General comments:

The authors present a nested regional ocean model of Halifax Harbour and part of the Scotian shelf which is validated against measurements. A simple dissolution model is implemented and pulse releases of an alkaline effluent are modelled, consisting of a mix of dissolved and particulate alkalinity. The subsequent changes in alkalinity and DIC (from the induced CO2 uptake) are evaluated and analyzed. 

Overall the manuscript is well laid out, focused and easy to follow. The simulations presented establish an important standard of rigor for future OAE deployments in other areas. I recommend publication.

Specific comments

The authors show that alkalinity addition inside a natural enclosed harbour enables a substantial fraction of the theoretically maximal CO2 uptake to occur quickly and within the simulation domain, due to the long residence time and relatively shallow waters. As pointed out in L556-559, this makes MRV much easier both experimentally and from a simulation perspective. Of course the flipside of this is that a confined body of water which does not quickly spread any added ∆TA over large ocean areas will also limit the total sustained alkalinity addition rate in that area, limiting scaling of OAE.

It would be useful to add an estimation of this in the manuscript. For a rough, first pass estimate, perhaps one could assume that the response of ∆TA and ∆DIC are roughly additive and linear with respect to addition rate. Then, for each of the three locations, one could calculate what the maximum addition rate would be which would raise the maximal ∆pH to some acceptable limit (what that limit is is of course arbitrary, but perhaps something conservative like +0.1 or +0.05 units would be illustrative).

Another approach would be perhaps to examine the export rate of alkalinity out of the simulation boundary and try to estimate what sustained alkalinity addition rate (rather than a pulse) could be achieved, again within some ∆pH or ∆TA limit set within the domain.

A discussion of this and the tradeoffs of release locations would be useful to the reader to understand better what sort of scale OAE can achieve.

L317 k_{diss}TA_p term:

The treatment of dissolution as an exponential decay process (i.e. dTAp/dt = -k TAp) was surprising at first glance. Usually dissolution of particular matter is treated with a shrinking core model, where the dissolution rate has units of mol cm-2 s-1, the radius of particles shrinks linearly and fully dissolves in a finite amount of time. For a very narrow (as indicated in L335, “a particle size of 12µm”) or uniform distribution of particle sizes I believe an exponential dissolution curve is only a mediocre fit. 

I can see that an exponential model could perhaps capture the behaviour of a gaussian or log-normal distribution of particle sizes, but a short discussion of this and a justification of the choice of model here would be helpful. 

L317 w_{p}TA_{p} term:

It’s unclear to me how the sinking term is applied. As written it looks like there is an exponential decay, i.e. each time step some fraction of TA_p is lost to sinking from any given simulation grid voxel. What happens to that TA_p ? Does it get added to the cell below, until the bottom cell is reached after which it disappears in to the sediment ? Or does the model assume the sunk particles are removed completely (i.e. they sink out entirely at a rate of W_p*TA_p from anywhere in the column ?). As currently written it seems more like it’s the latter, as there is no term that accounts for sinking particles that arrive from a cell above (i was expecting a second term like +w_p*TA_p^{z=i-1}  )

Please clarify how the sinking mechanism is implemented and justify its construction. 

The sinking rate is stated as 5.5 m^{-1} later (L337) but that can’t be w_p since the units wouldn’t be right (w_p should have units of inverse time, like k_{diss}). How is w_p calculated from the 5.5m^{-1} ?

L326 The treatment of sediment loss in layer N is a little unclear. It says a term is “added” to ∂∆TA/∂t ? Or does this replace the regular dissolution term in ∂∆TA/∂t (last term in Equation 9) ? It might be clearer here to just rewrite the full Equation 9 (and perhaps Equation 8) in the case of the bottom cell, for clarity.

It’s also confusing to me that the loss of TAp due to sinking/burial  is already explicitly treated in equation 8 using w_p and then it’s treated again here with the  \theta_{loss} term. Is \theta_{loss} a constant ? Or is it calculated from w_p ?

L424ff The comparison of H2 and H3 is very interesting and suggests perhaps a resolution as high as H3 isn’t necessary. A similar comparison of H1 vs H2 would also be useful if the releases can be reasonably implemented at the coarsest level. Even if the release location would have to be assumed to be wider or poorly matched in terms of exact location, injection of the same amount of alkalinity in the coarsest model could be interesting to determine to what extent the H2 level is required.

