the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Apr 2023
F-region drift current distribution by X wave ionospheric heating
Abstract. We present a theoretical and numerical study of drift current model in the ionosphere by incorporating the ohmic heating model and the magnetohydrodynamic (MHD) momentum equation. Based on these equations, the ionospheric electron temperature and drift current are investigated. The results indicate that the maximum change of electron temperature ΔTe is about 570 K, and the ratio is ΔTe / Te ~48 %. The maximum drift current density is 8 × 10−10 A ⋅ m−2, and its surface integral is 5.76 A. Diamagnetic drift current is the main form of current. The low collision frequency between charged particles and neutral particles has little effect on the current, and the collision frequency of electrons and ions is independent of the drift current. The current density profile is a flow ring. We present the effective conductivity as a function of the angle between the geomagnetic field and the radio wave; the model explains why the radiation efficiency in Kotik's experiment was strongest when the X wave is heating along the magnetic dip angle.
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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.
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Preprint
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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.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2023-610', Anonymous Referee #1, 03 Jun 2023
- In the abstract, the authors mentioned the following statement which is not appropriate.
the model explains why the radiation efficiency in Kotik's experiment was strongest 15 when the X wave is heating along the magnetic dip angle.
You may revise the sentence as follow:
the model explains why the radiation efficiency was strongest when the X wave is heating along the magnetic dip angle as reported in recent observations by Kotik et al…..
- There are many grammatical mistakes and very long sentences that make it difficult for the reader to follow. As an example please lines 30-34 and many more examples to be find.
- Lines 44-46 have to be revised. This is not an appropriate way to promote your work. You may mention that your work is including more physics that was neglected in the previous studies.
- Another issue that is not discussed or addressed properly here is the work done by Mahmoudian and Kalaee, 2019.
This new study which is a continuation of previous work by Eliasson and Papadapoulos 2012, has shown that the VLF signal may not penetrate to the D-region as efficient as the ELF signal. I suggest that authors provide the explanation on ELF or VLF excitation during HF modulation (Beat wave) and try to provide a more general conclusion rather than just studying the excited diamagnetic current and its aspect angle dependency.
Study of ULF-VLF wave propagation in the near-Earth environment for earthquake prediction, Advances in Space Research, Volume 63, Issue 12, 2019,
- It is critical that authors include the geomagnetic angles for other latitudes such as mid latitude (Arecibo Observatory) or equatorial region (possible facility coming at Hicamarca Peru). The efficiency of HF pump heating at those latitudes and possible variation of excited diamagnetic current should be discussed. If the proposed model is not capable of simulating such condition this weakness should be admitted in the text.
Citation: https://doi.org/10.5194/egusphere-2023-610-RC1 -
AC3: 'Reply on RC1', yaung li, 24 Jul 2023
We are grateful to the reviewer for accepting and making time to review our manuscript. Next we respond to reviewer comments by point.
Reviewer:
In the abstract, the authors mentioned the following statement which is not appropriate.
There are many grammatical mistakes and very long sentences that make it difficult for the reader to follow. As an example please lines 30-34 and many more examples to be find.
Lines 44-46 have to be revised. This is not an appropriate way to promote your work. You may mention that your work is including more physics that was neglected in the previous studies.
Authors:
These comments are valuable and all these shall reflect in the upcoming review of the paper. Since this is my first paper, there are many grammatical and expression errors, I will fix them according to the comments in the subsequent revision.
Reviewer:
Another issue that is not discussed or addressed properly here is the work done by Mahmoudian and Kalaee, 2019.
This new study which is a continuation of previous work by Eliasson and Papadapoulos 2012, has shown that the VLF signal may not penetrate to the D-region as efficient as the ELF signal. I suggest that authors provide the explanation on ELF or VLF excitation during HF modulation (Beat wave) and try to provide a more general conclusion rather than just studying the excited diamagnetic current and its aspect angle dependency.
