Simulating enhanced ocean alkalinity experiments in a high-latitude fjord using nested ROMS simulations coupled with MARBL biogeochemistry

Heede, Ulla K.; Long, Matthew C.; Karspeck, Alicia; Bachman, Scott; Loose, Nora; Stephenson, Dafydd; Ho, David T.; Gerke, Lennart; Koffman, Tobias; Benoit-Cattin, Alice; Harðardóttir, Sara; Macrander, Andreas

doi:10.5194/egusphere-2026-2920

Preprints

https://doi.org/10.5194/egusphere-2026-2920

Preprints

12 Jun 2026

| 12 Jun 2026

Simulating enhanced ocean alkalinity experiments in a high-latitude fjord using nested ROMS simulations coupled with MARBL biogeochemistry

Ulla K. Heede, Matthew C. Long, Alicia Karspeck, Scott Bachman, Nora Loose, Dafydd Stephenson, David T. Ho, Lennart Gerke, Tobias Koffman, Alice Benoit-Cattin, Sara Harðardóttir, and Andreas Macrander

Abstract. Ocean-based carbon dioxide removal (CDR) technologies have the potential to make significant contributions to climate change mitigation, yet more research is needed to deepen our understanding of their effectiveness and safety. One proposed method, ocean alkalinity enhancement (OAE), involves increasing seawater alkalinity to promote additional carbon uptake and long-term storage in the ocean. Ocean models are crucial tools to accompany OAE field trials and research, as alkalinity signals are rapidly diluted, and observations alone cannot capture the spatiotemporal scales at which interventions evolve. The C-Star open source regional ocean-biogeochemical modeling system is designed to support OAE research and quantification. Here, we present results from deploying C-Star in a nested regional modeling configuration established for Hvalfjörður, a fjord located in western Iceland. We compare the model solution with observations collected during a 2024 field campaign. These include repeated measurements of the fjord’s physical and chemical state, as well as a tracer release and sampling program used to assess the model’s ability to reproduce tracer transport and dispersal. We find that the model captures key features of the circulation in the fjord, including tidally driven currents and sea-surface height variations, tracer dispersal, and seasonal stratification. Next, we use C-Star to simulate six 96 hr OAE releases in the fjord under varying seasonal, tidal, and weather conditions. The OAE experiments produce a ~1 km² plume with detectable anomalies in alkalinity, pH and pCO₂ during the release. The uptake of CO₂ from the atmosphere is 0.05 to 0.15 mol of carbon absorbed per mol of added alkalinity during and four days following the release, and surface winds and seasonal stratification are key for both alkalinity dispersal and air-sea gas exchange. The model exhibits background biases in alkalinity, dissolved inorganic carbon (DIC), and nutrients, arising from limitations in initial and boundary conditions and representation of in situ biogeochemical processes. While these biases are a target for improvement, we show that they do not significantly degrade the model’s ability to simulate OAE-relevant anomalies. Overall, this work enhances confidence in the applicability of C-Star nested model domains as OAE research and field-trial support tools in fjord and estuary systems.

Received: 22 May 2026 – Discussion started: 12 Jun 2026

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.

Download & links

Preprint (PDF, 2260 KB)

Supplement (2406 KB)

Download & links

Status: final response (author comments only)

RC1:
'Comment on egusphere-2026-2920', Anonymous Referee #1, 08 Jul 2026

Review of Heede et al.
In this study authors construct ROMS model configuration for high latitude fjord Hvalfjörður. The model performs generally well in simulating the physics, although some biases were reported. Using MARBL biogeochemistry module, idealized OAE experiments were then performed on this model domain to understand the feasibility of this set up in quantifying CDR effect, which in general is difficult by solely relying on observations.
Keeping in mind the recent push for mCDR through OAE, this kind of regional model set up is a timely work which will benefit over all OAE-mCDR community. However, the present version of the manuscript is lacking discussion on the other works this field which needs to be addressed before publication. For example, I see Laurent et al. (2026) is cited, but this was not discussed in discussion. They have done a very similar work on the other side of Atlantic, using similar nested ROMS model configuration. These examples need to be discussed.
The current OAE simulations represent highly simplified approach by adding NaOH which instantaneously elevates the TA concentration. While this is fine for idealized simulations, it is important to discuss if this kind of material would be suitable/feasible in practical deployments. As far as I understand, most real-life deployments are based on alkaline mineral addition, so they are in particulate/slurry forms, which undergoes dissolution at different rates depending on a number of variables. This generates TA that would then be available for CDR. These limitations need to be mentioned in the discussion.

Other comments:
The model underestimates productivity in the surface layer, and remineralization at surface to subsurface depths. This is likely due to iron limitation in the model leading to low PP. Is it possible to show (in supplement) the OM (POC) concentration in the water column, PP production and POC flux to bottom if the relevant model outputs/obs are available?

Line 129: what is NHy?
Line 160-161: briefly state the benefit of dual tracer, either here or in the discussion.
Line 191: typo. ‘biogeochemistry’
Line 228: What would be the unit of I ? Is it the added alkalinity?
Line 248: η_max?
Line 347: For readers, please explain how the salinity-normalized DIC, Alk was calculated, and what information it provides.
Line 391: There’s no Fig 3f. 10f?
Line 393: No Fig S3g.
Line 414-416: It is interesting that for Nov simulations CO2 uptake is higher, even though model simulation shows lower fraction of added alkalinity within the surface layers for Nov compared to July (Fig S11). Fig 11 a,c shows higher cumulative CO2 uptake in Nov. But b,c show DIC anomaly is higher in July compared to Nov. I am having hard time understanding this, and was expecting the DIC signal to be other way around. Could you clarify how the patterns observed in Fig 11 emerges? I see later that due to mixed condition in Nov, even though lower frac of added alkalinity remains in the surface, CO2 draw down continues. Still, I did not understand how the integrated DIC anomalies are higher in July than Nov.

