Plume spreading test case for coastal ocean models

Fofonova​​​​​​​, Vera; Kärnä, Tuomas; Klingbeil, Knut; Androsov, Alexey; Kuznetsov, Ivan; Sidorenko, Dmitry; Danilov, Sergey; Burchard, Hans; Wiltshire, Karen Helen

doi:https://doi.org/10.5194/gmd-14-6945-2021

Articles | Volume 14, issue 11

https://doi.org/10.5194/gmd-14-6945-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/gmd-14-6945-2021

© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.

Articles | Volume 14, issue 11

Methods for assessment of models

|

17 Nov 2021

Methods for assessment of models |

| 17 Nov 2021

Plume spreading test case for coastal ocean models

Vera Fofonova, Tuomas Kärnä, Knut Klingbeil, Alexey Androsov, Ivan Kuznetsov, Dmitry Sidorenko, Sergey Danilov, Hans Burchard, and Karen Helen Wiltshire

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Final revised paper (published on 17 Nov 2021)
Supplement to the final revised paper
Preprint (discussion started on 26 Feb 2021)
Supplement to the preprint

Interactive discussion

Status: closed

CEC1:
'Comment on gmd-2020-438', Juan Antonio Añel, 03 Apr 2021

Dear authors,
Reviewing your manuscript, we have found some issues with your 'Code and Data availability' statement that you must fix. For the GETM and Thetis models, you point to their web pages to access the code. Unfortunately, such web pages can not be considered trustful repositories for long-term code storage.
My proposed solution is as follows: Given that GETM and Thetis are released as free software (GPLv2 and MIT licenses, respectively) and have their code available in Github, you must take the frozen version of the code that you have used in your manuscript and create suitable repositories for them (e.g., Zenodo - Github does not ensure long-term archiving). In this way, you will have a D.O.I. that you can use to cite it in your manuscript.

Also, please, fix the hyperlink to the Zenodo repository of FESOM-C in the preprint of your manuscript. It does not work.
Best regards,
Juan A. Añel
Geosc. Mod. Dev. Executive Editor

Citation: https://doi.org/10.5194/gmd-2020-438-CEC1
- AC1: 'Reply on CEC1', Vera Fofonova, 16 Apr 2021
  
  Dear Editor,
  Thank you for the comment. We have created DOIs for the Thetis, GETM and FESOM-C codes used in the current study:
  Thetis: https://doi.org/10.5281/zenodo.4683743 ,
  GETM/GOTM: http://doi.org/10.5281/zenodo.4695259 ,
  FESOM-C: https://doi.org/10.5281/zenodo.4696058 .
  The correct link to the FESOM-C v2 version is https://doi.org/10.5281/zenodo.2085177 .
  We promise to include these links to the 'Code and Data availability' during 'response to review' phase. Excuse us for the inconvenience.
  Kind regards, Vera on behalf of the authors
  
  Citation: https://doi.org/10.5194/gmd-2020-438-AC1
RC1:
'Comment on gmd-2020-438', Anonymous Referee #1, 22 Apr 2021
General Comments

This work is a detailed study of the reproduction of a river plume by some state-of-the-art unstructured mesh models. The problem is introduced with an excellent analysis of the analytical solution and the results show the reproduction of various characteristics of the plume by the models. The use of different numerical schemes and other model parameters is discussed. The paper presents a considerable amount of work of very good quality and of great interest. However, although the first part is well written, the second part with results and discussion needs a substantial revision. Below are the main comments, which refer from section 5 onwards.

This part of the paper is written as a technical report. The authors speak to a reader interested in reproducing their experiments. This greatly limits the paper and makes it less useful for readers interested in applying a model in a real situation. In particular, the paper should answer questions such as: what is the best numerical scheme for reproducing a river plume? What are the minimum horizontal and vertical resolutions still good? I would suggest adding a section of conclusions after section 6, which answers these questions, those posed in the Introduction (p.3, r80-83) and discusses the last sentence of the abstract;

The part of the results is too long and difficult to read, it should be reduced where possible. Furthermore, after section 4, the English must be carefully checked and improved (you could contact a native English speaker), trying to use shorter sentences, better use of punctuation and to extend the explanation of some parts with complex concepts which, sometimes, are sketched out;

I would move section 7 to the appendix, trying to use some tables. I would finish the paper, in a more traditional way, with the Conclusions.