Authors:
The propagation issues raised by the reviewers are essential. The given literature discusses in detail the propagation of ULF-VLF wave propagation in the near-Earth environment, and we will include a reference to it in Introduction. However, the main focus of this paper is to discuss the currents generated by ionospheric heating and to analyze their influence. The propagation of the current-excited magneto-fluidic waves can be neglected because it is unnecessary.
Reviewer:
It is critical that authors include the geomagnetic angles for other latitudes such as mid latitude (Arecibo Observatory) or equatorial region (possible facility coming at Hicamarca Peru). The efficiency of HF pump heating at those latitudes and possible variation of excited diamagnetic current should be discussed. If the proposed model is not capable of simulating such condition this weakness should be admitted in the text.
Authors:
Our model can explore the influence of the geomagnetic angles for other latitudes; however, we do not specifically go into this issue in this paper because the available experiments focus on high latitudes.
Citation: https://doi.org/10.5194/egusphere-2023-610-AC3
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AC1: 'Comment on egusphere-2023-610', yaung li, 27 Jun 2023
We are grateful to the reviewer for accepting and making time to review our manuscript. Next we respond to reviewer comments by point.
Reviewer:
In the abstract, the authors mentioned the following statement which is not appropriate.
There are many grammatical mistakes and very long sentences that make it difficult for the reader to follow. As an example please lines 30-34 and many more examples to be find.
Lines 44-46 have to be revised. This is not an appropriate way to promote your work. You may mention that your work is including more physics that was neglected in the previous studies.
Authors:
These comments are valuable and all these shall reflect in the upcoming review of the paper. Since this is my first paper, there are many grammatical and expression errors, I will fix them according to the comments in the subsequent revision.
Reviewer:
Another issue that is not discussed or addressed properly here is the work done by Mahmoudian and Kalaee, 2019.
This new study which is a continuation of previous work by Eliasson and Papadapoulos 2012, has shown that the VLF signal may not penetrate to the D-region as efficient as the ELF signal. I suggest that authors provide the explanation on ELF or VLF excitation during HF modulation (Beat wave) and try to provide a more general conclusion rather than just studying the excited diamagnetic current and its aspect angle dependency.
Authors:
The propagation issues raised by the reviewers are essential. The given literature discusses in detail the propagation of ULF-VLF wave propagation in the near-Earth environment, and we will include a reference to it in Introduction. However, the main focus of this paper is to discuss the currents generated by ionospheric heating and to analyze their influence. The propagation of the current-excited magneto-fluidic waves can be neglected because it is unnecessary.
Reviewer:
It is critical that authors include the geomagnetic angles for other latitudes such as mid latitude (Arecibo Observatory) or equatorial region (possible facility coming at Hicamarca Peru). The efficiency of HF pump heating at those latitudes and possible variation of excited diamagnetic current should be discussed. If the proposed model is not capable of simulating such condition this weakness should be admitted in the text.
Authors:
Our model can explore the influence of the geomagnetic angles for other latitudes; however, we do not specifically go into this issue in this paper because the available experiments focus on high latitudes.
Citation: https://doi.org/10.5194/egusphere-2023-610-AC1 -
CC1: 'Comment on egusphere-2023-610', Alex Lee, 20 Jul 2023
I think author may add simulated results for other latitudes and make a comparison for them to enhance the practicality of this manuscript.
Citation: https://doi.org/10.5194/egusphere-2023-610-CC1 -
AC2: 'Reply on CC1', yaung li, 24 Jul 2023
We are grateful to the reviewer for accepting and making time to review our manuscript. In this paper, the computational focus concentrates on high latitudes, which is easier to verify on existing experimental facilities， such as HAARP or EISCAT. In addition, selecting a location allowed for a more in-depth discussion of the nature and distribution of the currents, such as (1) an analysis of the impact of collisions, and (2) the impact of the ground transmitter launch angle on the currents. Therefore, we believe that adding simulation locations may be slightly trivial. But we would be happy to devote some future work to this issue.
Citation: https://doi.org/10.5194/egusphere-2023-610-AC2
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AC2: 'Reply on CC1', yaung li, 24 Jul 2023
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RC2: 'Comment on egusphere-2023-610', Anonymous Referee #2, 09 Aug 2023
Review of "F-region drift current distribution by X wave ionospheric heating" by Li et al..
