Data-Driven Interpolation of Sea Surface Suspended Concentrations Derived from Ocean Colour Remote Sensing Data

Round 1

Reviewer 1 Report

Results presented in this paper indicate clearly that new method of the data interpolation in this study outperforms a number of other more or less conventional (established) approaches to the recovery of the signal from noisy, data-poor samples. I think, this paper would be of interest to the practitioners working in environmental modelling and observations. Having said this, I believe, the paper (as well as the readership of this paper) would greatly benefit from clarifying a number of questions and from refining the presentation of this study. See comments follow.

Comment 1.

The problem I had reading this paper was to understand the new method advocated in this document. Authors give a very brief outline of it, referring to a couple of other papers for more details (references 23 and 36, see below).

One of such references (ref No. 36) was not available for at least several days I was trying to reach it ( System Unavailable (lanl.gov) )

I managed to  get an arXiv version of it, but this was not particularly helpful either since the arXiv paper has not being properly polished. For example in page 2 (arXiv paper), equation 2, operator I(U,Y,W) is introduced as a function of 3 variables, and immediately after that it is referred to as a function of 2 variables   I(Y, W). Page 2 is referring to formula (5) which is introduced later in the paper.  Page 3 states “This algorithm at the basis of DINEOF algorithm and XXX for matrix completion under subspace constraints [2, 15] involves the following iterative update ….” Which would require the reader to dive into another paper to understand the meaning of XXX. What is XXX? It is not a common name or abbreviation.

Same comment goes for the reference No, 23 – it does not provide enough details and instead is referring to another paper.

To summarise, neither the reviewed paper nor the papers it is referring to provide a comprehensive description of the new method.

I think, the paper and the readership of this paper would greatly benefit from this article having a sound description of the new method. May be some simple/toy example with specific inputs and outputs instead of an abstract generalising formulations would help here.

23. Beauchamp, M.; Fablet, R.; Ubelmann, C.; Ballarotta, M.; Chapron, B. Intercomparison of data-driven and learning-based interpolations of along-track nadir and wide-swath swot altimetry observations. Remote Sensing 2020, 12, 1–29. doi:10.3390/rs12223806.

36. Fablet, R.; Drumetz, L.; Rousseau, F. End-to-end learning of energy-based representations for irregularly-sampled signals and images 2019. pp. 3–7, [1910.00556] http://xxx.lanl.gov/abs/1910.00556

Comment 2.

The authors should explain why they have selected synthetic observations to illustrate this method instead of applying it directly to the remote sensing data.

Comment 3.

The numerical model simulates transport of mud, sand and gravel. Why do you simulate gravel? Does it contribute to the suspended sediment?

Comment 4.

Another common technique for the data interpolation in geophysical applications is Gaussian Process modelling (eg Kriging). Do you think this approach would be suitable for the kind of applications reported in this paper?

Author Response

ANSWERS TO REVIEWER 1

GENERAL COMMENT FROM REVIEWER

Results presented in this paper indicate clearly that new method of the data interpolation in this study outperforms a number of other more or less conventional (established) approaches to the recovery of the signal from noisy, data-poor samples. I think, this paper would be of interest to the practitioners working in environmental modelling and observations. Having said this, I believe, the paper (as well as the readership of this paper) would greatly benefit from clarifying a number of questions and from refining the presentation of this study. See comments follow.

GENERAL ANSWER TO REVIEWER

Thanks to the reviewers' specific comments, the article has been largely improved in form. First, as a consequence, the title of the article has been modified. Also Figures 1 and 2 are new. Figures 3, 5 and 6 were modified, and Tables 1 and 2 have been corrected or improved. Sections "2.1 Data", "3.4. 4DVarNet" and "5. Discussion" were completely re-written and Section "2.2. OSSE and benchmarking framework" largely updated. 6 new article references are now included in the reference list: 22, 27, 28, 33, 35, and 40.

COMMENT 1:

The problem I had reading this paper was to understand the new method advocated in this document. Authors give a very brief outline of it, referring to a couple of other papers for more details (references 23 and 36, see below).One of such references (ref No. 36) was not available for at least several days I was trying to reach it ( System Unavailable (lanl.gov) )I managed to  get an arXiv version of it, but this was not particularly helpful either since the arXiv paper has not being properly polished. For example in page 2 (arXiv paper), equation 2, operator I(U,Y,W) is introduced as a function of 3 variables, and immediately after that it is referred to as a function of 2 variables   I(Y, W). Page 2 is referring to formula (5) which is introduced later in the paper.  Page 3 states “This algorithm at the basis of DINEOF algorithm and XXX for matrix completion under subspace constraints [2, 15] involves the following iterative update ….” Which would require the reader to dive into another paper to understand the meaning of XXX. What is XXX? It is not a common name or abbreviation.Same comment goes for the reference No, 23 – it does not provide enough details and instead is referring to another paper.To summarise, neither the reviewed paper nor the papers it is referring to provide a comprehensive description of the new method.I think, the paper and the readership of this paper would greatly benefit from this article having a sound description of the new method. May be some simple/toy example with specific inputs and outputs instead of an abstract generalising formulations would help here.
Beauchamp, M.; Fablet, R.; Ubelmann, C.; Ballarotta, M.; Chapron, B. Intercomparison of data-driven and learning-based interpolations of along-track nadir and wide-swath swot altimetry observations. Remote Sensing 2020, 12, 1–29. doi:10.3390/rs12223806.
Fablet, R.; Drumetz, L.; Rousseau, F. End-to-end learning of energy-based representations for irregularly-sampled signals and images 2019. pp. 3–7, [1910.00556] http://xxx.lanl.gov/abs/1910.00556

ANSWER 1:

Yes the new method can be more detailed in the article. More description has been added though. In particular this NN methodology was initially tested with a toy model based on a MNIST dataset, with other details put forward. In consequence Section 3.4 "4DVarNet interpolation schemes" has been rewritten. Since the present article is not intended to introduce a new method but a new application, the desciption of the method is still a summary of the description found in the original reference n°36.
 
Indeed this reference n°36 was a preprint (badly referenced as XXX). It is now an article published in Frontiers. It provides a much better description of the new method with experiments carried out on the toy model (MNIST) and an experiment with SST dataset. Both AE and GENN architecture are now fully explained. And there are no more issue with the mathematical formulation you identified. The new reference, with an Internet link at the end, can be found here:
Fablet,  R.;   Beauchamp,  M.;   Drumetz,  L.;   Rousseau,  F. "Joint  Interpolation  and  Representation Learning  for  Irregularly Sampled Satellite-Derived Geophysical Fields". Frontiers in Applied Mathematics and Statistics 2021,7, 1–13. doi:10.3389/fams.2021.655224.
https://www.researchgate.net/publication/351485345_Joint_Interpolation_and_Representation_Learning_for_Irregularly_Sampled_Satellite-Derived_Geophysical_Fields

Concerning the reference 23, it is another application of the NN methods to SWOT satellite data, by adding satellite tracks in an OSSE context. The main difference between this OSSE and the OSSE presented in the present article concerns the observations (inputs of the interpolation model). In the reference 23 SWOT satellite nadir tracks are simulated. Those type of simulation give a quite different interpolation context. In the present case we work on 2D maps which give more irregulary sampled information than the NADIR tracks (which give the quite the same rate of available data at each iteration). 

COMMENT 2:

The authors should explain why they have selected synthetic observations to illustrate this method instead of applying it directly to the remote sensing data.

ANSWER 2:

OK, the following paragraph has been added to the Section dedicated to OSSE (2.2. OSSE and benchmarking framework):
"Observing System Simulation Experiments (OSSE) [29] provide a  well-posed  framework  to  carry  out  such  benchmarking  experiments  when  dealing  with  high missing data rates,  typically above 80%.   This explains why OSSE schemes are widely exploited for benchmarking experiments for the reconstruction of sea surface fields [30,30,31] from observation data. Especially, within an OSSE setting, the definition of the evaluation metrics do not depend on the sampling patterns of the observation data, which result in better characterization of space-time scales the interpolation methods can resolve."

COMMENT 3:

The numerical model simulates transport of mud, sand and gravel. Why do you simulate gravel? Does it contribute to the suspended sediment?

ANSWER 3:

OK, the following sentence has been added to the Section dedicated to the data (2.1. Data):
"The gravel class had been defined in the MARS-MUSTANG model to model the bedload transport [25]. As this class does not contribute to the SSSC, it was not retained in this study"

COMMENT 4:

Another common technique for the data interpolation in geophysical applications is Gaussian Process modeling (eg Kriging). Do you think this approach would be suitable for the kind of applications reported in this paper?

ANSWER 4:

Yes kriging methodology are regularly used in this type of interpolation issue. Here we compare our methods with the Optimal Interpolation (OI). OI and kriging methods give same results, in fact the kriging resolves the same least-squares problem but in the parameter space (the spatial grid) instead of the data space. The difference happens only in the CPU time, depending on the number of parameters or data present in the inverse problem (least-squares).
Also it is true that many other geostatistical and kriging methods can be used in this kind of benchmark (natural neighbourhood, local neighbourhood etc.), but we take one of the most used as a reference in order to better focus on DA and NN interpolation models. Now, following this interesting comment that can be useful for the readers, we decided to complete the following sentence in the Section "3.1. Optimal Interpolation" giving also a reference to kriging methods:
"The Optimal Interpolation (OI), also referred to as kriging [33] is a method widely applied ingeophysics."
[33] Cressie, N.A.C.; Wikle, C.K.Statistics for spatio-temporal data; Wiley, 2011; p. 588.

