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arxiv: 2606.04590 · v1 · pith:VUDS2DSGnew · submitted 2026-06-03 · ⚛️ physics.ao-ph · physics.geo-ph

The relationship between atmospheric stratification and internal wave processes

A. V. Kochin This is my paper

Pith reviewed 2026-06-28 03:22 UTC · model grok-4.3

classification ⚛️ physics.ao-ph physics.geo-ph
keywords atmospheric stratificationinternal gravity wavespressure fluctuationsradiosondewave spectravertical temperature gradientatmospheric parameterssurface measurements
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The pith

Spectra of surface pressure fluctuations can be inverted to recover atmospheric stratification parameters that match radiosonde data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to establish that the atmosphere behaves as a resonant system whose internal gravity wave frequencies are fixed by the vertical temperature gradient. Measuring the spectrum of pressure fluctuations at the ground therefore supplies the frequencies needed to calculate the stratification parameters. The authors invert the observed spectra, compare the resulting parameters against the ascent rates of radiosondes, and report good agreement. A reader would care because the approach offers a route to infer vertical atmospheric structure from surface records alone. The central mechanism is the direct dependence of wave frequency on the temperature gradient, which permits the inversion.

Core claim

The stratification parameters were calculated based on the frequency of internal gravity waves and showed good agreement with the upper-air sounding data. The frequency of internal gravity waves depends on the vertical temperature gradient, so spectra of internal wave processes can be used to estimate the spatial distribution of atmospheric parameters. The rate of ascent of the radiosondes served as reference information that was compared with the spectra of pressure fluctuations at the surface.

What carries the argument

The dependence of internal gravity wave frequency on the vertical temperature gradient, inverted from measured surface pressure fluctuation spectra to obtain stratification parameters.

If this is right

  • Surface pressure records alone can supply estimates of vertical atmospheric structure.
  • The method supplies an independent consistency check on radiosonde profiles.
  • Internal wave activity can be detected and characterized from ground-based pressure time series.
  • The agreement between inverted parameters and sounding data supports treating surface spectra as direct tracers of stratification-controlled wave frequencies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the inversion is reliable, networks of surface barometers could supplement sparse radiosonde coverage for routine stratification monitoring.
  • The same spectral analysis might be applied to historical pressure archives to reconstruct past vertical temperature gradients.
  • Discrepancies in future comparisons would point to additional wave sources or non-stratification effects that must be accounted for.

Load-bearing premise

The observed spectra of pressure fluctuations at the surface are produced by internal gravity waves whose frequencies are determined solely by the vertical temperature gradient.

What would settle it

A new set of simultaneous surface pressure spectra and radiosonde profiles in which the stratification parameters calculated from the spectra disagree with the sounding results.

Figures

Figures reproduced from arXiv: 2606.04590 by A. V. Kochin.

Figure 1
Figure 1. Figure 1: Standard atmosphere temperature graph (ISA) https://aviationperformance.wordpress.com/2020/08/29/basic-performance/. The use of the ratio (1) and the vertical temperature profile in the standard atmosphere makes it possible to calculate the vertical profile of the Brunt-Väisälä frequency period, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Fig.2. Vertical profile of the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Fig.3. Conditional view of the spectra of the T oscillation periods in the stratosphere and [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Data of launch of two radiosondes with an interval of 300 seconds to indicate vertical movements by changing the speed of ascent of radiosondes. On the left is the speed of ascent of radiosondes m/s, on the right is the spectrum of the difference in the speed of ascent of radiosondes at the same altitude. The horizontal axis in the left figure represents the flight time in seconds, and the oscillation peri… view at source ↗
read the original abstract

The atmosphere is a resonant system and its oscillation spectrum is determined by the spatial distribution of parameters. For example, the frequency of internal gravity waves depends on the vertical temperature gradient. Therefore, the study of the spectra of internal wave processes can be used to estimate the spatial distribution of atmospheric parameters. The work is aimed at detecting wave fluctuations in the atmosphere and calculating atmospheric parameters based on the measured spectra. The rate of ascent of the radiosondes was used as a reference information, which was compared with the spectra of pressure fluctuations at the surface. The stratification parameters were calculated based on the frequency of internal gravity waves and showed good agreement with the upper-air sounding data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that spectra of surface pressure fluctuations can be analyzed to detect internal gravity waves, whose frequencies are then used to calculate atmospheric stratification parameters (such as those related to the vertical temperature gradient), with the resulting values showing good agreement when compared against reference data from the rate of ascent of radiosondes.

