the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 30 Oct 2025
Estimation of Doppler Velocity from Incoherent Scatter Spectra Using Context-Aware Transformers
Abstract. We present a context-aware transformer model for estimating Doppler velocity from incoherent scatter radar (ISR) spectra. The model is based on the standard transformer encoder with adaptations from the Vision Transformer. Trained entirely on theoretical spectra, the AI model generalizes well for Arecibo ISR data and outperforms the traditional fitting methods significantly. Simulations show that the velocity error of the conventional least-squares fitting (LSF) is 1.5 to 3.5 times that of the AI model using 5 input heights. An inference from the AI model is approximately 100 times faster than the LSF method and requires minimal hardware, making it practical for large-scale or real-time processing. The AI approach applies to all situations where the spectrum can be parameterized.
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Status: final response (author comments only)
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RC1: 'Comment on egusphere-2025-5022', Anonymous Referee #1, 01 Dec 2025
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AC1: 'Reply on RC1', Qihou Zhou, 12 Dec 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-5022/egusphere-2025-5022-AC1-supplement.pdf
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AC1: 'Reply on RC1', Qihou Zhou, 12 Dec 2025
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RC2: 'Comment on egusphere-2025-5022', Anonymous Referee #2, 05 Dec 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-5022/egusphere-2025-5022-RC2-supplement.pdf
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AC2: 'Reply on RC2', Qihou Zhou, 12 Dec 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-5022/egusphere-2025-5022-AC2-supplement.pdf
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AC2: 'Reply on RC2', Qihou Zhou, 12 Dec 2025
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- 1
The manuscript reports results of line-of-sight plasma velocity fits to Arecibo ISR data using artificial intelligence (AI), namely context-aware transformers. The manuscript seems to be continuation to a series of papers by the same authors [1,2,3], in which they apply different data analysis techniques to archived coded long pulse (CLP) data from the Arecibo radar. The results suggest that AI may produce high-quality results in ISR data analysis.
While the idea to replace the traditional least-square fitting techniques with computationally less expensive (after the expensive training has been done) AI techniques is novel and the results look promising in general, I have several critical comments about the text and interpretation of the results.
1. The manuscript lacks critical references and fails to explain key principles of the AI model. If the idea is to introduce the AI techniques to the ISR community, skipping most of the key information "for brevity" may not be the best choice. It is understandable that Section 3.1, which describes the AI architecture, is full of field-specific jargon, but the terminology should be explained to the reader in such a level that reading the text is possible also for a non-expert of the field without reading all the references, and references to the key concepts should be given for readers who are interested in more details.
2. The actual scientific target of the measurements considered remains unclear. The authors first give a few very general motivations for measuring the Doppler velocities (without references). The AI model, which solves only for plasma velocities, is then compared with a least-squares fitting technique, which fits also several other parameters. Is there some specific application, for which the velocities alone are important? Would it be possible to use the AI model to fit the same parameters that are fitted with the least-squares solver? On line 300 the authors finally claim that focus of this study is around 110 km altitude. What exactly is the focus and why not to mention it in the abstract and in the introduction?
3. Least-square fits contain several tunable parameters that may greatly affect quality of the results, but these are not considered at all. In particular, stopping criteria for the iterations and initial values of the fitted parameters may affect both standard deviation and bias of the results. These should be carefully evaluated when comparisons between the AI model and the least-squares fits are performed.
4. Computational requirements are not discussed at all until the Conclusions section, where the authors claim that "Velocity inference is roughly 100 times faster than the fitting method and requires significantly fewer computational resources.". This may be true, but some key figures about computational resources needed for both training the model and the final velocity inference should be given. Also the training part is important for potential users of the technique, because it seems that one may need to train the model for each radar and radar operation mode separately.Â
5. The Arecibo radar collapsed a few years ago, but there are several other incoherent scatter radars in the world. Re-analysis of the archived Arecibo data is indeed valuable, but the authors could also comment if their technique might be usable for data from other radars that have considerably lower SNR and operate in completely different geophysical environments. In particular, other radars may observe much larger velocities and the users are typically interested also in electron densities and electron and ion temperatures, not just plasma velocities. At very end of the conclusions the authors claim, without any justification, that the model can be applied more broadly, but the very different noise levels and very much larger line-of-sight velocities observed with many other ISRs are not discussed at all.Â
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Detailed comments:
Lines 22-23: "particularly during disturbed conditions."
