the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 02 Oct 2025
Storm-Time Asymmetries at Magnetic Conjugate Points: A Distribution-Aware Benchmark for GNSS
Abstract. Geomagnetic storms disrupt the Global Navigation Satellite System (GNSS) and transionospheric links through rapid asymmetric ionospheric variability. In this study, three widely used empirical models (IRI-2016, IRI-Plas, and NeQuick2) were used against GNSS-derived Total Electron Content (TEC) at two magnetic conjugate pairs (mid- and low-latitude) during the geomagnetic storm of August 25–27, 2018. Rather than assessing storm-time predictability, these models were employed as quiet-time reference baselines to quantify storm-time deviations and hemispheric asymmetry. Model performance was evaluated using the Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and distribution-aware Kullback–Leibler divergence (KLD). This study introduces a novel conjugate-point validation framework augmented by KLD that uniquely captures both magnitude errors and structural distributional mismatches between hemispheres. This is a critical aspect of GNSS reliability that is overlooked by conventional metrics. The results indicate a phase-dependent performance: all models exhibit degradation during the main phase, with the largest errors and structural mismatches occurring at the equator. KLD reveals distributional distortions (variance, skewness, tails) that MAE and RMSE cannot, particularly at the storm onset. NeQuick2 demonstrates superior performance only during the recovery phase, which is consistent with its solar-flux-driven parameterization but limited topside representation. By integrating a conjugate-point framework with distribution-aware validation, this study elucidates where empirical baselines fail under storm conditions, and why hemispheric responses diverge. This approach clarifies the model limitations relevant to GNSS reliability and motivates the development of hybrid data-assimilative schemes that incorporate dynamic drivers while being evaluated with both magnitude- and structure-sensitive metrics.
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Status: final response (author comments only)
- RC1: 'Comment on egusphere-2025-4594', Anonymous Referee #1, 17 Oct 2025
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RC2: 'Comment on egusphere-2025-4594', Anonymous Referee #2, 18 Nov 2025
The study uses empirical models (IRI, NEQuick etc) as baseline to compare TEC changes during the geomagnetic storm of 25-27 August 2018 at two pairs of mid and low latitude stations across the two hemispheres. The authors claim that the station pairs are conjugate, and rightly emphasize the need to investigate the hemispheric asymmetry from magnetic conjugate points. They evaluated the model performance was using the Mean Absolute Error (MAE), Root Mean Square Error (RMSE) Kullback–Leibler divergence, but insisted that the aim is not to evaluate the models but develop a “framework” for studying hemispheric asymmetry using the models as baseline. The idea was to develop a “distribution aware framework” by using Kullback–Leibler divergence, since according to the authors, the ionospheric variability during storm time is similar to the variability of the communication channels where KLD is usually employed. The methodology is not validated or justified properly, and the findings of the study are vague, since no concrete conclusions except the inability of the models to match the storm time changes is highlighted.
The manuscript has several serious short comings. First the methodology is not yet proven, and therefore requires very strong justification and validation. This was missing, since all the literature justifying the method of KDL in the introduction were fake (AI generated?), in a sense that these previous studies, which were cited were not directly related to the context or the methodology employed (described in detail below). Second, the use of the empirical models as baseline for the stations concerned is not justified by any method. It is well established that the empirical models like IRI don’t properly represent even the quiet time TEC variation in the low latitude, due to the inherent variability. Therefore, estimating how the storm time TEC over a station differed from the model TEC may not represent the actual storm time divergence for that station. Finally, the discussion about the advantage of the new framework, and the speculation about the physical drivers are without any evidence. Therefore, even though the approach may be novel, the justification and validation for the implementation is weak. The conclusions do not provide any new insight, as expected from a new approach. Therefore, the manuscript cannot be accepted for publication at the current state.
The detail comments are given below.
