A Space-Time Partial Differential Equation Based Physics-Guided Neural Network for Sea Surface Temperature Prediction

Round 1

Reviewer 1 Report

Adv. Space Res-22-01340 Review

A Space-time partial differential equation based Physics-guided neural network for sea surface
Temperature prediction
Yuan T. et al.

General comments
Sea surface temperature is one of the most important parameters of the world's ocean. It plays a fundamental role in the exchange of energy between the oceans and the atmosphere, and, as a consequence, to global climate.

The main idea of the paper, I think, lies in the fact the predicted model will contains physics knowledge and deep learning. But, it seems that it is strongly necessary to select sufficiently related variables to establish this model.

It is not the first paper based on deep learning. Even if the proposed model(s) were highly promising but for short and mid-term (daily) sea surface temperature.
But in already published papers, the arguments used to characterise the
improvement are encrypted ; with %, with RMSE, with MAPE, etc.
(see Xiao et al., 2019).
In the present paper, the reader can find many aspects about introducing
physics into DL model ; I think, however, that the paper do not give enough explicite arguments in order to appreciate and finally, make the proof, of all the benefits (which are described in section 5. (P12, L380-4135).

As a consequence, there is nothing in the paper that permits to describe the precision of the used data, even if it is model’s outputs instead of data.
I don’t say that it is necessary to perform a sensitivity study in order
to investigate a range of plausible error budgets. But local error levels,
error variance-covar matrices, SST trends (and even accelerations) should be provided (or at least discussed) with their corresponding uncertainties.

In addition, it is difficult to (finally) understand that authors are working on a medium-to-long term sea surface temperature forecasting. I think that, in the Introduction, authors should specify, thus very early in the text, the interest of that specific period (around 10 yrs) e.g. for global climate studies : daily, monthly or a few years or a decade (like here) : what are the challenges beyond ?

It is difficult to use the ‘’Supporting information’’ even if it contains a lot of informations; but the relationship between both documents (paper and support) is not easy.
In addition :
Introduction P1 : what are the ‘’various state-of-the-art models ? Please add references
 

Figures 3, 4, 5 and S1 to S9 : please use the same scale for RMSE, e.g. 0.7 to 1.3, for all plots.

Abstract
P1, L 9-12 : the reader has no idea about about the expected performance
of the adopted STPDE method for prediction of the daily Sea Surface Temperature. Authors should adopt some criteria, i.e. by only giving a % or a number characterising this new performance.


1. Introduction
It is unclear for me, after reading the introduction, why authors do not describe (at leats briefly), the observed connection between SST and sea level pressure variabilities. Because it is the result of the atmosphere driving the ocean.

L66-68 : please give a reference
L76 : ‘’we obtain more accurate SST predictions …’’ : please give a number !

Please add 1-2 lignes at the end in order to give a idea of the different sections of the paper.

Generally, the problem of using different approaches is well explained but partially justified ; I would say that authors should use, some times along the text, some numerical value(s) to better characterise the existing solutions and also the expected performance of their model… (e.g. the idea is to improve the prediction by a factor of xxxx, on that period of time).

2. Data
P3, Table 1: Authors should add a new column in order to help
characterising the input variables and/or data : uncertainties and origine (e.g. reference) of the variable

3. Methods

4. Results
4.1.
For the figures (1, 2, 3, etc.) authors should indicate the unit of RMSE and, above all,should describe (at least briefly) in what extend the SST prediction error(s) lead to uncertainties in term of energy or in term impact on sea level (steric effect) etc.

4.2.
Figure 6 : please add a reference for the HYCOM model

4.3 Limitation analysis of pure…
The first paragraph is unclear… (in particular L281-283) Please re-write.


5. Discussion and Conclusions
I think that arguments must be clearly encrypted ; with regard to
other prediction models and/or from large geophysical effects ;
i.e. to what extend the more accurate long (medium) term prediction of
sea surface temperature would help climate model, global sea level trend, etc.

The quality of English language is high ; being not a native English, it's difficult for me to add more pertinent comments or arguments about that.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Although this is an interesting study, it could be useful for predicting SST to track climate change. However, the article needs extensive revisions. Please address the comments to improve the quality of your article. 

