the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 21 May 2026
The composite radar-GNSS spectrum of auroral plasma turbulence
Abstract. In the auroral ionosphere, plasma turbulence acts as an important dissipation mechanism for magnetospheric energy and the primary cause of radio wave scintillation. Characterizing auroral plasma turbulence across its full spatial extent has historically been limited by the narrow bandwidths of individual instruments. Our investigation approaches the problem of obtaining accurate, scale-dependent information using the physics of the Farley-Buneman (FB) instability, a modified two-stream plasma instability. In this study, we construct a composite spatial powerspectrum of plasma turbulence in the auroral electrojets spanning roughly four orders of magnitude in scale (from ~100 km down to ~20 m). This is achieved by combining a recent Monte-Carlo-based method of spatial clustering of very-high-frequency (VHF) radar echoes, with phase screen information derived from global navigation satellite system (GNSS) signals, using ground-based instrumentation in Canada. Through multi-instrument conjunctions with the European Swarm and Japanese Arase missions, we observe that the clustering of electrojet turbulence matches the structuring of field-aligned currents, and correlates with magnetospheric electron fluxes. Statistical analysis of the composite spectra, as well as a very large database of radar clustering spectra only, reveals a consistently steep decay of spectral power in the auroral electrojets, with the most probable spectral index being near −8/3. The observations suggest a continuous, scale-invariant cascade that frequently preserves the spatial signature of its magnetospheric drivers, where we outline a way for Alfvén waves to structure the turbulent E-region. Furthermore, we demonstrate that the plasma structures guilty of causing GPS scintillations (~270 meters in size) were moving at the ion acoustic speed, implying that those structures were, in fact, FB waves, and we thereby establish an observational basis for low-frequency electrojet turbulence. The method that we present, the composite radar-GNSS spectra, will on both counts offer useful empirical constraints for future efforts seeking to simulate the "sub-grid" turbulence that complicates the magnetosphere-ionosphere coupling around aurorae.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Annales Geophysicae.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 25 Aug 2026)
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RC1: 'Comment on egusphere-2026-2344', Anonymous Referee #1, 26 Jun 2026
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AC1: 'Reply on RC1', Magnus Ivarsen, 13 Jul 2026
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We thank the referee for a constructive report. All comments are addressed below. During the revision we found and corrected a convention error that impacts comparisons between the composite spectrum and in-situ (one-dimensional) power spectra observed by satellites (Swarm). We describe this discrepancy first, since several of the responses follow from it.
A correction: the spectral convention of the composite spectrum
The Hankel transform of the two point correlation function of echo positions (Eq. 3) returns the two dimensional spectral density of the echo field, defined per unit area in the wavenumber plane. A one dimensional cut through the same field carries an index shallower by one power of k. The GNSS spectra share the two dimensional convention: by the projection slice theorem, the areal spectrum of the phase field preserves the transverse index of the density spectrum, and the measured temporal spectrum involves one marginalization over transverse wavenumber, where a one dimensional in situ measurement involves two. Both halves of the composite are therefore two dimensional spectral densities, one power of k above one dimensional spectra. The overlap between 750 m and 3000 m confirms this empirically.
The foregoing carries two consequences. First, the composite spectrum is internally consistent and its measured indices remain methodologically sound. Second, two comparisons in the original manuscript crossed conventions: the overlay of Swarm along-track FAC spectra (one dimensional) on the composite (two dimensional), and the identification of the index near -8/3 with the kinetic Alfven prediction of David and Galtier (2019), which is a reduced one dimensional spectrum. The two dimensional -8/3 corresponds to a one dimensional -5/3, and the identification does not survive the correction. We have removed both comparisons and everything that rested on them; see the responses to comments 2, 4, and 6. Section 2.4 of the revision states the convention; the full treatment is in Ivarsen et al. (2026, in review). This has led to large cuts in the manuscript, such as the old Appendix B in its entirety, a reduction in figures and figure panels, and any discussion of kinetic Alfvén waves as a driver of FB waves (which is deferred to a future investigation).
