Round 1

Reviewer 1 Report

Reviewing comments to the Article “A comparison of stochastic and deterministic downscaling in eddy resolving ocean modelling: the Lakshadweep Sea case study” submitted by Shapiro*, Gonzalez-Ondina, Salim and Tu, in Journal of Marine Science and Engineering (Manuscript Number: jmse-2146621).

 

I have finished reading this manuscript regarding its work in the Lakshadweep Sea of Indian Ocean. The authors aim to conduct the skill assessments for 3 models (mainly 2 models) and compare the computational efficiency between the stochastic model (LD20-SDD) and deterministic model (LD20-NEMO). They both use the larger deterministic model CHEMS (Copernicus Marne Service) at 1/20 degree resolution as boundary conditions, and they both use the 1/20 degree resolution for their own model. The temperature and salinity are compared with 3 observation sources (i.e., OSTIA data, GHR-MUR observations, and Argo floats). They finally conclude the high-resolution model can better capture smaller scale processes (e.g., meso to sub-meso scale eddies), and the selected stochastic model has much higher computational efficiency than the deterministic model. The authors have done good works in the numerical simulations and comparisons. However, there are a couple of issues still need be addressed (e.g., lacking a deeper discussion on the mechanisms of the phenomenon or simulations from both methods). I recommend Major Revision and my specific comments are listed as follows.

 

1.      Abstract L12: Please double check that whether the first letter needs to be initialized for “Stochastic-Deterministic Downscaling”.

2.      Introduction L35: It seems you add more than one space that as needed between two words.

3.      The literature review in this Introduction needs to be strengthened. For example, what are the recent status of the stochastic and deterministic model? Why this work is important (e.g., the novelty of this manuscript). Only the comparison of the computational accuracy and efficiency may be not sufficient for a scientific publication. Please consider improve it.

4.      Material and Methods. Because the focus of this study in on the model skill assessment, the description of the observation should be in a more detailed way. Please a more give descriptions of the observations from GHR-MUR, OSTIA, and Argo data.

5.      L91-92: The space seems too large between symbols and texts. Please check and revise it accordingly herein and other places over the manuscript.

6.      L155: the selected station of 7.3 degree N and 76.2 degree E is out of the study domain indicated by the authors (7.5-14.5 degree N).

7.      L161-165: The authors discuss Eq. (2) and correlation function in this paragraph. I think it may be more proper to introduce Eq. (2) first before this equation to be discussed.

8.      L180-181: Please rewrite this sentence for clarity.

9.      L189-192: Could you explain this equation to me briefly?

10.   L195: What’s meaning of “BLUE” in here?

11.   L213: It may be better to delete these words shown in the computational program and use expression with physical meaning. For example, compilation Keys key-traldf_c3d and key-traldf_smag). Similar suggestions are also for other places with this issue.

12.   L235: []11 -> [11].

13.   L236-237: “…… other oceanographic parameters …..”, please specify these oceanographic parameters.

14.   Results: The comparison for the three models: the authors have compared temperature and salinity. I was thinking that for the hydrodynamic model (e.g., simulating eddies), it is better to conduct model comparisons regarding sea surface height (e.g., geostrophic flows), surface current velocities etc.

15.   L248-264, are all these equations (Eq. 6-13) used in the following analysis? Please only include the parameters that will be discussed.

16.   L275: I believe the time series comparison is in Figure 3 not Figure 1. Please correct it accordingly.

17.   L308: what corrections are made in 2015 for the NWP768 radiance data? Please briefly introduce it.

18.   Table 2: this is a following questions for the data source. Since the authors have not introduced the observations in detail, I was wondering that why the correlation coefficients between two observations (i.e., OSTIA SST and GHR-MUR) are so low. Which data source is more reliable and why choose OSTIA for model-to-data comparison instead of GHR-MUR? Please explain it.

19.   L321-322: I believe the authors refer to Table 2 instead of Table 4. Please correct it accordingly.

20.   L345: “which provides either boundary (to LD20-NEMO) of full 3D data (LD20-SDD) to other models”. Here, “either … of” should be changed to “either … or”.

21.   Figure 5: what do the column stand for? 2 different stations?

22.   L358-359: “Vorticity is calculated using derivatives of current velocity, and hence an overly-smoothed representation of velocity will result in underestimation of vorticity”. Based on my knowledge, this is not necessarily true. Please explain it.

23.   Figure 6: why just choose one day (2015.5.15) from this 4-year simulations (2015.1.1-2018.12.31) herein?

24.   L369-372. “The LD20-SDD model gives higher values of vorticity than CMEMS and resolves some smaller scale features which are only embryonically seen in CMEMS, in particular in the NW corner of the domain and around the islands”. This statement is not obvious to me, could you show/mark them in figure?

25.   L383-384: the authors indicate that the enstrophy is the square of vorticity. Is that should be the half of the square of the relative vorticity? Please double check it.

26.   L387-388: why do you choose daily data to calculate the enstrophy?

27.   L396: “… dynamics and ageostrophic flows []”. Please add the cited reference herein.

28.   L401-402: “The Kibel number in this case is equal to the ratio of ageostrophic to geostrophic velocity”. Do you mean “equal” or “as an indicator”? If the Kibel number is equal to this ration, could you show it to me mathematically?

29.   Figure 8: Again, why do you choose this time period? The authors use different time periods during the study but without an explanation. Note a typo is also in this figure for 01-17 (the corrected one should 02-17 following 01-17 in the x-axis).

30.   L417-419: It is better to give the specific value of the percentage area for the high nonlinearity.

31.   L419: “It [is] likely that …”.

32.   L421: Here and in the following texts the authors mention “early spring” several times, but the figure shows the “winter” time. Please be consistent.

33.   L429-433: If the computational efficiency is defined as the ratio between one simulation day and computed core hours, then it is clear that the stochastic model is 120 times more efficient than the deterministic model.

34.   L450: “about 100” -> “120”; L521-522: “approximately 100” -> “120”.

35.   L511-512: “Kilbel number larger than 0.5”. This expression seems awkward to be put in here.

36.   References 29: “Geophysical research letters” -> “Geophysical Research Letters”. Please also double check the format of other references.

Author Response

Authors’ responses to Reviewer 1 comments on jmse-2146621

A comparison of stochastic and deterministic downscaling in eddy resolving ocean modelling: the Lakshadweep Sea case study.

Following reviewers’ comments, the text was amended, the MS was extended by 70 lines of text, 1 new Figure and 7 new literature references.

Comment: They both use the larger deterministic model CHEMS (Copernicus Marne Service) at 1/20 degree resolution as boundary conditions, and they both use the 1/20 degree resolution for their own model.

Response: The CMEMS model has a coarser resolution of 1/12^th. This is crucial because the two child models aim to improve the resolution to 1/20th.

