A Fuzzy-Logic-Based Covariance Localization Method in Data Assimilation
Round 1
Reviewer 1 Report
This is a resubmitted manuscript that I have reviewed. It has been improved somehow since some details have been added, e.g., sentences in lines 273-275. However, I think one important component is still missing from the manuscript that has made it not ready for publication. Below the authors can find my comment for the last submission about the lack of the application for the algorithm to large 3D atmosphere and ocean model. The authors need to do additional work to address it.
In this study, the newly developed covariance localization algorithm has been applied to two low-order models: the Lorenz-96 model and the quasi-geostrophic (QG) model. As previous studies have shown, algorithms developed for data assimilation may work well for low-order models, but it is possible that they perform poorly when applied to large 3D atmosphere and ocean models. The authors have actually briefly discussed this in the manuscript (L550-558), but they failed to perform and show this kind of applications. In my opinion, this application is significant because it will include the consideration of vertical localization.
Author Response
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Author Response File: 
Author Response.docx
Reviewer 2 Report
I appreciate the authors’ effort on revising the manuscript. However, I am not fully convinced with the authors’ response to my major comments.
Re-response to comment 1:
I am still fully not convinced. Please show RMSE instead of Kalman gain matrix. Also, please put the results with different localization scale and fuzzy logic parameters in the manuscript as well. Please summarize the results as in Figure 6.
Re-response to comment 2: “Although the improvement is not significant in this study, we are planing to test more algorithms in our future studies. If possible, please give us this chance to bring those new ideas to atmosphere community.” I think the authors misinterpreted my comment. I did not mention to reject the paper. If the results are not statistically significant, please provide the results of a statistical test in the manuscript. However, I generally think the significance of results is important part of a paper. If we can achieve similar results with more simple method, we do not need to use such complicated method. If you can achieve significant results with other atmospheric models, please also provide it in the manuscript.
Author Response
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Round 2
Reviewer 2 Report
Thank you for your revisions. However, related to my previous comment 2, the percentage of RMSE reduction do not tell anything about statistical significance. Please show the results of statistical test (t-test, bootstrap, permutation, ... whichever most appropriate in this context). Currently, the word choices of "small error", "moderate error", and "severe error" are subjective and not scientific.
Author Response
please see the attachment
Author Response File: Author Response.docx
This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.
Round 1
Reviewer 1 Report
This manuscript presents a study that develops and tests a covariance fuzzy localization method in data assimilation that couples a covariance localization method with a fuzzy logic control algorithm. This study is in general well written and fits well in the scope of Atmosphere. However, I think one important component is missing from the manuscript that has made it not ready for publication.
In this study, the newly developed covariance localization algorithm has been applied to two low-order models: the Lorenz-96 model and the quasi-geostrophic (QG) model. As previous studies have shown, algorithms developed for data assimilation may work well for low-order models, but it is possible that they perform poorly when applied to large 3D atmosphere and ocean models. The authors have actually briefly discussed this in the manuscript (L550-558), but they failed to perform and show this kind of applications. In my opinion, this application is significant because it will include the consideration of vertical localization.
L18-20: This sentence is confusing in that it makes an impression that the Lorenz-96 and the quasi-geostrophic models are combined. Please rewrite.
L36: Please be more specific about ‘small’ ensembles.
L97: Write out ‘QC’ here since this is where it first shows.
Figure 3b: Please separate ‘20’ and ‘19’ in top x-axis.
L272: “…we set the model time step to 0.05 UNITS…’
L414-416: I think this statement is too strong considering it was based on only one experiment.
Author Response
Please see the attachment.Author Response File: Author Response.docx
Reviewer 2 Report
This manuscript investigates the potential of the covariance fuzzy method as a replacement for covariance localization in data assimilation. There are many parts that are unclear and not explained sufficiently. I suggest authors to greatly improve the manuscript based on the following comments.
Major comments
First of all, I am fully not convinced that CF is better than CL. Although the authors tested with different ensemble members and inflation factors, the authors have never mentioned the sensitivities of the parameters used in CF and CL. The quantification scaling factor, quantification scaling factor, and localization radius were used as constants. I am not an expert on fuzzy logic, but at least the localization length scale in DA is known to change results a lot. You could easily choose a localization length scale that does not perform as well as others.
In abstracts, the authors have mentioned CL “results in poor assimilation”, and “CF can obtain a more effective observation”, but the results in the main text are not as obvious as authors claim. Are these improvements statistically significant?
In general, there are many unexplained processes especially on fuzzy logic that is almost impossible for readers in other fields to understand. The authors should try to improve the text so that it would be easier to follow for non-experts.
Table 1 & Table 2: These are problematic. I do not think this will help readers to understand the algorithm. Please explain in text with detailed descriptions.
Minor comments:
Line 46: “will have” -> “have”
Line 92-93: “However, these experiments were only conducted with toy models such as the Lorenz-96 model, and the proposed methodology needs to be tested with a more realistic atmosphere model” but it was not conducted in this study either
Line 96: “a fuzzy thought-based transition from absolute truth to partial truth” I do not get the meaning.
Figure 1 and Figure 2: What are the differences between these two figures? What are the “coded parameters”?
Line 193: What do you mean by “determine the structure of the fuzzy controller”? How do you define?
Line 193; “single-input-single-output fuzzy controller”?
Throughout: “Euclidean distance dist”, “inflation factor infl”... Are these necessary? They are distracting and confusing. If authors want to use them, consider writing them in mathematical/italic font and/or use Greek letters.
Line 216: “According to the operational experience of experts” ?
Line 218: “the researcher's knowledge” ?
Line 238-239: Do you have any references?
Line 256: “a set of accurate weight coefficients” how do you know they are accurate?
Line 271: What do you mean by “Generally”?
Figure 4: Why are there some large values in the off-diagonal edges of K(CL) and K(CF)?
Figure 4: What is shown in the 4th column? This is not explained in the caption.
Figure 5: I suggest removing the first 50 periods or so to remove the effects of initial conditions and also to make the differences easier to see.
Figure 5: There are peaks in RMSEs with CF methods. Why? Also it is difficult to see the improvements in this figure. How about adding box plots of RMSEs on the side?
Figure 9: Many things are not explained in this figure. Please add labels and explain them in the caption.
Author Response
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Author Response File: Author Response.docx