What follows is an outline of our revisions.
Comment 1. "The physical meaning of the composite spectrum should be clarified."
Response: Section 2.4 now states what the composite spectrum is: the two dimensional spectral density of the turbulent irregularity field. The radar measures it through the Hankel transform of the echo position correlation function, which is a two-dimensional isotropic sampling of the echo point distribution. The GNSS spectrum measures the irregularity field through the weak scatter phase screen. The shared convention is verified empirically by the 750 m to 3000 m overlap (and theoretically described in Section 2.4), and the abstract and conclusion state the observable. Break point positions do not depend on the convention, and so the comparison of knee scales with the literature is unaffected.
Comment 2: "The −8/3 spectral slope needs stronger uncertainty and robustness analysis."
Response: The -8/3 value no longer carries a mechanism (see the correction above), and the revised paper claims constancy of the index, not a particular value. The requested statistics are reported in Section 3: the ten events give overall indices between -1.93 and -2.83 (Figure 9d), with mean -2.50, median -2.52, and standard deviation 0.24 (mean -2.56, standard deviation 0.15 without the shallowest event). The database of 7,700 radar-only spectra, which conditions only on echo activity, peaks at -2.7 (Figure 9a), and the conjunction sample lies within that distribution. All indices are quoted in the two dimensional convention; the one dimensional equivalents are one power of k shallower, and the discussion attaches no mechanism to the value in either convention.
On the synthetic pipeline and reduced processing tests: the two constituent methods are documented, including slope analyses, in four papers in JGR: Space Physics, Ivarsen et al. (2023a, 2023b) for the radar spectra and Song et al. (2025) and Meziane et al. (2025) for the GNSS spectra. We rely on those published analyses for pipeline fidelity, and the revision confines the interpretation to what the reported statistics support (omitting any inferred mechanisms responsible for those results).
Comment 3: "The 270 m Farley–Buneman interpretation is suggestive, but too strong as currently written."
Response: The abstract, results, and conclusion now read "consistent with long wavelength FB-like structures", and "only reasonable explanation" is removed. Section 4.1 calls the FB identification "the simplest explanation" on the strength of the velocity discrimination (Figures 4b and 8b), while a new paragraph on alternatives (GDI, mixed GDI and FB regimes, nonlinear coupling) states that a mixed scenario cannot be excluded and that the sample is conditioned on amplitude scintillation.
The sensitivity of the GPS derived speed is bounded in the now-extended sensitivity appendix (Appendix C of the original, Appendix B of the revision). Assumed altitude: plus or minus 10 m/s for a plus or minus 5 km offset. This also addresses pierce point motion: under roughly 25 m/s at the elevations of our sample; a new table lists date, PRN, and median elevation for the ten events, all at 60 degrees or above. Finite layer thickness: under plus or minus 4 percent spread in the Fresnel scale for a 15 km layer, which broadens the knee without moving it. Isotropy: bounded by the agreement between the phase screen drifts and the Doppler speeds, since an anisotropy artifact would have to shift drifts near 1000 m/s by a factor of two onto the independently measured Doppler peak near 500 m/s. Especially Figure 3b (but also Figures 3, 5 and 8 in the revised paper) make this point very clear: the phase screen drifts are observed far from the tracked radar speeds, and the latter have been confirmed by Ivarsen et al. (2024a, b) to trace magnetospheric drifts. The combined uncertainty on the phase screen drifts (Appendix B of the revised paper) is an order of magnitude below the separation between the two velocity populations, which is the quantity the interpretation rests on.
Comment 4: "The Alfvénic-driver interpretation should be toned down or better supported."
