Thank you for your reading and pointing out this mistake.

We will surely add the corrected symbol in the revised version.

We sincerely thank the reviewer for their generous and positive feedback on our manuscript. We are glad that the review was considered insightful and a valuable contribution to microplastic modelling in estuarine environments.

Regarding the suggestion to emphasise the role of ocean (and estuarine) current modelling in microplastic transport studies, we fully agree with this important point. In the revised version, we will expand our discussion on the critical importance of hydrodynamic modelling, particularly its role in simulating complex estuarine currents. While we have noted this aspect in the recommendations section, we will further highlight the need for accurate and high-resolution current models as a fundamental requirement for advancing microplastic transport simulations.

Dear Reviewer,

We sincerely thank you for taking the time to thoroughly review our manuscript and for providing constructive comments and valuable suggestions. We will try to address your feedback in the revised version to improve the overall clarity and impact of our paper. Here are our responses to each of the comments.

"My major comment is that this review is weighted too heavily toward listing the details of what other studies of done and does not provide enough synthesis that would add value beyond the references to the individual studies. The discussion also wanders into related but distinctly different topic areas (such as hydrodynamic modeling) and provides excessive levels of details in equations and parameter choices that can easily be found in the citations, other topical reviews, or textbooks.  This results in an overly long manuscript that risks losing reader interest before the main discussion on advantages and disadvantages of different approaches and recommendations for future steps.  Trimming and reorganizing the text as suggested in the comments below would make for a more accessible review.  The review has good quality content and appropriate scope, and some reorganization and streamlining of the text could greatly enhance its impact."

We agree that enhancing the synthesis could improve the manuscript’s accessibility and will work toward this in the next version. At the same time, we would like to emphasize that this review is intentionally aimed at a broad audience interested in microplastics, from master's students to researchers from diverse disciplines, many of whom may not be familiar with modeling approaches and require sufficient contextual detail to understand the differences between existing methods and parameterizations.

We believe that a certain level of technical elaboration (e.g. the introduction of key parameters and parameterization choices) is valuable not only for beginners and non-specialists engaging with modeling literature, but also for more specialized readers, given the rapid evolution of this field and the lack of consolidated references. Ultimately, we see this as a matter of stylistic balance rather than content quality. The manuscript is designed to understandable even with partial or selective reading, with distinct sections covering the state of the art, synthesis, and recommendations. For example, the integrative comparison of the advantages and disadvantages of different approaches draws explicit connections across earlier sections. We will, however, revise the structure to make this clearer and will streamline selected parts to maintain reader engagement. Many of the reviewer’s specific comments relate to this broader concern, and we address them in detail below. In summary, our preference is to first establish a consistent overview of the modeling choices made in the reviewed studies, and then build upon that to discuss challenges and formulate recommendations based on the key findings.

[16]      missing “by” after “research”

[19]      “both” is used twice in the sentence and is only needed once.

[22]      It’s not clear what “privileged” means here.

We will check the typos and add or remove the words as per the suggestion.

[85]      The topical organization here is confusing.  Four categories of models are identified: Eulerian analytical or idealized, realistic Eulerian, realistic Lagrangian, and Population Balance Equation. All of them rely on interfacing with a hydrodynamic model that represents the transport, mixing, and ambient conditions the plastic particles are experiencing, which is explained later in the text but still ambiguous at this point. The estuary being simulated could be idealized or realistic.  The hydrodynamic model can solve the transport equations analytically (requiring simplifying assumptions) or numerically.  The representation of the particles can be in Eulerian as concentration or Lagrangian as discrete particles. The distribution of particles sizes and characteristics can be done in numerous ways, including a single size class, multiple separate size classes, or multiple interacting size classes, which is what the Population Balance approach sounds like. Particle characteristics such as settling, resuspension, degradation, and biofouling can be represented at various levels of complexity. It would be more logical and informative to identify these distinct dimensions of model characteristics and discuss the tradeoffs along each dimension independently rather than grouping them more arbitrarily, as is currently the case.  For example, idealized estuary models can use Lagrangian particle tracking to represent plastic transport (e.g., Bo et al. 2024, https://doi.org/10.1073/pnas.2401498121), but that approach does not fit in the organizational framework here.  Similarly, it seems like the Population Balanced approach could be applied in a realistic or idealized hydrodynamic models, so it overlaps with other categories. More thoughtful organization of the orthogonal model attributes would help readers organize the topic and help guide more coherent synthesis of the studies.

