The work of Nordam et al. compares the Eulerian and Lagrangian formulations of the vertical transport equation of buoyant (or negatively buoyant) particles in the seawater column. Specifically, three types of particles were analyzed, namely: buoyant fish eggs, positive/negative buoyant microplastic, and buoyant oil drops, each one characterized by specific boundary conditions and rising/settling velocity. The study shows the accuracy and the convergence of the two approaches by varying several parameters; among those, the most relevant is the number of classes describing the particle population (Eulerian approach) and the number of particles (Lagrangian approach). The results indicate that both the Eulerian and Lagrangian schemes predict the same distribution with an error that reduces with the square of the class number and the square root of the particle number, respectively.

In general, I found the analysis rigorous, but the draft organization could be improved. For instance, there are many subsections and continuous cross-references to other sections in the text. The overall result is often a redundancy of notions and a not fluent reading in some parts. I suggest defining and developing the methods and the results separately.

Finally, The relevance of the research questions and the outcomes of the present work are not evident. The fact that Eulerian and Lagrangian Schemes give similar results is not surprising and trivially expected. The implementation of the boundary conditions adopted is also well-established. Finally, how can one transpose the present results, which are based on a 1D scheme, to more realistic 3D scenarios where the dynamics of the particles are more complex than those implemented here? What is the best approach in the latter cases?

Below I report some specific comments.

- L210. w instead of v within the square brackets?

- L270-279. This long paragraph seems more suited for an Introduction.

- L283. Why do you use the reflection of the particle displacement? Which is the physical meaning? The free surface should dampen the particle velocity independently of the mechanism involved (advection or scattering by diffusivity).

- Fig.1. The GOTM simulation predicts null diffusivity at the water interface. This seems consistent we the null diffusivity flux at the boundary. Is much more demanding to use the output from GOTM instead of Equation (15) in the transport equation?

- L416. Why this difference? Is it maybe owing to a substantial variation of the velocity distribution for the two classes?

- Fig.4. The graduation of the two y-axes overlaps.

- Eq. (19). Which is the value of H_s?

Review of ‘A comparison of Eulerian and Lagrangian methods for vertical particle transport in the water column’ by Nordam et al.

General comments:

The authors provide a very thorough commentary on the current state of the modelling of particle transport and movement within the water column, as well as addressing both the benefits and disadvantages of Eulerian and Lagrangian methods for this application. The description of their one-dimensional model and the approaches used to apply Eulerian and Lagrangian schemes was detailed and clearly laid out (both in the main text and the appendices). As a general note, the descriptive balance did feel slightly tipped in favour of Lagrangian methods, but the evaluation of both methods was fair and balanced, which is also reflected in the overall discussion and conclusion of the performance of the schemes in each of the test cases. The choices of the test cases are relevant and reflective of common usages of both Eulerian and Lagrangian modelling frameworks. Overall, the manuscript presents an interesting discussion on the advantages and disadvantages of each approach in terms of efficacy within a one-dimensional domain, but I wonder how applicable these results would be in a three-dimensional domain.

Specific comments:

1. Introduction:

As mentioned in the general comments, the discussion and description of Eulerian and Lagrangian methods does feel slightly imbalanced in favour of Lagrangian methods. There is only “a challenge” discussed for an Eulerian approach, whereas there is only “an advantage” included for a Lagrangian approach. Both have advantages and disadvantages and are useful for certain applications than the other. A brief mention of the fact that they are quite complementary methods and can be used in conjunction (e.g. to model larval dispersal (Young et al. 2015) and (on a slightly larger scale) to implement transport of interactive icebergs (Marsh et al 2015) to give a couple of examples) would maybe make a good addition to the discussion.

The phrase “implementing different boundary conditions and a simple reaction term” (and variations) is repeated several times in the introduction, and maybe doesn’t need to be reiterated quite that frequently.

2. Components of the advection-diffusion reaction model:

In Section 2.5, the reader is pointed to both Section A1.4 and Section A2.2 for further details of the reaction term. However, there is not much further discussion of the reaction term aside from that the study only considers reaction terms that add mass, and then points the reader to section 4.3 for more details. This cross-referencing is a little frustrating and would make for an easier read if further detail was provided in one place. I’m not sure that the appendix sections are necessary.

3. Implementation:

In Section 3.1.2 L206-208, some more clarity on what “some cases” and “other cases” would be insightful and less vague (are the cases the ones discussed in this study, or just generally?), similarly clarifying what “available directly” means.

In Section 3.2.1, the discussion around boundary conditions (L270-278) would maybe better placed in the introduction, appendix or in Section 5.1 where boundary conditions (and the associated challenges) are further discussed.

4. Case studies

Figures 2, 3 and 5: For all of the left panels of these figures, a clearer distinction between the colours for 0 hours and 2 hours would be very beneficial (and perhaps a less dark colour for 12 hours). Although it is clear which is which from the description of the initial Gaussian vertical distribution of the particles, I think it would be more accessible/easier to understand for those who are perhaps not so familiar with the topic (or those who may have not thoroughly read the text and are heading straight for the figures).

5. Discussion

L507: The Lindeberg-Lévy CLT acronym should be defined either earlier on in the text when it is mentioned previously or here.

Typological comments:

L28: largel -> large

L32: correct reference for the NEMO manual is Madec et al. (2022), this also needs addressing in the references

L186/L255: “we wish to use” should perhaps be reworded as a more definite statement – you have already used the boundary conditions

L210: should it be w (not v) in the square brackets?

L273: particle -> particles

L275: missing closing bracket

L556: … both broad and changing time… -> changing over time