Specific Comments

Throughout the paper, references should be made to the numbers of the sections, not to their name;

Table 1 would be more convenient at the beginning of section 5, where it is cited many times;

From section 5 the Authors use "second (first) inertial period", which is a bit misleading. I would use "two (one) inertial periods" or "two rotational periods", in accordance with the first part of the paper;

I think that the comparison with analytical results and laboratory studies should be used more, both in the text and in the figures. In the figures, it would be useful to see these quantities. In any case, I leave the decision to the authors;

The figures with the vertical profiles have the x-axis inverted. I find this unintuitive; anyway, it is not so important;

p21r465-467: Explain more;

Fig. 6: Explain the various panels more. A line Fr = 1 would be useful;

p23r478-479: Explain more;

p24r495-500: Explain better;

Section 5.3: Some parts of the text are missing (p27r516). Another error in r522. The text describes the differences in a concise way, with short comments. Sometimes it is difficult to understand;

Section 5.4: Like the previous one, it is hard to understand. Use shorter sentences and describe better the methodology;

p29r557: not clear;

p30r563-564: explain better;

p30r569: why? Explain more;

Fig.11 The curves are different in the panels, use the legends in each panel;

p32 605-615 Not clear, write better;

p34r650: compared to? Run 1?

p35r669: First explain the purpose and then describe the runs.

p36r688: Remove the text in brackets, it is not clear;

p37r690: Where? Explain better where the reader should look;

p38r726: Rephrase the sentence describing your findings not your suggestion.

Technical Corrections

p3r74: the

fig1: r is r_0?

p5r131: brackish -> fresh

p5r142: we recommend.. -> we increased ... Describe the set-up, don’t give recommendations.

p5r146: we suggest -> What did you use? As before, describe the set-up.

p7r158: below. Specify the section number.

p9r200: a

p12r302-305: u_b and h_0 are defined in sec2.1, say it somewhere or remember their definitions;

p14r357: angel…

p21r464: typo

p23r490: there

Fig. 7: surface v-component?

p24r505: Fig3, which panel?

p28r547: intervening? I don't understand this sentence;

p23r550:.) ->).

p30r559 signalizing?

p32r591 than

p39r752 general
Citation: https://doi.org/10.5194/gmd-2020-438-RC1
- AC2: 'Reply on RC1', Vera Fofonova, 29 Jul 2021
  
  Dear Reviewer 1,
  Thank you for your effort to review the paper and your insightful comments! Please, find attached the answers.
  Kind regards, Vera on behalf of the team
  
  Citation: https://doi.org/10.5194/gmd-2020-438-AC2
RC2:
'Comment on gmd-2020-438', Anonymous Referee #2, 08 Jul 2021

Authors have done a lot of experiments, and some of them should be useful. While some of them duplicated with previous plume modeling, such as Xia’s Cape Fear River Modeling (North Carolina State University, 2007) to discuss how the numerical scheme to impact plume’s structure modeling, which is the key part of this manuscript. The horizontal resolution and vertical layers were given discussion in Xia et al., 2007 and other papers which were listed below. Numerical mixing can be considered as numerical errors, and authors need be carefully to utilize the error for the physical explanation. Please re-format this work and do a more than major revision to provide insight the plume community. Please remove most experiments which was conducted from these papers below and other literatures, make this manuscript concise and useful. I will provide more comments after new version, not this long, wordy unclear one. Also did authors simulate the internal wave (line 68?)

Niu, Q., Xia, M. (2021) “The behavior and wind-driven dispersions of two dynamically distinctive limnetic river plumes in a semi-enclosed basin,” (In press)

Niu, Q., Xia, M., Ludsin, S.A., Chu, P.Y., Mason, D.M., Rutherford, E.S. (2018). “Highâurbidity events in Western Lake Erie during ice-free cycles: Contributions of river-loaded vs. resuspended sediments,” ,00, 1-18.

Jiang, L., & Xia, M. (2016). “Dynamics of the Chesapeake Bay outflow plume: Realistic plume simulations and its seasonal, interannual variability,” , 121, 1424-1445.

Xia, M., Xie, L., Pietrafesa, L.J., Whitney, M.M. (2011). “The ideal response of a Gulf of Mexico estuary plume to wind forcing: Its connection with salt flux and a Lagrangian view,” , 116, C08035.

Xia, M., Xie, L., Pietrafesa, L.J. (2010). “Winds and the orientation of a coastal plane estuary plume,” ,37, L19601.

Xia, M., Xie, L., Pietrafesa, L.J. (2007). “Modeling of the Cape Fear River estuary plume,” , 30(4), 698-709.

