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https://doi.org/10.5194/egusphere-2026-807
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/egusphere-2026-807
© Author(s) 2026. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
23 Feb 2026
| 23 Feb 2026
Status: this preprint is open for discussion and under review for Atmospheric Chemistry and Physics (ACP).
Variability of local gravity wave spectra from data of a high-resolution icosahedral-grid global model
Abstract. Atmospheric gravity waves influence the general circulation through transport of energy and momentum. Even with increasing computing capacities, parametrisation of their effects is still needed. Here, we diagnose gravity wave spectra from the data of a high-resolution ICON simulation on subdomains defined by a low-resolution ICON grid. A unique methodology is applied that avoids unnecessary interpolations and filters the data by projection on the linearised gravity wave modes, providing precise and detailed information about the gravity wave spectra. The dependence of these spectra on latitude is then studied, highlighting the importance of the zonal wind direction in the shape of the spectra. Finally, we see that the spectra can be highly simplified by using tens to hundreds of principal components, which is a key property allowing for an increase in efficiency of current gravity wave parametrisations.
How to cite. Procházková, Z., Mahmoudi, E., Chew, R., Dolaptchiev, S., Stephan, C. C., Völker, G. S., and Achatz, U.: Variability of local gravity wave spectra from data of a high-resolution icosahedral-grid global model, EGUsphere [preprint], https://doi.org/10.5194/egusphere-2026-807, 2026.
Competing interests: Supervisor of ZP is an editor at this journal.
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Zuzana Procházková
CORRESPONDING AUTHOR
Department of Atmospheric Physics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Erfan Mahmoudi
Institute for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Germany
Institute for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Germany
Department of Planetary and Geosciences, California Institute of Technology, Pasadena, California, US
Stamen Dolaptchiev
Institute for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Germany
Claudia Christine Stephan
Leibniz Institute of Atmospheric Physics at the University of Rostock, Kühlungsborn, Germany
Georg Sebastian Völker
Institute for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Germany
Department of Physical Oceanography, Leibniz Institute for Baltic Sea Research Warnemünde, Rostock, Germany
Ulrich Achatz
Institute for Atmospheric and Environmental Sciences, Goethe University Frankfurt, Germany
Short summary
The study analyzes gravity waves in a high-resolution simulation. A unique methodology is applied to compute three-dimensional gravity wave spectra while keeping the data on the original triangular model grid and using linear wave theory. The results show the structure of gravity waves that would remain unresolved by a model with lower horizontal resolution. It is shown that the spectra can be highly simplified, which can help constructing precise but efficient gravity wave parametrisation.
The study analyzes gravity waves in a high-resolution simulation. A unique methodology is...
The paper is a very thorough introduction into the application of spectral analysis to the icosahedric grid of the ICON model avoiding spurious effects necessarily generated by interpolating the data on a rectangular grid first. The data gives some convincing examples of the application. I feel, however, that the paper should be strengthened in the intuitive physical interpretation. Also, when it comes to discussion of global distributions there is a wealth of previous work from both models and satellite observations which you can compare against. This shouldn't be lengthy, but also not completely ignorant. I am wondering that you are not considering phase speed spectra and would suggest this. The paper is generally well written and of high presentation quality, thus strongly recommended for publication as soon as these points raised have been taken into account.
General comment:
The aim of the paper is, I think, to motivate other scientists working with ICON to use your tool to analyze ICON data. This means, you are aiming to a large fraction to GW physicists and people interpreting models. I think a few minor modifications (as indicated below) would help them to better understand what you propose. The paper contains no introduction to the code. I hope the tool is reasonably self explaining, otherwise I am voting for an appendix C with ashort technical introduction.
Specific comments:
L51 With a horizontal resolution of 2.5km you are expected to reasonably represent wavelengths of 25km and longer, which would correspond to GWs emitted from a single convective tower (though that would of course not be really resolved). You would then expect 20min the dominant period (works of Fovell and Lane), i.e. you are just at the Nyquist limit -> direction flips to be expected. For introducing a new method, that's all fine, but from a physical point of view I think one should do 5min time step.
L55 Only a comment, no action needed: Just to remember that this is only an estimate, since the interaction of scales would be missing in a 160km run.
L67 A picture illustrating this would be really nice. If you really care it takes minutes to understand these three senetences.
L90 Perhaps one sentence why, in contrast to a FFT on a regular rectangular grid you need a regularization?
L104 Why do you want a symmetric range? At some point you can resolve ambiguities by GW polarization relations. If that is the motivation, include here? For instance: The symmetric range is later used in Section ... to ...
L107 equidistant in a regular x-y grid I think you need to say this, because the sides of the triangles are of equal length -> equidistant
L116 For comparison with other methods and observations it would be interesting to do temp as well, in particular as b includes a vertical derivative which introduces new sources of uncertainty
L121 Do you see infrasound waves in ICON? If yes then the 10min sampling become really questionable
L139 I think at this point you need to explain a bit more. In which way are the polarization relations a vector? And what are you gaining by the projection in a physical sense. A few additional senetnces should help. Please keep in mind that you need to keep the average atmospheric scientist in the boat, if you want your method to be applied.