Does this mean that the radars are more reliable than other instruments during disturbed conditions?
Line 25-26: References to studies where these measurements are valuable would be useful.
Line 28: To my understanding, the moment and autocorrelation methods are not commonly used for ISR data analysis, because computers are powerful enough for the least-squares fits and the users are typically interested in many other plasma parameters as well. Please correct me if I am wrong.Â
Lines 33-34: "Their easy implementations and computational efficiency make them a popular first choice."
Again, is this still true for IS radars nowadays?
Lines 39-40: "Unlike traditional methods,..."
Does this refer to some traditional machine learning methods, or to the traditional radar data analysis methods?
Line 59: Please give a reference to the coded long pulse technique.
Line 64: "...with the traditional curve fitting method."
Please explain what is "the traditional curve fitting method", and give a reference.
Equation (1): Shape of this profile seems to affect the final results, because the context-aware AI model learns this profile shape. Is there some physical justification for the selected function?
Lines 85-86: "context-aware" and "context-unaware" are here used without explaining the terms first.
Lines 93-94: Please give references to the "broader definitions".
Section 2: It would be useful to show some examples of the synthetic IS spectra with different noise levels.Â
Sections 3.1, 3.2 and 3.3: Please explain the AI terminology so that also readers who are not familiar with it can follow the description at least superficially, and give sufficient references. I will not list every single point separately in these comments.Â
Lines 124-125: "In transformer architectures such as BERT or ViT (Devlin et al. 2019; Dosovitskiy et al. 2020)."
This sentence seems to be completely detached from the surrounding text.
Line 199: "...context-unaware model is trained on standalone 101-point spectra with artificial noise..."
Is this noise somehow different from the noise added to the 5x101 input of the context-aware model?
Lines 208-217 & Figure 2. I do not understand what LSF-ideal and LSF-realistic mean here and how the comparison is done. The contours in Figure 2 are as function of bandwidth and noise std, but then the authors claim that there was no added noise (noise std=0?) in the LSF-ideal case. Please explain what happens in the comparison.Â
Lines 234-235: "...frequently used moment method..."
Please provide references that demonstrate the frequent use of the moment method in ISR data analysis.
Lines 243-244: Is the bias in the LSF results possibly affected by the initial parameter values? One might expect this kind of bias profile if the iteration starts from zero velocity and tends to stop a bit too early.
Lines 244-246: "The LSF and moment methods underestimate the true velocity for the same reason that the mean velocity tends to zero in the absence of noise."
I do not understand this sentence. What is "the same reason"?
Lines 248-249: Does the LSF standard deviation depend also on stopping criteria of the iteration? If the criteria are too loose, the iteration might stop at random locations around the true minimum of the cost function, increasing the noise.
Figure 3, panel c: please change the colors, especially yellow is almost invisible.
Lines 279-280: "For a slowly varying quantity, the standard deviation of the second-order difference of independent samples is √6 times of the random error, as measured by the standard deviation."
Please give a reference.
Lines 294-296: Is it possible that the fluctuations are true temporal variations in the wind field?
Lines 299-300: "In any event, the AI error is still 30% smaller than the LSF method around 110 km, which is the focus of the current study"
What exactly is the focus of the current study, and why is this mentioned only on line 300?
Caption of Figure 5: (divided by 20) -> (divided by 40)?
Conclusions: The conclusions should summarize the results and they should preferrably be understandable without reading the whole manuscript. Neither of these conditions is fulfilled in this case. The contents of the first paragraph would better fit to the preceding sections, and the discussion about computing resources should be expanded there.Â
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[1] Li, Y., and Zhou, Q.: Measurements of F1-region ionosphere state variables at Arecibo through
quasi height-independent exhaustive fittings of the incoherent scatter ion-line spectra, J.
Geophys. Res. Space Phys., 129(11), e2024JA032620, 2024.
[2] Li, Y., and Zhou, Q.: Accurate spectral fitting in the upper F-region using the randomly coded data
of the Arecibo 430 MHz radar, J. Geophys. Res. Space Phys., 130, e2025JA033877,
https://doi.org/10.1029/2025JA033877, 2025a.
[3] Zhou, Q., Li, Y., and Gong, Y.: Variance estimations in the presence of intermittent interferences
and their applications to incoherent scatter radar signal processing, Atmos. Meas. Tech., 17(14),
4197–4209, https://doi.org/10.5194/amt-17-4197-2024, 2024.