 

Comment: The authors have done good works in the numerical simulations and comparisons. However, there are a couple of issues still need be addressed (e.g., lacking a deeper discussion on the mechanisms of the phenomenon or simulations from both methods). I recommend Major Revision and my specific comments are listed as follows.

Response: We assume that the specific comments contain all the suggestions that the reviewer has with the paper. The aim of this paper is not to discuss the physical phenomena happening the Lakshadweep Sea, only the skills of the two different models, one is traditional and the other one is new. The text is re-worded accordingly namely ‘In this study, we conduct an extensive analysis of the properties, efficiency and accuracy of a novel ocean model based on the SDD method against a traditional deterministic ocean circulation model in the Lakshadweep Sea located in the tropical Indian Ocean.’.

 

Comment: Abstract L12: Please double check that whether the first letter needs to be initialized for “Stochastic-Deterministic Downscaling”.

Response: They need to be capitalized because they are the initials of SDD. We have added “(SDD)” after it to make this clearer.

 

Comment: Introduction L35: It seems you add more than one space that as needed between two words.

Response: Corrected as advised.

Comment: The literature review in this Introduction needs to be strengthened. For example, what are the recent status of the stochastic and deterministic model? Why this work is important (e.g., the novelty of this manuscript). Only the comparison of the computational accuracy and efficiency may be not sufficient for a scientific publication. Please consider improve it.

Response: Traditional ocean circulation models have been developing since early 1960s and resulted in hundreds if not thousands of publications. Their current status can be found in papers [1-7] which are referenced in the introduction. For the status of the SDD model, we know of only one publication [8], which is also referenced in the introduction. A very detailed comparison of a traditional versus new modelling approaches is the element of novelty of the paper. We refer to Reviewer 3 report which states:’ This paper addresses an important issue in oceanic numerical modelling regarding providing improved horizontal resolution in large-scale and global models. The research is scientifically sound and the paper is generally well written’.

 

Comment: Material and Methods. Because the focus of this study in on the model skill assessment, the description of the observation should be in a more detailed way. Please a more give descriptions of the observations from GHR-MUR, OSTIA, and Argo data.

Response: These observations are results of large multi-national projects, are held on major operational and climate data centres in the US and Europe [11-13]. The data sets are described in much detail by their originators on the relevant websites. Following the reviewer’s advice, we added generic description of the datasets in the revised MS.

 

 

Comment: L91-92: The space seems too large between symbols and texts. Please check and revise it accordingly herein and other places over the manuscript.

Response: We agree. As far as we are aware from the Journal guidelines, the formatting, including removal of extra spaces, will be done during the copyediting stage.

 

Comment: L155: the selected station of 7.3 degree N and 76.2 degree E is out of the study domain indicated by the authors (7.5-14.5 degree N).

Response: For the correlations we used an enlarged domain so nodes near the limits do not suffer from boundary effects (see also Fig. 2). Fig1.b shows one of these cases, where a node near the boundary includes correlations with points outside of the domain. Clarification is added in the text.

 

Comment: L161-165: The authors discuss Eq. (2) and correlation function in this paragraph. I think it may be more proper to introduce Eq. (2) first before this equation to be discussed.

Response: We agree. Eq. (2) is indeed introduced before this paragraph.

 

Comment: L180-181: Please rewrite this sentence for clarity.

Response: We have made the sentence clearer.

 

Comment: L189-192: Could you explain this equation to me briefly?

Response: This is the basic linear equation for the weights in the Objective Interpolation method [14,19]. The sum symbol  represents the product of matrices  and .

 

Comment: L195: What’s meaning of “BLUE” in here?

Response: “Best Linear Unbiased Estimate” as explained in lines 196-197 of the original manuscript:

“In these conditions Eq(4) provides the best unbiased linear estimate (BLUE) to the true value [14,19,20].”  We have capitalised “best unbiased linear estimate” in the revised version of the text for clarification.

 

Comment: L213: It may be better to delete these words shown in the computational program and use expression with physical meaning. For example, compilation Keys key-traldf_c3d and key-traldf_smag). Similar suggestions are also for other places with this issue.

Response: As indicated in the text, these keys are related to the Smagorinsky approach, which can be found in many textbooks. The keys are useful for NEMO users to fully understand our setup.

 

Comment: L235: []11 -> [11].

Response: Thanks, corrected as advised.

 

Comment: L236-237: “…… other oceanographic parameters …..”, please specify these oceanographic parameters.

Response: We agree. Modified as: ‘The LD20-NEMO model outputs 3-hourly instantaneous and daily average values for temperature, salinity and U, V components of current velocity. ‘

 

Comment: Results: The comparison for the three models: the authors have compared temperature and salinity. I was thinking that for the hydrodynamic model (e.g., simulating eddies), it is better to conduct model comparisons regarding sea surface height (e.g., geostrophic flows), surface current velocities etc.

Response: We are not aware of observations of surface currents or sea surface height with the required resolution to perform comparisons.

 

Comment: L248-264, are all these equations (Eq. 6-13) used in the following analysis? Please only include the parameters that will be discussed.

Response: Yes, they are all used in Figs. 3-4 and Table 1. Please note that SSTA_M and SSTA_OSTIA are used to define CORR.

 

Comment: L275: I believe the time series comparison is in Figure 3 not Figure 1. Please correct it accordingly.

Response: Thank you. Corrected as advised.

 

Comment: L308: what corrections are made in 2015 for the NWP768 radiance data? Please briefly introduce it.

Response: Here we rely on the explanation given by the data provider [30] which states that at that time (15.03.2016) they introduced: “Variational bias control for satellite radiances, UM 10.2”. Clarification is given in the text.

 

Comment: Table 2: this is a following questions for the data source. Since the authors have not introduced the observations in detail, I was wondering that why the correlation coefficients between two observations (i.e., OSTIA SST and GHR-MUR) are so low. Which data source is more reliable and why choose OSTIA for model-to-data comparison instead of GHR-MUR? Please explain it.

Response: The correlation between OSTIA SST and GHR-MUR for the four years 2015-2018  is 0.67 which shows a reasonable level of correlation. OSTIA is regarded as a very reliable, good quality data source (https://data.marine.copernicus.eu/product/SST_GLO_SST_L4_REP_OBSERVATIONS_010_011/description ] it is available from both American and European data centres. An additional reference was added to the revised MS. Table 2 is now Table 1.

 

Comment: L321-322: I believe the authors refer to Table 2 instead of Table 4. Please correct it accordingly.

Response: Thanks. Sorry for relying too much on the automatic numbering in MS Word. Table 2 is now Table 1. Corrected as advised.

 

Comment: L345: “which provides either boundary (to LD20-NEMO) of full 3D data (LD20-SDD) to other models”. Here, “either … of” should be changed to “either … or”.