We agree that modeling approaches can be classified according to different criteria (e.g., analytical vs. numerical; Eulerian vs. Lagrangian; idealized vs. realistic), and that our initial distinction—particularly labeling 2DV Eulerian models as “idealized”—may be confusing. While this terminology is common in hydro-sedimentary modeling, we acknowledge that other approaches can also be applied to idealized or academic configurations, as already noted in lines 531–536. In the revised version, we will clarify the classification scheme and introduce four main types of transport models used in the literature, each based on different particle transport equations: 2DV (semi-)analytical models, numerical Lagrangian, numerical Eulerian, and Population Balance Equations (PBE). We will anticipate that both numerical Eulerian and Lagrangian approaches can be applied to either realistic (as it's the case of previous works on microplastic transport) or idealized configurations, while the semi-analytical approach is inherently restricted to idealized setups. The same currently holds for the PBE framework, although future developments may enable more realistic applications. We will also better explain the particularity of the PBE approach in using a continuous distribution of particle size classes. While we will try to avoid excessive technical detail, we believe that including representative equations is necessary to make the differences between 4 modeling strategies intelligible to a broad readership.

[98]      should be “Tables 1 and 2 compile and compare”

We will rewrite the typos.

[143]    Since this is a review, it would be reasonable to leave out the details of model applications such as the governing equations and direct readers to the references cited.  That might help streamline the text for a manuscript that is quite long. 

As noted above, we agree that streamlining the text is important, and we will certainly remove some of the more general equations to improve readability. That said, we consider it important to retain a few key formulations to clarify the specificities of each modeling approach, particularly for readers less familiar with these methods, so as to ensure a self-contained and accessible comparison. We will revise the relevant sections accordingly.

[162]    Is the “F_E” here the same as “E” in equation (5) and in the next paragraph?  If so, please make them consistent.

Yes, we will rewrite the equation with consistency.

[165]    This section seems to be interchanging sediment transport and plastics transport, which is confusing. There are analogies between the topics, but there can also be big differences. For example, the statement here is that the parameters are determined based on morphodynamic equilibrium, but that seems irrelevant to plastics transport.  Suggest keeping the focus here on how sediment transport approaches can be adapted to plastics rather than getting into the details of the sediment transport equations.

We agree with the reviewer that this part is well suited for removal or summarization, and we will revise it accordingly, summarizing details of sediment transport and providing some details on the links and differences between sediment and plastic transport approaches.

[190]    Maybe this is coming later, but I expected more of a synthesis of the studies using the approach described in this section -- key findings, sources of uncertainty, benefits and limitations.  Identifying the approaches used is an important start, but it would be valuable to assimilate the diverse sources into coherent guidance for readers.

As noted, the synthesis of benefits, limitations, challenges, recommendations from key findings, is provided later in the manuscript, in a dedicated section. This structure was chosen deliberately to make the main messages easy to locate for readers who may be reading selectively or in a non-linear way, and to allow us to summarize and reflect upon insights from the preceding sections in a coherent and accessible manner. Nevertheless, in the next version, we will carefully consider whether other elements of synthesis can be more clearly highlighted throughout the manuscript.

[205]    Similar to the comment above, the focus here should be on the microplastic aspects of the modeling rather than the hydrodynamics.  Textbooks have been written about the tradeoffs between finite difference and finite element, or sigma vs z-coordinates, and it would be a disservice to try to cover those topics here.  Instead provide context on the choices that go into using circulation models to simulate plastic transport, either with Eulerian or Lagrangian representation of the plastics.

We agree that the primary focus of the review should remain on the microplastic aspects of modeling. Our intention in including a brief overview of hydrodynamic discretization methods and vertical grid systems was to provide context for how these choices influence microplastic transport simulations, especially adapting from sediment transport modeling. We will revise this section to reduce the emphasis on general hydrodynamic modeling.