How did the authors decide that the two station pairs are magnetically conjugate? Needs elaboration. In the African sector the magnetic field has very complex declination (opposite in the two hemispheres), which makes it difficult to ensure that the two locations are magnetically conjugate.
The 30⁰ elevation is not suitable in low latitude as multipath effects can be very high.
Line 46-47: The “distribution-aware metrics” attributed to Chou et al., 2023 and Peng et al., 2024
Whereas these two papers did not discuss anything related to distribution aware metrics.
Adolfs et al. (2022) has no reference to Kullback–Leibler Divergence method as indicated in line no 101-103.
Similarly, Bojilova et al., 2024; Li et al., 2024 does n’t refer to distribution aware validation.
Line 50: “disturbance dynamo currents” if this reference is to the well known disturbance dynamo electric field, then DDEF was proposed by Blanc and Richmond, 1980 and not by Lee et al., 2025.
Most references make no sense to the reviewer since the attributed link to the text doesn’t exist.
This raises the question whether the introduction was written with the help of AI tools, which are known to create such false references.
In some key points, in the introduction, the references are wrongly attributed. Example is the bridging the gap between space weather science and wireless communication? No such connection was available in the cited literature.
Again for the “validation framework”- Did these previous works made such comments? As far as the reviewer could read these, he could not find the such comments in these articles. The referred papers mostly dealt with validation in ML approach.
Line 115-116: “...as both ionospheric TEC 115 variability and wireless channel fluctuations exhibit similar distribution-sensitive error characteristics”.
Is there any study which report this similarity? Or is it just assumption of the authors? For justifying the use of KLD, the authors have to mathematically show that these are similar in nature. Otherwise, it is just a speculation.
Line no : 123-126- “…the role of empirical ionospheric models in storm-time contexts, not as predictive tools for disturbed conditions, but as reference baselines whose limitations, when properly characterized, provide critical insights into GNSS reliability and wireless system vulnerability”
How the limitation of the empirical models can provide insight into GNSS reliability and wireless system vulnerability? Elaborate.
Are you suggesting GNSS systems uses these models? As per existing system they don’t.
As the reviewer can understand, the using the model as reference baseline is necessitated by the absence of such quiet time base line with the authors for the stations under study. But since the models actually doesn’t represent the quiet time values very well (numerous reports of IRI short comings, particularly at low latitudes during quiet time are published), this approach is not valid. Or atleast the authors must show that the IRI model represent the quiet time base line for the stations well enough to justify their use. What the reviewer wonders is-why the authors just don’t use the quiet time base line TEC for the stations which can be the monthly mean, and can be calculated very easily.
Line 191-193 : These standard versions (“IRI”) are the most widely implemented in operational GNSS receivers and communication systems for real-time error correction.
The reviewer is not aware that the IRI is actually used for error correction in real time GNSS systems. Is there any reference, where the authors can point to prove this point?
Line 250-252. The supplementary Figures and Table S2 are missing in this document and therefore, it is not possible to verify the author’s claim. Consider this as serious lapse.
Line 258: which theoretical model anticipate symmetry? Provide reference.
Line 263: “Beyond its geophysical importance, this framework elucidates the mechanisms by
which ionospheric storms impair Global Navigation Satellite System (GNSS)..”
Which framework? It is a bit confusion as what a framework is in this context.
If the framework refers to the use of the conjugate stations, then very little use of the conjugacy was made to derive mechanism. For example, conclusions section has not highlighted any mechanism.
Line 266: “The theoretical expectation of both coupling and asymmetry directly…”
The reviewer is really confused. Only in previous paragraph, the authors said that theoretical models anticipate symmetry? Line no 258.
Line 295:” This underscore two critical aspects: (i) even moderately driven storms with sustained southward Interplanetary Magnetic Field (IMF) Bz can induce strong interhemispheric ionospheric coupling ..”
The authors are yet to show any results (plots of TEC) but already reached a conclusion, how?