Response: The phrase is reworded: ‘… which provides either boundary data in the case of  LD20-NEMO model or full 3D data in the case of LD20-SDD’.

 

Comment: Figure 5: what do the column stand for? 2 different stations?

Response: The caption in Fig. 5 answers this question: “… temperature (left panels) and salinity (right panels)”

 

Comment:.   L358-359: “Vorticity is calculated using derivatives of current velocity, and hence an overly-smoothed representation of velocity will result in underestimation of vorticity”. Based on my knowledge, this is not necessarily true. Please explain it.

Response: In agreement with our own statement, reviewer 2 confirms that “Higher resolution model should develop its own dynamics and larger variability, which is exactly the reason for doing so.” and “You find that the stochastically downscaled model shows higher values of vorticity than the global model. This is a good result, suggesting that the methods works well”.

 

Comment: Figure 6: why just choose one day (2015.5.15) from this 4-year simulations (2015.1.1-2018.12.31) herein?

Response: We present selected results from a very large set of more than 140,000 maps.

 

Comment: L369-372. “The LD20-SDD model gives higher values of vorticity than CMEMS and resolves some smaller scale features which are only embryonically seen in CMEMS, in particular in the NW corner of the domain and around the islands”. This statement is not obvious to me, could you show/mark them in figure?

Response: In agreement with our own statement, reviewer 2 confirms that “Higher resolution model should develop its own dynamics and larger variability, which is exactly the reason for doing so.” and “You find that the stochastically downscaled model shows higher values of vorticity than the global model. This is a good result, suggesting that the methods works well”. Additional clarification is added to the discussion of vorticity and enstrophy.

Comment:.   L383-384: the authors indicate that the enstrophy is the square of vorticity. Is that should be the half of the square of the relative vorticity? Please double check it.

Response: Thank you. We have double checked and our formula is correct, see Doering, C. R. and Gibbon, J. D. (1995). Applied Analysis of the Navier-Stokes Equations, p. 11 eq (1.3.19), Cambridge University Press, Cambridge. ISBN 052144568-X..

 

Comment:.   L387-388: why do you choose daily data to calculate the enstrophy?

Response: The enstrophy is mostly produced by mesoscale circulation and from Fig. 7 it is clear that the temporal resolution of one day is sufficient to resolve the enstrophy variability.

 

Comment:.   L396: “… dynamics and ageostrophic flows []”. Please add the cited reference herein.

Response: Thank you, corrected as advised.

 

Comment: L401-402: “The Kibel number in this case is equal to the ratio of ageostrophic to geostrophic velocity”. Do you mean “equal” or “as an indicator”? If the Kibel number is equal to this ration, could you show it to me mathematically?

Response: We agree. Amended as follows: The Kibel number in this case is an indicator of the ratio of ageostrophic to geostrophic velocities.

 

Comment: Figure 8: Again, why do you choose this time period? The authors use different time periods during the study but without an explanation. Note a typo is also in this figure for 01-17 (the corrected one should 02-17 following 01-17 in the x-axis).

Response: We like to present different time periods in order to avoid unconscious bias of presenting only the best results that may occur if a single set of dates is used throughout the manuscript. Figure corrected as advised.

 

Comment:  L417-419: It is better to give the specific value of the percentage area for the high nonlinearity.

Response: The percentage is given in line 426: “highly non-linear processes can be as high 20% or more”

 

Comment: L419: “It [is] likely that …”.

Response Thank you. Corrected as advised.

 

Comment: L421: Here and in the following texts the authors mention “early spring” several times, but the figure shows the “winter” time. Please be consistent.

Response: Corrected as advised. ‘In winter and early spring, the area occupied with highly non-linear processes can be as high 20% or more’

 

Comment: L429-433: If the computational efficiency is defined as the ratio between one simulation day and computed core hours, then it is clear that the stochastic model is 120 times more efficient than the deterministic model.

Response: We agree with the Reviewer’s calculation for this particular case, but the computational times depend on many factors (e.g. how many processes are running at the same time) so we prefer to give an approximate figure.

 

Comment: L450: “about 100” -> “120”; L521-522: “approximately 100” -> “120”.

Response: See our response to the previous comment.

 

Comment: L511-512: “Kilbel number larger than 0.5”. This expression seems awkward to be put in here

Thank you. Reworded as: ‘The areas of highly non-linear dynamics ( i.e. with Kibel number larger than 0.5) occupy as much as 20–25% of the Sea in early spring and as low as 5% in the summer.’

.

Comment: References 29: “Geophysical research letters” -> “Geophysical Research Letters”. Please also double check the format of other references.

Response: Thank you. We have made amendments as advised, and we will double check at the copyediting stage.

 

Note: All numbered references in this document refer to the bibliography in the original manuscript. Same applies to figures and tables.

 

 

Reviewer 2 Report

Review of a paper entitled ”A comparison of stochastic and deterministic downscaling in eddy resolving ocean modelling: the Lakshadweep Sea case study” by George L. Shapiro, Jose M Gonzales-Ondina, Mohammed Salim and Jiada Tu.  

The paper under review compares different ocean models with each other. The ocean models under consideration are a global data assimilating ocean model (CMEMS) with 1/12 resolution that is used to downscale 2 higher horizontal resolution (1/20 degree) models. The main aim is to assess differences in the higher resolution models due to their different modelling approaches. One model uses a stochastic dynamical downscaling method while the other higher resolution ocean model uses a standard dynamical downscaling approach. The authors compare model results with each other and additionally use observational data sets to determine and intercompare skills on various metrics.  

Overall, the authors note that the statistical downscaling model is computationally efficient. About 100 times faster than the dynamically downscaling model, with similar (if not better) mean statistics but deficiencies in reproducing smaller scale features which are shown in e.g. vorticity fields.  

The paper is well written and there is nothing too much wrong with it. I find some additional information and discussion should be included in the document. I’ll outline them below. The main aim of this paper is to compare statistical downscaling with dynamical downscaling. The statistical downscaling method has been described in Shapiro et al, 2021. This is an application of that method over the Lakshadweep Sea which, arguably, is novel in itself.  

I find the paper is acceptable for publication after some review. The changes I suggest are between minor and major. I find that some additional clarification and discussion is necessary. Also additional data examination is suggested.  

 

Main points 

One of the comparison metrics used (for OSTIA) is based on domain averaged values. The authors find that the stochastic downscaled model gives similar metrics compared to the global model. Is this surprising (if not please explain)? Although the downscaling method has the ability via the introduction of stochastic length scales to better represent some mesoscale feature than the global model the mean statistics should be very similar. The downscaling method is an enhancement of the OI method therefore the data assimilation aspect will make the solution very similar and this includes mean features. I suppose if one was to assimilate a large amount of observation into a dynamical model and assumes that the observations are perfect and have a large impact the resulting analyses will be very close to the observed field. The dynamically downscaled model on the other hand will have introduced a wider range of variability which generally increases the error. Furthermore so, as the dynamical downscaled model is not constrained in the interior via e.g. a DA approach.  

