the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Oct 2025
Harmonic Content of Ap Index
Abstract. Zajtsev et al. (1993) applied fast Fourier transform (FFT) (Cooley et al., 1969) of the magnetic field components measured by a particular magnetic observatory. They reported that some patterns could be recognized in the contour plots of Fourier coefficients versus time for different phases of sub-storm evolution. Similar techniques can be applied to the planetary geomagnetic indices Ap and Dst. The spectral content changes prior to the growth phase of the sub-storm. The higher frequency coefficients, the larger the power spectrum is shifted upwards. This feature can serve as a precursor, if spotted. We present an analysis of the February 2001, 2003, and 2017 time intervals. The technique can be potentially used as a forecast tool for predicting geomagnetic activity.
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Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Preprint
(16401 KB)
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(16401 KB) - Metadata XML
- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2025-4629', Anonymous Referee #1, 28 Nov 2025
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AC1: 'Reply on RC1', Evgeny Romashets, 29 Nov 2025
We thank the Referee for compliments and suggestions.Spectral content of the geomagnetic indices consists of that 1. of solar activity, frequency of appearance and decay of Active regions and associated events like flares, coronal mass ejections, 2. of interplanetary magnetic field and solar wind irregularities, like sector and sub-sectors of interplanetary magnetic field with complicated structure of heliospheric current sheet and heliospheric plasma sheet, as well as interfaces between fast and slow solar wind flows, and 3. of magnetospheric and ionospheric response to geo-effective interplanetary disturbances arriving to Earth's orbit. These include of course frequencies of Alfven waves in ionospheric and magnetospheric plasma, but also the rate of convection, as well as of compression/expansion of lobe part of the magnetosphere and of ring current. With the development of reliable Fourier analysis enabling reconstruction of the geomagnetic indices, we will be able in future to identify the physical cause of the disturbances by analyzing the frequency content.Thank you.AuthorsCitation: https://doi.org/
10.5194/egusphere-2025-4629-AC1 -
RC3: 'Reply on AC1', Anonymous Referee #1, 07 Dec 2025
It's all ok, what the authors mention in their reply. Of course in the future they want to apply their method to real problems, this is normal and no news. Otherwise ny mehtod makes no sense at all. However, here we are takung about amanuscript in advance of its publication, and so far it is incomplete. it presents a method but does not apply it nor say what will be expected when applied to observations (which is intended to be applied!).
From a complete publication in some physics journal I do not expect the presentation of a mathematical or numerical programmwe but an ooutlook what it willm be good for. In the Reply the authors mention a numberr of points. These should be, maybe even a little bit polished and expanded in publicable form but nevertheless included into a final section either under the title Oulook or Prospects or whatever the authors feel best (not Results of course because no applicationn has been given). I simpy expect that those points which are in very rough form contained in the Author's Reply become contained in that section. Otherwise the paper remains incomplete. The Authors have left the house but did not close the door.
I do not demand anything impossible here. Just the reasonable completion of the text.
My personal procedure reading a paper is after the title and a glace at the Abstract (which in most cases does not tell much) to look for the final Section on the Concusions/Outlook/Application to become informed where and why the ppaper has been written. This is missing here.
But
Citation: https://doi.org/10.5194/egusphere-2025-4629-RC3 -
AC3: 'Reply on RC3', Evgeny Romashets, 08 Dec 2025
Dear Referee,Thank you for your comments and suggestions.We will add a description of the computer program used. The points mentioned in the Reply will be polished. The Abstract and Conclusions will be rewritten accordingly.Sincerely,Authors.Citation: https://doi.org/
10.5194/egusphere-2025-4629-AC3
-
AC3: 'Reply on RC3', Evgeny Romashets, 08 Dec 2025
-
RC3: 'Reply on AC1', Anonymous Referee #1, 07 Dec 2025
-
AC1: 'Reply on RC1', Evgeny Romashets, 29 Nov 2025
-
RC2: 'Comment on egusphere-2025-4629', Anonymous Referee #2, 06 Dec 2025
This manuscript applies Fast Fourier Transform (FFT) techniques to analyze the geomagnetic Ap index. The authors examine amplitude and phase coefficients over three selected time intervals. While the topic is potentially interesting, several major issues must be addressed before the work can be considered further.