This paper is a theoretical and numerical study of drift current model in the ionosphere by incorporating the ohmic heating model and the MHD momentum equation. The authors found that the ionospheric currents are mainly driven by a diamagnetic drift effect due to the ionospheric heating. The intensity of the ionospheric currents tended to decrease with an increase of the propagation direction angle of X wave. The main reason is that the effective conductivity becomes small for the large propagation angle. This result is clear and interesting, and I recommend that this paper should be published for Ann. Geophys. journal after some minor revisions. The revision points are shown below.
1. Line 55: The authors assume that the magnetic field inclination is 90 degrees for the calculation of X-wave heating. However, the magnetic field line has an inclination that is different from 90 degrees except for the magnetic pole. The authors should explain the validity of this assumption in this paper.
2. Equation (9): Please replace ERP with one character. In this case, the reader may regard ERP as ExRxP.
3. Line 91: ...the electric force should be ...The electric force...
4. Lines 105-107: Please include the references for each model. Further, the authors should show the version of the IGRF model used in this study. Please spell out IGRF.
Citation: https://doi.org/10.5194/egusphere-2023-610-RC2 -
AC4: 'Reply on RC2', yaung li, 12 Aug 2023
We are grateful to the reviewer for making time to review our manuscript. The comments are valuable and helpful for revising and improving our paper, We have studied the comments carefully and have made corrections which we hope meet with approval. Below are your comments and our responses and modifications
This paper is a theoretical and numerical study of drift current model in the ionosphere by incorporating the ohmic heating model and the MHD momentum equation. The authors found that the ionospheric currents are mainly driven by a diamagnetic drift effect due to the ionospheric heating. The intensity of the ionospheric currents tended to decrease with an increase of the propagation direction angle of X wave. The main reason is that the effective conductivity becomes small for the large propagation angle. This result is clear and interesting, and I recommend that this paper should be published for Ann. Geophys. journal after some minor revisions. The revision points are shown below.
Re: Your acknowledgment of our work is an excellent incentive for us to keep going.
1. Line 55: The authors assume that the magnetic field inclination is 90 degrees for the calculation of X-wave heating. However, the magnetic field line has an inclination that is different from 90 degrees except for the magnetic pole. The authors should explain the validity of this assumption in this paper.
Re: There are two reasons why we assume a magnetic inclination angle of 90°.
First, the location we chose for our study is HAARP. A query reveals that the magnetic inclination of the place is 75°, which is relatively close to the magnetic inclination of the magnetic pole. Therefore, the magnetic inclination angle always defaults to 90° in previous studies, and this paper adopts the previous literature setting.
Second, it can be found that the current (or effective conductivity) depends mainly on the angle between the magnetic inclination and the launching angle; the effect of the initial value is not so significant. Therefore, to simplify the calculation, we simplify the magnetic inclination to 90 °
2. Equation (9): Please replace ERP with one character. In this case, the reader may regard ERP as ExRxP.
Re: ERP is the effective radiated power of the transmitter. To avoid ambiguity, we rewrite ERP in Eq. 9 as PER
3. Line 91: ...the electric force should be ...The electric force...
Re: Thank you for your comments on; we have made corrections in the manuscript.
4. Lines 105-107: Please include the references for each model. Further, the authors should show the version of the IGRF model used in this study. Please spell out IGRF.
Re: According to the comments, the section was rewritten as follows. “Background data were acquired at HAARP on 2 October 2011. The ionospheric and atmospheric background profiles are given by the International Reference Ionosphere (IRI-2016)(Bilitza et al., 2022) model and the neutral atmosphere model (MSIS)(Picone et al., 2002), as well as geomagnetic field data from the International Geomagnetic Reference Field(IGRF-11) model(Geomagnetism et al., 2010)”.