[233]    Is the sense of the inequality in equation (9) correct?  It seems to be saying that deposition only happens for stress greater than the threshold rather than less than the threshold, which is counterintuitive.  Similar for equation (8).  Or consider removing these equations since they are standard for sediment transport modeling and can be found in the references.

We will check the equations and rewrite or (if appropriate) remove them, aiming to strike a balance between conciseness and the clarity of the section.

[239]    Is this “E” from Equation (10) the same as that in Equation (5)?  If not, change the nomenclature so they are not confused.

It is not the same. We will rewrite the equation correctly.

[243]    “Traditionally, modelling efforts are focused mostly on the floating particles leading to a stronger emphasis on the approaches suited for surface transport.” This is confusing following the previous paragraphs, since they presume that particles are negatively buoyant and act like sediment. It would be helpful to discuss the role of buoyancy for plastics earlier on in the manuscript, and how that influences modeling choices.

We will take this into account and will consider including a discussion on particle buoyancy in the context of microplastic modeling.

[245]    “Furthermore, transport processes such as beaching, which involves the interaction of the particles with coastlines, cannot be effectively captured using ERMs, due to their fixed spacial framework.”   This is not true, as ERMs with wetting and drying would be able to deposit particles (sediment or plastics) in intertidal regions such as beaches.  Please clarify.

Thank you for pointing this out. You are correct that Eulerian models with wetting and drying capabilities can simulate beaching and particle deposition in intertidal zones. This is most done by combining the hydrodynamical and transport equations with an Exner-type approach, assuming that the bed evolution in time is driven by the divergence of the sediment flux. Similar approaches can certainly be used for microplastic deposition, provided that the related parameterization initially developed for sediments can be adapted and validated for plastic particles.  However, the studies we referenced in this review that employed Eulerian frameworks did not consider beaching processes explicitly. We will revise the text to clarify this distinction and avoid generalizing it as a limitation of ERMs.

[247]    How is this “lower preference for ERMs” identified? By less prevalence of Eulerian applications compared to Lagrangian?  It's not obvious why practitioners would gravitate toward one approach or the other simply because of popularity...perhaps there are additional factors such as ease of implementation or efficiency that favor Lagrangian approaches?

Thank you for raising this point. Yes, there are other factors discussed in detail in Section 2.5, We will review this part of the text in the next version.

[250]    Not sure what “precedent” means here...suggest removing.

We will remove this word.

[258]    Similar to a comment on the previous section, this section goes into unnecessary levels of detail on what the previous studies did (all of which can be found in the citations) and provides little synthesis on what the studies learned or what we can learn by comparing and contrasting them. 

As explained above, this section aims to review the state of the art; synthesis is provided in the last section on challenges and recommendations based on key findings from these studies. We will revise the section and streamline the descriptions with a better balance by retaining essential information while improving the comparative analysis and highlighting key insights.

[270]    Presumably the Dietrich (1982) settling velocity formulation was developed for sediment rather than microplastic, as is suggested here.  Please clarify.

We will do it.

[355]    Is this advection scheme analysis specific to plastics or more general for LPTMs?  If the latter, that is getting away from the focus of this review.  If the former, please add context on what makes the choice of advection scheme specific to or particularly important for plastics.

The study by Pilechi et al al. (2022) is specific to microplatics in estuaries and for that reason we have included it in our review (Tables 1-2). But the conclusion can be still valid more general for LPTMS. We will try to provide clearer context on these aspects in the revised version.

[369]    The manuscript has a lot of unfamiliar acronyms, and I often have had to scroll back to figure out what they are.  Suggest reducing the use of acronyms and instead use the words when possible -- e.g., "random walk model" doesn't take up much ink on the page, and “RWM” is not a common term in the literature.

We will minimise the use of acronyms to avoid confusion.

[374]    This is another example where the text stops at reporting what the previous authors did rather than explaining why it matters or how it is relevant to the best practices for modeling plastics.  There are lots of random walk models out there, and reviews of that topic that synthesize pros and cons.  Here it would be helpful to distill how that choice influences outcomes for modeling plastics.