Response: Removed. The Swarm FAC spectral overlays, the impedance analysis (former Figures 5d to 5g), the former Appendix B, and the Alfvénic causal narrative in Section 4.2 are gone. The removal follows from the convention correction: the spectral agreement supporting the identification compared a one dimensional spectrum with a two dimensional one. The Swarm data retain the velocity comparison (Figure 5a, b), which confirms that the radar target motions track the F region ion drift. Section 4.2 was rebuilt around the scale-free organization, the two knees, and the Arase precipitation correlation, which compares the same observable with itself and is therefore convention independent. The magnetospheric causal chain involving kinetic Alfvén waves is deferred to future work.
Comment 5: "Event-selection effects should be discussed more clearly."
Response: Section 2.3 now gives the selection procedure with numbers. We first selected 49 one hour intervals of strong radar activity, with no GNSS input. Within those, ten conjunctions were identified by overlap with scintillating pierce points. Amplitude scintillation is a prerequisite of the phase screen method: without it, neither the Fresnel frequency nor the IFLC spectrum is defined, so a radar-active, GNSS-quiet composite spectrum cannot be constructed. The GNSS segment therefore characterizes scintillation-producing conditions by construction. Whether the conditioning biases the spectra is tested against the radar-only database: the ten event index distribution lies within it (Figure 9a). The Fresnel knee is treated separately; Section 4.2 states that the knee position, unlike the surrounding indices, may reflect the selection and should be generalized with caution.
Comment 6. "The discussion should stay closer to what is demonstrated."
Response: The discussion has been cut. Removed: the Alfvén wave energy extraction narrative, impedance matching and the preferred auroral altitude, polar cap potential saturation, self organized criticality, and the companion framing of the renormalization group manuscript (which is no longer a companion paper in any proper sense of the word). Section 4.2 was retitled and rebuilt as described under comment 4.
Minor comments: "Only reasonable explanation" is removed. "Universal", "continuous scale-invariant cascade", "preserves the magnetospheric driver", and "directly structures" are removed. The thin layer assumption is stated in Section 2.3, with the quantitative bounds in the sensitivity appendix. The break point method is described in Section 2.4: piecewise linear Hermite polynomials with free knots, a five segment fit for the composite spectra, and a parallel single fit providing the overall index. Typos are fixed, the placeholder references are resolved, panel lettering and cross references are corrected, the abstract is rewritten to match the revised scope, and the title punctuation is changed to "radar and GNSS".
For the referee's benefit, we state the abstract here, as it is difficult to read in the attached "bluetext" PDF:
"In the auroral ionosphere, plasma turbulence acts as an important dissipation mechanism for magnetospheric energy and as the primary cause of radio wave scintillation. Characterizing this turbulence across its full spatial extent has historically been limited by the narrow bandwidths of individual instruments. In this study, we construct a composite spatial powerspectrum of plasma turbulence in the auroral electrojets spanning roughly four orders of magnitude in scale (from ~100 km down to ~20 m). This is achieved by combining a recent Monte-Carlo-based method of spatial clustering of very-high-frequency (VHF) radar echoes, with phase screen information derived from global navigation satellite system (GNSS) signals, using ground-based instrumentation in Canada. Both measurements yield the two-dimensional spectral density of the turbulent irregularity field, and the two spectra agree closely across their shared band between 750 m and 3000 m. Across ten radar and GNSS conjunction events, the composite spectra exhibit a steady, scale-free decay of spectral power, with overall spectral indices of mean -2.50 and standard deviation 0.24 in that two-dimensional convention, consistently interrupted by spectral knees near 5~km and near 270~m. We further compare three independent velocity measurements in the same volume: radar Doppler velocities, tracked radar target motions, and GNSS phase screen drifts. The ~270~meter structures responsible for GPS scintillation moved at the ion acoustic speed, near 500 m/s, well below the concurrent ExB drifts near 1000 m/s traced by the target motions, a velocity signature consistent with long-wavelength Farley-Buneman (FB) waves, complementing the 3 m FB waves the radar observes directly. Conjunctions with the Japanese Arase mission show that spectral steepening correlates with precipitating magnetospheric electron flux, while conjunctions with the European Swarm mission confirm that the radar target motions track the F-region plasma drift. The method that we present, the composite radar and GNSS spectra, may offer useful empirical constraints for future efforts seeking to simulate the "sub-grid'' turbulence that complicates the magnetosphere-ionosphere coupling around aurorae."