- The abstract claims that the study analyzes the Dst index, but the manuscript contains no such analysis. It also states that the spectral content prior to the substorm growth phase is examined, yet no analysis relating to the substorm growth phase appears in the paper.
- A substantial portion of Section 2 simply reproduces standard FFT formulations. Since these are well-established and widely known, it is unnecessary to present them in such detail. Moreover, the expressions for a_nl and b_nl are mathematically equivalent to the formulation in terms of C_{nl} and ϕ_nl. Because only C_{nl} and ϕ_nl.are used in the subsequent analysis, the extensive derivations of unused quantities are redundant.
- Line 101. The statement about “linear interpolation” is unclear. It is not clear what type interpolation has been performed, how the interpolation modifies the sampling rate, or how the Nyquist frequency is affected. This requires explicit clarification.
- Line 114-115. “In other words, all coefficients and phases are calculated in (3)–(5) for every three-hour interval”. It is unclear whether a moving time-window is used, what the total window length is (e.g., 27 days?), and how the three-hour stepping is implemented. This should be explained precisely.
- Figure 1, The inverse FFT reconstruction of Ap is a routine check applicable to any FFT analysis. It does not provide new insight into either the method or the dataset. This figure should be removed or moved to supplementary material.
- Standard practice in space-physics FFT analysis is to express coefficients as functions of frequency ω (or period), not as a function of index n. The physical meaning of n in Figures 2–6 is not immediately obvious, and readers cannot interpret the results without knowing the corresponding frequencies or periods.
- It is very hard to interpreted Fig.2, Fig.3. If the goal is to relate coefficient variations to substorms or magnetic storms, the relevant geomagnetic indices (e.g., AL/AE for substorms or Dst for storms) should be plotted alongside the spectral coefficients on the same timescale. Without this, interpretation is very limited.
- Fig.5 and Fig.6. The manuscript does not justify why phase is normalized by n, nor does it explain the near-linear trend seen in the figures. This raises concerns that the behavior might be an artifact of the analysis method rather than a physical signal.
- A major issue is the absence of contextual background on the Ap/Kp indices. Ap is the linearized form of Kp and provides a widely used measure of magnetospheric convection strength (e.g., Thomsen 2004; Rowland & Wygant 1998; Wang et al. 2025). Large-scale magnetospheric convection is driven by dayside and nightside magnetic reconnection (e.g., Siscoe & Huang 1985; Cowley & Lockwood 1992; Dai et al. 2024; Zhu et al. 2024, 2025) and penetrates deep into the inner magnetosphere (e.g., Wygant et al. 1998; Dai et al. 2015; Thaller et al. 2015).
These previous studies should be discussed to establish the physical context and significance of analyzing the Ap/Kp indices.
Thomsen, M. F. (2004). Why Kp is such a good measure of magnetospheric convection. Space Weather, 2(11), S11004. https://doi.org/10.1029/2004SW000089
Rowland, D. E., & Wygant, J. R. (1998). Dependence of the large‐scale, inner magnetospheric electric field on geomagnetic activity. Journal of Geophysical Research, 103(A7), 14959–14964. https://doi.org/10.1029/97JA03524
Wang, X., et al. (2025). Inner magnetospheric convection electric fields and corresponding geomagnetic indices during high-speed solar wind streams. Space Weather, 23, e2025SW004548. https://doi.org/10.1029/2025SW004548
Cowley, S. W. H., & Lockwood, M. (1992). Excitation and decay of solar-wind–driven flows in the magnetosphere–ionosphere system. Annales Geophysicae, 10(1–2), 103–115.