Fig 11e: would it be more appropriate to write as ∑ΔDIC / ∑ΔALK ?
Fig. S10: mention units for oxygen.

Citation: https://doi.org/10.5194/egusphere-2026-2920-RC1
- AC1: 'Reply on RC1', Ulla Heede, 04 Sep 2026
  
  Reviewer 1
  Review of Heede et al.
  In this study authors construct ROMS model configuration for high latitude fjord Hvalfjörður. The model performs generally well in simulating the physics, although some biases were reported. Using MARBL biogeochemistry module, idealized OAE experiments were then performed on this model domain to understand the feasibility of this set up in quantifying CDR effect, which in general is difficult by solely relying on observations.
  Keeping in mind the recent push for mCDR through OAE, this kind of regional model set up is a timely work which will benefit over all OAE-mCDR community. However, the present version of the manuscript is lacking discussion on the other works this field which needs to be addressed before publication. For example, I see Laurent et al. (2026) is cited, but this was not discussed in discussion. They have done a very similar work on the other side of Atlantic, using similar nested ROMS model configuration. These examples need to be discussed.
  Thank you for this comment. We agree that more context for this study would improve the manuscript. We have now added the following paragraph in the introduction:
  “Several regional modeling studies have examined how release location and site-specific conditions influence OAE signal detectability and near-field CO₂ uptake. For example, Laurent et al. (2023) demonstrated in Halifax Harbour, Nova Scotia using 3-nest ROMS model coupled with a combination of explicit and reduced biogeochemistry modules, that release location dictated both the retention time of added alkalinity and the spatial extent of surface pH and pCO2 anomalies. They found that an in-shore release had a much longer residence time, and over twice as much CO2 uptake within the domain after 6 months compared to a location in the outer harbor, which was closer to the open ocean. Other studies using OAE releases in single-nest regional ocean modeling systems have similarly found regional features greatly impact regional scale CO2-uptake. For example, studies in the Bering Sea showing a very high regional CO2-uptake efficiency (0.96 after three years) (Wang et al., 2023) and locations in the North Sea showing coastal releases have a higher CO2-uptake efficiency that open ocean releases prone to deep-sea loss of added alkalinity (Liu et al., 2025) Overall, these studies highlight the need for high-resolution, site-specific modeling efforts to accompany OAE research.”
  And in the discussion we modified the following paragraph to compare our results with other studies:
  “The uptake efficiency—defined as the moles of additional carbon absorbed from the atmosphere per mole of added alkalinity—ranged from 5–15% after 8 days from the start of the experiment. This efficiency is derived from the air–sea CO₂ flux and reflects uptake within the domain. The peak DIC anomalies were low relative to background variability, indicating that confirming CO2 uptake in the fjord via in situ DIC sampling would be difficult. Surface wind speed proved to be a key driver of CO2 uptake in the domain, as strong winds led to rapid CO2 uptake, particularly during the November experiments, when the water column was colder than in the July experiments. While studies such as Laurent et al., (2023) and Lui et al., (2025) focus on differences in CO2 uptake depending on release location, we show here, complimentarily, that near-field CO2-uptake from the same location may vary depending on wind conditions as well as differing seasonal conditions within the water column. In addition, a primary focus in this study is on the near-field detectability of processes associated with alkalinity addition, relevant for field-trial planning and permitting purposes, as well as near-field carbon uptake. To determine the total CO2-uptake from the experiments, a larger ocean domain would be necessary, or an application of an upscaling technique that passes the alkalinity and DIC values from a smaller domain to a larger domain.”
  The current OAE simulations represent highly simplified approach by adding NaOH which instantaneously elevates the TA concentration. While this is fine for idealized simulations, it is important to discuss if this kind of material would be suitable/feasible in practical deployments. As far as I understand, most real-life deployments are based on alkaline mineral addition, so they are in particulate/slurry forms, which undergoes dissolution at different rates depending on a number of variables. This generates TA that would then be available for CDR. These limitations need to be mentioned in the discussion.
  Thank you for this comment. We chose to simulate NaOH addition because this is the material chosen for use in the planned Hvalfjörður field trial. NaOH addition can be thought of as representing the operation of electrochemical alkalinity addition. To address this comment we have added the following paragraph to the discussion section:
  “It is further important to note that our model setup simulated alkalinity addition via NaOH, which represents a simplified, liquid-phase deployment. We intentionally selected NaOH to simulate the planned field-trial, where the goal is to evaluate physical transport and chemical signal detectability in a context representative of electrochemical OAE. Mineral deployments introduce additional complexity because particulate material undergoes sinking, settling, and variable dissolution rates governed by ambient temperature, particle size, and localized saturation states before alkalinity is released into the water column (Laurent et al., 2026). As such, applying this modeling framework to a broader range of alkalinity addition methods would require an integration of particulate dissolution kinetics and mineral settling dynamics.”
  Other comments:
  The model underestimates productivity in the surface layer, and remineralization at surface to subsurface depths. This is likely due to iron limitation in the model leading to low PP. Is it possible to show (in supplement) the OM (POC) concentration in the water column, PP production and POC flux to bottom if the relevant model outputs/obs are available?
  Thank you for this comment. In a new iteration of the model integration, we have disabled the Fe limitation to better match the coastal conditions in the fjord. In this new integration we indeed see much more primary productivity and nutrient drawdowns that match the observations better, and we plan to include results from this new iteration in the revised manuscript. We do not have observations of OM, PP and POC available, but we have included DOC and PP from the model output in an updated supplementary (there is no POC pool in MARBL).
  Line 129: what is NHy?
  In the revised manuscript we have clarified that NHy refers to reduced nitrogen species such as ammonia and ammonium.
  Line 160-161: briefly state the benefit of dual tracer, either here or in the discussion.
  Thank you for pointing out that we missed an explanation for the dual tracer. In the revised manuscript, we have added:
  “ A separate analysis measured both ³He and SF₆ for the purpose of determining air-sea gas exchange rates (Gerke et al. (2026)). Here, for the purpose of tracer dispersal, we only use the SF₆.”
  Line 191: typo. ‘biogeochemistry’
  We have fixed this, thank you.
  Line 228: What would be the unit of I ? Is it the added alkalinity?
  We have specified that the added alkalinity is measured in concentration (mmol/m3)
  Line 248: ηmax ?
  Thank you for catching this, which we have now fixed. Yes indeed, ηmax
  Line 347: For readers, please explain how the salinity-normalized DIC, Alk was calculated, and what information it provides.
  We have added in the methods section a description of how the salinity-normalization is done:
  X_norm=((X-X₀)/S)*S_ref+X₀
  Where X denotes the variable of interest (alkalinity or DIC), X₀ denotes the value of the variable in freshwater (see Supplement for riverine tracer values), X_norm is the salinity-normalized value, S is the corresponding salinity value at the location and time of X, and S_ref is a reference salinity constant set to 34 psu.
  Line 391: There’s no Fig 3f. 10f?
  Thank you for catching this, which we have now fixed. Yes indeed it is Fig. 10f.
  Line 393: No Fig S3g.
  Thank you for catching this, which we have now fixed. It should be Fig. S12g.
  Line 414-416: It is interesting that for Nov simulations CO2 uptake is higher, even though model simulation shows lower fraction of added alkalinity within the surface layers for Nov compared to July (Fig S11). Fig 11 a,c shows higher cumulative CO2 uptake in Nov. But b,c show DIC anomaly is higher in July compared to Nov. I am having hard time understanding this, and was expecting the DIC signal to be other way around. Could you clarify how the patterns observed in Fig 11 emerges? I see later that due to mixed condition in Nov, even though lower frac of added alkalinity remains in the surface, CO2 draw down continues. Still, I did not understand how the integrated DIC anomalies are higher in July than Nov.
  Thank you for this comment. With regards to Fig 11, we discovered a typo in the code for the plot, and we have now corrected the plot, which shows much larger DIC anomalies for the November experiments, consistent with the higher uptake efficiency in those experiments. In addition, we have updated Fig. S11 to show the fraction of alkalinity within the mixed layer rather than the surface layer. Because the mixed layer is much deeper in the November experiments, this more accurately reflects which fraction of added alkalinity is subject to change the surface pCO2.
  Fig 11e: would it be more appropriate to write as ∑ΔDIC / ∑ΔALK ?
  Thank you for this comment. We have applied changes to the figure to reflect the used method of calculating the CO2 uptake efficiency.
  Fig. S10: mention units for oxygen.
  Thank you for pointing out the missing units, we have updated Fig. 10.
  