The references:
Bilitza, D., Pezzopane, M., Truhlik, V., Altadill, D., Reinisch, B. W., and Pignalberi, A.: The International Reference Ionosphere Model: A Review and Description of an Ionospheric Benchmark, Reviews of Geophysics, 60, e2022RG000792, https://doi.org/10.1029/2022RG000792, 2022.
Picone, J. M., Hedin, A. E., Drob, D. P., and Aikin, A. C.: NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues, Journal of Geophysical Research: Space Physics, 107, SIA 15-11-SIA 15-16, https://doi.org/10.1029/2002JA009430, 2002.
Geomagnetism, I. A. o., Aeronomy.: International Geomagnetic Reference Field: the eleventh generation, Geophysical Journal International, 183, 1216-1230, https://doi.org/10.1111/j.1365-246X.2010.04804.x, 2010.
Thanks again for your comment.
Citation: https://doi.org/10.5194/egusphere-2023-610-AC4
-
AC4: 'Reply on RC2', yaung li, 12 Aug 2023
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2023-610', Anonymous Referee #1, 03 Jun 2023
- In the abstract, the authors mentioned the following statement which is not appropriate.
the model explains why the radiation efficiency in Kotik's experiment was strongest 15 when the X wave is heating along the magnetic dip angle.
You may revise the sentence as follow:
the model explains why the radiation efficiency was strongest when the X wave is heating along the magnetic dip angle as reported in recent observations by Kotik et al…..
- There are many grammatical mistakes and very long sentences that make it difficult for the reader to follow. As an example please lines 30-34 and many more examples to be find.
- Lines 44-46 have to be revised. This is not an appropriate way to promote your work. You may mention that your work is including more physics that was neglected in the previous studies.
- Another issue that is not discussed or addressed properly here is the work done by Mahmoudian and Kalaee, 2019.
This new study which is a continuation of previous work by Eliasson and Papadapoulos 2012, has shown that the VLF signal may not penetrate to the D-region as efficient as the ELF signal. I suggest that authors provide the explanation on ELF or VLF excitation during HF modulation (Beat wave) and try to provide a more general conclusion rather than just studying the excited diamagnetic current and its aspect angle dependency.
Study of ULF-VLF wave propagation in the near-Earth environment for earthquake prediction, Advances in Space Research, Volume 63, Issue 12, 2019,
- It is critical that authors include the geomagnetic angles for other latitudes such as mid latitude (Arecibo Observatory) or equatorial region (possible facility coming at Hicamarca Peru). The efficiency of HF pump heating at those latitudes and possible variation of excited diamagnetic current should be discussed. If the proposed model is not capable of simulating such condition this weakness should be admitted in the text.
Citation: https://doi.org/10.5194/egusphere-2023-610-RC1 -
AC3: 'Reply on RC1', yaung li, 24 Jul 2023
We are grateful to the reviewer for accepting and making time to review our manuscript. Next we respond to reviewer comments by point.
Reviewer:
In the abstract, the authors mentioned the following statement which is not appropriate.
There are many grammatical mistakes and very long sentences that make it difficult for the reader to follow. As an example please lines 30-34 and many more examples to be find.
Lines 44-46 have to be revised. This is not an appropriate way to promote your work. You may mention that your work is including more physics that was neglected in the previous studies.
Authors:
These comments are valuable and all these shall reflect in the upcoming review of the paper. Since this is my first paper, there are many grammatical and expression errors, I will fix them according to the comments in the subsequent revision.
Reviewer:
Another issue that is not discussed or addressed properly here is the work done by Mahmoudian and Kalaee, 2019.
This new study which is a continuation of previous work by Eliasson and Papadapoulos 2012, has shown that the VLF signal may not penetrate to the D-region as efficient as the ELF signal. I suggest that authors provide the explanation on ELF or VLF excitation during HF modulation (Beat wave) and try to provide a more general conclusion rather than just studying the excited diamagnetic current and its aspect angle dependency.
Authors:
The propagation issues raised by the reviewers are essential. The given literature discusses in detail the propagation of ULF-VLF wave propagation in the near-Earth environment, and we will include a reference to it in Introduction. However, the main focus of this paper is to discuss the currents generated by ionospheric heating and to analyze their influence. The propagation of the current-excited magneto-fluidic waves can be neglected because it is unnecessary.