Significance. A validated, independent method to invert surface pressure spectra for stratification parameters would enable continuous, ground-based monitoring of atmospheric stability without requiring frequent soundings. The direct comparison to radiosonde data is a necessary validation step, but the absence of methodological detail on frequency extraction and the unaddressed wavenumber dependence in the dispersion relation prevent the result from being assessed as robust or reproducible.

major comments (2)
  1. [Abstract] Abstract: The central claim that stratification parameters 'were calculated based on the frequency of internal gravity waves' and showed 'good agreement' with radiosonde data rests on the assumption that observed frequency determines N (or equivalent) uniquely. This is contradicted by the IGW dispersion relation ω = N (k_h / |k|), which requires an assumption or measurement of the propagation angle or wavenumber ratio that is neither stated nor validated against the sounding profiles.
  2. [Abstract] Abstract: No methods are supplied for frequency extraction from the pressure spectra, no sample sizes, no error bars on the comparisons, and no discussion of confounding factors (e.g., other sources of pressure fluctuations or mode identification). These omissions make the reported agreement impossible to evaluate quantitatively.
minor comments (1)
  1. [Abstract] Abstract: The phrasing 'the rate of ascent of the radiosondes was used as a reference information' is grammatically awkward and should be clarified to specify exactly which parameter (e.g., ascent rate as proxy for density or temperature gradient) is being compared.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and for highlighting issues that affect the clarity and reproducibility of the work. We address each major comment below and will revise the manuscript to incorporate the necessary clarifications and additional details.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that stratification parameters 'were calculated based on the frequency of internal gravity waves' and showed 'good agreement' with radiosonde data rests on the assumption that observed frequency determines N (or equivalent) uniquely. This is contradicted by the IGW dispersion relation ω = N (k_h / |k|), which requires an assumption or measurement of the propagation angle or wavenumber ratio that is neither stated nor validated against the sounding profiles.

    Authors: The referee is correct that the dispersion relation requires the horizontal-to-total wavenumber ratio. The manuscript implicitly treats the observed frequencies as corresponding to N under the assumption of near-horizontal propagation (k_h / |k| ≈ 1), which is a standard simplification when only frequency spectra are available. This assumption was not stated explicitly. We will revise the abstract and main text to articulate the assumption, note its limitations, and discuss consistency with the radiosonde profiles where vertical structure information is available. revision: yes

  2. Referee: [Abstract] Abstract: No methods are supplied for frequency extraction from the pressure spectra, no sample sizes, no error bars on the comparisons, and no discussion of confounding factors (e.g., other sources of pressure fluctuations or mode identification). These omissions make the reported agreement impossible to evaluate quantitatively.

    Authors: We agree that the current manuscript lacks the required methodological transparency. We will add a methods section that specifies the spectral analysis and peak-identification procedure used to extract IGW frequencies from surface pressure records, report the number of spectra and comparison cases, include uncertainty estimates or error bars on the derived stratification parameters, and discuss potential confounding sources together with the criteria applied for mode identification. revision: yes

Circularity Check

0 steps flagged

No circularity: independent comparison to radiosonde data keeps derivation self-contained

full rationale

The paper extracts frequencies from surface pressure spectra, inverts them to stratification parameters using the stated dependence of IGW frequency on vertical temperature gradient, and validates the result against separate radiosonde ascent-rate data. No equations, self-citations, or fitted quantities are shown that reduce the calculated parameters to the input spectra by construction; the external benchmark comparison supplies independent content. The noted incompleteness of the dispersion relation (ω = N kh/|k|) is a question of modeling assumption rather than a definitional or self-referential loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only abstract available; main reliance is on the standard dispersion relation for internal gravity waves.

axioms (1)
  • domain assumption Frequency of internal gravity waves depends on the vertical temperature gradient.
    Invoked in abstract as the basis for calculating stratification parameters from observed frequencies.

pith-pipeline@v0.9.1-grok · 5627 in / 1122 out tokens · 46739 ms · 2026-06-28T03:22:53.773571+00:00 · methodology

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Reference graph

Works this paper leans on

6 extracted references · 3 canonical work pages

  1. [1]

    Waves in the Atmosphere

    Gossard E., Hooke W. Waves in the Atmosphere. 1975

    1975

  2. [2]

    An Introduction to Dynamic Meteorology

    Holton J. An Introduction to Dynamic Meteorology. Elsevier. 2004

    2004

  3. [3]

    Khaykin, S. M., A. Hauchecorne, N. Mzé, and P. Keckhut (2015), Seasonal variation of gravity wave activity at midlatitudes from 7 years of COSMIC GPS and Rayleigh lidar temperature observations, Geophys. Res. Lett., 42, doi:10.1002/2014GL062891

    work page doi:10.1002/2014gl062891 2015

  4. [4]

    Kochin A. V. 2023. V olumetric Acoustic Oscillations in the Atmosphere. January

    2023

  5. [5]

    DOI: 10.2139/ssrn.4385069

    SSRN Electronic Journal. DOI: 10.2139/ssrn.4385069

    work page doi:10.2139/ssrn.4385069

  6. [6]

    Kshevetsky S., Kulichkov N. 2015. Influence of internal gravity waves from convective clouds on atmospheric pressure and spatial distribution of temperature disturbances. Izvestiya, Atmospheric and Oceanic Physics. DOI: 10.7868/S000235151501006X

    work page doi:10.7868/s000235151501006x 2015