Dai, L., et al. (2015). Near-Earth injection of MeV electrons associated with intense dipolarization electric fields: Van Allen Probes observations. Geophysical Research Letters, 42(15), 6170–6179. https://doi.org/10.1002/2015GL064955
Dai, L., et al. (2024). Global-scale magnetosphere convection driven by dayside magnetic reconnection. Nature Communications, 15(1), 639. https://doi.org/10.1038/s41467-024-44992-y
Siscoe, G. L., & Huang, T. S. (1985). Polar cap inflation and deflation. Journal of Geophysical Research, 90(A1), 543–547. https://doi.org/10.1029/JA090iA01p00543
Thaller, et al. (2015). Van Allen Probes investigation of the large-scale duskward electric field and its role in ring current formation and plasmasphere erosion in the 1 June 2013 storm. Journal of Geophysical Research: Space Physics, 120(6), 4531–4543. https://doi.org/10.1002/2014JA020875
Wygant, J., et al. (1998). Experimental evidence on the role of the large spatial-scale electric field in creating the ring current. Journal of Geophysical Research, 103(A12), 29527–29544. https://doi.org/10.1029/98JA01436
Zhu, M., et al. (2025). Response of magnetospheric convection to the southward turning of the IMF in fast and slow solar wind streams. Journal of Geophysical Research: Space Physics, 130, e2025JA034529. https://doi.org/10.1029/2025JA034529
Zhu, M.,et al. (2024). The influence of ionospheric conductance on magnetospheric convection during southward IMF. Journal of Geophysical Research: Space Physics, 129(9), e2024JA032607. https://doi.org/10.1029/2024JA032607
Citation: https://doi.org/10.5194/egusphere-2025-4629-RC2 -
AC2: 'Reply on RC2', Evgeny Romashets, 07 Dec 2025
Dear Referee,Thank you for the corrections and suggestions.We agree with all of them and will implement the corresponding changes.In the abstract, for example, we will summarize what actually was done but not what will be done and not what we thought about before the work started.Sincerely,AuthorsCitation: https://doi.org/
10.5194/egusphere-2025-4629-AC2
Peer review completion
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-4629', Anonymous Referee #1, 28 Nov 2025
This is kind of a new Fourier harmonic analysis of a aprticular Ap event which b itself is certainly interesting. As such it is a technical paper of how to analyse irreegularl distributed data to make them a continuum and represent it as a function which can be smoothl represented as a Fourir seires within the interval of observation.
This is all ok. There is nothing to against the method in as far as it is new or new in parts because Fourier analysis is, of course, an old methodology to analyse data. I have not gone into the literature to check whether similar mehtods have also been applied, but this is not important. The authors show that their representation works even in takeingg its inverse to reconstruct the data.
All that is ok. What is, however, missing, is the physical meaning, the insight gained by formally appling such an analysis. The paper is lacking that completely. It stops at an intermediate formal point. One may ask: and so what? What should one do with that? What is the result? Cleaning a road which nobody is using makes lilttle sense. The authors shuld absolutely add what the physical meaning of their method is even applied to the event they are using it. Without such an effort, result, information I cannot accept the paper .
Citation: https://doi.org/10.5194/egusphere-2025-4629-RC1 -
AC1: 'Reply on RC1', Evgeny Romashets, 29 Nov 2025
We thank the Referee for compliments and suggestions.Spectral content of the geomagnetic indices consists of that 1. of solar activity, frequency of appearance and decay of Active regions and associated events like flares, coronal mass ejections, 2. of interplanetary magnetic field and solar wind irregularities, like sector and sub-sectors of interplanetary magnetic field with complicated structure of heliospheric current sheet and heliospheric plasma sheet, as well as interfaces between fast and slow solar wind flows, and 3. of magnetospheric and ionospheric response to geo-effective interplanetary disturbances arriving to Earth's orbit. These include of course frequencies of Alfven waves in ionospheric and magnetospheric plasma, but also the rate of convection, as well as of compression/expansion of lobe part of the magnetosphere and of ring current. With the development of reliable Fourier analysis enabling reconstruction of the geomagnetic indices, we will be able in future to identify the physical cause of the disturbances by analyzing the frequency content.Thank you.AuthorsCitation: https://doi.org/
10.5194/egusphere-2025-4629-AC1 -
RC3: 'Reply on AC1', Anonymous Referee #1, 07 Dec 2025
It's all ok, what the authors mention in their reply. Of course in the future they want to apply their method to real problems, this is normal and no news. Otherwise ny mehtod makes no sense at all. However, here we are takung about amanuscript in advance of its publication, and so far it is incomplete. it presents a method but does not apply it nor say what will be expected when applied to observations (which is intended to be applied!).