Reviewer 2 Report

Please see attachment.

Comments for author File: Comments.pdf

Author Response

ANSWERS TO REVIEWER 2

GENERAL COMMENT FROM REVIEWER

This  manuscript  discussed  some  methods  to  interpolate  “satellite  images”  of  surface suspended sediment concentrations (SSSC). Data used in this study are not real satellite products. The high-resolution numerical simulation results of SSSC was thought as the references dataset, and the cloud masks taken from real MODIS images were then applied to stimulate a MODIS-like observation dataset. After comparison of four kinds of interpolation methods, the performance of GE-4dVarNet model was found to be the best. However, from this paper we still couldn’t know the performance of these models for real satellite images. I have some questions about this manuscript.
Considering all the points listed above, I think at this stage this manuscript needs major revision.

GENERAL ANSWER TO REVIEWER

Thanks to the reviewers' specific comments, the article has been largely improved in form. First, as a consequence, the title of the article has been modified. Also Figures 1 and 2 are new. Figures 3, 5 and 6 were modified, and Tables 1 and 2 have been corrected or improved. Sections "2.1 Data", "3.4. 4DVarNet" and "5. Discussion" were completely re-written and Section "2.2. OSSE and benchmarking framework" largely updated. 6 new article references are now included in the reference list: 22, 27, 28, 33, 35, and 40.

COMMENT 1:

How about the differences between the numerical simulations from MARS-MUSTANG model and the real satellite products of SSSC in this study area? Or with that in situ observations?

ANSWER 1:

OK, A new paragraph (in red) has been added in Section "2.1: Data" between Fig.1 and Fig.2

COMMENT 2:

We know that the SSSC in the open ocean are quite low. Could you please show us a spatial distribution of SSSC based on model results? How large is the area with SSSC below 0.1 mg/L?

ANSWER 2:

Yes this first version of article does not provide enough information about the initial distribution of the SSSC from the model. 
In the new present version we then added in Section "2.1. Data" a map of the mean SSSC resulting from the MARS MUSTANG model (Fig.1), which illustrates the spatial distribution of SSSC below the limit of 0.1 mg/L. In order to give a better understanding of the area we also juxtapose in parallel a bathymetric map showing the major isobaths of the Bay of Biscay. Finally a description of the SSSC distribution with regard to bathymetry has also been added to this Section. 

COMMENT 3:

Does the RMSE in Table 1 and 2 has units(mg/L)? If yes, we should add it. Otherwise, we can use another abbreviation by noting logarithm transformed.

ANSWER 3:

Yes, the unit of the RMSE need to be precised. In our case the RMSE is calculated directly with the log10 output maps compared to the MARS/MUSTANG log10 maps. So the unit is log10[g/l]. It has been added to Table 1 and 2.

COMMENT 4:

There are many differences among the results of four methods, but what’s the reason? Some explanations are expected in the discussion part.

ANSWER 4:

Indeed we added a paragraph (in red) in the Section "5. Discussion" giving some possible explanations of why the results are so: please see the text enlighted in red in this section.

COMMENT 5:

How about the results of these data-driven interpolation methods if applied for real satellite image? I think this question should be answered, if use this title.

ANSWER 5:

Actually we are working on this article only in a OSSE context. Indeed the formulation of the title may be considered as hazardous. For our case we don't use direct remote sensing data but derived ones from MODIS cloud cover only. About the use of real satellites images we are beginning to answer this question in the Discussion section citing the work of Bart et al 2020. They actually used SST satellite products with similar methods as ours. But the present work here deals with OSSE only especially because we have a very hight rate of missing data in our zone of study: while Barth et al 2020 have a mean 30% of missing data, we are at about 70%. This hight amount of missing data will introduce a lot of bias, particulary on validation points.
For all this reason and for a better understanding of the article then we are proposing now a modified title, as following: "OSSE assessment of sea Surface Suspended Sediment Concentrations interpolated from ocean colour remote sensing".

COMMENT 6:

What’s the meaning of “w.r.t”? “with respect to“？Does is very popular in scientific writing?

ANSWER 6:

Yes the w.r.t. meaning was "with respect to". It's now written in full in the paper.

Round 2

Reviewer 1 Report

Good work

Reviewer 2 Report

I recommend publication of this manuscript.

One point is about the new title. Is "OSSE" a popular abbreviation? I think maybe the old title is better.