L769 It was a surprise to read here that the sediment loss term was set to zero. I feel like this should have been mentioned earlier, perhaps even right when the loss term(s) are introduced in L317ff. Is both wp and \theta_{loss} set to zero or just the latter ? If it’s just the latter, does the model currently just settle all the particles on the floor and let them dissolve from there until completely dissolved ?

Technical corrections:

L120:  I assume the conversion factor is 1025 kg m^-3, not 1.025kg m^-3 (remove dot or change dot to comma)

L243  In equation (3), it appears that the parameter “c1” is duplicate as a coefficient to t and as an exponent. Likely it is meant to be c2 instead ?

L325 change to “is added that mimics” or “is added to mimic” 

L331 “1.29 ml s-1”, exponentiate the “-1”

L475 In such cases, 

Fig.1D consider using a different color scheme for the bathymetry as the scale is different.

Figs. 3, 5,6,7, 10: Is it possible to indicate the release location in these plots with a small black arrow or similar. I know they are shown in Fig 1 D, but it would be very helpful to have that info on each of the other plots too. 

Figure 7: It would be nice to add a horizontal dashed line to the two graphs indicating the theoretical maximum uptake (at your CO2 efficiency of 0.89) to get a sense for what fraction of the ultimate uptake occurs within the simulation domains.

Fig S4-S8 The observations of the depth profiles are sparse enough in time that it’s difficult to assess visually how closely the corresponding model predictions match. Perhaps, for each observation time and depth simply make a scatter plot against the corresponding prediction value ? Could be color coded by depth perhaps to see if correlation is better at surface vs depth. 

This is a very interesting and thoughtful paper on a numerical modelling approach to detect and evaluate the effects of OAE. It represents a significant step forward towards realistic simulations of an actual alkalinity release field experiment. I think the paper can be accepted for publication after moderate revisions and clarifications.

There are several questions I hope the authors can clarify.

I like the approach to separate the slurry additions into dissolved TA input and particulate form which later dissolve and sink. This is more realistic than the previous modelling approach which adds TA in dissolved form. It also counts for lost TA due to particle sinking onto the seabed. It was interesting to see the result that the maximum CO₂ uptake from this mixture is lower. On the other hand, the more realistic model representation comes at the expense of introducing three additional parameters: the particle dissolution rate, the particle sinking rate and the fraction of slurry particles incorporated onto the sediment, the last of which would be difficult to estimate. In reality, there would be a size spectrum of slurry particles which dissolve and sink. As shown in Fig. S10 in Wang et al. (2025), the sinking velocity varies by two orders of magnitude for alkaline feedstocks of various sizes. It is possible that the dissolution rate may also change with the particle size. Wang et al. (2025) also showed the results are very sensitive to the particle dissolution rate and sink velocity. How does one choose one “representative” particle with a particular size, dissolution rate and sinking velocity? I understand the need to keep the model manageable, but these are model assumptions that could be discussed. There are approaches to model a size spectrum of bubbles generated by breaking waves (Garrett et al., 2000). The bubbles are injected into the upper ocean, rise due to buoyancy and dissolve under partial pressure differences. Maybe some of these modelling approaches could be discussed. Sediment transport modelling has to deal with a spectrum of particle sizes too and it is well known the settling site of sediment depends critically on the particle size.

I am also curious about the author’s approach to use a high-resolution hydrodynamic model but a simplified biogeochemical model. I can understand the need for high resolution hydrodynamic to resolve the near-field transport and dispersion of added slurries in the inner model domains but do not quite understand the use of a simplified biogeochemical model. Was it due to the high computational cost of the full biogeochemical model? I thought the biogeochemical model can be run very efficiently if done on an offline mode. It would be good to discuss why the authors took this modelling approach. It will be instructive to other modelers.

There is also this broad question how we can validate the model results and document the OAE effects. The authors did a lot of model validation without OAE but none for the model results with OAE. How can the model help the documentation and verification of alkalinity addition? The latter is a nagging issue facing all OAE studies, due to a combination of large natural variability in the carbonate system and the policy restriction/regulation on exposure impacts.    