From a complete publication in some physics journal I do not expect the presentation of a mathematical or numerical programmwe but an ooutlook what it willm be good for. In the Reply the authors mention a numberr of points. These should be, maybe even a little bit polished and expanded in publicable form but nevertheless included into a final section either under the title Oulook or Prospects or whatever the authors feel best (not Results of course because no applicationn has been given). I simpy expect that those points which are in very rough form contained in the Author's Reply become contained in that section. Otherwise the paper remains incomplete. The Authors have left the house but did not close the door.
I do not demand anything impossible here. Just the reasonable completion of the text.
My personal procedure reading a paper is after the title and a glace at the Abstract (which in most cases does not tell much) to look for the final Section on the Concusions/Outlook/Application to become informed where and why the ppaper has been written. This is missing here.
But
Citation: https://doi.org/10.5194/egusphere-2025-4629-RC3 -
AC3: 'Reply on RC3', Evgeny Romashets, 08 Dec 2025
Dear Referee,Thank you for your comments and suggestions.We will add a description of the computer program used. The points mentioned in the Reply will be polished. The Abstract and Conclusions will be rewritten accordingly.Sincerely,Authors.Citation: https://doi.org/
10.5194/egusphere-2025-4629-AC3
-
AC3: 'Reply on RC3', Evgeny Romashets, 08 Dec 2025
-
RC3: 'Reply on AC1', Anonymous Referee #1, 07 Dec 2025
-
AC1: 'Reply on RC1', Evgeny Romashets, 29 Nov 2025
-
RC2: 'Comment on egusphere-2025-4629', Anonymous Referee #2, 06 Dec 2025
This manuscript applies Fast Fourier Transform (FFT) techniques to analyze the geomagnetic Ap index. The authors examine amplitude and phase coefficients over three selected time intervals. While the topic is potentially interesting, several major issues must be addressed before the work can be considered further.
- The abstract claims that the study analyzes the Dst index, but the manuscript contains no such analysis. It also states that the spectral content prior to the substorm growth phase is examined, yet no analysis relating to the substorm growth phase appears in the paper.
- A substantial portion of Section 2 simply reproduces standard FFT formulations. Since these are well-established and widely known, it is unnecessary to present them in such detail. Moreover, the expressions for a_nl and b_nl are mathematically equivalent to the formulation in terms of C_{nl} and ϕ_nl. Because only C_{nl} and ϕ_nl.are used in the subsequent analysis, the extensive derivations of unused quantities are redundant.
- Line 101. The statement about “linear interpolation” is unclear. It is not clear what type interpolation has been performed, how the interpolation modifies the sampling rate, or how the Nyquist frequency is affected. This requires explicit clarification.
- Line 114-115. “In other words, all coefficients and phases are calculated in (3)–(5) for every three-hour interval”. It is unclear whether a moving time-window is used, what the total window length is (e.g., 27 days?), and how the three-hour stepping is implemented. This should be explained precisely.
- Figure 1, The inverse FFT reconstruction of Ap is a routine check applicable to any FFT analysis. It does not provide new insight into either the method or the dataset. This figure should be removed or moved to supplementary material.
- Standard practice in space-physics FFT analysis is to express coefficients as functions of frequency ω (or period), not as a function of index n. The physical meaning of n in Figures 2–6 is not immediately obvious, and readers cannot interpret the results without knowing the corresponding frequencies or periods.
- It is very hard to interpreted Fig.2, Fig.3. If the goal is to relate coefficient variations to substorms or magnetic storms, the relevant geomagnetic indices (e.g., AL/AE for substorms or Dst for storms) should be plotted alongside the spectral coefficients on the same timescale. Without this, interpretation is very limited.
- Fig.5 and Fig.6. The manuscript does not justify why phase is normalized by n, nor does it explain the near-linear trend seen in the figures. This raises concerns that the behavior might be an artifact of the analysis method rather than a physical signal.
- A major issue is the absence of contextual background on the Ap/Kp indices. Ap is the linearized form of Kp and provides a widely used measure of magnetospheric convection strength (e.g., Thomsen 2004; Rowland & Wygant 1998; Wang et al. 2025). Large-scale magnetospheric convection is driven by dayside and nightside magnetic reconnection (e.g., Siscoe & Huang 1985; Cowley & Lockwood 1992; Dai et al. 2024; Zhu et al. 2024, 2025) and penetrates deep into the inner magnetosphere (e.g., Wygant et al. 1998; Dai et al. 2015; Thaller et al. 2015).