Also interhemispheric coupling was not discussed at all.
Line 425: “This asymmetry cannot be attributed solely to model deficiencies; it reflects genuine geophysical influences, including solar illumination…”
How did the authors reach this conclusion? The deficiency of the models in low latitude is well established. Since the models don’t represent the baseline anyway, is it possible to infer geophysical influence? Please plot the model baseline to show that the asymmetry is not inherent in the model.
Please elaborate how the changes are attributed to different drivers like solar illumination, since no analysis of the solar flux condition or contribution was estimated. Discuss how different geophysical drivers like the electric field, winds or solar insolation affect the hemispheric variation.
Line 492:” These findings collectively highlight the imperative for the development of hybrid or data-assimilative models that integrate solar-wind coupling, E×B drifts (Fejer, 2002), and variations in thermospheric composition”
Again, the reviewer is at loss, how such a conclusion was reached, since nothing related to solar wind or plasma drift was discussed, analysed or estimated in this study. Also indicate how the IRI is to assimilate these data since others models which does that are already available.
While the authors repeatedly insisted that the theme of the study was not to assess the performance of the model, the first conclusion (line no 505 ) “The analysis of the storm from August 25 to 27, 2018, indicated that the performance of the models was significantly contingent upon the storm phase; all models exhibited degradation during the main phase, with NeQuick2 demonstrating superior performance during the recovery phase”
Line 512: “The Kullback-Leibler Divergence (KLD) effectively identified structural discrepancies,..”
Please point out these deficiencies in conclusion.
Line 524: “The findings indicate that empirical models should be considered as reference benchmarks rather than predictors”
The study uses the empirical models as reference baseline and does some analysis with storm time observations which, as expected show major differences. The authors attribute the differences to physical drivers without showing any evidence that the differences are not due to the model short comings as baseline. What is the justification that the models should be used as reference baseline? Were they compared to the actual baseline data? Do observations not count for something? If we can use the model, why have observations at all?
Authors reach the obvious conclusion that models should not be used as predictor for storm time observations, which is already well-accepted in the community.
Citation: https://doi.org/10.5194/egusphere-2025-4594-RC2
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The paper evaluates three empirical ionospheric models (IRI-2016, IRI-Plas, NeQuick2) during a geomagnetic storm. Combining magnetic conjugate-point analysis with a distribution-aware metric (Kullback–Leibler Divergence, KLD) is useful, though not entirely novel. The approach allows the authors to quantify magnitude errors (via MAE and RMSE) and reveal structural differences in TEC distributions between hemispheres. However, the manuscript’s contribution is not yet significant. I recommend the following revisions:
The authors utilize IRI-2016. However, given that the IRI model is continuously improved, the IRI-2020 version has been available for some years. Since IRI-2020 incorporates significant updates, it would be more worthwhile and relevant to investigate this improved version to understand if its advancements mitigate the storm-time discrepancies your framework so effectively reveals.
One significant point is the LT confounding factor. The authors correctly note (lines 273-277, 433-439) that conjugate points do not share the same Local Time at a given Universal Time. Since TEC is heavily influenced by solar illumination (i.e., local time), a portion of the observed "hemispheric asymmetry" could simply be a diurnal effect. While the authors state this will be addressed in future work, the current study's conclusions about hemispheric asymmetry would be significantly stronger if this factor had been controlled for by using LT-aligned data (this could be an important scientific improvement).
The analysis is based on a single storm event. The authors explicitly state that future work will expand to a statistical ensemble of storms (lines 530-533), which is necessary to establish the generalizability of the findings across different seasons and solar cycle conditions. Doing this in the present manuscript (especially since there is no major hinderance to doing so) could also add more value to the manuscript.
The IRI model includes a storm-time option, while NeQuick does not. There doesn't seem to be a justification for using the NeQuick for such storm-time study. The authors should clarify the model settings used and justify applying NeQuick for storm-time analysis.