Citation: https://doi.org/10.5194/gmd-2020-438-RC2
- AC3:
  'Reply on RC2', Vera Fofonova, 29 Jul 2021
  Dear Reviewer 2,
  Thank you for your comments. This manuscript deals with a much more basic problem than assumed by the reviewer. It diagnoses numerical diffusion in coastal models, showing that it is related to advection schemes rather than to discretization or mesh type. There are many other important factors that influence plume propagation in realistic configurations, as explored in the papers cited by the reviewer, but all they work on the top of model numerical factors. We surely agree that the questions raised in the papers cited by the reviewer are important in real-world applications, that many important aspects of plume dynamics were carefully explored in the papers cited by the reviewer. However, the level of numerical diffusion is also important, which is sometimes not fully appreciated. The present manuscript is addressing this question using a specially designed plume configuration that does not characterize a particular river.
  It is important to note that all simulations considered in the manuscript
  do not consider the wind, wave or tidal forcing as all of the listed by Reviewer 2 articles;
  
  are done without physical eddy diffusivity (except one to see the difference) to be able to trace the level of numerical mixing accurately;
  
  are performed by different models using different schemes.
  
  So, we present a novel test case and diagnostic metrics by which the numerical mixing in ocean models can be quantified. Such a test case can be rather helpful for model developers, especially as it allows comparing models with very different numerical discretizations (in the present paper we consider finite volume C and quasi-B grid models on unstructured and structured meshes, as well as a discontinuous Galerkin finite element model on an unstructured mesh). We believe that the novel test case and metrics are of interest to the model development community.
  The references proposed by the reviewer are all examples of excellent work, but they go beyond the present study as they deal with processes not considered by us (e.g. impact of winds, river discharge, or tides) or focus on model assessment in realistic river plume simulations. They do not focus on the systematic assessment of numerical mixing as the present work does. We also note that there are numerous regional studies (some of them are cited in the manuscript), which focus on plume behaviour under different conditions in the different areas worldwide, and we are citing a few of them, including the work proposed by this reviewer.
  We have revised the manuscript substantially, shortening and making it easier to read.
  
  Citation: https://doi.org/10.5194/gmd-2020-438-AC3
  - EC1: 'Reply on AC3', Sandra Arndt, 02 Aug 2021
    
    Dear Authors,
    reviewer 2 posted a comment on your reply before the interactive discussion closed, but has mistakenly used the abusive comment reporting to provide their feedback. Please find their feedback below and please also respond to the feedback in your revised submission.
    
    "I don't think authors have read these references. Clearly Xia 2007 discussed how the numerical schemes impact the plume dynamics, and this submission has overlap with other references. Ideal experiments is very simple, and plume should be investigated with realistic as well. Under the strong river runoff, most mixing scheme won't work well."
    
    Thank you, Sandra Arndt
    
    Citation: https://doi.org/10.5194/gmd-2020-438-EC1
    
    AC4: 'Reply on EC1', Vera Fofonova, 03 Aug 2021
    
    Dear Reviewer 2,
    Suggested reference to Xia et al. 2007 “Modeling of the Cape Fear River estuary plume” does not analyze performance of different tracer advection schemes or limiters with respect to numerical mixing. The individual and coupled effects of the astronomical tides, river discharge, and atmospheric winds were considered to investigate the Cape Fear River Estuary dynamics. On page 699 (right side) the paper provides a brief description of the used EFDC model. Only here the advection scheme is mentioned : ‘The model includes the anti-diffusion upwind advection scheme that is more suitable for the plume study than the upwind scheme or the central difference scheme (Berdeal et al. 2002). ’
    It looks like a misunderstanding, because we do not consider different mixing schemes, indeed physical eddy diffusivity is set to 0, eddy viscosity is calculated based on k-eps style turbulence closure or set to background value. We consider the numerical mixing level attributed to the different tracer advection schemes and limiters. This is clearly written through the paper.
    As we have mentioned in our first reply, we propose the test case and diagnostic metrics by which the numerical mixing in ocean models can be quantified. Spurious numerical mixing in circulation models can destroy stratification and frontal features, and significantly alter the plume dynamics. While considering the effect of physical forcings on the plume dynamics is certainly relevant, it is out of the scope of the present article. The community needs benchmark test cases (see attached Lemarié et al., 2019 summary ) that are reproducible, can be compared against analytical solutions and offer the analysis of "isolated" effects (not blurred by the interplay of many different processes as in complex realistic scenarios) and the direct connection to specific numerical choices in the model core. The suggested idealized plume scenario with a unique set of parameters is reproduced differently by different, but commonly used, advection schemes+limiters. And this is not surprising because the plume dynamics in some zones can be characterized by nonlinear flow regimes with sharp frontal boundaries. Simplicity or non-simplicity of idealized experiments depend on the accuracy level you chose as acceptable.
    We have read all the papers suggested by the Reviewer. However, their scopes are beyond that of our study. Please, find below a brief report on the suggested articles:
    Niu, Q., Xia, M. (2021) “The behavior and wind-driven dispersions of two dynamically distinctive limnetic river plumes in a semi-enclosed basin,” Estuarine, Coastal and Shelf Sciences.(In press)
    
