Review Report

This manuscript presents a significant methodological advancement for multistatic meteor radar wind retrievals by formulating the Volume Velocity Processing (VVP) in a rigorous spherical coordinate system (SVVP). The authors demonstrate the impact of this new implementation using four years of observations from the Nordic Meteor Radar Cluster and provide a thorough intercomparison with both the traditional plane‑geometry VVP and the more sophisticated 3DVAR+DIV tomographic retrieval. The topic is timely, the analysis is comprehensive, and the results convincingly show that accounting for Earth’s curvature is essential—particularly for vertical wind estimates and higher‑order kinematic quantities. The manuscript is generally well structured and the figures effectively support the narrative.

Nevertheless, several aspects require improvement before the paper can be recommended for publication in Atmospheric Measurement Techniques. These concern the presentation and discussion of the validation/uncertainty aspects, the quality of the language, and the completeness of the figure captions and citations. Below I list specific comments and suggestions, separated into major and minor issues.

Major Comments

       1. Treatment of vertical wind bias and uncertainty. The manuscript mentions that a bias correction of 1−4 cm s⁻¹ is subtracted from the vertical winds (lines 225–227, 417–423) based on the assumption that the long‑term mean vertical wind should be zero.

       This correction is critical because the absolute values of the vertical wind are central to the conclusions. The authors should provide more details: how exactly is the bias estimated? Is it a single constant per station, per altitude, or per domain size?

       The statistical significance of the debiased vertical wind patterns (e.g., upwelling of ~10 cm s⁻¹ in summer) should be evaluated, perhaps with confidence intervals or by showing that the bias‑subtracted values indeed vary seasonally and not merely as residual noise.

       Moreover, the 3DVAR+DIV vertical winds are an order of magnitude larger (lines 328–330). The authors attribute this to lower meteor counts per grid cell and the Tikhonov regularization. A more quantitative explanation (e.g., typical measurement response, averaging kernels) would strengthen the discussion.

       2. Intercomparison with 3DVAR+DIV and sensitivity to Tikhonov parameter. Section 4.3 presents a single snapshot (1 January 2021) to illustrate the effect of the regularization parameter.

       The representativeness of this single case should be commented on. Are the differences shown robust across many days/seasons?

       The text states that “the 3DVAR+DIV performs best with regularization strengths between α = 0.4~5. How was this range determined? A brief description of the metric used (e.g., cross‑validation, spectral analysis) would be helpful.

       The comparison between VVP and 3DVAR+DIV vertical winds (Fig. 14) shows a regression slope of only 0.105 (spherical) and 0.019 (plane). The discussion merely notes that this “validates and [is] consistent with the climatology results”. Given the huge difference in magnitude, a deeper analysis of why the two methods disagree so strongly is warranted. The role of the divergence‑derived vertical wind in 3DVAR+DIV versus the Doppler‑derived vertical wind in SVVP should be explicitly addressed.

       3. Temporal and spatial resolution sensitivity. The analysis of temporal resolution (15, 30, 60 min) and domain radius (200–400 km) is well motivated.

       In Fig. 9 the vertical wind regression slopes deviate markedly from unity (1.965 for 15 vs 30 min, 0.530 for 60 vs 30 min). The authors suggest this reflects the gravity‑wave spectrum, but they do not investigate whether this scaling is linear or whether a “true” reference exists. A more systematic treatment—e.g., power spectral density comparisons or an estimate of the gravity‑wave contribution—would elevate the discussion.

       The optimal radius (200–250 km) is justified by the 3DVAR+DIV measurement response (Fig. 15). However, the measurement response shown is for the 3DVAR+DIV retrieval, not for SVVP. It would be more direct to show, for the SVVP, how the number of meteors and the condition number of the least‑squares matrix vary with radius. The current argument is indirect and should be clarified.

