the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Assessing Atmospheric Gravity Wave Spectra in the Presence of Observational Gaps
Irina Strelnikova
Robin Wing
Gerd Baumgarten
Abstract. We present a thorough investigation into the accuracy and reliability of gravity wave (GW) spectral estimation methods when dealing with observational gaps. GWs have a significant impact on atmospheric dynamics, exerting influence over weather and climate patterns. However, empirical atmospheric measurements often suffer from data gaps caused by various factors, leading to biased estimations of the spectral power-law exponent (β). This exponent describes how the energy of GWs changes with frequency over a defined range of GW scales. In this study, we meticulously evaluate three commonly employed estimation methods: the Fast Fourier Transform (FFT), Generalised Lomb-Scargle periodogram (GLS), and Haar Structure Function (HSF). We assess their performance using time series of synthetic observational data with varying levels of complexity, ranging from a single sinusoid to superposed sinusoids with randomly distributed wave parameters. By providing a comprehensive analysis of the advantages and limitations of these methods, our aim is to provide a valuable roadmap for selecting the most suitable approach for accurate estimations of β from sparse observational datasets.
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Mohamed Mossad et al.
Status: open (until 12 Oct 2023)
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RC1: 'Comment on egusphere-2023-1598', Anonymous Referee #1, 28 Sep 2023
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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
toolsl131: 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.
Citation: https://doi.org/10.5194/egusphere-2023-1598-RC1
Mohamed Mossad et al.
Mohamed Mossad et al.
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