Review Reports - Reconstruction of Rainfall Field Using Earth–Space Links Network: A Compressed Sensing Approach

Round 1

Reviewer 1 Report

Summary: This manuscript details the reconstruction of the CMORPH precipitation field using a ‘new’ technique, specifically a compressed sensing methodology. This methodology is compared against a more traditional inverse distance weighting (IDW) algorithm and found to be superior, as defined by the RMSE, mean bias and spatial correlation.

Recommendation: Major revisions

There is a critical lack of detail in key aspects of the methodology (section 2.2) that makes it impossible to reproduce these results, even if one were to download the CMORPH precipitation product. Given that this research is proposing a new algorithm, it is necessary to show the mathematics, if only in supplemental material.

· The k-SVD sparse basis functions employed, PSI, are not detailed/presented.

· The index, n, defined as ‘the scale of the rainfall field’, is not quantified, yet this is used as an integer in equation (7). CMORPH has a resolution of ~ 8 km x 8 km resolution. Is n then the total domain area divided by the area of one CMORPH grid?

· What is the actual measurement matrix, A, for the examples? How is this produced?

· Please better explain the restricted isometry property. How sensitive are the results to the choice of delta?

This research needs to detail the computation cost involved with the new algorithm, in comparison to the IDW methodology.

This research also needs to address the robustness of the algorithm. What happens when links are temporarily unavailable? With the IDW algorithm, this is not a concern. It only uses the links available, no matter how good or bad, For the new algorithm, do we need to go back and redefine the system?

Is the algorithm robust to different precipitation processes? I.e., will the same defined algorithm be optimal for squall lines, frontal passages and supercell thunderstorms?

The use of the k-means algorithm to set the optimal location of the grid is a bit of gimmick (unnecessary) given that there will be very real logistical constraints to where the links can be located. But I have little doubt that no matter how a reasonable network is constructed, the proposed algorithm will be superior to the traditional IDW algorithm, as defined by RMSE, mean bias and correlation. Am I correct? If so, state this clearly.

For this manuscript, the explanation of the rainfall retrieved by ESL (section 2.1) is an unnecessary digression, since only CMORPH fields are used in the example. This level of detail is even a distraction, as a reader may be expecting to see ESL retrievals for the examples.

Minor points:

There is no need to disparage weather radar observations in the introduction. As noted, they are expensive and not available everywhere. If they exist, however, they are still considered to be a superior product, which is part of why they are so heavily used.

Overall, much of the writing is acceptable. I commend the authors for that, assuming that English is not their native language. I will note that the abstract had a few minor issues that should be addressed, since it is the first thing people will read.

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Comments for author File: Comments.pdf

Author Response

Response to Reviewer 1

Thank you for your comments on the paper, which are all valuable and very helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have modified the manuscript according to your comments. The detailed responses are as attached.

Best wishes

Yingcheng Zhao

Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper, compressed sensing is used to reconstruct rain field surfaces using limited amounts of data samples with high precision. The core idea is to use distributed earth–space links networks for sampling along with compressed sensing reconstruction. Experimental results demonstrate that the method is effective and leads to improvements over alternative methods based on inverse distance weighting. The paper reads well and the experimental results are relatively convincing. I have the following comments to be considered before publication: 1. How do you know that the \theta matrix satisfies the RIP condition? Is there any theoretical or empirical justification? 2. When K-SVD is used to train the matrix \psi, how the user should select the dimension of this matrix? 3. I would like to see the effect of noise on the quality of reconstruction. Can you expand table 1 by adding results when different levels of noise are added to measure the field samples? I would like to see how robust the proposed method is with respect to measurement noise. 4. There are prior works that use compressed sensing for the reconstruction of spatial fields in other applications: a. Three-dimensional morphology of iron oxide nanoparticles with reactive concave surfaces. A compressed sensing-electron tomography (CS-ET) approach. Nano letters, 11(11), pp.4666-4673. b. A compressed sensing approach for partial differential equations with random input data. Communications in computational physics, 12(4), pp.919-954. c. Compressed sensing of diffusion fields under heat equation constraint. In 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (pp. 4271-4274). IEEE. I think the above works should be discussed to provide readers with the context for which compressed sensing has been used successfully to reconstruct spatial data. 5. In Figure 4, please add the comparison metrics below each subfigure to provide the reader with a quantitative way of comparison, too. Currently, this is left for visual inspection. 6. Is it possible to release code in a public domain to help other researchers to reproduce your results?

Author Response

Response to Reviewer 2

Best wishes

Yingcheng Zhao

Author Response File: Author Response.pdf

Reviewer 3 Report

Review of remotesensing-1913826: " Reconstruction of Rainfall Field Using Earth–Space Links Network: A Compressed Sensing Approach".

I have received the manuscript remotesensing-1913826 for reviewing. The author carries out the research of reconstructing the high‐precision rainfall fields using the earth–space links (ESL) network with compressed sensing (CS) in the case of the sparse distribution of the ESL. The description of the manuscript is clear and the structure is reasonable, and the author has done a very excellent job I think this manuscript should do a minor revision before acceptance for publication. I would like to give my specific comments as following:

1. Why the author chooses the precipitation on 10 August 2019?

2. How effective is the method proposed in the manuscript in reconstructing extreme precipitation? I think the reconstruction of extreme precipitation can highlight the significance of this study.

3. What reference significance does it have for other regions, such as those with snow in winter?

Author Response

Response to Reviewer 3

Best wishes

Yingcheng Zhao

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The authors' addressed many of my major revisions well. That said, there were a few points where I felt the response didn't address my comments well. With regards to item 3, I was specifically interested in what happens if one or more ground links is temporarily unavailable (e.g. a power outage or routine maintenance.). Do you need to reconstruct the algorithm with fewer stations? Or can you readily use this algorithm even with missing observations? This is a different question than about noise in the system.

I also don't believe they addressed my concern on item 6. Since we are using CMORPH in the case study here, the details of the ESL calculation are irrelevant. You can use this methodology whether the rainfall comes from ESL, CMORPH, individual rain guages, ERA5, GPCC or any one of many different precipitation products. Making a connection to ESL precipitation allows for this to be in Remote Sensing, but otherwise it's irrelevant to the methodology. Ideally the authors would acknowledge this.

Reviewer 2 Report

The authors have addressed my concerns and reflected the suggestions.