Minor Comments

1. Figures 4 and 5 (monthly and seasonal composites) are redundant; consider merging them or moving one to supplementary material.
2. In Fig. 6 (correlation plots) the robust regression method should be named (e.g., Theil‑Sen, iteratively reweighted least squares).
3. The comparison of information content / Shannon entropy is only briefly mentioned and not shown. Either remove this remark or add a figure/table that supports it.
4. The paragraph about the influence of the circle of influence on vertical wind is very insightful. It would be even stronger if the authors could show a simple plot of the retrieved vertical wind (or its bias) as a function of radius for a fixed time/altitude.
5. The conclusion that SVVP is “more physically consistent” is well supported, but the limitations of the method (e.g., inability to capture non‑linear gradients, reliance on a single reference point) should be acknowledged more explicitly.

This manuscript presents an innovative extension of the traditional VVP technique by explicitly accounting for spherical geometry and Earth curvature effects. This is an important and often overlooked issue in large-scale radar wind retrievals. The mathematical derivation is rigorous and the analysis is comprehensive. The study represents a valuable methodological contribution to MLT wind retrievals.

However, I have several concerns that should be addressed before publication.

Major comments:

1. The primary conclusion of the manuscript is that SVVP provides more physically realistic vertical winds than the conventional VVP approach. However, the current analysis only demonstrates differences between retrieval methods and does not establish which solution is closer to the true atmospheric state.Therefore, the current results demonstrate that SVVP produces different retrievals from VVP, but do not yet conclusively demonstrate that SVVP is more accurate. If possible, comparisons with independent observations (e.g., nearby Na lidar) would substantially strengthen the manuscript. At minimum, the authors should discuss the current limitations and opportunities for validating MLT vertical wind retrievals.
2. I strongly encourage the authors to perform a leave-one-radar-out sensitivity experiment by excluding each radar in turn and repeating the retrieval. Such an analysis would provide a quantitative assessment of the robustness of the derived vertical winds and help determine whether the results are strongly dependent on the network geometry.
3. The vertical wind bias correction plays a central role in the final results. However, the manuscript does not sufficiently discuss the assumptions behind this procedure. It is unclear whether the correction is derived from the entire multi-year dataset or shorter temporal intervals. Different choices may influence the resulting climatology and long-term variability, and it remains unclear to what extent the apparent improvement in vertical winds originates from the SVVP formulation itself versus the adopted bias-correction procedure.A sensitivity analysis of the retrieved vertical winds to the adopted bias-correction strategy would strengthen confidence in the conclusions.
4. As a broader perspective, the authors may consider discussing whether the method could be adapted to weather radar networks and tropospheric wind retrievals, where more independent observations are available for validation.
5. The manuscript concludes that radii between 200 and 250 km provide the best performance. Is there a quantitative criterion that favors one radius over the other, or are both considered equivalent within uncertainty?

Minor comments:

1. Figures 7–10 contain a substantial amount of overlapping information. The authors may consider combining these figures into one or two multi-panel figures to facilitate direct comparison between VVP, SVVP, and 3DVAR+DIV. In addition, some of the quantitative comparisons could be more effectively summarized in tables.
2. The manuscript would benefit from a summary table quantifying the differences among VVP, SVVP and 3DVAR+DIV retrievals (e.g., bias, RMSD, correlation coefficients), rather than relying primarily on visual inspection of multiple figures.
3. The statement that the SVVP method produces “more realistic” vertical winds may be somewhat strong given the lack of independent validation. Consider using more cautious wording such as “more physically consistent” or “more self-consistent”.

This manuscript presents a spherical formulation of the Volume Velocity Processing (VVP) technique and applies it to four years of observations from the Nordic Meteor Radar Cluster. The topic is relevant and the mathematical formulation is carefully developed. However, the manuscript does not provide sufficient evidence to support its central claim that the spherical formulation produces more accurate or physically realistic wind retrievals, particularly for the vertical wind component. The analysis demonstrates differences between retrieval methods, but does not establish improved retrieval accuracy.

Demonstrating differences between retrieval methods is not equivalent to demonstrating improved accuracy. Consequently, several fundamental issues are insufficiently addressed and require substantial additional work before the scientific conclusions can be considered adequately supported.

Major comments:



1. Lack of rigorous validation

The primary weakness of the manuscript is the absence of a validation framework capable of assessing retrieval accuracy. The manuscript repeatedly concludes that the spherical formulation yields more realistic vertical winds and reduces biases present in conventional VVP. However, these conclusions are based on comparisons between retrieval methods rather than comparisons against a known reference. Agreement or disagreement with VVP or 3DVAR+DIV does not establish which solution is closer to the true atmospheric state.

