Reviewer Follow-Up Comments
While I appreciate the authors’ additional clarifications, the fundamental concerns raised in the original review remain unresolved. The manuscript continues to rely on assumptions that are not physically justified for the MAARSY head-echo dataset and presents results that are inconsistent with established models and climatologies. The following points elaborate on these issues.
1. Applicability of the trajectory model
The manuscript references the energy equation from Vondrak et al. (2008) and uses CABMOD as its physical foundation. To clarify, when the entry angle is measured with respect to the zenith, CABMOD is applicable to trajectories between 0° and ~85°, with 90° corresponding to a horizontal path. Thus, the concern is not that CABMOD disallows shallow entries per se, but that the simplified form of Eq. (1) used here does not capture the relevant physics of low-elevation, long-path meteoroid entries, which constitute a significant portion of MAARSY head-echo detections (Schult et al., 2017).
At such shallow geometries, several effects become first order and must be treated explicitly:
Extended atmospheric path length: Energy deposition depends on the evolving thermospheric temperature and density along the trajectory, not on velocity alone.
Gravitational curvature and deceleration: The long flight path alters both ablation timing and altitude of maximum ionization.
Variable heating history: Shallow entries experience significant pre-heating before main ablation, shifting RCS peaks independently of neutral density.
Differential ablation and fragmentation: Extended residence times amplify selective element release (especially alkalis) and fragmentation, changing radar cross-section and mass-loss functions.
Without validating Eq. (1) for these geometries, applying it directly introduces systematic bias in derived ablation heights and neutral-density retrievals. The analysis should therefore (i) demonstrate validity through simulations, (ii) restrict analysis to an angular regime where assumptions hold, or (iii) incorporate a trajectory-dependent treatment that accounts for long-path and heating effects.
2. Flight physics and differential ablation
Differential ablation governs the radar cross section (RCS) and detection altitude but is largely absent from the manuscript’s discussion. For shallow entries, the extended atmospheric path leads to unique heating–cooling cycles. The low heat capacity of most meteoroids allows ambient thermospheric temperatures to preheat the surface, altering the onset of ablation. The release of alkali metals (Na, K) at higher altitudes can generate strong echoes with minimal mass loss, collapsing the core assumption that detection altitude traces neutral density.
Moreover, the organic compounds present in meteors act as a glue-like matrix which binds the various mineral phases together (Flynn et al., https://doi.org/10.1016/j.gca.2003.09.001). Although the organic phases may undergo some degree of thermal degradation or pyrolysis during atmospheric – particularly for particle diameters below 200 microns (Bones et al., https://doi.org/10.1029/2021EA001884) – larger bodies may experience fragmentation (Subasinghe et al., https://doi.org/10.1016/j.pss.2016.12.009), generating multiple fragments whose combined plasma cross section differs substantially from a single solid body. The manuscript neither discusses nor quantifies how these processes impact the results, leaving a major gap in the physical interpretation.
3. Physical consistency and claimed accuracy
The manuscript claims to infer neutral density variations with accuracies of several percent, despite presenting variability amplitudes of 20–40 %. Given that meteoroid mass, density, and atmospheric density contribute comparably to the kinetic energy budget, such precision is unrealistic without modeling each parameter.
Additionally, the number of head echo detections per solar longitude is limited, and a large fraction correspond to retrograde orbits (OCC or HTC), while specular radar detections—typically used for such studies—are dominated by JFC meteors. These populations differ in speed, angle, and composition, all of which influence detection altitude.
Since the relevant processes follow power-law and exponential dependencies (e.g., velocity³, density⁴), reliable uncertainty quantification requires simulations using multiple ablation and scattering models (e.g., 10.1029/2021JA029525). Even advanced models yield substantial uncertainty in mass estimates (10.1029/2023JA032281). Without such modeling, the precision claimed here is not supported.
4. Data provenance and acknowledgement
The dataset used is part of the Meteor Shower Catalogue by Peter Jenniskens (Meteor Showers and Their Parent Comets). This provenance should be explicitly stated when introducing the observations. The authors should also acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) under grant STO 1053/1-1 (AHEAD), as noted in the same source.
5. Neutral density variability and consistency with prior work
The revised manuscript presents neutral air density variations that diverge sharply from prior studies. Vida et al. (Icarus, https://doi.org/10.1016/j.icarus.2020.114051) derived neutral density variability using NAVGEM-HA, validated against temperature and wind observations. The variability amplitudes and spatial patterns in the current manuscript are neither comparable nor physically consistent with those results or any established climatology of the mesosphere and lower thermosphere.
This inconsistency indicates a fundamental flaw in the analysis, as the underlying assumptions appear invalid for this type of retrieval. The authors neither acknowledge nor reconcile these discrepancies. Given the extensive validation of NAVGEM-HA, any alternative climatology would require compelling physical evidence and quantitative justification.