Some basic information is missing for example how many observations were available over the domain of interest (you give some information on the ARGO floats in section 3)? I suggest to add a table/ or figure of some sort ? How many of the observations that you compare the models to were actually assimilated into the global model as well? Do have independent observations to base the statistics on?   

When you assess the ability of the downscaled models to represent smaller scale features. You find that the stochastically downscaled model shows higher values of vorticity than the global model. This is a good result, suggesting that the methods works well. However, you also find that the dynamically downscaled model shows rather different fields and you describe them as “more chaotic than the other model”. Is this not the point of dynamic downscaling – yield larger variability? You then assume that the global model, because it is data assimilating, should be more realistic in the area – but we do not know how many observations went into the DA over the region for that day. Are there enough observations to constrain the velocity fields?  

You should discuss differences in the atmospheric forcing used for the global model and the dynamic downscaled model (also give a better description of the global model). Can difference in the atmospheric forcing for example explain the larger error of the dynamic downscaled model in the earlier time period? What about topographies? How different are they? 

 

Minor comments  

Line 16: “...LD20 NEMO uses only 2d data set of data from CMEMS as lateral boundary conditions...”. That sounds like you are not applying baroclinic fields to the downscaled model but I assume you are using standard downscaling/ nesting including temperature, salinity, velocity and sea surface height? Please clarify.   

2 Material and methods 

Line 61: Since you are comparing to CMEMS you should add some more information on the model. What forcing has been used etc./ information on DA.  Which of the observations you are comparing to are already assimilated in CMEMS ?  

Line 67: “The child SDD-LD20 model has the same geographical limit as the parent model”? The parent model is global - does this means the SDD model covers the whole globe? I might misunderstand the model approach or setup in this case. Please clarify. 

Line 179: Would be interesting though to see if/ what the differences are.  

Line 206-: LD20 Model setup., Can you discuss differences between the atmospheric forcing applied to LD20 NEMO and CMEMS. 

Line 227: Boundaries are including baroclinic and barotropic fields (2d and 3d) this seems to contradict what you write in the abstract. Please clarify. 

Line 230: “...for baroclinic velocities”. What boundary conditions are you using for temperature and salinity? 

Line 233: What do you mean by first guess tuning parameters ? 

Line 336: Are the ARGO floats independent or are they assimilated in the global model?  

3 Results 

Line: 238-272: Not quite clear.  Did you interpolate the observation onto the respective model locations and then calculate the error stats and then average. Or did you calculate domain average and then do statistics  

Line 336: Have the ARGO floats also been assimilated ? 

Line 344: Largest difference at around 200m might be related to large uncertainty in modelling thermocline depth. Atmospheric forcing mainly influence in the planetary boundary layer  

Snapshot of velocity falls in bad modelled period (2015) ? 

Line 368-372 : SDD shows smaller scale feature – supposed to do that 

Line 368-380: I think conclusion drawn not quite OK. Higher resolution model should develop its own dynamics and larger variability, which is exactly the reason for doing so. Maybe compare mean EKE or mean vorticity as well.  

Line 378: The vorticity pattern from LD20-SDD are model consistent...”. Shouldn’t that be the case given the stochastic method? 

 

Figures 

Figure 2: Please add titles indicating what we are looking at (I.e. T surface, T 156m, etc.) 

Figure 9: Missing latitude and longitude.   

 

 

Shapiro GI, Gonzalez-Ondina JM, Belokopytov VN (2021) High-resolutionstochastic downscaling method for ocean forecasting 573models and its application to the Red Sea dynamics. Ocean Science 17(4):891-9075749. 

Author Response

Authors’ responses to Reviewer 2 comments on jmse-2146621

A comparison of stochastic and deterministic downscaling in eddy resolving ocean modelling: the Lakshadweep Sea case study.

Following reviewers’ comments, the text was amended, the MS was extended by 70 lines of text, 1 new Figure and 7 new literature references.

Comment: One of the comparison metrics used (for OSTIA) is based on domain averaged values. The authors find that the stochastic downscaled model gives similar metrics compared to the global model. Is this surprising (if not please explain)? Although the downscaling method has the ability via the introduction of stochastic length scales to better represent some mesoscale feature than the global model the mean statistics should be very similar.

Response: The statement of the similarity of the area averaged statistics between the parent (1/12 deg) and LD20_SDD (1/20) models is largely true for the area mean bias. The stochastic downscaling is performed on fluctuations, which reduces the area averaged differences between the parent and child model by design, see Shapiro and Ondina (2021).

The situation with non-linear operations (RMSD and RMSDA) is different and the similarity of the metrics is surprising to some extent. It has to be noted that OSTIA has higher resolution (1/20 deg) than the global model but the same resolution as LD20 model. Therefore, if the skill of the downscaling is not good enough, one can expect potentially greater mismatch between data in the finer resolution grid points and OSTIA than between the coarser resolution parent model and OSTIA. Therefore, the area averaged differences in non-linear statistics, Eq (9) and Eq(10) as well as in Person correlation Eq (13) could be much greater for finer models. The reason for this is that the finer resolution model may have greater gradients and be prone to the ‘double penalty effect’. For example, a finer resolution ORCA12 model has larger small-scale forecast errors compared to coarser ORCA025 in regions of high temperature  gradients (D.Carneiro , R.King, M.Martin and A.Aguiar, Met Office Technical Report No: 645, 2021, https://www.metoffice.gov.uk/binaries/content/assets/metofficegovuk/pdf/research/weather-science/frtr_645_2021p.pdf.)     Clarification is added to the text ( Discussion section).

 

Comment:  I suppose if one was to assimilate a large amount of observation into a dynamical model and assumes that the observations are perfect and have a large impact the resulting analyses will be very close to the observed field.

Response: We agree with this. In this study we use a downscaled dynamical model without data assimilation.

Comment: The dynamically downscaled model on the other hand will have introduced a wider range of variability which generally increases the error. Furthermore so, as the dynamical downscaled model is not constrained in the interior via e.g. a DA approach.

Response: We agree. This is why we developed and presented the SDD model which is much faster to run than the dynamical model and it is indirectly constrained by observation via the parent data assimilating model. Our LD20-NEMO model is also not bad even  without DA. It  introduces only a small amount of error as seen in Fig. 4 and Table 2 even after a few years of free  run.

Comment: Some basic information is missing for example how many observations were available over the domain of interest (you give some information on the ARGO floats in section 3)? I suggest to add a table/ or figure of some sort?