If independent observations are unavailable (e.g., rockets, MST radars, and/or from satellites), the authors should perform validation using realistic synthetic atmospheric fields generated from direct numerical simulations or global circulation models. Such approaches are standard in the atmospheric remote sensing community and allow retrieval biases, uncertainties, and resolution limits to be quantified under controlled conditions. Examples include the Observing System Simulation Experiments (OSSE) framework described by Cucurull et al. (2024), which provides a systematic methodology for retrieval validation, and its application to MLT wind retrievals by Urco et al. (2024).

Such experiments would allow the authors to quantify retrieval bias, random error, uncertainty propagation, and the effective spatial and temporal resolution of the proposed method.

More fundamentally, the manuscript does not define an objective performance metric by which the proposed method can be judged superior to conventional VVP. Without a quantitative success criterion, the interpretation of “improvement” remains subjective.

Validation deferred to a companion paper or future publication cannot be used to support conclusions made in the present manuscript. The proposed method requires validation within the manuscript itself.

2. Failure to demonstrate that spherical geometry is a dominant source of error

The central premise of the manuscript is that Earth curvature introduces significant biases in VVP retrievals and that these biases are mitigated by the spherical formulation. However, the manuscript does not quantify the relative importance of geometric effects compared to other error sources.

Potential contributors include measurement uncertainty, meteor sampling variability, network geometry, temporal averaging, regularization choices, vertical-wind bias correction, and inversion assumptions. The current analysis therefore demonstrates that SVVP produces different retrievals than conventional VVP, but does not demonstrate that these differences arise primarily from the spherical representation.

The manuscript currently assumes that curvature effects are responsible for the observed differences, but this assumption is never tested quantitatively.

A quantitative error budget is needed to establish whether curvature effects are indeed a dominant source of retrieval error. Without such analysis, the attribution of the observed differences to spherical geometry remains largely qualitative.

3. Insufficient sensitivity and robustness analysis

The robustness of the proposed retrieval method is insufficiently characterized.

Several sensitivity analyses are required. In particular, a leave-one-radar-out experiment would provide valuable information regarding the dependence of the retrieved winds on network geometry and station availability. The argument that removing major stations degrades the retrieval is not a justification for omitting the experiment. On the contrary, quantifying the degradation is precisely the purpose of such a sensitivity study.

Similarly, robustness could be assessed through leave-random-measurements-out experiments, where a fraction of the meteor detections (e.g., 10–50%) is removed and the retrieval repeated. Such analyses would help quantify the stability of the inferred winds and their sensitivity to sampling density.

The vertical-wind bias correction also plays a central role in the manuscript’s conclusions. However, no systematic sensitivity analysis is presented to determine how strongly the results depend on the adopted bias-correction strategy. It remains unclear how much of the apparent improvement originates from the SVVP formulation itself and how much originates from the subsequent correction procedure.

Furthermore, the need for an externally imposed bias correction raises additional questions regarding the robustness of the vertical wind retrieval itself. If the proposed formulation substantially reduces geometric biases, the manuscript should clarify why a subsequent empirical correction remains necessary and quantify its impact on the reported results.

4. Lack of uncertainty characterization and scale-dependent analysis

The manuscript does not adequately characterize retrieval uncertainty, effective resolution, or recoverable scales.

Many conclusions are based on differences in vertical wind magnitude, smoothness, divergence, and temporal variability. However, the manuscript does not establish which spatial and temporal scales can be reliably reconstructed by either method. Consequently, it is difficult to determine whether the reported differences reflect improved physical reconstruction, changes in effective filtering, or different regularization behavior.

In particular, the manuscript does not establish the smallest recoverable scales, the scales dominated by regularization, or the scales for which the retrieval becomes unreliable.

Several issues raised by the analysis—including the interpretation of vertical-wind amplitudes, the dependence on temporal averaging, the selection of the optimal domain radius, and the comparison with 3DVAR+DIV—ultimately require a quantitative assessment of retrieval uncertainty and resolution. Without such information, the physical interpretation of the results remains ambiguous.