We agree with the reviewer’s point. However, in this section, our intention was not to compare different random walk models, but rather to highlight the novelty of this topic within the context of microplastic simulations. Based on previous studies, we found that the diffusion calculation using Equation 20 is particularly appropriate when accounting for spatio-temporal variations in diffusivity, an approach applicable to both sediments and microplastics. We will clarify this point more explicitly in the revised version.

[382]    Given the common sources of uncertainty in the different modeling approaches (e.g., plastic terminal velocity), it would be useful to address that as a cross-cutting topic, in parallel with the division between Lagrangian and Eulerian transport frameworks.

We agree that this is a valuable suggestion and in fact considered this option during the writing process. However, while some sources of uncertainty are shared across modeling frameworks, others are specific to particular approaches. For that reason, we chose to structure this section, intended to be more descriptive, by modeling approach, which we still believe is a reasonable choice, especially since common parameters are discussed later in Section 3.2 and 4 to discuss the choices from different studies and the challenges and recommendations.

[393]    maybe I missed these acronyms...are PE, PS, and PP types of plastic?  Please clarify.

We have already provided the acronyms below the table, as they are used directly within it. However, we agree it would be helpful for clarity, and we will include the acronyms in the main text as well.

[395]    “and rising” typo

We will rewrite the typos.

[443]    Is “bubble’s oxygen” modeling the oxygen inside bubbles?  It’s an unfamiliar term.

Yes, it is the oxygen inside the bubbles, which we will clarify using the studies done.

[445]    The continuum of particle sizes seems like another topic which is cross-cutting and would be common to Eulerian or Lagrangian approaches.  Presumably the assumption in the cases above is that there is a single plastic size class, but that does not have to be the case. Suggest making the size distribution a separate point of discussion and including this Population Balance approach in its assessment.

While all approaches can account for more than one particle size class, a key distinction between the Eulerian/Lagrangian frameworks and the PBE lies in their treatment of particle size/characteristics: the former use discrete classes, whereas the latter employs a continuous distribution (see e.g. description in line 446). This continuous formulation is specific to the PBE and will be more clearly emphasized in the revised version. As for settling velocity, a discussion of this topic for all approaches is given in subsequent sections. We would also like to note that the author of the study introducing the PBE approach provided feedback on our review and did not raise any concerns regarding its presentation.

[452]    Should the “eta” in this sentence be “xi”?  There doesn't appear to be an eta in equation (28).

Thank you for noticing this. Yes, it is 'xi' which is an error while writing the equation. We will make it correct.

[459]    The transport equation (28) is very similar to the transport equation (7) for the ERM, which raises questions about why it is categorized separately.  It would be helpful to clarify the advantages of PBE that make it more efficient than ERM, and what that depends on (e.g., number of size classes, discretization of the Eulerian model, time step limitations for particle settling).

This is indeed the objective of the work of Shettigar et al. (2024). We will provide a few more details on it in our review as suggested.

[461]    The suggestion here is that PBE handles “all particle sizes”.  Is PBE discretized in multiple, yet still discrete, size classes or a continuous function of particle size?  Seems like there is still a tradeoff in the number/size of particle classes being represented, which would also be the case in a Eulerian or Lagrangian approach representing more than one particle size.

As mentioned above, we will better clarify that PBE uses a continous function.

[473]    Even if there are few examples, it would be useful to assess the PBE approach rather than just stating that it exists. 

We agree that a more detailed assessment of the PBE approach would be valuable; however, to the best of our knowledge, the study we included is currently the only published application of this method in the context of microplastic modeling. Given that it is a very recent contribution, we focus on discussing its key aspects and highlighting it as a promising and novel direction.

[476]    These assessments of advantages and limitations would fit better following the description of the approach, while the subject is still fresh in readers’ minds.  The description of each approach could be significantly shortened, and the pros and cons presented here could form the main message of that combined section.

Placing the advantages and limitations immediately after the description of each approach is also a good choice, that we also considered during the writing processes. However, we prefer to highlight the comparative strengths and weaknesses of each approach by discussing them together in a dedicated section. This comparative format allows for a clearer understanding of how the methods differ in terms of their suitability and limitations across various scenarios.