These previous studies should be discussed to establish the physical context and significance of analyzing the Ap/Kp indices.
Thomsen, M. F. (2004). Why Kp is such a good measure of magnetospheric convection. Space Weather, 2(11), S11004. https://doi.org/10.1029/2004SW000089
Rowland, D. E., & Wygant, J. R. (1998). Dependence of the large‐scale, inner magnetospheric electric field on geomagnetic activity. Journal of Geophysical Research, 103(A7), 14959–14964. https://doi.org/10.1029/97JA03524
Wang, X., et al. (2025). Inner magnetospheric convection electric fields and corresponding geomagnetic indices during high-speed solar wind streams. Space Weather, 23, e2025SW004548. https://doi.org/10.1029/2025SW004548
Cowley, S. W. H., & Lockwood, M. (1992). Excitation and decay of solar-wind–driven flows in the magnetosphere–ionosphere system. Annales Geophysicae, 10(1–2), 103–115.
Dai, L., et al. (2015). Near-Earth injection of MeV electrons associated with intense dipolarization electric fields: Van Allen Probes observations. Geophysical Research Letters, 42(15), 6170–6179. https://doi.org/10.1002/2015GL064955
Dai, L., et al. (2024). Global-scale magnetosphere convection driven by dayside magnetic reconnection. Nature Communications, 15(1), 639. https://doi.org/10.1038/s41467-024-44992-y
Siscoe, G. L., & Huang, T. S. (1985). Polar cap inflation and deflation. Journal of Geophysical Research, 90(A1), 543–547. https://doi.org/10.1029/JA090iA01p00543
Thaller, et al. (2015). Van Allen Probes investigation of the large-scale duskward electric field and its role in ring current formation and plasmasphere erosion in the 1 June 2013 storm. Journal of Geophysical Research: Space Physics, 120(6), 4531–4543. https://doi.org/10.1002/2014JA020875
Wygant, J., et al. (1998). Experimental evidence on the role of the large spatial-scale electric field in creating the ring current. Journal of Geophysical Research, 103(A12), 29527–29544. https://doi.org/10.1029/98JA01436
Zhu, M., et al. (2025). Response of magnetospheric convection to the southward turning of the IMF in fast and slow solar wind streams. Journal of Geophysical Research: Space Physics, 130, e2025JA034529. https://doi.org/10.1029/2025JA034529
Zhu, M.,et al. (2024). The influence of ionospheric conductance on magnetospheric convection during southward IMF. Journal of Geophysical Research: Space Physics, 129(9), e2024JA032607. https://doi.org/10.1029/2024JA032607
Citation: https://doi.org/10.5194/egusphere-2025-4629-RC2 -
AC2: 'Reply on RC2', Evgeny Romashets, 07 Dec 2025
Dear Referee,Thank you for the corrections and suggestions.We agree with all of them and will implement the corresponding changes.In the abstract, for example, we will summarize what actually was done but not what will be done and not what we thought about before the work started.Sincerely,AuthorsCitation: https://doi.org/
10.5194/egusphere-2025-4629-AC2
Peer review completion
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Marek Vandas
Evgeny Romashets
Tasmina Imam
Tanvir Hasan
Pranab Majumder
Sanjay Karki
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(16401 KB) - Metadata XML
This is kind of a new Fourier harmonic analysis of a aprticular Ap event which b itself is certainly interesting. As such it is a technical paper of how to analyse irreegularl distributed data to make them a continuum and represent it as a function which can be smoothl represented as a Fourir seires within the interval of observation.
This is all ok. There is nothing to against the method in as far as it is new or new in parts because Fourier analysis is, of course, an old methodology to analyse data. I have not gone into the literature to check whether similar mehtods have also been applied, but this is not important. The authors show that their representation works even in takeingg its inverse to reconstruct the data.
All that is ok. What is, however, missing, is the physical meaning, the insight gained by formally appling such an analysis. The paper is lacking that completely. It stops at an intermediate formal point. One may ask: and so what? What should one do with that? What is the result? Cleaning a road which nobody is using makes lilttle sense. The authors shuld absolutely add what the physical meaning of their method is even applied to the event they are using it. Without such an effort, result, information I cannot accept the paper .