This manuscript presents a useful methodological contribution to multistatic meteor radar wind retrievals by reformulating Volume Velocity Processing in spherical coordinates. The topic is timely and relevant for Atmospheric Measurement Techniques, since multistatic meteor radar networks now cover domains of several hundred kilometers, where plane-geometry assumptions may introduce projection errors. The multi-year Nordic Meteor Radar Cluster observations and the comparison among plane-geometry VVP, spherical VVP, and 3DVAR+DIV provide a valuable basis for assessing geometric effects on retrieved MLT winds and higher-order kinematic quantities.

However, I think the manuscript needs substantial revision before publication. My main concern is not the usefulness of the spherical formulation, but the interpretation and positioning of the method. The discussion sometimes gives the impression that SVVP is a more reliable alternative to 3DVAR+DIV, especially for vertical winds. This is not sufficiently justified. SVVP is an important geometric improvement of VVP, but it remains a reduced-order, first-order representation of the wind field. By contrast, 3DVAR+DIV is theoretically a more general tomographic framework that can resolve spatially heterogeneous three-dimensional winds and include physical constraints. Therefore, the differences between SVVP and 3DVAR+DIV should not be interpreted simply as evidence that SVVP is superior. They may instead indicate limitations in the present 3DVAR+DIV implementation, including geometry, continuity constraints, regularization, and sparse-sampling treatment.

I recommend major revision. The paper has clear potential, but the conclusions should be more balanced, and the retrieval uncertainty, validation, and method comparison need to be strengthened.

Major comments:

1. The manuscript should more clearly distinguish between the improvement of SVVP relative to plane-geometry VVP, the broader theoretical capability of 3DVAR+DIV, and the limitations of the current 3DVAR+DIV implementation. SVVP is a geometrically improved version of VVP, but it does not remove the reduced-order nature of VVP, which still represents the wind field using mean winds and first-order spatial gradients within a finite volume. In contrast, 3DVAR+DIV is designed to retrieve spatially varying three-dimensional wind fields with physical constraints. The manuscript should therefore avoid implying that SVVP supersedes 3DVAR+DIV. The larger vertical winds from 3DVAR+DIV should be discussed in terms of spherical/ellipsoidal geometry, continuity assumptions, Tikhonov regularization, and sparse meteor sampling. A better framing is that SVVP provides a geometrically self-consistent benchmark for reduced-order retrievals, while an improved 3DVAR+DIV remains the more general framework for future multistatic meteor radar tomography.
2. The observational comparison shows that SVVP, plane VVP, and 3DVAR+DIV produce different results, especially for vertical winds and higher-order kinematic quantities. However, this does not fully isolate the role of spherical geometry. I recommend adding a synthetic or closed-loop retrieval experiment. The authors could prescribe known wind fields, generate synthetic line-of-sight velocities using the actual NORDIC radar geometry and meteor sampling locations, and then retrieve the winds using both plane VVP and SVVP. Test cases could include uniform horizontal wind with zero vertical wind, known divergence/vorticity, prescribed vertical velocity, and simple gravity-wave-like perturbations. Such experiments would directly show whether SVVP reduces projection errors and whether plane VVP produces spurious vertical wind or divergence.
3. The paper retrieves not only mean winds but also horizontal divergence, relative vorticity, stretching deformation, and shearing deformation. These quantities are sensitive to sampling geometry, station distribution, and the conditioning of the least-squares problem. The manuscript mainly presents retrieved fields and correlations, but it does not sufficiently show whether all fitted parameters are well constrained. The authors should include diagnostics such as condition numbers, singular values, parameter covariance, and correlations among retrieved coefficients. This is particularly important for vertical wind and gradient terms. The contribution of each radar station should also be quantified, since uneven spatial overlap and different meteor counts may cause the retrieval to be dominated by certain stations or viewing directions.
4. The manuscript subtracts a long-term or seasonal vertical-wind bias based on the assumption that the long-term mean vertical wind should vanish. This correction is critical because its magnitude is comparable to the retrieved vertical winds. The authors should describe how the bias is estimated in much greater detail. It should be clarified whether the correction is derived separately by altitude, radius, temporal resolution, season, station combination, or from the full dataset. The authors should also test whether the seasonal upwelling/downwelling pattern remains under different bias-correction strategies. The uncertainty associated with this correction should be propagated into the final vertical-wind climatology.
5. The comparison between SVVP and 3DVAR+DIV needs a more careful interpretation. Since 3DVAR+DIV is a more general framework, the comparison should not simply emphasize that SVVP gives smaller or more physically plausible vertical winds. The authors should analyze why the two methods differ. First, the current 3DVAR+DIV implementation may not include the same spherical geometric treatment as SVVP. Second, vertical wind in 3DVAR+DIV is constrained differently from the Doppler-derived vertical wind in SVVP. Third, the influence of Tikhonov regularization should be quantified more systematically, rather than illustrated mainly with selected cases. This would help clarify whether the discrepancy reflects method hierarchy, geometry, physical assumptions, sampling sparsity, or regularization choices.
6. The manuscript discusses the relation between horizontal divergence and vertical velocity using a simplified continuity equation. However, the MLT is strongly density-stratified, and an incompressible continuity equation may not be appropriate without qualification. An anelastic form involving density stratification may be more relevant. Even if the main SVVP climatology is based on Doppler-derived vertical velocity, divergence and 3DVAR+DIV results are still used to support the interpretation of vertical motion. The authors should clarify how the continuity constraint is used in 3DVAR+DIV, whether density stratification is included, and how this affects the comparison with SVVP vertical winds.
7. The SVVP method still assumes that the wind field within the analysis volume can be represented by a first-order expansion. This may be restrictive over 200–400 km domains, where gravity waves, tides, planetary waves, and polar-region dynamics can produce nonlinear spatial structures. The manuscript should better quantify the representation error associated with this first-order approximation. For example, the authors could show line-of-sight residuals as a function of radius, altitude, local time, or season. Synthetic tests using sinusoidal or gravity-wave-like wind fields would also help identify the spatial scales over which SVVP remains valid. This is important because some SVVP–VVP differences may arise from model truncation errors, not only from geometric effects.
8. The manuscript concludes that reliable vertical winds are obtained for 15–30 min temporal resolution and a 200–250 km spatial radius. This is plausible, but the selection criterion is not sufficiently quantitative. The authors should state whether the optimal range is based on meteor counts, radar overlap, retrieval uncertainty, condition number, residual error, comparison with 3DVAR+DIV, or physical plausibility. These criteria are not equivalent. A larger radius may improve sampling but worsen the first-order approximation, while a smaller radius may reduce representation error but degrade conditioning. A summary table or figure showing these metrics as a function of radius and temporal resolution would make the conclusion more convincing.
9. Because the paper focuses on geometric implementation, the definition of the vertical direction must be precise. The manuscript should state whether the retrieved vertical wind is relative to the geocentric radial direction, the geodetic normal, the local ENU up direction at each meteor location, or the reference point. Over a 200–400 km domain, local vertical directions are not parallel, and small projection differences may matter for cm s⁻¹ vertical winds. The authors should explain how line-of-sight velocities measured in local radar coordinates are transformed into the common retrieval coordinate system, and whether residual differences in local vertical directions can project horizontal wind into the retrieved vertical component.

This paper proposes a new Volume Velocity Processing method in spherical coordinates to improve the wind retrieval in MLT. Its performance is compared against the conventional VVP method in plane geometry and the 3DVAR+DIV method, which result shows that the proposed SVVP method generally resolves more variability than the conventional VVP, and provides a more robust framework than 3DVAR+DIV for the study of MLT dynamics in terms of longer time series. The manuscript is generally well written. My main concerns are as follows:

1. The caption of table 1 should appear on top of the table. Moreover, it would be nice to see the relevant parameters of radar antenna beam as well.
2. The authors demonstrate the difference between SVVP and VVP clearly, notably for the retrieval of vertical wind component. However, their superiority cannot be intuitively judged due to the lack of comparison with ‘actual’ wind field.
3. The comparison against 3DVAR+DIV is not straightforward, since they are two different frameworks. The advantages/disadvantages of SVVP w.r.t. 3DVAR+DIV should be highlighted.
4. The authors demonstrate the importance of geometric effects. While the contribution of geometric effects to the wind retrieval errors is not well addressed.