Response: We present the number of Argo profiles in Line 338 (original MS): ‘… in total there are 325 profiles’. We do not know how many observations were used for DA in the global model (CMEMS) as the originators do not give such information. We do not know how many SST data points were used to create OSTIA for the same reason. OSTIA is a very complex product, which uses satellite data from sensors that include the Advanced Very High Resolution Radiometer (AVHRR), the Advanced Along Track Scanning Radiometer (AATSR), the Spinning Enhanced Visible and Infrared Imager (SEVIRI), the Advanced Microwave Scanning Radiometer-EOS (AMSRE), the Tropical Rainfall Measuring Mission Microwave Imager (TMI), and in situ data from drifting and moored buoys (https://podaac.jpl.nasa.gov/dataset/UKMO-L4HRfnd-GLOB-OSTIA). OSTIA is regarded as a very reliable, good quality data source it is available from both American and European data centres.  Clarification is added.

 

Comment: You find that the stochastically downscaled model shows higher values of vorticity than the global model. This is a good result, suggesting that the methods works well.

Response: We agree, this is why we present data on vorticity.

Comment: you also find that the dynamically downscaled model shows rather different fields and you describe them as “more chaotic than the other model”. Is this not the point of dynamic downscaling – yield larger variability?

Response: “more chaotic than the other model” means that a free run of LD20-NEMO is likely to be prone to the ‘double penalty effect’, meaning that it produces larger variability, but in the wrong place, as many fine resolution models do both in ocean and atmosphere, see  e.g. (Rossa, A., Nurmi, P., & Ebert, E. (2008). Overview of methods for the verification of quantitative precipitation forecasts. In Precipitation: Advances in measurement, estimation and prediction (pp. 419-452). Springer, Berlin, Heidelberg.). The shochastic downscaling replicates larger scale features from the coarser model and therefore keeps the small scale features constrained by their large scale counterparts.     Clarification is added.

Comment: You then assume that the global model, because it is data assimilating, should be more realistic in the area – but we do not know how many observations went into the DA over the region for that day.

Response: We use OSTIA and the global CMEMS model due to their high reputation for accuracy and reliability. For example the quality control document on the global CMEMS model (https://catalogue.marine.copernicus.eu/documents/QUID/CMEMS-GLO-QUID-001-030.pdf) gives the following estimates of error. ‘The global mean sea surface temperature is close to the observations with a weak (warm) misfit of less than 0.1°C all along the reanalysis…. The sea surface salinity  is generally fresher than both the climatology with regional biases of less than 0.2 psu…GLORYS12V1 reanalysis reproduces well the main ocean currents…RMSD are generally smaller than 0.25 m.s-1 in the water column with a maximum in the lower part of the Equatorial Under Current’. CMEMS model is considered to be the most advanced global reanalysis produced in Europe [10]. For our study we used the product GLOBAL_REANALYSIS_PHY_001_026 which was available at the time of conducting our research. It has recently been updated to version GLOBAL_REANALYSIS_PHY_001_030.    Clarification to the text and an updated reference are added.

 

Comment: Are there enough observations to constrain the velocity fields?  

Response: It is difficult to assess or even set a criterion to judge if there are ‘enough’ observations. This is why we analyse the accuracy of the final result, i.e. the actual model output against various observations.

 

Comment: You should discuss differences in the atmospheric forcing used for the global model and the dynamic downscaled model (also give a better description of the global model). Can difference in the atmospheric forcing for example explain the larger error of the dynamic downscaled model in the earlier time period? What about topographies? How different are they? 

Response: We agree that all these components of a model influence the result of the simulation. Changing these components, e.g. bathymetry, atmospheric forcing, turbulence closure scheme, parameterisation of horizontal diffusion and viscosity, vertical discretization  etc. or changing the software engine (e.g. ROMS or HYCOM instead of NEMO) will create a different model. CMEMS uses NEMO v3.1 while LD20-NEMO uses a more modern version v3.6.  In this study we assess our existing model LD20-NEMO with its specific choice of its components. We have chosen them as best as we could based on our modelling experience. We do not claim that it is not possible to create, in the future, a better dynamical model. We are comparing the two specific models which do exist.   Clarification is added to the text in section 2.2.

 

Comment: Line 16: “...LD20 NEMO uses only 2d data set of data from CMEMS as lateral boundary conditions...”. That sounds like you are not applying baroclinic fields to the downscaled model but I assume you are using standard downscaling/ nesting including temperature, salinity, velocity and sea surface height? Please clarify.

Response: ‘2D data set’  means the data set along the boundary, therefore each data point ( tempreature, salinity etc) has 2 coordinates, one along the boundary, the second one is depth. Clarification is added in section 2.2

Comment: Line 67: “The child SDD-LD20 model has the same geographical limit as the parent model”? The parent model is global - does this means the SDD model covers the whole globe? I might misunderstand the model approach or setup in this case. Please clarify. 

Response: Thank you. We meant ‘The child SDD-LD20 model has the same geographical limit as the extract from the parent model used in this study.’ Text corrected as advised.

Comment: Line 179: Would be interesting though to see if/ what the differences are.  

Response: The differences in the correlation length are shown in Figure 2 (a-h) for temperature, salinity, U and V velocities at the surface and 156 m depth. The maps at other depth levels are similar. This is explained in the manuscript as follows: “Figure 2 shows that the values of the short correlation length are similar at different depth levels and different field variables: T, S, U, V”.

Comment:  LD20 Model setup. Can you discuss differences between the atmospheric forcing applied to LD20 NEMO and CMEMS. 

Response: The oceanographic component of the CMEMS model is the NEMO v3.1 platform driven at the surface by ECMWF ERA-Interim reanalysis until end of 2018 at 3h and 24 hour frequency (https://catalogue.marine.copernicus.eu/documents/QUID/CMEMS-GLO-QUID-001-030.pdf). LD20-NEMO uses NEMO v3.6 modelling engine and is driven by the meteo forcing at 3-hour interval for all variables except winds and 1-hour interval for wind.      Clarification is added in section 2.2 and Section 3.

 

Comment: Line 227: Boundaries are including baroclinic and barotropic fields (2d and 3d) this seems to contradict what you write in the abstract. Please clarify. 

Response: Please see our response to the comment re Line 16.

Comment: Line 230: “...for baroclinic velocities”. What boundary conditions are you using for temperature and salinity? 

Response: We are using the Flow Relaxation Scheme ( see https://www.nemo-ocean.eu/doc/node61.html) for temperature, and salinity with the width of the relaxation zone of 6 grid points. See line 232 of the original manuscript.

Comment: Line 233: What do you mean by first guess tuning parameters ? 

Response: Some model parameters may not be entirely known a priori, they include diffusion and viscosity coefficients for laplacian and bilaplacian operators and Smagorinsky coefficients among others, for which only typical ranges may be known. It is standard practice to guess them by using previous knowledge of similar systems. This can be further improved by performing a calibration process.       Clarification is added in Section 2.2.

