The manuscript describes a thorough comparison of different methods to 

quantify spectral characteristics of geophysical one-dimensional data 

such as profiles or timeseries. The motivation comes from analyses 

of gravity waves in observations. An important focus is on the 

effect of potential gaps in the data, with gaps present for a significant 

fraction of the data. Three methods are compared: Fast Fourier Transform, 

Generalised Lomb-Scargle periodogram, and Haar Structure Function. The

study constitutes a useful and interesting contribution to the literature: 

the topic is rather technical and only interests a specific readership, 

but this is very well carried out, well explained and generally well 

presented. A very positive aspect is that an open code is made available 

to use these three analysis methods. Some changes would constitute 

improvements, and in particular the conclusion section deserves to 

be rewritten in less technical terms. Minor revision is recommended, and 

this shall constitute a valuable study, although for a somewhat specific 

audience.  

Main concern

The authors have made appreciated efforts for clarity throughout the text, 

and for pedagogy in presenting the different methods. This is particularly 

useful as these methods are not necessarily familiar to all, making 

this study a valuable opening towards uncommon methods that may be 

of relevance for certain purposes (data with significant gaps in particular). 

However, the conclusion appears less polished than the rest of the text: a list

of key messages has been identified, and this is positive and useful, but

this list remains too technical, and too long. It makes the conclusion 

less readable and less efficient than it could be. There should be more of

an effort to come back to recommandations for concrete analyses of observations, 

with less acronyms and simpler messages and recommandations for the different 

situations and the advantages / disadvantages of the different methods. There

is a contrast between the conclusion, which reads more like a summary of a 

technical report, and the synthetic sketch of figure 8, which carries simple 

and clear messages. 

Minor points

l30 'universal GW spectrum': odd formulation given that different power laws have

been documented in different contexts as recalled in table A1

Additionnally, although the table does not aim to be exhaustive, it could 

include observations from long-duration balloons, as these provide original 

insights into Lagrangian spectra of gravity waves, which is uncommon (Hertzog 

Vial 2001,  Podglajen et al 2016)

l50-51: the FFT is likely known by almost anyone doing data analysis; however, 

how common are the other two methods? How commonly are they used in geosciences? 

Could the authors give some hint or suggestion on that? 

 

l129: it is very good that there is an open code available for part of these 

tools 

l131: the study may be motivated by the analysis of gravity waves, but the 

conclusions and the methods described are more general. Signals are analyzed 

for their periodic components or for their spectral slopes, but no use is 

made of specific aspects of gravity waves such as polarization relations. 

Other scientists dealing with observations including gaps, and analyzing

nearly periodic signals and / or spectra, could be very interested in this. 

The authors are thus encouraged to put less stress on the gravity wave aspect, 

and to broaden the scope of the study (by a few appropriate sentences, in the 

introduction for instance). 

l162: it could be recalled that in many observational cases, the f is not a

frequency but a vertical wavenumber.

l204: a reference ofr the MLE could be included 

l205: why is the observation O noted as a vector? 

Figure 5: in the right panel, the figure includes the mean and standard 

deviation. This should be added in the left panel. The comparison for HSF 

is particularly important. 

l325-331: prewhitening and postdarkening should be explained a bit more. How 

does this relate to derivation and integration? Can the factor on line 330

be explained or interpreted in a few words? 

Figure 8: rather than "simple sinusoid", which describes the synthetic data used 

for the study, the authors should find a phrasing that could better describe 

potential observations ("conspicuous periodic signal"? "signal with one dominant

frequency"? ). How (un-)important is the sinusoidal character of the oscillations? 

l350: the authors should take into account that readers may skip to the conclusion 

for the main messages: some redundancy between the conclusion and the preceding 

text is not a problem and rather desirable if it makes the conclusion more 

self-consistent. For instance, it is worth recalling what "the methods" are. 

l354: the editor may judge otherwise, but redefining acronyms could be welcome. 

l365: recall that beta is the spectral slope

l367: 'competent', for a method? Efficient? 

l380: reexplain prewhitening and postdarkening, very briefly; part of the 

readers will be unfamiliar with these. 

Hertzog, A., & Vial, F. (2001). A study of the dynamics of the equatorial lower stratosphere by use of ultra‐long‐duration balloons: 2. Gravity waves. Journal of Geophysical Research: Atmospheres, 106(D19), 22745-22761.

Podglajen, A., Hertzog, A., Plougonven, R., & Legras, B. (2016). Lagrangian temperature and vertical velocity fluctuations due to gravity waves in the lower stratosphere. Geophysical Research Letters, 43(7), 3543-3553.

See attached file.