  Citation: https://doi.org/10.5194/egusphere-2026-2920-AC1
RC2:
'Comment on egusphere-2026-2920', Anonymous Referee #2, 14 Aug 2026
Stated goal: Use C-Star nested regional ocean modeling to simulate the background flow and carbonate system in Hvalfjörður, Iceland, evaluate the model against observational data, and use it to simulate OAE deployments in the fjord.
This manuscript addresses an important need for high-resolution, site-specific modeling tools to support the design and monitoring, reporting, and verification (MRV) of ocean alkalinity enhancement (OAE) field trials. Unfortunately, there is not sufficient methodological detail or evaluation provided to sufficiently judge at this stage and there are some concerns with the results because of that confusion. The comments below are offered to help strengthen the model evaluation, clarify several methodological choices, and improve the overall presentation. With these edits, the paper maybe be suitable for publication in this journal.
Major Comments
The manuscript would benefit from a fuller discussion of prior and related work that this modeling framework builds on. Situating C-Star relative to previous regional ocean modeling and mCDR simulation studies will help readers assess the novelty and contribution of this work.

Section 2.2 states that river forcing is excluded from the two outermost nests and included only for the two innermost nests. Please clarify the reasoning (e.g., data availability constraints) and discuss the implications for the initial and boundary conditions of the inner nests, which are derived from the outer "parent" nests. Additionally, please justify — and, where possible, validate — the choice to source surface iron, NOx, NHy, ammonium, and DOM from the CESM simulation rather than a more regionally resolved product.

Section 2.5 describes the OAE experimental setup (a 4.5% NaOH solution applied at 30 L/min over 96 hours). This design is well suited to testing the model's ability to produce an observable OAE signal. To strengthen the manuscript, please add justification for the chosen alkalinity source, flow rate, and perturbation duration, and discuss the real-world feasibility of this style of alkalinity addition for field deployment.

