The manuscript is very difficult to read, with serious grammar and spelling issues from the abstract on.  While some of these can be taken care of during the editorial process, many were extremely distracting from the message of the manuscript, and the vast majority should have been corrected prior to submission.  The errors in language were compounded by some strange typesetting, including changes of font in mid sentence, and mathematical equations that were mixed between in the text and as separate equations.  If it needs a superscript.subscript combination it belongs on its own line.  I did not get the sense that the latex template provided by NPG was used to produce the manuscript, but perhaps it is just a different flavour from the one I use.

The manuscript is heavily reliant on acronyms, and while some of this is ameliorated by the algorithms in Figures 1-3 (these are probably the strongest point of the manuscript), it is very difficult to imagine readers not already invested in the method using the manuscript to learn and implement the method.

The methods discussed are applied to a single time series (ozone) and presented in figures that show decompositions and the derived trend.  There is repetition between the figures, but over all they are of good quality.  I was surprised that only a single time series was used, since presumably it takes very little time to produce the type of results shown.  In my own work on developing data centric methods we typically applied our methods to three case studies.  This is not a hard and fast formula, but a single, rather simple, time series seems like not enough to convince the reader.  An example for which traditional methods fail, and the new method succeeds seems to me like a reasonable requirement.  Many standard mathematical software packages have a wavelet package (e.g. Matlab) and apply it to geophysical data.  A reader shopping for new methods should clearly see why they should be adopting the present method.

A discussion of the consistency of the method with atmospheric variability, using a single table, is provided.  It is reasonable, if somewhat uninspired.

I was very surprised that there was no discussion of code availability.  I think this is a must in modern methods papers.

I am thus left to conclude that the manuscript makes a contribution to a detailed area of study, and will perhaps find an audience in this area.  It is so poorly presented that there is very little chance that the ideas will penetrate beyond this small audience.  Were I to be writing a traditional review, I would have no choice but to suggest that the manuscript be rejected.  Given the nature of the peer review for NPG, I will leave it to the authors to try to improve the manuscript via what I see as rather fundamental revisions.

The manuscript by Delage et al. presents a new method for adaptive filtering with the aim of combining the advantages of empirical mode decomposition (EMD) and empirical wavelet transform (EWT). The concept of combining EMD and EWT to overcome issues inherent with both decomposition techniques is interesting and somewhat novel. The new method could represent another useful tool for analysing non-linear time series.  However, in its current form there are several major issues with the manuscript.

First and foremost, representation of the benefits of the method could be far more substantial. The manuscript relies on a single example and would strongly benefit from more than one example of its application. It would also be interesting if the results of the EMD compared to the new EAWD method were explored more in depth. I feel the manuscript would benefit if there were much more substantial discussion of the results obtained by EAWD compared to EMD in these different examples. I would at least expect to see enhanced discussion of how and why the results are different in different examples, as well as some contemplation on which situations the new method is likely to be most beneficial. Currently, I do not believe the argument for using the new method is especially compelling.

Furthermore, the manuscript is currently very difficult to read. Regular grammatical and spelling errors are apparent throughout the manuscript. As it is, it is difficult to follow how exactly to interpret the method. I would strongly recommend that the manuscript would benefit from proof reading and rewriting to greatly improve readability.

In addition, it would be extremely beneficial to provide a sample script and sample data as a supplement to the manuscript. In its current form it would vastly reduce the potential outreach of the paper to not provide this.

The manuscript will require substantial and significant revisions to be acceptable for publication, although I do believe the core idea behind the manuscript is of sufficient interest to the readership of nonlinear processes in geophysics.

Specific points:

Abbreviations – The paper manuscript would benefit from an abbreviation list at the beginning. Consistency in abbreviations is also needed throughout, IMF for example doesn’t get defined until its 4^th use

Abstract – This could be improved a lot, currently the new method is not even mentioned till the 4^th line from the end. The abstract should be written to better describe why there is a need for this new method, what the new method is, and how it is shown to be useful in this manuscript.

Introduction – The introduction is currently one block paragraph and would benefit from being broken up.

Section 2.1 – This is often repetitive of things already stated in the introduction

Section 2 – I think some discussion of requirements for the data if they’re to be used in this method would be helpful.

Equations – these should be consistently listed throughout, it is confusing that they are often in text.

Figure 1-3 – French used instead of English numerous times

Figure 4-5 – Y-axis should be labelled Ozone, and Dobson made clear as the unit

Figure 5 – Time unit needs labelling, and y-axis should be made bigger