The citation of Kunze et al. (2024) as showing similar structures in UA-ICON is also inaccurate; that paper does not present seasonal neutral density variations. The authors must clarify which aspects of Kunze et al. are being invoked and provide physical reasoning for the differences.
6. Neutral density retrieval from specular meteor radars versus meteor head echoes
The inference of neutral density variability from meteor head echoes is not physically equivalent to that from specular meteor radars, yet the manuscript conflates the two. Specular radars measure underdense trails, providing direct access to velocity and electron line density, which define the leading-order terms of the ablation energy equation. Radiative heating/cooling, fusion heat, and velocity can thus be constrained, while the heat capacity term can be solved iteratively—yielding statistically valid density retrievals.
Head-echo detections, by contrast, provide only speed and an approximate radar cross section, leaving all other energy-balance terms unknown. The manuscript’s claim that velocity³ dominates neglects higher-order terms—especially the temperature dependence (T⁴) and the exponential vaporization term governed by the Clausius–Clapeyron relation.
These are not secondary corrections but primary controls of ablation behaviour.
Therefore, the assertion that neutral density can be retrieved with 20–40 % accuracy is mathematically unsupported. Achieving such precision would imply knowledge of meteoroid mass, shape, and composition to within 10 %, which is unrealistic without detailed modeling. A defensible approach would require coupling head-echo observations to a complete ablation–scattering model for each meteor and propagating uncertainties accordingly.
Summary
In summary, the revised manuscript remains misaligned with the physical and methodological standards expected for Atmospheric Measurement Techniques. The analysis employs simplified assumptions that are not valid for the geometry and physics of the dataset, lacks comparison with established climatologies, and overstates the precision of its results without adequate modeling or uncertainty analysis. To render the study publishable, substantial revision would be required—either incorporating a rigorous ablation–scattering framework or explicitly limiting the scope of claims to reflect the methodological constraints. |
This paper describe the use of a large data set of radar echoes from meteor head ionization to infer density fluctuations at altitudes around 90-110 km. The work is well explained and presented and adequately cited. Of particular interest is the authors’ use of velocity cubed as a proportional proxy for atmospheric density. The writing is of an overall high quality and figures are both easy to read and complimentary to the text. The paper provides a useful introduction to the authors’ methodology and will serve as a useful foundation for their future publications on the topic. It is recommended for publication with the following minor changes.
General: This is perhaps pedantic, but “bulk density” may be more appropriate than “neutral density” While the atmosphere is relatively lightly ionized in the meteor ablation region, collisional heating at entry speeds does not distinguish between neutral molecules and those missing a full complement of electrons. It is recognized that “neutral density” is commonly used in literature, but this may be an opportunity to use more precise language.
Line 20-21: It would also be worth mentioning Yi et al. 2018 (doi: 10.1002/2017JA025059)
Line 27 change “signal” to “line of sight vector” or similar
Should define MST acronym at first use in main text.
Line 54: remove “A”, use commas
Line 84-85: It would be good to also cite the work of Campbell-Brown in generating precise maps and models of the sporadic background e.g. Campbell-Brown et al. 2008 (doi: 10.1016/j.icarus.2008.02.022)
Line 85: Maybe use autumn instead of fall to avoid confusion.
Line 103/figure 2: Is this mean detection altitude or mean initial detection altitude?
Line 110a/section 4: This assumes that the size distribution and composition of meteoroids remains constant throughout the year. While this may be a reasonable assumption for the sporadic sources, it is less so for shower sources. This raises the possibility of transient contamination of the results during strong shower activity.
Line 110b: Equation 1 describes the energy balance of collisional heating, radiation, and vaporization, but does not describe the amount of plasma generated or the reflectivity near the meteoroid. Readers would benefit from an expression describing meteor head plasma density and echo strength at the wavelengths considered. It also seems important to mention the aspect sensitivity of meteor head echoes, which may affect the average seasonal results. This only affects the absolute terms in figures 1 and 2, but not the later figures, which portray relative fluctuations between years.
Line 114: Would substitute “plasma density” for “ablation rate”. The latter refers to material loss rate, not specifically generation rate of detectable plasma
Figure 2: These are well constructed and easy to read plots. The correlation in the top panel is clear, but the deviation of the 60 and 40 km/s heights from associated iso-density contours in the bottom panel for the first half of the year goes unremarked in the text, except the disclaimer in lines 108-109. Do the authors think that this could be a shortcoming of the MSIS model, dynamical features of the atmosphere, or something to do with temporal changes in head echoes?
Line 120: “…panel of the background…”
Line 129: incomplete sentence ending in “…to compare with.”
Section 4.4: The summer/autumn reduction in density above 100 km is not obvious to me in figure 3. Is there some other way of presenting the data to make this claimed feature stand out?
Section 4.5: This section could benefit from the inclusion of a wavelet spectrogram that should clearly show the presence of planetary waves. Alternatively, a line plot showing the velocity cubed ratio variation at a fixed height may provide readers with a clearer depiction of oscillations.