The boundary conditions draw on GLORYS for physics and on GLODAPv2/WOA for biogeochemistry, and neither BGC product is particularly well resolved regionally. Please discuss the coverage of these BGC products around Iceland, the rationale for pairing disconnected physical and BGC boundary products, whether a more regional or empirical BGC product was considered, and how sensitive the results are to these boundary-condition choices.

Please report the prescribed river end-member values used for each tracer, and clarify whether temperature was included as an end-member variable. Total alkalinity in rivers influenced by glacial or ice meltwater is difficult to constrain given the limited available data — please note this as a limitation and discuss how it may affect the results.

Please expand the model evaluation description in the Methods to specify which performance metrics were used and why. A substantial literature exists on multi-metric regional-model evaluation (see, e.g., Kessouri et al., 2021); adopting quantitative bias and skill metrics — rather than the largely descriptive, qualitative comparisons currently presented — would strengthen the manuscript and align it with the rigor increasingly expected for MRV protocols.

If direct CO2 observations are available, please include a comparison against them in the evaluation section.

Please clarify what the approximately 60 mmol/m3 bias (as Table 2 appears to be limited to July 2024 only) corresponds to in terms of pCO2 or CO2 uptake, and how this bias is being factored into the MRV process. Consider expanding Table 2 to cover a longer period than a single month.

Please add methodological detail on which biogeochemical processes are represented in MARBL — for example, whether calcium carbonate burial is included — and note any known biases from the existing literature that would help readers interpret this paper's results.

Please provide more methodological detail on how salinity normalization was performed in this estuarine setting, given that vertical mixing in seasonally stratified shelf environments continually resets density and complicates this calculation.

Please discuss whether current observational methods could detect the simulated signal in practice, including over what timeframe and spatial extent this would be feasible.

Since the model output allows full carbon tracking, please consider adding a carbon budget showing where the added carbon ends up, whether CO2 is the only carbon species affected or others change as well, and the transported/advected component.

Given the small magnitude of the simulated OAE signal, please compare it against the model's internal variability (e.g., using a perturbed-initial-condition ensemble) to demonstrate that the signal is distinguishable from natural variability.

Please describe how the ensemble was constructed, particularly with respect to addressing the signal-to-noise ratio that affects the results, and expand the Methods accordingly.

Table 2 suggests that the DIC and TA biases act in opposing directions and partially cancel. Please discuss how the authors plan to address these conflicting biases, which appear to contribute to a pCO2 anomaly error that is large relative to the intervention signal.

Please report the total simulation length and describe the spin-up procedure, given the stated importance of initial conditions.

The conclusion that circulation-driven variability — particularly wind-driven variability — is the dominant source of variability in short-term pH excursions and near-field pCO2 anomalies would be better supported by a quantitative budget analysis. Please add this analysis or temper the claim accordingly.

Minor Comments
Table S2: Please add detail on how the salinity normalization for alkalinity and DIC was computed.

Line 235: Please clarify the rationale for multiplying theta by I (the intervention term).

Lines 294–297: Please clarify the connection between the salinity biases noted in the outermost and innermost fjord and the river-forcing configuration — for example, whether the outer-nest bias reflects the absence of river forcing and the inner-nest bias reflects limited river-data coverage. Additionally, the statement that "simulated estuarine circulation in the fjord is too weak" appears to be in tension with the SF6 results (Figs. S6–S7), where modeled average SF6 concentrations are consistently lower than observed — a pattern that would suggest the opposite. Please reconcile this discrepancy or clarify the reasoning.

Lines 330–331: The bulk fjord characteristics appear reasonably well captured by the SF6 results, though a magnitude difference exists between some timestamps in Figs. S6 and S7. The discussion of potential sampling bias as a contributing explanation is a reasonable and sufficient treatment.

Line 391: Figure 3f is referenced in the text but does not appear to be included — please add.

Line 393: Figure S3g is referenced in the text but does not appear to be included — please add.

Line 514: Please provide additional quantitative support for the claim that the seasonal salinity evolution is captured by the model.
Citation: https://doi.org/10.5194/egusphere-2026-2920-RC2
- AC2: 'Reply on RC2', Ulla Heede, 05 Sep 2026
  