Reference

Garrett, C., M. Li and D.M. Farmer. 2000. The connection between bubble size spectra and energy dissipation rates in the upper ocean, Journal of Physical Oceanography, 30, 2163-2171.doi: https://doi.org/10.1175/1520-0485(2000)030<2163:TCBBSS>2.0.CO;2       

Review for: A high-resolution nested model to study the effects of alkalinity additions in Halifax Harbour, a mid-latitude coastal fjord

The manuscript describes a novel BGC model that is run within a physical model (ROMS) which itself can be run at 3 described resolutions (ROMS-H1, ROMS-H2, ROMS-H3). ROMS-H2 is the workhorse resolution here. The novel BGC model here is a cut-down version of a more complete BGC model (not clearly named here) that essentially simplifies the BGC to DIC, TA and O2, with major missing processes parameterised and described here. This model is then used in a series of OAE experiments. The manuscript details coupled physics-biogeochemistry model specifically designed for OAE in a nested grid configuration and reduced biogeochemistry with increasing spatial resolution from Scotian Shelf to Halifax harbour. To ensure that the model is suitable for the location, hindcast simulation of the model is validated against observation on the shelf. Alkalinity enhancement experiment is simulated at the inner, mid, and outer harbour with two different feedstocks; fully dissolved and fully particulate.  Then the effect of alkalinity addition to the carbonate system is analysed. A major conclusion is around the relative success (69%) of CO2 absorption driven by OAE within the modelled coastal domain.

General comments:

Overall, the manuscript is an interesting investigation into OAE in a very specific locale, Halifax Harbour. In most places, the manuscript is written quite well, and the model has been generally shown to capture the observations. The manuscript also explores different locations of alkalinity addition and types of feedstocks, which are relevant and can be insightful for field study and MRV. However, while we generally appreciated it, there are a few suggestions that would make the manuscript stronger.

A general comment we’d make is that the structure of the manuscript impedes its interpretation. In particular, it merges model description, experiment design and results from the OAE side of the work into a single and lengthy section. There’s nothing special in the work that precludes a conventional method-results-discussion structure, so please reformulate the manuscript this way.

Another general comment is that the use of a novel BGC model here introduces the requirement for a lengthy digression into the formulation and skill of this model. Ideally, such a model would be described in a separate manuscript and then used for the problem at hand. As written, it is sometimes unclear whether the paper’s primary aim is to describe the novel OBGC model itself or to address OAE research problem, which in our opinion, makes the narrative harder to follow. We would suggest clarifying the manuscript’s focus and streamlining the model description, so that this description is largely moved to supplementary and shortened in the main body.

On a related point, because the model used here is novel, it would be extremely beneficial to compare it with its parent model. At present, the validation in Supplementary Material appears to compare / validate the parent and novel models separately rather than together. For example, Figures S3 to S8 appear to use the parent, while Figures S10-S19 appear to use the novel model, but there are none intercomparing the shared properties of the models with observations. Given how different the models appear to be in their state variables and formulation, it is critical for readers to understand how strong the relationship between the models is.

We would also suggest that the manuscript would be more complete if the authors also discussed other diagnostics that are relevant for impact assessments. Such as how OAE affects Halifax Harbour’s pH and saturation states (e.g. Ω aragonite) over the course of alkalinity addition. Those are liable to be important for natural ecosystems in the region.

Specific comments:

Abstract: A little light on actual results. I would have expected a statement regarding either the efficacy or challenges encountered during the work.

Line 90: some models, e.g. Palmieri & Yool (2024), assumes that particulate material is added, and uses the calculated dissolution rate of this to specify the flux. In this specific model, yes, the model only sees a flux of TA, but this is achieved through the temperature-dependent dissolution rate of an implicit particulate source (which is assumed to have already settled on the seafloor).

Line 96-103: It might have expected to see some articulation of the key research questions here. This seems primarily a breakdown of how the manuscript is organised. (Of which, see below.)

Methods: There are 6.5 pages of model description before we get to the OAE part. Ideally, the model used would be an existing model, previously described elsewhere. However, we are where we are. We would suggest abbreviating this to a ~1 page summary that cites prior work and moving the more expansive text to an appendix. It’s useful – in fact, given this is a novel model, *critical* – to have all of this, but this level of detail tends to distract from the focus of the paper.