1. The introduction needs improvement. For example, in the introduction line 15-16, authors stated that "Sea Surface Temperature (SST) plays a fundamental role in understanding global ocean atmosphere ecosystems and the Earth’s climate system...". I suggest that the authors provide the following references to support the argument: Sarker, Shiblu. "Fundamentals of Climatology for Engineers: Lecture Note." Eng 3.4 (2022): 573-595.

2. My first question is why do we need to consider STPDE along with conventional ANN/DL? Usually nural network doesn't consider spatial and temporal feature? Have you checked that? I suspect usually it optimizes based on PDE during backpropagation. 

3. Methods' writing doesn't impress me! Poorly written! Review more papers to improve your methodology. In addition, illustrate the models with very small schematics. Please improve your figure 1 and 2. 

4. RMSE is a well known facts! what about other metrics. Please improve figures 3, 4, 5, 6 and 7. Currently they are unclear to me! I think Python is able to generate publishable figures. Reduce the space between subplots. Please review this python toolbox. https://timcera.bitbucket.io/plottoolbox/docs/command_line.html#time 

5. How do you reformulate Mixed-Layer Heat Budget Equation in a so called STPDE? Can you explain little bit more with schematic figures? Authors can review the following references for explanation. (a) Sarker, Shiblu. "A short review on computational hydraulics in the context of water resources engineering." Open Journal of Modelling and Simulation 10.1 (2021): 1-31, (b) Sarker, S. (2022). Essence of mike 21c (fdm numerical scheme): Application on the river morphology of bangladesh. Open Journal of Modelling and Simulation, 10(2), 88-117.

6. What is the importance of this study? Please explain the implications of this study in the context of climate change. Currently it does not persuade me that it provides a basis for climate change/environmental protection. Please describe in a distinct section (prior to the conclusion) the potential implications of this study. 

Perhaps it would be beneficial for the authors to revise their compositions, particularly the sentence structure. 

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Many thanks for your work and positive responses;

concerning response 10 & 12, I think yes, it would be beneficial to include a Table that provides prediction results/performances.

About P8 and P9 of your new version, v2; please check the number of the employed formulas before P8 (1, 2, 3 and 4) and then after on P9 with number 3 and 4 already used...

In addition, if you could adopt the same scale (on the vertical axis), at least on Fig. 4 (not easy on Fig. 5, 6 ...), it would be much more easy for the reader to have a quick look about differences between the methods.

Thank you again for the cover letter.

Author Response

Thank you for taking the time to review our paper and for providing valuable feedback. We sincerely appreciate your effort in carefully evaluating our work and your constructive comments that have helped improve the quality of our research.

Your feedback has been instrumental in strengthening our findings and addressing certain shortcomings in our previous version. We would like to express our gratitude for your insightful suggestions, which have allowed us to enhance the presentation of our results and clarify important aspects of our methodology.

We acknowledge the importance of including a table showcasing the improvement of our method compared to traditional algorithms. We have promptly incorporated this suggestion and believe that the addition of this table will significantly enhance the reader's understanding of our approach and its performance.

Furthermore, we genuinely appreciate your attention to detail in pointing out the inconsistency in the numbering of the formulas. We have carefully revised the relevant sections according to your observation to ensure clarity and accuracy.

Regarding the suggestion to adopt a consistent scale, especially in Figure 4, we acknowledge its merits in facilitating quick comparisons between methods. We have taken your recommendation into consideration and have made the necessary adjustments to provide a more consistent visual representation throughout our figures.

Once again, we are grateful for your time and effort invested in reviewing our paper. Your feedback has been instrumental in strengthening the quality of our research, and we are confident that these revisions enhance the overall contribution of our work. We sincerely appreciate your continued support and valuable insights.

Thank you once again for your invaluable contribution to our manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

Thanks for the revision. 

Please check the English again.

Author Response

Thank you for taking the time to review our paper and for providing valuable feedback. We sincerely appreciate your effort in carefully evaluating our work and your constructive comments that have helped improve the quality of our research.