  Stated goal: Use C-Star nested regional ocean modeling to simulate the background flow and carbonate system in Hvalfjörður, Iceland, evaluate the model against observational data, and use it to simulate OAE deployments in the fjord.
  This manuscript addresses an important need for high-resolution, site-specific modeling tools to support the design and monitoring, reporting, and verification (MRV) of ocean alkalinity enhancement (OAE) field trials. Unfortunately, there is not sufficient methodological detail or evaluation provided to sufficiently judge at this stage and there are some concerns with the results because of that confusion. The comments below are offered to help strengthen the model evaluation, clarify several methodological choices, and improve the overall presentation. With these edits, the paper maybe be suitable for publication in this journal.
  Major Comments
  The manuscript would benefit from a fuller discussion of prior and related work that this modeling framework builds on. Situating C-Star relative to previous regional ocean modeling and mCDR simulation studies will help readers assess the novelty and contribution of this work.
  Thank you for this comment. We agree that the manuscript will be improved with better context of previous works. In response to this point and to reviewer 1, We have added the following to the introduction:
  To highlight the novelty and contribution of this work, we have further rewritten this paragraph:
  “Several regional modeling studies have examined how release location and site-specific conditions influence OAE signal detectability and near-field CO₂ uptake. For example, Laurent et al. (2023) demonstrated in Halifax Harbour, Nova Scotia using 3-nest ROMS model coupled with a combination of explicit and reduced biogeochemistry modules, that release location dictated both the retention time of added alkalinity and the spatial extent of surface pH and pCO2 anomalies. They found that an in-shore release had a much longer residence time, and over twice as much CO2 uptake within the domain after 6 months compared to a location in the outer harbor, which was closer to the open ocean. Other studies using OAE releases in single-nest regional ocean modeling systems have similarly found regional features greatly impact regional scale CO2-uptake. For example, studies in the Bering Sea showing a very high regional CO2-uptake efficiency (0.96 after three years) (Wang et al., 2023) and locations in the North Sea showing coastal releases have a higher CO2-uptake efficiency that open ocean releases prone to deep-sea loss of added alkalinity (Liu et al., 2025) Overall, these studies highlight the need for high-resolution, site-specific modeling efforts to accompany OAE research.”
  To highlight the novelty and contribution of this work, we have further rewritten this paragraph:
  “The goal of this study is to use C-Star nested regional ocean modeling capabilities to simulate the background flow and carbonate system in Hvalfjörður, Iceland, to evaluate the model solution against observational data, and to simulate potential OAE deployments in the fjord. By establishing the Hvalfjörður domain, which has not previously been modeled with a regional ocean model, we provide a demonstration of the technical feasibility of configuring high-resolution regional ocean-biogeochemical models with C-Star. Furthermore, while other studies deploying ROMS for OAE research focus on CO2-uptake, here we, in addition, establish the model as a tool for supporting CDR field trial planning with focus on signal detectability and evaluating different release results under varying seasonal and weather conditions. Note that the purpose of the study is providing insights on a deployment-relevant scale, and the aim is not to calculate the total carbon uptake from a given CDR intervention for which a larger ocean domain would be required.”
  And to the discussion, we have revised this paragraph to put more context to our findings:
  “The uptake efficiency—defined as the moles of additional carbon absorbed from the atmosphere per mole of added alkalinity—ranged from 5–15% after 8 days from the start of the experiment. This efficiency is derived from the air–sea CO₂ flux and reflects uptake within the domain. The peak DIC anomalies were low relative to background variability, indicating that confirming CO2 uptake in the fjord via in situ DIC sampling would be difficult. Surface wind speed proved to be a key driver of CO2 uptake in the domain, as strong winds led to rapid CO2 uptake, particularly during the November experiments, when the water column was colder than in the July experiments. While studies such as Laurent et al., (2023) and Lui et al., (2025) focus on differences in CO2 uptake depending on release location, we show here, complimentarily, that near-field CO2-uptake from the same location may vary depending on wind conditions as well as differing seasonal conditions within the water column. In addition, a primary focus in this study is on the near-field detectability of processes associated with alkalinity addition, relevant for field-trial planning and permitting purposes, as well as near-field carbon uptake. To determine the total CO2-uptake from the experiments, a larger ocean domain would be necessary, or an application of an upscaling technique that passes the alkalinity and DIC values from a smaller domain to a larger domain.”
  Section 2.2 states that river forcing is excluded from the two outermost nests and included only for the two innermost nests. Please clarify the reasoning (e.g., data availability constraints) and discuss the implications for the initial and boundary conditions of the inner nests, which are derived from the outer "parent" nests. Additionally, please justify — and, where possible, validate — the choice to source surface iron, NOx, NHy, ammonium, and DOM from the CESM simulation rather than a more regionally resolved product.
  We have replaced the original model runs with new integrations that address several shortcomings in the original configuration. Notably, riverine forcing is now applied at all nest levels, and we have updated the text accordingly. While providing an improved representation of aspects of the background biogeochemistry in the fjord, the new integrations do not change any fundamental aspects of the simulated response to alkalinity addition.
  With respect to surface iron, NOx, NHy and DOM, we are not aware of a regionally resolved product to force these variables and we have amended the text to make this point clear and justify our choice of forcing. We do not expect these surface forcing inputs to be of first order for the accuracy of the Iceland fjord integration.
  Section 2.5 describes the OAE experimental setup (a 4.5% NaOH solution applied at 30 L/min over 96 hours). This design is well suited to testing the model's ability to produce an observable OAE signal. To strengthen the manuscript, please add justification for the chosen alkalinity source, flow rate, and perturbation duration, and discuss the real-world feasibility of this style of alkalinity addition for field deployment.
  Thank you for this comment. In the revised manuscript, we have updated the description of the NaOH experiment to address the reviewer’s concern:
  “Each of the 6 ensemble members simulated the discharge of a 4.5% NaOH solution (1.18 × 10⁶ mmol m⁻³) and a flow rate of 30 L min⁻¹ over a 96-hour period (204 kmol alkalinity released in total). Sodium hydroxide (NaOH) was selected as the alkalinity source due to its immediate dissolution, enabling the model to simulate a clean alkalinity representative of electrochemical OAE signal without added complexity of particle dissolution dynamics. The concentration, flow rate , and 96-hour duration were chosen to reflect realistic logistics for conducting a small-scale coastal trial, such as temporary shore-based tank storage and a small pump, while maintaining local pH perturbations within acceptable environmental safety thresholds.