References:
David, Vincent, and Sébastien Galtier. ‘K_\perp ^-8/3 Spectrum in Kinetic Alfvén Wave Turbulence: Implications for the Solar Wind’. The Astrophysical Journal Letters 880, no. 1 (2019): L10. https://doi.org/10.3847/2041-8213/ab2fe6.
Ivarsen, Magnus F., Kaili Song, Jean-Pierre St-Maurice, and Glenn C. Hussey. ‘Excursion-Set Structure Factor of the Auroral Electric Field (in Review at Physical Review Letters)’. arXiv:2606.26854. Preprint, arXiv, 29 June 2026. https://doi.org/10.48550/arXiv.2606.26854.
Ivarsen, Magnus F., Adam Lozinsky, Jean-Pierre St-Maurice, et al. ‘The Distribution of Small-Scale Irregularities in the E-Region, and Its Tendency to Match the Spectrum of Field-Aligned Current Structures in the F-Region’. Journal of Geophysical Research: Space Physics 128, no. 5 (2023): e2022JA031233. https://doi.org/10.1029/2022JA031233.
Ivarsen, M. F., Jean-Pierre St-Maurice, Glenn Hussey, et al. ‘Measuring Small-Scale Plasma Irregularities in the High-Latitude E- and F-Regions Simultaneously’. Scientific Reports 13, no. 1 (2023): 1. https://doi.org/10.1038/s41598-023-38777-4.
Song, K., K. Meziane, A. M. Hamza, and P. T. Jayachandran. ‘Investigation of the Fresnel Scale From Ionospheric Scintillation Spectra’. Journal of Geophysical Research: Space Physics 130, no. 2 (2025): e2024JA033239. https://doi.org/10.1029/2024JA033239.
Meziane, K., A. M. Hamza, K. Song, and P. T. Jayachandran. ‘Identifying Scales of the Ionospheric Structure Through Scintillation Events’. Journal of Geophysical Research: Space Physics 130, no. 10 (2025): e2025JA034326. https://doi.org/10.1029/2025JA034326.
Ivarsen, M. F., Jean-Pierre St-Maurice, Glenn C. Hussey, Devin R. Huyghebaert, and Megan D. Gillies. ‘Point-Cloud Clustering and Tracking Algorithm for Radar Interferometry’. Physical Review E 110, no. 4 (2024): 045207. https://doi.org/10.1103/PhysRevE.110.045207.
Ivarsen, M. F., Jean-Pierre St-Maurice, Devin R. Huyghebaert, et al. ‘Deriving the Ionospheric Electric Field From the Bulk Motion of Radar Aurora in the E-Region’. Journal of Geophysical Research: Space Physics 129, no. 11 (2024): e2024JA033060. https://doi.org/10.1029/2024JA033060.-
RC2: 'Reply on AC1', Anonymous Referee #1, 13 Jul 2026
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I thank the authors for their detailed response and for the substantial revision of the manuscript. I find the revised version much improved. In particular, I appreciate the correction of the spectral-convention issue and the removal of the kinetic-Alfvén interpretation based on the −8/3 slope. This was an important point, and the authors have dealt with it in a careful and scientifically honest way.
The manuscript is now much stronger as an observational and methodological paper. The physical meaning of the composite spectrum is clearer, the spectral indices are now reported with useful statistics, and the broader Alfvénic-driver interpretation has been removed or substantially softened. I also appreciate that the authors now describe the event selection procedure more clearly and acknowledge that the GNSS part of the composite spectrum is conditioned on scintillation-producing events.