 

Comment: Line 336: Are the ARGO floats independent or are they assimilated in the global model?  

Response: We do not know which specific ARGO profiles were assimilated in the CMEMS global model. The originators do not disclose this information in their documentation. Anyway, assimilation of profiles does not mean a zero difference between data assimilating CMEMS and original ARGO profiles as shown in Fig.5. None of our own LD20 models assimilate Argo profiles.   Clarification is given in section 2.2.

Comment: Line: 238-272: Not quite clear.  Did you interpolate the observation onto the respective model locations and then calculate the error stats and then average. Or did you calculate domain average and then do statistics  

 

Response: The profiles from the models are interpolated in time and space to Argo locations and in the vertical to the depth levels of Copernicus CMEMS model. Then we calculate the misfit and the square of misfit at each profile and then calculate statistics (BIAS, RMSD, RMSDA)  using equations similar to Eq 8-10, i.e. averaging over all profiles.   Clarification is added as requested.

 

Comment: Line 336: Have the ARGO floats also been assimilated ? 

Response: LD20-SDD and LD20-NEMO do not assimilate Argo profiles (or anything else). Clarification is added.

Comment: Line 344: Largest difference at around 200m might be related to large uncertainty in modelling thermocline depth. Atmospheric forcing mainly influence in the planetary boundary layer  

Snapshot of velocity falls in bad modelled period (2015) ? 

Response: We agree. In our experience, the large differences at the top of the thermocline are due to insufficient vertical resolution in that depth range in most ocean models. We hope that the new generation of models which would use a multi-enveloping vertical discretisation system see (Bruciaferri et al, 2020, https://doi.org/10.1016/j.ocemod.2019.101534) would help solve this issue. We decided to show results from different times not just present an unconsciously biased selection of ‘best’ results.     Clarification is added.

Comment: Line 368-372 : SDD shows smaller scale feature – supposed to do that 

Response: We agree. Also LD20-NEMO.

 

Comment: Line 368-380: I think conclusion drawn not quite OK. Higher resolution model should develop its own dynamics and larger variability, which is exactly the reason for doing so. Maybe compare mean EKE or mean vorticity as well.  

Response: We agree that ‘Higher resolution model should develop its own dynamics and larger variability’ . Both LD20-SDD and LD20-NEMO show this, see Fig 7 of the original MS. We provide the time series of area averaged enstrophy rather than vorticity. The reason for this is that area averaged vorticity is identical for all models due to the Stokes circulation theorem.    Clarification is added.

Comment: Figure 2: Please add titles indicating what we are looking at (I.e. T surface, T 156m, etc.) 

Response:  Figures are updated as advised.

Comment: Figure 9: Missing latitude and longitude.   

Response: Corrected as advised

 

Note: All numbered references in this document refer to the bibliography in the original manuscript. Same applies to figures and tables.

Reviewer 3 Report

General Comments

This paper addresses an important issue in oceanic numerical modelling regarding providing improved horizontal resolution in large-scale and global models.

The research is scientifically sound and the paper is generally well written. However, there are segments where the clarity of the writing could be improved. The content could be improved in some areas and section 4 should be reduced and/or incorporated into other sections. The figures and tables are well presented.

Detailed comments are provided in the attached .pdf file.

Comments for author File: Comments.pdf

Author Response

Authors’ responses to Reviewer 3 comments on jmse-2146621

A comparison of stochastic and deterministic downscaling in eddy resolving ocean modelling: the Lakshadweep Sea case study.

Following reviewers’ comments, the text was amended, the MS was extended by 70 lines of text, 1 new Figure and 7 new literature references.

General Comments

Comment: This paper addresses an important issue in oceanic numerical modelling regarding providing improved horizontal resolution in large-scale and global models.

The research is scientifically sound and the paper is generally well written. However, there are segments where the clarity of the writing could be improved. The content could be improved in some areas and section 4 should be reduced and/or incorporated into other sections. The figures and tables are well presented.

 

Response: Thank you.

 

Detailed Comments

 

Comment: Line 21  “ant” should be “and”

Response: Thank you. Corrected as advised.

Comment: Line 30: "physical models" usually mean lab-based models using physical constructs rather than computer-based models.

Response: Corrected to ‘numerical models of ocean dynamics’

Comment: Line 41. ‘One of such algorithms’ is incorrect grammatically – please reword.

Response: We amended the text to ‘One example is the algorithm titled Stochastic-Deterministic Downscaling (SDD) which was proposed in [8].…’.

Comment: Line 49: "against traditional" should be "against a traditional"

Response: Thank you. Corrected as advised.

Comment: Line 52-53: The first sentence might be better if placed in section 1 Introduction. More information about this oceanic area should be provided here, such as the comments in the first two paragraphs of Section 4. A map of the Lakshadweep portion of the Indian Ocean should be included showing the coastline and bathymetry.

Response: In structuring the paper, we following the style that Introduction sets the scene by introducing previous research, and everything that is new or specific to the current study is presented in the following section. Following the reviewer’s suggestion we added more information of the Lakshadweep Sea and included a  map showing the coastline and bathymetry.

 

Comment: Line 54-60. The "parent model", later identified as the CMEMS model, needs to have a more detailed description, especially since the url link for Reference [10] does not work. Does this data assimilation system actually included a numerical model incorporating the equation of motion for fluid dynamics?

Response: The EU Copernicus Marine Environment Monitoring Service (CMEMS) has evolved since we downloaded their product called ‘GLOBAL_REANALYSIS_PHY_001_026’.  Now it is called the EU Copernicus Marine Service, and their global reanalysis product has been upgraded to version GLOBAL_MULTIYEAR_PHY_001_030. The model component is the NEMO platform driven at surface by ECMWF ERA-Interim then ERA5 reanalyses for recent years. Observations are assimilated by means of a reduced-order Kalman filter. Along track altimeter data (Sea Level Anomaly), Satellite Sea Surface Temperature, Sea Ice Concentration and In situ Temperature and Salinity vertical Profiles are jointly assimilated. Moreover, a 3D-VAR scheme provides a correction for the slowly-evolving large-scale biases in temperature and salinity (https://data.marine.copernicus.eu/product/GLOBAL_MULTIYEAR_PHY_001_030/description).This is arguably the most advanced global ocean reanalysis available in Europe, there are tens if not hundreds of publications explaining how it works. A short reference list is publicly available on https://catalogue.marine.copernicus.eu/documents/QUID/CMEMS-GLO-QUID-001-030.pdf. We added a comment that the ‘CMEMS’ model has evolved to a new version.

 

Comment: Line 68: "different depth levels”.  In what way were depth layers different?

Response: CMEMS and LD20 meshes have different computational depth layers below the sea surface.