L146 O.k., here is the why. Still I don't see how the projection does it.
L151 in Appendix B from the extremal vertical wavenumber values m->inf and m=0, respectively.
L154 I don't think the model can really simulate waves at its vertical Nyquist. Should be a safeguard only?
L163 the wave ... generates -> is generated also not fully satisfactory
L168 arbitrary, exemplarily ? Or did you really use a (computer) dice? And why not use something where other studies exist?
F1 Lucid writing rules: same colors for same things, different colors for different things. There are more color scales than viridis. Confirming is a bit strong.
In the explanation you discuss the limits by f, N creeps in via changes in color between e and f (correct?), the extent of the k scale is Nyquist. In principle k=0 is part of the Fourier grid, but you cut to the domain size, so the white stripe in the middle (?). That this is naturally not very populated (e) is from the tapering? An additional background removal? Because b is at a mean value of 11m/s.
L187 This irritates me slightly. Physically, time is the dimension which runs only in one direction, so you should break symmetry here (same as nature). m>0 should be downward propagating, m<0 upward propagating waves and it should make sense to compare both of them in order to search for reflections and middle atmosphere sources. Mathematically, you can break of course as you like, but I am nota able to send my sensor backward in time. At least mention that you have both possibilities and do a choice here which makes it easier to discuss some features.
L191 This is a bit simpler than the limit you have stated above (Equ 20). At one point you should include, how the two relate to each other. I would suggest after equ 20 something for GWs with such and such properties these become the well known limits ...
L197 58% is surprisingly symmetric.
L203 For me I would again discuss along the physical case. Scandinavia is known to excite mountain waves. (I find the suitable... a bit awkward). Accordingly, we find a predominance of waves with ground-based frequencies close to zero. There obviously is a stronger dominance of upward propagating waves with a well defined source below. That the ridge is N-S and thus most power is in k you don't discuss in the spectra, maybe omit? What you mean by circular I don't understand. Explain or omit.
L217 Why "Although"? Mission A accomplished now comes mission B. We now extent our analysis to the global scale ... or something like that
L220 e.g. Andes or Himalayas -> These are the two you would not necessarily expect and which will disappear when you move a little higher in analysis altitude. (Andes -> summer, Himalaya a general wind shear). Not against quoting them, but I would do a few more e.g. Delany, Rocky Mountains, Greenland, Iceland, Mongolia, Catabatic winds at Antarctica. Interestingly, at this particular day, not so much Scandinavia. In addition to this you see the subtropical convection on the SH, without pointing at special locations, should be mentioned.
F3 Please do not use judgemental language: simple -> only How good or bad the removal works will depend a lot on the details of the removal.
L235 What is a non-linear GW? Do they really exist as a pure form or are GWs rather usually well described but may deviate somewhat from linearity? In particular, you would then expect deviations from the quadrature phase relations between temperatures and winds. which indead would reduce the projected energy in the cospectra. Please rethink the formulation.
L238 Why Finally ?
L242 ITCZ -> this would be the small peak around 10S on top of a wider GW maimum form 10N to 25S. Convection about subtropical sources is also known.
L248 ... are chosen narrower ... Or did you really make them conatining equla amounts of cells?
3.3 in general:
For me it would now be logical to switch to spectra in terms of phase speed and direction. This helps you very intuitively to see different wave sources and wind filtering - quite a bit of work out in the literature. The vertical wavelength then mixes the wind and the source effect and the zonal means and the variations of winds with longitude is not really helping.
The PCA on the other hand is not motivated. Why do you want to do this? What does the modes tell us? Wouldn't it be better to perform PCA on phase-speed spectra? And how would results change if you go to a different day, e.g. in March?
L271 retrograde -> generally opposite ?
L303 GW filtering -> this is for me associated with (critical level) wind filtering. You mean the projection/identification/extraction ... still not the right word, but come up with something more positive saying afterwards we have the GW only
L305 flow -> dynamics ? Its not only u and v
L306 This is here not connected and would need to be introduced in the discussion of the model setup. You may also overestimate some scales.
L311 You cannot expect the readers to know the Chew paper. Should be introduced in the intro or really discussed in the math part, if you want to delineate your method from others.
L323 I think if you have the input data, i.e. model output at high frequency its better to use frequency rather than m as it is less subject to changes by e.g. refraction. However, of course, when you have it is a strong constraint as you need to foresee the application when you do the model run and you can apply it to short runs only. A fair one sentence statement would be good to make.
For dedicated experiments which are saved at short time steps a k,l,frequency analysis is the better choice ...
L324 Please have a look at Strube et al as well. This paper discusses an altitude dependency of how well this may work. (DOI: {10.5194/amt-13-4927-2020})