KaRIn Noise Reduction Using a Convolutional Neural Network for the SWOT Ocean Products

Round 1

Reviewer 1 Report

Comments for author File: Comments.pdf

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper addresses an important issue in oceanography, which is the need for high-resolution and accurate measurements of sea surface height for understanding fine-scale ocean dynamics and their role in global ocean variability and climate. However, the paper uses simulated data generated by the SWOT simulator, which may not fully capture the complexity and variability of real-world data. The paper acknowledges that the ground truth for real SWOT data may not be accessible, which could limit the ability to evaluate the performance of the proposed method on real-world data. Given, the SWOT is in space now, I would suggest to add a section to analyze on real data for clear contribution.

                                  

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

The authors study applicability of a non-linear filter based on a convolutional neural network for removal of KaRIn random noise from satellite altimetry measurements produced by the upcoming SWOT mission. Though the KaRIn noise is only one of many sources of errors in SWOT data, the authors argue that an accurate removal of this component of errors will potentially improve the ability to resolve small scale features of the ocean topography in SWOT data and will be particularly important for the analysis of spatial derivatives of the observed fields.

Simulated SWOT observations were generated as a set of snapshots of sea surface height anomaly (256 x 70 pixels) extracted from the solution of high resolution ocean model and superimposed with a replication of the KaRIn error as an uncorrelated random Gaussian noise. The convolutional neural network with U-Net architecture was trained to recognize the snapshots of modeled sea surface height anomaly in the simulated SWOT data. The authors demonstrate that such a non-linear filter outperforms several linear filtering algorithms for the simulated SWOT data.

It is obvious that for real SWOT data, the “ground truth” data set will not be available for training and testing the convolutional neural network. The authors suggest that the algorithm trained on simulated data could be applicable for filtering KaRIn noise in real data. The manuscript presents the results of the set of experiments where (without re-training) the filter is applied to the simulated data with correlated KaRIn noise and different significant wave heights which affects simulated KaRIn noise variance, the experiments with the simulated data generated for a different ocean region, and the experiments where simulated date are taken from the results of a different lower resolution numerical model. In these experiments, the proposed algorithm still outperforms linear filtering algorithms considered in the manuscript.

The manuscript is easy to read, the method and the results are presented with sufficient but not excessive details. The author provide a link to the archive with configuration of their experiments, input data and results as a “a controlled environment with predefined metrics” for the researches to test other algorithms of SWOT data noise filtering. I recommend publishing the manuscript with minor corrections outlined in my “minor comments”. On the other hand, in my view, the impact of this research could be increased significantly if the authors also attempt to address my “general comments” listed below.

General comments:

1.      The authors state that the manuscript (L14) “explores the feasibility, strengths and limits of a noise reduction algorithm based on a convolutional neural network” for filtering SWOT data. In my opinion, this study is incomplete and these goals are not accomplished unless the authors provide a comprehensive analysis on why the proposed filter appears to be insensitive to the properties of the training data set. The authors call this “robustness” of  the filter:

(L656): “we tested the robustness of the U-Net noise reduction in various scenarios where the inference is done on a dataset with very different properties than the training one’s. For all the scenarios the U-Net residuals are still functioning as expected: random noise is mitigated very efficiently …”.

For a prescribed neural network architecture, the properties of the filter should be defined entirely by the properties of the training data set. Why the results of the experiments with the validation data sets “with very different properties than the training one’s” appeared to be successful? Is that because of simple statistics of the KaRIn noise utilized in all experiments and a spectral gap between KaRIn noise and variability of model states? Or the training data set based on summer-fall 2009 eNATL60 solution is rich enough to represent SLA variability in other seasons and other regions of the ocean? I did not find the analysis of limitations of the presented filter in the manuscript to be sufficient to transfer the success of the experiments with simulated data to the applicability of the noise reduction algorithm for real SWOT data.

2.      The manuscript pays special attention to the performance comparison of the proposed non-linear filter and (L643) “the filter from Gomez-Navarro et al. (2020) which was …” considered as “… the state of the art for SWOT…”. The Gomez-Navarro filter is a simple semi-norm spline with quite unrealistic (polynomial) background correlation function associated with the squared Laplacian term in the cost function (see McIntosh, 1990, JGR, V95, C8). This linear filter is far from optimal since it does not account for a realistic background covariance of the modeled sea surface height anomalies. The tuning of the smoothness term weight (which was not done in the presented research) can be interpreted as adjusting of the KaRIn noise variance rather than tuning of the background covariance. For me, it would be much more important to see the comparison of the proposed non-linear filter with performance of a linear filter which is significantly closer to best linear unbiased filter. Such a filter can be built within the frames of the same 2D-var or Optimal Interpolation approach as the Gomez-Navarro filter but with a more realistic spatially non-homogeneous anisotropic background covariance model which is derived (tuned) from the same ensemble of realizations of modeled sea surface height anomalies used for training in the presented research (e.g., see Yaremchuk and Nechaev, 2012, Monthly Weather Review).  

Minor comments:

1.      L75: “The data used do not contain the effect of oceanic tides but include the effect of the wind and pressure (no DAC correction used) provided by an atmospheric forcing (ERA-interim).” What is DAC correction?  Some other abbreviations require explanation, e.g.  Signal-to-Noise Ratio on L341.

2.      L105: “These data are available from 01/07/2009 to 31/07/2010 over the North Atlantic Ocean.”

This is the mixture of U.S. and European date format. I suggest to use 1 July 2009 to …

3.      L114: “To improve the performance of the model, two steps are done. The first one is to remove the temporally averaged of the SSH model to work on Sea Level Anomalies (SLA). Second, the data is scaled: a Standard Scaler is used which centers the data by removing the mean and scaling to unit variance”.  Please specify is the time averaging was over 2009, one year of model results or over the 13 months of the results. Also it is not clear is the data scaling is performed for each snapshot (256 x 70 pixels) separately. Does the step 1 really improve performance?

4.      L237: The formula for relative vorticity is wrong. First of all, the vertical component of geostrophic relative vorticity is proportional to the Laplacian of SSH, second, the coefficient is different. The property defined here has the units of s/m, vorticity has the units of 1/s. Also, the authors recognize that the units are wrong and do not show vorticity units in Fig.6 and Tables 1, 2, 3.

5.      Fig.4: “ (c) Errors mad by the noisy field”

6.      Fig.5: change “True SSH (m)” to relative vorticity with appropriate units. Also for errors.

7.      Fig. 7, 10, 11, 12, 14, 15: axes labels and text of figures is too small and nearly impossible to read.

8.      Please explain how the power spectrum density was computed and averaged to produce Fig 10, 11, 12, 15. The fundamental frequency for a single snapshots data (256 x 70 pixels) should not allow for so detailed PSD plots.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

It's Ok for this current form.