Ln. 137: It would be helpful if the BGC models here were given names so that they can be clearly identified, and clearly separated from the physical frameworks they are coupled to.

Line 300: Section 5 appears to combine model description with model results. This doesn’t seem a helpful way to present the work. We would suggest creating / merging into separate sections to 1. describe the model (part of methods), and 2. describe findings from its use (the results section). Similarly, the validation of the model ahead of its use could either be arranged formally part of the methods (as it kind-of is now) or moved to be part of the results.

Line 301-303: a verbal overview description of the OAE scheme might fit well here. Specifically, that OAE TA is added to the ocean in dissolved TA and particulate TA forms (the latter requiring a new tracer), and that the latter dissolves into the former with time. Also, this whole model description completely overlooks Figure 2 which rather clearly indicates how the model works.

Line 306: It could be helpful to explain why new delta tracers were added rather than the more conventional compare-and-contrast with a control simulation. One can imagine what the explanation is, but readers would benefit from understanding this.

Ln. 310-312: This describes the split between dissolved and particulate TA additions but does not clarify what the fraction is or how it may vary. It also seems like this is something that isn’t explored elsewhere in the manuscript, e.g. a sensitivity analysis on the importance of this fraction might be expected. In any case, one would at least expect to be told what its value was, or – if this is variable – under what conditions it varies.

Eqn. 8-9: We would suggest adding the equation for TA so that the relationships between TAp and delta-TA are easy to understand. Same for DIC.

Ln. 329: This section is sorely missing a clear non-narrative description of the experiments undertaken and the simulations performed. A table listing the simulations and their roles would make it very easy for readers to understand the work undertaken.

Ln. 329: Technically, it could be argue that this subsection is methods, but the organisation of subsection 5.2 is compromised by a subsubsection 5.2.1 which is more results than methods. Reorganising into the conventional methods-results-discussion format would greatly improve this manuscript.

Ln. 331: superscript typo, 1.29 mol s^-1

Ln. 363-371 and Ln. 383-403: these sections of text quantify the results found verbally rather than, more obviously, in a table (or tables). This would allow the reader to clearly understand distinctions being drawn between experiments and locations that currently require the reader to hold a lot in their heads at once just to make basic sense of the results.

Ln. 364: The manuscript presents a maximum achievable uptake of 0.89 mol CO2 per mol TA, perhaps we are missing something, but can the authors elaborate more on how this number came up? Will this number change with seawater condition / location / model resolution?

Ln. 448: The balance in this manuscript between the base model and the OAE experiments is generally off, and this section (6.1) continues this. Manuscripts like this one generally present just enough information about the base model to satisfy readers that it’s an appropriate choice for the experiments in question. Also, and more importantly, it blends in details about the OAE experiments that might better be discussed in the relevant section (6.2, 6.3).

Ln. 449-450: Why “not surprisingly”? Also, similar performance to what? Is there maybe a grammatical error in this sentence.

Ln. 551: “Tufts Cove is the location for alkalinity …” should this be “Tufts Cove is the ideal location …”?

Ln. 591: “These results stress the importance of operational design as well as the use of high-resolution regional models when quantifying additionality.” – Can you be clearer on what, specifically, is meant by “operational design” here? Is it geographical / depth choice of TA release, the balance of dissolved / slurry supply of TA, the timing of application of slurry (w.r.t. tides)?

Figure 2: This shows pH in a similar way to model state variables. But it’s a calculated property rather than a state variable. Maybe alter the line style of the box so that it’s clear that it’s not a state variable?

Figure 3: while I have used Ocean Data View-style palettes like this before in my own work, I now appreciate that they present particular difficulties for readers with colour vision issues. To which end, please convert this figure to a more suitable palette, plus subsequent ones using the same palette.

Figure 5-6: This seems to use a different geographical domain to Figure 3 onward. Is there a reason for this? More generally, why do these figures include satellite imagery while the others don’t? (Figure 1d also shows slightly different domain limits than in Figure 3.)

Figure 7: needs rotating.

Figure 10: needs rotating.