancement efficiencies in virtual alkalinity deployments differ due to differences between ocean biogeochemistry models. The upshot is that uncertainties (or biases) in vertical transport in the upper ocean are associated with pretty substantial uncertainties (or biases) in OAE efficiency in popular global ocean biogeochemical models. This is a valuable contribution to the literature, building on recent work to map OAE efficiency and understand its sensitivity to deployment location and ocean circulation regime. It should be published after revision.
Comments/suggested revisions line-by-line:
Table 1. If you’re going to include this Biological Ablation Experiment, I think you should include some reference to and discussion of the actual equations in Darwin and specifically the coupling between Alk, Dic and biology, and whether it is realistic. In general, I think you should have more explicit caveats about potential missing processes, e.g. small-scale plume processes, microscale processes on particles, etc.
L121: State the definition of the brackets [..]
Eq1-2 / Supplemental Material. I didn’t check all the calculations completely. That said, they feel out of scope for this paper. Can you justify why this is needed or appropriate in this context? Why can’t you just use available tools? Is there some reason why you can’t make these calculations using existing infrastructure in pyCO2SYS, e.g. finite differences or automatic differentiation? Are sensitivities like d DIC/ dCO2 or d ln DIC/d ln CO2 not already available from existing outputs of pyCO2SYS? Is this critical to making your computations efficient, i.e. speeding up pyCO2SYS for this application?
The map in Fig S1 would be better in the main text.
Fig S2. If you’re going to keep this material, it would help to discuss how frequently/where DIC/Alk > 1 occurs in the real ocean and thus whether this parameterization improvement beyond Tyka et al. 2022 has practical relevance. The approximation from Tyka et al. 2022 is nice to have here, but how important are these adjustments. Also, I’m wondering if OAE could push the system into low DIC/Alk< 0.5, where the approximations start to fail? (I don’t see how it could push it to high DIC/Alk)
Eq (2): I’m a little wary about this. Be careful to discuss units on these. The Revelle factor d ln CO2/d ln DIC has the advantage of making this type of sensitivity unitless.
Section 2.6: What does “surface dilution” versus “surface distribution” mean? This is not very intuitive. Does it mean vertical vs lateral distribution of the plume? Be more precise and maybe show and discuss examples.
L169/Eq 3: To me, “fully re-equilibrate with the atmosphere (not accounting for reservoir feedbacks (Tyka 2025))” is not quite the right wording. It is not clear what you mean by “equilibrate” or “re-equilibrate”. The equation is also a bit imprecise here, because d DIC/dAlk varies spatially and temporally, as the plume moves. So it is not really a partial derivative. I think of this more precisely as representing a theoretical scenario in which co2 flux adjustment to surface alkalinity perturbations are instantaneous and leave pCO2sw unchanged, in which the partial derivatives make more sense. However, I appreciate the desire to frame it as the limit of a long-term adjustment when the ocean is fully mixed, which is related because the partial derivatives do not vary that much in space and time… Try to frame better.
Related to the above/Eq 7 I think the relationship between pCO2sw and DIC is non-linear, so expressing beta as a partial derivative can introduce errors for large D. By contrast, the partial derivative in eta_max is reasonably linear and thus not so sensitive to large perturbations. I’d appreciate seeing some initial plots of 1/D dD/dt and r, which should not be the same due to the various approximations, maybe in the appendix. Showing errors and giving some intuition. It feels like you jump to the model comparisons without illustrating this initial methodology.
Section 2.7.1/Figures 9-10: I’m confused. I don’t follow what is interchanged and what the 4 lines on the plot represent. Shouldn’t there be a matrix of 9=3 x 3 scenarios for each parameter and virtual deployment? 3 different physical plumes (reflecting same changes in both numerator and denominator in each scenario) and 3 different ratios reflecting different values in numerator and denominator (ECCO 99/CESM99; ECCO92/CESM99; ECCO99/ECCO92) or more if oceanSODA is included as an option for k and beta? Please clarify what is happening here and in the comparisons in Fig 9-10.
Figs 1/4: Move the map in Supplemental to the Main Manuscript.
Fig 3: It would help if you could show zoomed in the first 1-2 years by making the x axis non-uniform. Legend in (a) could be moved to the top right of the panel.
Fig 3-5: We need a more precise definition and maybe plot showing example of how “surface fraction” and “surface-ocean excess alkalinity fraction” are defined. See my comment above about this.
Fig 6f: perhaps use eta_max on the x axis rather than the partial derivative? also what are the units in panels e-f?
Fig 8: I don’t think this Biological Ablation experiment is worth publishing. See my comments above regarding the model formulation. The lack of sensitivity is unsurprising to me, and I’m not sure the Darwin model adequately captures the sensitivities of biology to DIC and Alk (to the extent these sensitivities are significant at all). (I'm more surprised by the difference near Oman)
Figs 9-10: What is the black line? (See my related comment in Section 2). I get a bit overwhelmed by the examples here. I suggest: a) try to reduce the content in Figs 9-12 to a table if possible and/or b) synthesize the narrative and reduce the number of plots. Questions to think about: What is the message you are trying to convey here? Could most of this be in supplemental? Why 6 examples or 12 examples or 2 examples? Why just time series? Why no plots of depth and time if vertical distribution is so important?
Fig 10/12: Use of the term “tropical” rather than “near-equatorial” is more appropriate for these regions.

Citation: https://doi.org/10.5194/egusphere-2025-3713-RC2

Michael Dominik Tyka, Mengyang Zhou, Elizabeth Yankovsky, and Dustin Carroll

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Michael Dominik Tyka, Mengyang Zhou, Elizabeth Yankovsky, and Dustin Carroll

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Short summary

Quantification of the kinetics of the induced ocean CO₂ uptake following application of marine carbon dioxide removal technologies (mCDR) is crucial for such technologies to gain scientific and social acceptance. Here, we compare two circulation models commonly used for this purpose and find substantial differences in their predictions. We analyze which physical aspects of the models contribute the most to the inter-model discrepancies, and thus require future research.


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