I am generally satisfied with the response. I still think the authors should be careful in the final clean version to keep the language cautious, especially regarding the 270 m structures. The wording “consistent with long-wavelength FB-like structures” is appropriate, whereas stronger wording implying a firm identification should be avoided unless further evidence is added. I also note that the requested synthetic-data and reduced-processing tests were not newly performed, but the concern is less serious now because the revised manuscript no longer uses the −8/3 value as a strong mechanistic argument.
Overall, I think the authors have addressed the main scientific concerns. I would recommend acceptance after minor revision, mainly to ensure that the cautious language is retained throughout the abstract, results, discussion, and conclusion, and that no residual wording from the previous stronger interpretation remains in the final manuscript.
Citation: https://doi.org/10.5194/egusphere-2026-2344-RC2
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RC2: 'Reply on AC1', Anonymous Referee #1, 13 Jul 2026
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AC1: 'Reply on RC1', Magnus Ivarsen, 13 Jul 2026
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Data sets
Icebear data Hussey, Ivarsen https://doi.org/10.5281/zenodo.7509022
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This manuscript presents an interesting observational study of auroral E-region plasma turbulence. The main new point, in my view, is the construction of a composite radar–GNSS spectrum by combining ICEBEAR radar echo-clustering spectra with GNSS/CHAIN phase-screen or TEC spectra. I think this is a useful and nice idea, because one instrument alone cannot cover such a wide range of spatial scales. The comparison with Swarm FAC observations and Arase particle measurements also gives the paper a useful magnetosphere-ionosphere coupling context.
I think the strongest part of the paper is observational and methodological. The composite spectra, the comparison between radar Doppler speeds, radar target motions, and GPS phase-screen speeds, and the attempt to connect radar-scale turbulence with scintillation-producing structures are all interesting. These results can be valuable for the community.
However, in several places I feel there is a sharp jump from the observations to a broader physical picture. The data show interesting spectral similarities and velocity relations, but some of the physical interpretations are stated stronger than what the evidence can support at this stage. In particular, the claims about a universal or near-universal −8/3 spectrum, long-wavelength Farley–Buneman waves at about 270 m, and direct Alfvénic structuring of the E-region need either stronger support or more careful language.
Major comments
1. The physical meaning of the composite spectrum should be clarified.
ICEBEAR echo-clustering spectra and GNSS phase/TEC spectra are related, but they are not exactly the same observable. One is based on coherent scatter echo locations, while the other comes from integrated density structure and phase-screen assumptions. The authors should explain more clearly what the final composite spectrum physically represents. Is it a density-irregularity spectrum, an echo-clustering spectrum, a scintillation proxy, or a combined observational spectrum? This is important, because the later physical interpretation depends on treating the composite spectrum as one meaningful physical object.
2. The −8/3 spectral slope needs stronger uncertainty and robustness analysis.
The spectral slope near −8/3 is used several times to support the physical interpretation of the paper. Because of this, the authors should show more clearly how well constrained this slope actually is. Please report the slope statistics more explicitly, including mean or median, standard deviation, confidence intervals, and event-to-event variability. The standard deviation is particularly important. If the slope distribution is broad, then a most-probable value near −8/3 may not be enough to support a strong interpretation based on that number.
I think two robustness checks are needed here. First, the authors should test their spectral-estimation pipeline using synthetic data with known input slopes. For example, they could generate spectra with slopes such as −2.4, −2.6, −8/3, and −3.0, add realistic noise/sampling effects, and then apply the same processing pipeline. This would show whether the method can recover the true slope, or whether the processing tends to push the result toward a value close to −8/3.
Second, the authors should report what slope is obtained with less processing. For example, what are the slopes from radar-only spectra, GNSS-only spectra, minimally smoothed spectra, and spectra closer to a raw FFT estimate? How much does the slope change after smoothing, normalization, truncation, splicing, binning, fitting-range selection, and automatic break-point detection?