Comment:  Line 74-75. ‘Markov-Gauss algorithm’ is this referring to the Gauss-Markov theorem? Perhaps a reference should be included?

Response: Yes, you are right. The wording is corrected as advised. This theorem is a common knowledge and is presented in many university texts as well as in Wikipedia.

 

Comment: Line 79. ‘allows to reveal’- wording is not clear

Response: Changed to ’ … method allows to expose details…’

Comment Line 95: "different 'central' nodes" how many central nodes are there? How are central nodes selected?

Response: All nodes of the parent grid become central in turn as the index n0 runs from 1 to N_p when computing the correlation function. This procedure is the same as used in optimal interpolation, see the (LS Gandin, 1965, reference  [14] in the MS). Clarification is added.

 

Comment: Line 108-109 . ‘ we only included the nodes which belong to the area of influence, in this case it was 1.7 x1.7 degrees in size’ - is the correlation for each 'central' node' computed within the 1.7 x1.7 degrees area of influence?

Response: Yes this is correct.

 

Comment: Line 169 "Figure 2" what are the units of the correlation length scales in the colour legend?

Response: The units are kilometres. Clarification is added in the caption. Also in the figure

 

Comment: Line 173. ‘values of the short correlation length are similar’ - U and V appear to have larger length scales, especially west of southernmost India?

Response:  The difference between correlation lengths for different variables is relatively small and comparable with differences between different depth levels. A few lines below we make a stronger simplification (using one map of Ls for all)- see our response to the next comment.

 

Comment: Line 177-178. ‘spatially varying value of correlation length calculated for the surface temperature was used for all variables and all depths of the child model grid’ - is this

simplification valid for the U and V variable given the results presented in Fig. 2?

Response: As usual, the validity of this any other simplification can be judged by the skill of the final product. This is why we present results of model validation against as many observations as we could find.

Comment: Line 195: " Is this an acronym for best linear unbiased estimate? If yes, the acronym should follow the words.

Response: We agree. The acronym does follow the words. The full sentence reads ‘In these conditions Eq(4) provides the best unbiased linear estimate (BLUE) to the true value [14,19,20]. We have clarified this in the revised manuscript as: “Best Unbiased Linear Estimate (BLUE)”

 

Comment: Line 199- 200.’The relieving fact is that the weighting factors are computed only once for the whole forecasting/hindcasting period’- wording should be improved.

Response: .Reworded as advised. ’The advantage of this approach is that the weighting factors are computed only once for the whole forecasting/hindcasting period’

Comment: Line 245: "area averaged" -what area is used for this averaging?

Response: This is explained in the MS a few lines below, namely ‘Area averaging takes place over the LD20 model domain but excluding a narrow flow relaxation sponge rim used by LD20-NEMO (approximately 90 km in width) around the open boundaries.’

Comment: Line 247: provide more detail on how the anomalies were computed

Response: Anomalies are calculated according to Eq (11). Clarification is added to the text.

Comment: Line 285: " seasonal variability” -  a large seasonal variability occurs for salinity but temperature is more complex - two cycles per year. Is there any physical understanding of why this is the pattern?

Response:  This is due to the monsoon circulation in the area. India receives south-west monsoon winds in summer and north-east monsoon winds in winter. Clarification is added.

 

Comment: Line 327- 329. ‘The slight deterioration of correlation in LD20-NEMO is probably due to the ‘double-penalty’ effect, which generates higher RMSD errors caused by small spatial shift in the distribution of field variables in finer-resolution models [31]’.- ‘the small spatial shift’ in higher resolution models is not clear. Can the wording be improved to provide better clarity?

Response: The ‘double penalty effect’ is a common phenomenon which occurs in both atmospheric and ocean models of higher resolution, see e.g (https://doi.org/10.5194/os-16-831-2020;  https://doi.org/10.1007/978-3-540-77655-0_16, 2008) . We give a reference [31] to (https://doi.org/10.1002/met.73) where this effect is analysed in great detail. Clarification is added.

Comment: Line 332. “The discrepancy between LD20_SDD and OSTIA” However, the discrepancy of the CMEMS model with observations is better than that of LD20_SDD, even though it has coarser resolution. Why is this?

Response: The discrepancies between LD20_SDD and OSTIA on the one hand and between CMEMS and OSTIA on the other are very similar, see Table 1.

Comment: Line 345- 346 “…which provides either boundary (to LD20-NEMO) of full 3D data (to LD20-SDD) to other models”. - clarify wording.

Response: The phrase is reworded: ‘… which provides either boundary data in the case of  LD20-NEMO model or full 3D data in the case of LD20-SDD’.

 

Comment: Line 280 (probably 380) ‘ could be caused by the ‘double penalty’ effect which is common to higher-resolution models’ - why would this effect be more pronounced for LD20_NEMO than for LD20_SDD?

Response: The double penalty effect is typical for dynamic models which can create small scale features that are present in the wrong place. Double penalty effect was not reported for stochastic models. Specifically, the larger-scale structure of LD20-SDD is constrained by larger scale structure of the coarser data assimilating model. Clarification is added. ‘could be caused by the ‘double penalty’ effect which is common to higher-resolution dynamic models and can create small scale features that are present in the wrong place. The SDD models are less prone to this effect by the design of the downscaling process, see [8]’.

Comment: Line 415-416: this sentence is this is redundant to the second last sentence of the previous paragraph.

Response: The repetition removed as advised.

 

Comment: Line 421-422.  ‘In early spring, the area occupied with highly non-linear processes can be as high 20% or more’ - Figure 8 shows area with Ki > 0.5 being more than 20% in winter rather

than early spring for LD20 runs only.

Response: Corrected as advised. ‘In winter and early spring, the area occupied with highly non-linear processes can be as high 20% or more..’

Comment: Discussion. This section could be eliminated. The first two paragraphs can be incorporated into Section 1. The middle paragraphs, especially paragraph 3, are not required. The last few paragraphs are partially redundant and should be merged into an expanded Conclusions section.

Response: We follow the journal rules, which require an extended discussion section and a short conclusion. The other 2 reviews did not require such restructuring.

Comment: Line 450-452: This should be presented earlier in the paper.

Response: We think that this sentence provides a reasonable link between the Introduction and Results sections. We are reluctant to put anything in the Introduction section which is our own result rather than present validated results of previous research. We have changed the tense of the sentence to make it fit better with the discussion section: “In this study we provided a comparative skill test for two ocean models of the same resolution”

Comment: Line 464-465: the limitations for the equations of motion for ocean modelling are dominated by resolution issues and ultimately by the very small scales of oceanic turbulence. In addition adequate representation of boundary condition and initial conditions as well as other issues are important. See Fox-Kemper et al (2019) Challenges and Prospects in Ocean Circulation Models. Front. Mar. Sci. 6:65. doi: 10.3389/fmars.2019.00065

Response: Thank you for this note. The reviewer’s suggestion is added verbatim to the text as well as the reference.