    We did not find an article which exactly matches the title, perhaps the Reviewer meant ‘The behaviors of two limnetic river plumes discharging into the semi-enclosed western basin of Lake Erie during ice-free seasons’ .
    The article is about wind-driven dynamics of the Detroit and Maumee River sediment plumes in the semi-enclosed western basin of Lake Erie on several temporal scales. In our case study the wind- driven dynamics has not been considered.
    Niu, Q., Xia, M., Ludsin, S.A., Chu, P.Y., Mason, D.M., Rutherford, E.S. (2018). “High turbidity events in Western Lake Erie during ice-free cycles: Contributions of river-loaded vs. resuspended sediments,” Limnology and Oceanography,00, 1-18.
    
    The article investigates the contributions of river loading (Detroit and Maumee Rivers) versus resuspension to high-turbidity events in Western Lake Erie during ice-free conditions in 2002–2012 using a wave-current forced sediment model (FVCOM based). The major result is that suspended sediment dynamics and high turbidity events in the area were dominated by wind and waves in the offshore regions, and were driven by river loadings near the mouths.
    We agree that it is a very important regional study, however, it has focus on sediment dynamics and is hardly relevant to our idealised plume scenario and its major aim.
    Jiang, L., & Xia, M. (2016). “Dynamics of the Chesapeake Bay outflow plume: Realistic plume simulations and its seasonal, interannual variability,” Journal of Geophysical Research: Oceans, 121, 1424-1445.
    
    The article identifies five types of real-time plume behavior regulated by wind and river discharge. Also it contains some sensitivity experiments related to the grid cell sizes considering fine and coarse grids. The article gives very valuable insights about Chesapeake Bay outflow plume behaviour. However, these five types are defined based on presenting physical conditions (preliminary by wind conditions) and there is no established connection to the numerical scheme performance. Therefore, the topic and analysis of the paper are beyond the topic and aims of our manuscript.
    “The ideal response of a Gulf of Mexico estuary plume to wind forcing: Its connection with salt flux and a Lagrangian view,” Journal of Geophysical Research, 116, C08035.
    
    The questions posted by the article are:
    1) How does wind forcing affect bay water as it encounters the Gulf?
    2) How do plume distribution, fluxes, and particle transport change with changing wind conditions?
    The questions are important to understand the regional dynamics. However, as they deal with physical forcings, the topic is beyond the current study.
    5. Xia, M., Xie, L., Pietrafesa, L.J. (2010). “Winds and the orientation of a coastal plane estuary plume,” Geophysical Research Letters,37, L19601.
    The suggested article deals with the Cape Fear River Estuary. and its river plume behavior (type) under different wind forcing and river discharge conditions. Results showed that wind direction, wind speed, and to a lesser extent river discharge contribute to plume transitions from one type to another among six defined major types. This topic is interesting, but not relevant for our study.
    6. Xia, M., Xie, L., Pietrafesa, L.J. (2007). “Modeling of the Cape Fear River estuary plume,” Estuaries and Coasts, 30(4), 698-709.
    Please, see the comment above.
    
    Citation: https://doi.org/10.5194/gmd-2020-438-AC4
    
    AC5: 'Reply on AC4', Vera Fofonova, 03 Aug 2021
    
    The numbering of the articles was changed automatically. The numbers of the articles are from 1 to 6.
    
    Citation: https://doi.org/10.5194/gmd-2020-438-AC5

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Vera Sidorenko on behalf of the Authors (29 Jul 2021) Manuscript

EF by Svenja Lange (04 Aug 2021) Author's tracked changes

EF by Svenja Lange (05 Aug 2021) Author's response

ED: Referee Nomination & Report Request started (30 Sep 2021) by Sandra Arndt

RR by Anonymous Referee #1 (12 Oct 2021)

ED: Publish as is (12 Oct 2021) by Sandra Arndt

AR by Vera Sidorenko on behalf of the Authors (18 Oct 2021) Manuscript

Short summary

We present a test case of river plume spreading to evaluate coastal ocean models. Our test case reveals the level of numerical mixing (due to parameterizations used and numerical treatment of processes in the model) and the ability of models to reproduce complex dynamics. The major result of our comparative study is that accuracy in reproducing the analytical solution depends less on the type of applied model architecture or numerical grid than it does on the type of advection scheme.