  The addition of alkalinity and freshwater in the model was specified as a volume flux within a single grid cell over the specified duration, and the salinity of the release volume was set to 1 psu (nominal value representative of freshwater) and the temperature to 10°C, while all other tracers were set to zero. This setup provides a sufficiently strong forcing to generate an observable, quantifiable OAE signal in alkalinity, pH, and pCO2 above background variability, without inducing large or long-term baseline alterations to the fjord’s biogeochemistry. These alkalinity release simulations were implemented via a specialized forcing module within C-Star.”
  Furthermore, in the discussion, we have added a caveat of using this type of idealized alkalinity forcing:
  “It is further important to note that our model setup simulated alkalinity addition via NaOH, which represents a simplified, liquid-phase deployment. We intentionally selected NaOH to simulate an idealized field-trial setting consistent with electrochemical OAE, where the goal is to evaluate physical transport and chemical signal detectability without the added complexity of mineral phase transitions. Mineral deployments introduce additional complexity because particulate material undergoes sinking, settling, and variable dissolution rates governed by ambient temperature, particle size, and localized saturation states before alkalinity is released into the water column (Laurent et al., 2026). As such, applying this modeling framework to a broader range of alkalinity addition methods would require an integration of particulate dissolution kinetics and mineral settling dynamics.”
  The boundary conditions draw on GLORYS for physics and on GLODAPv2/WOA for biogeochemistry, and neither BGC product is particularly well resolved regionally. Please discuss the coverage of these BGC products around Iceland, the rationale for pairing disconnected physical and BGC boundary products, whether a more regional or empirical BGC product was considered, and how sensitive the results are to these boundary-condition choices.
  Thank you for this comment. We agree that global climatologies like GLODAPv2 and WOA have coarse spatial resolution relative to modeled coastal/fjord dynamics.
  Around Iceland, GLODAPv2 and WOA incorporate repeat hydrographic measurements around Iceland (see attached figure), but are too coarse to resolve specific conditions within Hvalfjörður. We selected these dataset because, while some single point observational data with sporadic temporal coverage exists for select biogeochemical fields in Flaxafoi bay and Hvalfjörður, we are not aware of any high-resolution, 3D regionally tailored ocean biogeochemical state estimate for south-west Iceland that spans all required carbonate and nutrient variables.
  Pairing dynamic physical reanalyses (GLORYS) with climatological BGC fields is a standard approach in regional ocean modeling. Because our domain boundaries in the outer nest are positioned far from the region of interest (Hvalfjörður), we don’t expect a mismatch between physical and biogeochemical variables at the boundary to have a large influence on biogeochemistry in the fjord.
  As documented in our manuscript, mean biases in alkalinity and DIC values in the inner nest exist, which we determine to be, at least in part, a function of biases in the initial conditions and boundary conditions from the outer nest, forced by GLORYS and WOA. In future work, such biases could be alleviated by creating nest-specific forcing that nudges values of biogeochemical variables in the fjord to observed values and customized boundary forcing files that match observed values in the fjord. Here, as a first step, we instead provide a thorough analysis of the significance of these biases for the purposes of OAE research and MRV.
  Please report the prescribed river end-member values used for each tracer, and clarify whether temperature was included as an end-member variable. Total alkalinity in rivers influenced by glacial or ice meltwater is difficult to constrain given the limited available data — please note this as a limitation and discuss how it may affect the results.
  Thank you for these suggestions. We have updated the description of the riverine forcing data in the supplement to include river end-member values used for each tracer, including temperature. We have, in addition, described the single-point measurement of alkalinity and DIC in the Botnsá river that we use as river forcing for these tracers, and noted the seasonal uncertainty of these values associated with ice meltwater.
  Please expand the model evaluation description in the Methods to specify which performance metrics were used and why. A substantial literature exists on multi-metric regional-model evaluation (see, e.g., Kessouri et al., 2021); adopting quantitative bias and skill metrics — rather than the largely descriptive, qualitative comparisons currently presented — would strengthen the manuscript and align it with the rigor increasingly expected for MRV protocols.
  Thank you for this suggestion. To provide a more quantitative assessment of the model-observation comparison we have included a skill metrics summary table in the revised version of the manuscript, which notes, among other metrics, temporal observation-model correlations R2 values of key variables at select depths (salinity, temperature, east and northward velocities, alkalinity, DIC and nutrient fields) as well as noting the mean bias for each season. Furthermore, we have updated the methods section to describe these metrics, and refer to the values in the results section.
  If direct CO2 observations are available, please include a comparison against them in the evaluation section.
  Thank you for this suggestion. We have added a Figure to the supplement, which shows a model-observation comparison for pCO2.
  Please clarify what the approximately 60 mmol/m3 bias (as Table 2 appears to be limited to July 2024 only) corresponds to in terms of pCO2 or CO2 uptake, and how this bias is being factored into the MRV process. Consider expanding Table 2 to cover a longer period than a single month.
  The 60 mmol/m3 bias corresponds to the average model bias of alkalinity in the fjord in July, where the summer OAE experiments take place. The corresponding bias in terms of pCO2 is reported in table 2. (In response to the point above, we have also added the actual pCO2 bias from measurements). Note that we are not attempting here to do a full MRV analysis as the OAE experiment lengths are 8 days, and a longer timeframe would be needed to quantify the full CO2 uptake. Since our experiments are taking place in July, we only consider values in July. The goal of table 2 is to report on expected pCO2 anomaly biases induced near the release as a result of the intervention size and the known model background biases.
  Please add methodological detail on which biogeochemical processes are represented in MARBL — for example, whether calcium carbonate burial is included — and note any known biases from the existing literature that would help readers interpret this paper's results.
  Calcium carbonate burial is represented in MARBL. Rather than reproduce the full model description here, we direct readers to the comprehensive documentation of the biogeochemical processes represented in MARBL (Long et al., 2021; see, e.g., Section 2.2.7 for calcium carbonate burial). https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2021MS002647
  Regarding known biases, we note that the biogeochemical performance of MARBL cannot be characterized in isolation: biases that emerge in a given ocean region reflect the interplay between the physical ocean model and MARBL rather than the biogeochemistry alone.
  