Comment: Line 466 467.’ statistical properties of innovations defined as differences between the model and observations’  - use of the word "innovations" seems to be inappropriate.

Response: Amended as advised. ‘statistical properties of differences between the model and observations’

 

Comment: Line 511-512. ‘ …Kibel  number larger than 0.5 The seasonal variability…’ - this needs to be reworded for improved clarity

Response: Thank you. Reworded as advised. ‘The areas of highly non-linear dynamics ( i.e. with Kibel number larger than 0.5) occupy as much as 20–25% of the Sea in early spring and as low as 5% in the summer.’

Comment: Conclusions. This conclusion is minimal as some of the important findings related to vorticity and enstrophy which are provided in the latter half of Section 4, could be moved from that Section to the Conclusions section.

Response: We added some text related to vorticity and enstrophy, however we need to keep the Conclusions relatively short according to the journal guidelines.

 

Note: All numbered references in this document refer to the bibliography in the original manuscript. Same applies to figures and tables.

Round 2

Reviewer 1 Report

The re-reviewing of the manuscript “A comparison of stochastic and deterministic downscaling in eddy resolving ocean modelling: the Lakshadweep Sea case study” submitted by Shapiro*, Gonzalez-Ondina, Salim and Tu, in Journal of Marine Science and Engineering (Manuscript Number: jmse-2146621).

 

Thanks for addressing my comments. The authors have made substantial improvement to this manuscript. Therefore, Minor Revision is suggested before its publication in JMSE. The following is my comments:

 

1.     “Comment: Results: The comparison for the three models: the authors have compared temperature and salinity. I was thinking that for the hydrodynamic model (e.g., simulating eddies), it is better to conduct model comparisons regarding sea surface height (e.g., geostrophic flows), surface current velocities etc.”.

 

The authors state that “We are not aware of observations of surface currents or sea surface height with the required resolution to perform comparisons.” But I think these hydrodynamic data are key to the calibration/validation of the skill of numerical model. Therefore, I would suggest authors considering including these observations for model-to-data comparison.

 

2.     The selection of specified time for study needs to be explained. For example, my comments to Figure 6 and 8 etc.

Author Response

Manuscript ID jmse-2146621 : A comparison of stochastic and deterministic downscaling in eddy resolving ocean modelling: the Lakshadweep Sea case study

Reviewer 1 comments 2^nd round

Comment: Thanks for addressing my comments. The authors have made substantial improvement to this manuscript. Therefore, Minor Revision is suggested before its publication in JMSE. The following is my comments:

Comment
1. "Comment: Results: The comparison for the three models: the authors have compared temperature and salinity. I was thinking that for the hydrodynamic model (e.g., simulating eddies), it is better to conduct model comparisons regarding sea surface height (e.g., geostrophic flows), surface current velocities etc."

Response. We agree that the dynamic parameters such as current velocities are an important outcome of an ocean model either hydrodynamic or stochastic. Therefore we have provided maps of current velocity from all 3 models, which show the difference in the spatial patterns produced by different modelling approaches. CMEMS is data assimilating but at lower resolution, LD20-NEMO is a dynamic model at higher resolution and no DA, LD20-SDD is a stochastic model at higher resolution and no DA- see Fig 7 (a, c, e). To clarify further the difference between the models in representing currents we provided the maps of enstrophy< which is more sensitive to meso-submesoscale variations in the ocean current gradients – see Fig7 (b, d, f). In addition, the time series of surface current enstrophy is presented in Fig.8, which shows a systematic difference between lower and higher resolution models. We compare the full velocities rather than only their geostrophic components as the Lakshadweep Sea is an area of strong ageostrophic currents as shown in Fig.9.

Additional clarification is given in the text (lines 568-580 in the revised MS).

Comment. The authors state that "We are not aware of observations of surface currents or sea surface height with the required resolution to perform comparisons." But I think these hydrodynamic data are key to the calibration/validation of the skill of numerical model. Therefore, I would suggest authors considering including these observations for model-lo-data comparison.

Response. We agree that it would be beneficial to validate models against velocity observations in addition to model inter-comparison presented in Figs7-9. However we are not aware of observations of surface currents or sea surface height with the required resolution to perform comparisons model-to-observation comparisons. For example a reputable source of data (Permanent Service for Mean Sea Level -PSMSL) states ‘WARNING: THIS IS NOT RESEARCH QUALITY DATA. USE WITH EXTREME CAUTION’ in relation to the SSH data sets in the area, see  e.g. https://psmsl.org/data/obtaining/stations/2184.php, https://psmsl.org/data/obtaining/stations/1050.php.

Additional clarification is given in the text (Lines 587-591 in the revised MS)

Comment. 2. The selection of specified time for study needs to be explained. For example, my comments to Figure 6 and 8 etc.

Response. We have produced 1461 sets of maps. Each set includes temperature, salinity, velocity, vorticity, enstrophy at 50 depth levels, making the total number of maps=1461*5*50=362,250 maps. In the MS, we present a small selection of such maps. The date in Fig 7 is selected as a representative of a period of low mesoscale activity, so that the number of eddies is relatively small and they are clearly seen on the maps. The dates in Figure 10 are selected to show two contrasting seasons – winter and spring. Other figures (time series) cover a range of dates.

Additional clarification is given in the text (Lines 413-416 and 474-475 in the revised MS).

Reviewer 2 Report

I'd like to thank the authors for addressing my comments, which I am quite happy with.  

I am suggesting to accept the paper in the current format. 

One thing to note, there is a bit of talk about the "double penalty" for higher resolution dynamical models. Standard statistical analysis methods do not capture small displacements of oceanic features very well, therefore often giving the impression a lower resolution model performs better than a high resolution model compared to observations. This is a challenge that the community needs to start thinking about. The more so as, e.g. sub-mesoscale dynamics, internal tides, etc. are of increasing interest for the e.g. stakeholders

Author Response

Reviewer 2

Comment.

I'd like to thank the authors for addressing my comments, which I am quite happy with.  

I am suggesting to accept the paper in the current format. 

One thing to note, there is a bit of talk about the "double penalty" for higher resolution dynamical models. Standard statistical analysis methods do not capture small displacements of oceanic features very well, therefore often giving the impression a lower resolution model performs better than a high resolution model compared to observations. This is a challenge that the community needs to start thinking about. The more so as, e.g. sub-mesoscale dynamics, internal tides, etc. are of increasing interest for the e.g. stakeholders

Response. Thank you for supporting our study. We agree with your note that the ‘double penalty effect’ is a challenge to the community. We believe that our study contributes to resolving this challenge. As far as we are aware the scientists at the UK Met office are working on the problem as well but using a different approach.