|In the original review, I stated that "This is an interesting piece of work, potentially worthwhile for a publication". My basic position on this manuscript has not changed after the revision. Though I did not say this explicitly in initial review, I do not find any serious defect in this work. In this very respect, I do not wish to block the publication of this work in any fundamental manner. The only remaining question is the quality of the publication that both the Editor and the author wishes to achieve. My following comments intend to serve for this purpose:|
Most seriously, the two major points made in my initial review are practically not at all taken into account in revision:
1) review of the existing methodologies
2) proper review of the wavelet method
1) more specifically, I proposed to refer to Zagar et al (2015, 2016). However, the authors rejects to do so by simply stating that the normal mode approach is not relevant in the present context. Most seriously, this remark is found only the response to the reviews, and very strangely, not found in the manuscript text. As a result, as it stands for now, the text reads like claiming that this Fourier-wavelet method is an only possibility of describing the propagating waves. Of course, the readers who are familiar with those existing methodologies would just wonder why one must use this when an existing method works well enough: what is an advantage of this proposed methodology against the existing methodologies?
2) As it stands for now, there is even no proper lead sentence io introduce what the wavelet is. There is only a very short lead paragraph in Sec. 1.3, which is even misleading:
a) Torrence and Campo (1998) is just an introductory essay on wavelet. It would be misleading to state that the methodology of this paper is "described" in this essay: please cite a more proper textbook. my preference is one by Mallat.
b) As the authors states, with the continuous wavelet, a user can arbitrary select any frequency resolution, but only in a meaningless manner: this is just like trying to define the amplitude of noninteger wavenumbers over a finite domain, say, a wavenumber 1.345. Of course, one can do this, but we all know that this is meaningless. Strangely, the community simply does not realize the same with the continuous wavelet. The present author is not an exception. More formally stated, such an attempt contradicts with Heisenberg's uncertainty principle. Please refer to Mallat's text for the full discussions.
c) In short, there is no real advantage with the continuous wavelet against the discrete counterpart, apart from an easiness of using it. This very last point should be made absolutely clear in a final version with more relevant references (including a textbook by Mallat).
3) The introduction as it stands for now, mostly consists of a review of the existing studies on the plain planetary waves. The given review hardly motivates the present study.
In this context, the author totally neglects the following full paragraph from my initial review:
"In this respect, the introduction is slightly confused as it stands for now: its first half reviews previous works detecting "linear" planetary waves. Then, suddenly, at L55, the author decides to talk about the stratospheric sudden warming: this is clearly a nonlinear process that cannot be described by a single wave. The authors further begins to remark that the observed waves are rather "intermittent" (in own wording), and they can emerge even like bursts: that is all fine with me: these observed waves are not perfectly linear, and they are often generated by forcings as well as instabilities, and those evolution can be very nonlinear. However, after said all those (though the author does not comment on them), if one wishes to understand those phenomena as a part of the wave dynamics, an obvious way to go is to perform the normal-mode decompositions so that one can see explicitly which modes are involved in processes in which manner, etc. Those are very basic backgrounds of the atmospheric-wave dynamics, that should remind the readers."
An only hint for a need for the wavelet is a short phrase of "a burst of wave activity" (L57). However, without any proper elaboration, it is even not clear what the author is exactly referring to. Finally, at L73, the author states, "This is the motivation.....". However, unfortunately, I cannot identify a sentence that can be called a motivation in any earlier part: then what is this "This"? The author quickly adds a well known fact that "The wavelet analysis is useful for identifying wave activity that is localized in time" (L79): however, how often we observe such isolated waves in the atmosphere?etc The author simply fails even to provide such basic information.
The logic of the presentation is very loose at the best at many occasions. The most notable example is found in L80-81, which states: "the standard 1-D wavelet technique is not directly applicable to two-dimensional (2-D) longitude-time data...." If I understood the author's response to my comment correctly, this is nothing other than a trivial statement that any 1D transformation technique (wavelet or Fourier or else) is not directly applicable to any 2D data, because the transformation method is only 1d, and not 2D. Thus, we must adopt either 2D wavelet or 1D Fourier technique. It does not follow at all the we need to invoke Hayashi's method to overcome this difficulty. We just need to invoke any available 2D techniques.
In conclusion, I see that still substantial revisions are required before this manuscript becomes worthwhile for publication. [I click "major revision" because more than a cosmetic modification is required: the author clearly failed to note this point in then initial revision] As the very minimum, misunderstanding concerning the wavelet by the author must definitely be corrected.
L77: please add a reference discussing on the discrete wavelet in a more proper manner, for example: Yano et al (2001a, b)
L83, "Hayashi's method is combined with the wavelet technique": probably is would be more proper to say that "Hayashi's method is modified by adopting the wavelet in representation in time."
L130, Yano et al (2001, 2004): please also to refer to the second part (Yano 2001b) for a completeness.