  Please provide more methodological detail on how salinity normalization was performed in this estuarine setting, given that vertical mixing in seasonally stratified shelf environments continually resets density and complicates this calculation.
  Thank you for this comment. We have added an equation explaining the salinity normalization that we use in the methods section:
  
  X_norm=((X-X₀)/S)*S_ref+X₀
  Where X denotes the variable of interest (alkalinity or DIC), X₀ denotes the value of the variable in freshwater (see updated Supplement for riverine tracer values), Xn_ormis the salinity-normalized value, S is the corresponding salinity value at the location and time of X, and S_refis a reference salinity constant set to 34 psu.
  Note here that we use the salinity values that correspond to the tracer value of interest in time and space (we use modeled salinity for modeled values and observed salinity for observed values), so the salinity normalization value is what the tracer value would be at a 34 psu salinity and thereby accounts for seasonal stratification and vertical mixing.
  Please discuss whether current observational methods could detect the simulated signal in practice, including over what timeframe and spatial extent this would be feasible.
  A key purpose of Fig. 10 in the manuscript is to illustrate the spatial and temporal extent of signal detectability. The white contours on Figs a-d show the spatial extent of the ensemble and time average anomaly above one and two standard deviations of the background variability (as described in the methods). Furthermore, Figs e-h show the timeseries including ensemble spread of the maximum signal, and hence constrain the timeframe wherein a signal could be detectable. To clarify how Fig 10 relates to practical considerations of instrument placement, we have added the following to the manuscript:
  “From a practical monitoring perspective, detecting OAE signal in these field deployments requires sensor placements within 1 km of the outfall for July (100 m for November). Autonomous surface vehicles or fixed mooring arrays equipped with pH and pCO2 sensors, such as Sea-Bird SeapHOx pH sensor and Pro-Oceanus CO2-Pro CV pCO2 sensor (which were deployed during the 2024-2025 field campaign) with 0.05 pH units and 1 µatm pCO2 units precision could resolve the ensemble-mean signal over the 96-hour discharge window and the subsequent 12–24 hour decay period. In addition, discrete water sampling for alkalinity would require a tide-aware repeat sampling strategy that samples the footprint as well as baseline measurements.”
  Since the model output allows full carbon tracking, please consider adding a carbon budget showing where the added carbon ends up, whether CO2 is the only carbon species affected or others change as well, and the transported/advected component.
  In the revised manuscript, we have added a supplementary figure that shows the amount of DIC in the domain over time, including the amount generated from air-sea gas exchange and the amount leaving the domain due to advection. Fig 12 shows the ensemble-mean spatial distribution of DIC in the domain 8 days after release initiated. We note here that in the MARBL dual-carbonate tracer framework, DIC is the only carbon pool affected, so there is no change to biological productivity or standing stocks.
  Given the small magnitude of the simulated OAE signal, please compare it against the model's internal variability (e.g., using a perturbed-initial-condition ensemble) to demonstrate that the signal is distinguishable from natural variability.
  We note here that the variability in atmospheric conditions create a much larger spread in surface ocean conditions than using a perturbed-initial-condition approach would generate. Hence, to address the detectable signal compared with the model’s internal variability, including varying atmospheric conditions, we have generated an ensemble of releases by conducting the release on different days in two different seasons. Fig 10 and Fig S12 show the spatial extent of the time and ensemble averaged signal above one and two standard deviations of the background variability calculated from the observational datasets.
  Please describe how the ensemble was constructed, particularly with respect to addressing the signal-to-noise ratio that affects the results, and expand the Methods accordingly.
  We refer to the response above and in addition, we have added to the methods section:
  “To address signal detectability against background variability, the signal-to-noise ratio was quantified by computing the ensemble mean and ensemble spread across seasonal members (e.g., July vs. November), and mapping the mean anomalies against the standard deviation of natural background variability (Table S2). A signal was defined as statistically distinguishable from background noise where the ensemble-mean anomaly exceeded one to two standard deviations of background fluctuations. Time series of domain-wide maximum and minimum anomalies were further extracted across ensemble members to track peak perturbation magnitudes and quantify the ensemble spread over the release and relaxation phases.”
  Table 2 suggests that the DIC and TA biases act in opposing directions and partially cancel. Please discuss how the authors plan to address these conflicting biases, which appear to contribute to a pCO2 anomaly error that is large relative to the intervention signal.
  We estimate that the pCO2 bias that we expect from model background biases in alkalinity, DIC and temperature is about 10% of the intervention signal near the release site. We have added the following to the discussion, addressing the reviewer’s point:
  “While the physical model solution captured key characteristics of the observed flow, we documented several biases in alkalinity, DIC, oxygen, nutrients and biologic activity. The model exhibited negative biases in background alkalinity and DIC, likely stemming from the coarse resolution of the global datasets used to initialize the biogeochemical model, which affects the simulated pCO2 excursion, which could introduce errors in CO2-uptake calculation. To address these biases in future work, the outer model nest could be forced with improved biogeochemical boundary conditions, such as those generated by machine learning frameworks like PyESPER (Dai et al., 2025). Furthermore, internal nudging or data assimilation techniques could be applied to the inner domain nests to relax simulated biogeochemical state variables toward in situ observations collected directly within the fjord. In addition, the model had a positive bias in oxygen, oxygen saturation and nutrient concentrations. These discrepancies point to both biases inherited from initialization and boundary conditions, and specific local biological activity. Further evaluation and tuning would be required for MARBL to simulate these accurately, but this lies beyond the scope of the present study.”
  Please report the total simulation length and describe the spin-up procedure, given the stated importance of initial conditions.
  Thank you for this suggestion. We have now noted the total simulation length and spin-up procedure in the methods section. Note that in the new integration, we have added an additional year of spin-up.
  The conclusion that circulation-driven variability — particularly wind-driven variability — is the dominant source of variability in short-term pH excursions and near-field pCO2 anomalies would be better supported by a quantitative budget analysis. Please add this analysis or temper the claim accordingly.
  In a revised manuscript, we have added a statistical correlation between CO2 flux, winds, pH, and other environmental variables (local stratification, temperature and velocity) to further quantify the conclusion that wind-driven variability is the dominant source of variability in short-term pH excursions and near-field pCO2 anomalies
  Minor Comments
  Table S2: Please add detail on how the salinity normalization for alkalinity and DIC was computed. Done, please see response to previous comment.
  Line 235: Please clarify the rationale for multiplying theta by I (the intervention term). In the bracketed term in equation 5 (6 in the revised manuscript), units are µatm pCO2/mmol Alk m-3 per unit bias in state variables. It represents the error in slope (how wrong the pCO₂ sensitivity rate is per unit of added alkalinity). Multiplying by I converts the error in sensitivity (a rate/slope) into the actual total error in pCO₂ (an absolute value in µatm) for a specific dose concentration I. Without multiplying by I, you would only have the sensitivity bias rate, not the total error in pCO₂ caused by the intervention.
  Lines 294–297: Please clarify the connection between the salinity biases noted in the outermost and innermost fjord and the river-forcing configuration — for example, whether the outer-nest bias reflects the absence of river forcing and the inner-nest bias reflects limited river-data coverage. Additionally, the statement that "simulated estuarine circulation in the fjord is too weak" appears to be in tension with the SF6 results (Figs. S6–S7), where modeled average SF6 concentrations are consistently lower than observed — a pattern that would suggest the opposite. Please reconcile this discrepancy or clarify the reasoning. We have reconciled this contradiction in the manuscript. See response to previous comments regarding updates to riverine forcing and updates to the supplement describing the river forcing.
  Lines 330–331: The bulk fjord characteristics appear reasonably well captured by the SF6 results, though a magnitude difference exists between some timestamps in Figs. S6 and S7. The discussion of potential sampling bias as a contributing explanation is a reasonable and sufficient treatment.
  Line 391: Figure 3f is referenced in the text but does not appear to be included — please add. The reference was meant to be 10f, this has been fixed.
  Line 393: Figure S3g is referenced in the text but does not appear to be included — please add. The reference was meant to be S10g, this has been fixed.
  Line 514: Please provide additional quantitative support for the claim that the seasonal salinity evolution is captured by the model. We have now added a skill metric table summarizing salinity biases for each season as well as a temporal correlation between the model integration and observations.
  