[507]    The report here is that Lagrangian models rarely incorporate key processes related to the ambient conditions such as erosion and deposition or buoyancy effects. However, it seems straightforward to incorporate these factors based on information from the circulation model (salinity/temperature, bottom stress).  Is it a choice that previous applications have not done so or is there some basic technological limitation? The following sentence says that it is easy to take into account these processes, referencing Jalon-Rojas et al. (2024b). Please clarify.

In our review of existing studies using Lagrangian Particle Tracking Models (LPTMs) for estuarine microplastic transport, we found that most applications did not incorporate key parameterizations related to deposition–resuspension processes or variations in water density (e.g., due to salinity or temperature). As you correctly noted, this omission is not due to a technological limitation of LPTMs themselves—these processes can indeed be incorporated, which we pointed out. Rather, we intended to highlight that, despite their importance in estuarine systems, these processes have rarely been considered in past studies using LPTMs.

[517]    It is not obvious how initial conditions influence diffusion, either imposed by the turbulent diffusivities or due to numerical diffusion from advection.  Please explain.

We will check the sentence and will provide a proper explanation, or we will remove the sentence.

[543]    The overview framework described in this paragraph is clearly written and would be useful earlier in the manuscript, before the details on the different approaches to the transport modeling.

We agree with your proposal and will move this accordingly.

[578]    Perhaps it would be more succinct to say that the release strategy depends on the questions being addressed by the model, e.g., depending on the sources of plastic, forecast vs hindcast, environmental conditions influencing transport.

We will also add these elements.

[603]    Can convergence testing address questions on the number/concentration of particles to release, like what is done for evaluating model grid resolution or time stepping?

The sensitivity tests involving particle concentration were indeed mentioned in the recommendations sections after providing the issue (not here because previous studies did not do it).

[608]    For time stepping, it seems like the Courant condition relating grid size and advection length scale is an important consideration.  Or perhaps that can be relaxed for Lagrangian models where length scales for velocity gradients are much larger than the grid size?

Regarding the Courant condition, we described this in the recommendation section along with the challenge.

[615]    As above, it would be easier for readers to keep track of the issues and tradeoffs if the review sections and recommendations/analysis on each topic are presented together.

We have indeed structured each challenge followed by the corresponding recommendations within the last section.

[616]    It seems like the main message of this section (3.1) is that choices on release approach and simulation period depend on the study goals.  In the interest of streamlining the text, that could be said succinctly rather than listing numerous examples that don't provide much additional insight but take up several pages of text.

 While we agree that the main message of this Section is indeed that choices of the tracking parameters are closely tied to the study objectives, we believe it is important in the context of a review paper to provide a comprehensive overview of how these parameters have been handled in previous studies. Including these examples allows us to highlight the diversity of approaches used in the literature and helps readers understand the rationale behind different modeling decisions. We have aimed to balance clarity with completeness and believe this level of detail adds value for researchers looking to compare methodologies or design their studies.

[637]    Is there anything about the specification of these mixing parameters that have considerations for plastics, rather than the general question of mixing (e.g., for salinity, sediment, or biota)?  If so, that should be the focus of this section.  Otherwise, the topic of mixing in estuaries is broad and complex, and can be referenced to other work.

The reviewer is right. The key point here is to emphasize that multiple options exist, and our aim is to provide an overview of the choices made in previous microplastic studies—along with the rationale behind them when available—in order to support a later discussion of the associated challenges and recommendations. We will modify the text to make this clear.

[754]    This paragraph has broad generalities but little new content, and could be removed.

It is true that these are general recommendations; however, to our knowledge, no other review paper provides guidance specifically on modeling microplastic transport in estuaries, and we believe that such recommendations can be useful for researchers entering this field.

[778]    As with the previous comment, the value added by this paragraph is limited because its content has been covered already above.  Suggest moving the recommendations closer to where these issues are described earlier in this text and removing this rehash.

Already responded above.

[816]    As above, move the recommendations closer to the discussion of the literature on particle characteristics.

As noted above, we have presented the challenges and corresponding recommendations in a dedicated final section, as we found this structure to be a more effective and coherent way to convey the key insights and guidance rather than including it in the discussion about each approach.

[858]    Missing “be” after “can”

We will rewrite the typos.