These processing steps can reduce noise and make the spectra cleaner, but they can also introduce method-dependent bias or change the apparent slope and break points. If the −8/3 slope is a robust physical result, it should remain visible, within uncertainty, across reasonable levels of processing. Since the physical interpretation relies strongly on this value, this analysis is needed before making a strong claim about universality or kinetic-Alfvén-like scaling.
3. The 270 m Farley–Buneman interpretation is suggestive, but too strong as currently written.
The comparison between GPS phase-screen speed, radar Doppler speed, and ICEBEAR target motion is one of the most interesting parts of the paper. However, the conclusion that the ~270 m Fresnel-scale structures are FB waves should be written more carefully. The argument depends strongly on interpreting the GPS phase-screen speed as comparable to the radar Doppler speed and close to the ion-acoustic speed, while the target motion reflects a faster E×B/source-region motion.
The assumptions in this velocity comparison should be made more explicit. For example, how sensitive is the GPS-derived speed to scan geometry, anisotropy, pierce-point motion, layer thickness, and propagation direction? Since standard linear FB growth at 270 m is expected to be weak, the authors should also discuss other possible explanations more carefully, such as GDI, mixed GDI/FB processes, nonlinear coupling, or selection effects. If stronger support cannot be provided, the result should be phrased as “consistent with long-wavelength FB-like structures” rather than as a firm identification.
4. The Alfvénic-driver interpretation should be toned down or better supported.
The Swarm FAC comparison and impedance analysis are valuable, and they support an Alfvénic connection. However, similar spectral slopes do not by themselves prove that Alfvén waves directly structure the E-region turbulence down to all observed scales. The manuscript should avoid language implying a fully demonstrated causal chain from magnetospheric Alfvénic structure to the full E-region turbulent spectrum, unless more quantitative evidence is added.
A safer interpretation is that the observations are consistent with Alfvénic structuring and MI coupling, but do not yet prove direct scale-by-scale transfer.
5. Event-selection effects should be discussed more clearly.
The GNSS cases appear to be selected because they show clear scintillation or amplitude fluctuations. This is reasonable, but it may bias the sample toward Fresnel-scale structures and strong events. Since the 200–300 m knee is central to the paper, the authors should explain how the events were selected, how many candidate events were excluded, and whether radar-active but GNSS-quiet or weak-scintillation cases show similar spectra.
6. The discussion should stay closer to what is demonstrated.
The broader discussion includes interesting ideas about Alfvén-wave energy extraction, impedance matching, preferred auroral altitude, polar-cap potential saturation, self-organized criticality, and the companion RG interpretation. These may be useful future directions, but they are not demonstrated by this paper. The manuscript would be stronger if these parts were shortened or clearly marked as possible implications.
Minor comments
Please soften phrases such as “only reasonable explanation.” The proposed interpretation may be the most plausible one, but other mechanisms should not be ruled out too quickly.
Terms such as “universal,” “continuous scale-invariant cascade,” “preserves the magnetospheric driver,” and “directly structures” should be used more carefully.
The thin-layer phase-screen assumption should be mentioned more clearly in the main text, not only in the appendix.
The automatic slope and break-point detection method should be described more clearly, since the spectral index results depend strongly on it.
Please fix typos, formatting issues, and incomplete references, including the “?” placeholder in the discussion.
Overall assessment
This is a valuable observational paper with a nice methodological novelty. The composite radar–GNSS spectrum can be a useful contribution to auroral turbulence and space-weather studies. However, the manuscript should be more careful not to overclaim physical mechanisms based on limited conjunctions, spectral similarity, and fitted slopes. The main revisions should focus on clarifying the physical meaning of the composite spectrum, quantifying the robustness of the −8/3 slope, supporting or softening the 270 m FB interpretation, addressing selection bias, and reducing the strongest causal language about Alfvénic structuring.