  Citation: https://doi.org/10.5194/egusphere-2026-2920-AC2

Supplement

https://doi.org/10.5194/egusphere-2026-2920-supplement

Data sets

Seasonal oceanography of Hvalfjörður in southwest Iceland 2024-2025 - CTD data S. Harðardóttir et al. https://doi.org/10.17882/110439

Seasonal oceanography of Hvalfjörður in southwest Iceland 2024-2025 – discrete samples S. Harðardóttir et al. https://doi.org/10.17882/110401

Seasonal oceanography of Hvalfjörður in southwest Iceland 2024-2025 – mooring data S. Harðardóttir et al. https://doi.org/10.17882/113246

Model code and software

C-Star in Hvalfjordur Ulla Heede https://cworthy-ocean.github.io/C-Star-in-Hvalfjordur/

Viewed

Total article views: 239 (including HTML, PDF, and XML)

HTML	PDF	XML	Total	Supplement	BibTeX	EndNote
152	67	20	239	27	14	19

HTML: 152
PDF: 67
XML: 20
Total: 239
Supplement: 27
BibTeX: 14
EndNote: 19

Views and downloads (calculated since 12 Jun 2026)

Month	HTML	PDF	XML	Total
Jun 2026	59	15	5	79
Jul 2026	45	32	7	84
Aug 2026	32	16	6	54
Sep 2026	16	4	2	22

Cumulative views and downloads (calculated since 12 Jun 2026)

Month	HTML	PDF	XML	Total
Jun 2026	59	15	5	79
Jul 2026	45	32	7	84
Aug 2026	32	16	6	54
Sep 2026	16	4	2	22

Viewed (geographical distribution)

Total article views: 207 (including HTML, PDF, and XML) Thereof 207 with geography defined and 0 with unknown origin.

Country	#	Views	%

Latest update: 05 Sep 2026

Short summary

We use a new open-source ocean model system to conduct simulations of a fjord in Iceland and study how adding alkaline material to seawater can remove CO₂ from the air. We compare the model with field data to evaluate the model's accuracy. From our simulations, we show that the added alkaline material creates a short-lived, detectable signal in ocean chemistry in the fjord. Our motivation is to show how this ocean model system can support alkalinity enhancement field trials.


Total:	0
HTML:	0
PDF:	0
XML:	0