Reviewer:
It is critical that authors include the geomagnetic angles for other latitudes such as mid latitude (Arecibo Observatory) or equatorial region (possible facility coming at Hicamarca Peru). The efficiency of HF pump heating at those latitudes and possible variation of excited diamagnetic current should be discussed. If the proposed model is not capable of simulating such condition this weakness should be admitted in the text.
Authors:
Our model can explore the influence of the geomagnetic angles for other latitudes; however, we do not specifically go into this issue in this paper because the available experiments focus on high latitudes.
Citation: https://doi.org/10.5194/egusphere-2023-610-AC3
-
AC1: 'Comment on egusphere-2023-610', yaung li, 27 Jun 2023
We are grateful to the reviewer for accepting and making time to review our manuscript. Next we respond to reviewer comments by point.
Reviewer:
In the abstract, the authors mentioned the following statement which is not appropriate.
There are many grammatical mistakes and very long sentences that make it difficult for the reader to follow. As an example please lines 30-34 and many more examples to be find.
Lines 44-46 have to be revised. This is not an appropriate way to promote your work. You may mention that your work is including more physics that was neglected in the previous studies.
Authors:
These comments are valuable and all these shall reflect in the upcoming review of the paper. Since this is my first paper, there are many grammatical and expression errors, I will fix them according to the comments in the subsequent revision.
Reviewer:
Another issue that is not discussed or addressed properly here is the work done by Mahmoudian and Kalaee, 2019.
This new study which is a continuation of previous work by Eliasson and Papadapoulos 2012, has shown that the VLF signal may not penetrate to the D-region as efficient as the ELF signal. I suggest that authors provide the explanation on ELF or VLF excitation during HF modulation (Beat wave) and try to provide a more general conclusion rather than just studying the excited diamagnetic current and its aspect angle dependency.
Authors:
The propagation issues raised by the reviewers are essential. The given literature discusses in detail the propagation of ULF-VLF wave propagation in the near-Earth environment, and we will include a reference to it in Introduction. However, the main focus of this paper is to discuss the currents generated by ionospheric heating and to analyze their influence. The propagation of the current-excited magneto-fluidic waves can be neglected because it is unnecessary.
Reviewer:
It is critical that authors include the geomagnetic angles for other latitudes such as mid latitude (Arecibo Observatory) or equatorial region (possible facility coming at Hicamarca Peru). The efficiency of HF pump heating at those latitudes and possible variation of excited diamagnetic current should be discussed. If the proposed model is not capable of simulating such condition this weakness should be admitted in the text.
Authors:
Our model can explore the influence of the geomagnetic angles for other latitudes; however, we do not specifically go into this issue in this paper because the available experiments focus on high latitudes.
Citation: https://doi.org/10.5194/egusphere-2023-610-AC1 -
CC1: 'Comment on egusphere-2023-610', Alex Lee, 20 Jul 2023
I think author may add simulated results for other latitudes and make a comparison for them to enhance the practicality of this manuscript.
Citation: https://doi.org/10.5194/egusphere-2023-610-CC1 -
AC2: 'Reply on CC1', yaung li, 24 Jul 2023
We are grateful to the reviewer for accepting and making time to review our manuscript. In this paper, the computational focus concentrates on high latitudes, which is easier to verify on existing experimental facilities， such as HAARP or EISCAT. In addition, selecting a location allowed for a more in-depth discussion of the nature and distribution of the currents, such as (1) an analysis of the impact of collisions, and (2) the impact of the ground transmitter launch angle on the currents. Therefore, we believe that adding simulation locations may be slightly trivial. But we would be happy to devote some future work to this issue.
Citation: https://doi.org/10.5194/egusphere-2023-610-AC2
-
AC2: 'Reply on CC1', yaung li, 24 Jul 2023
-
RC2: 'Comment on egusphere-2023-610', Anonymous Referee #2, 09 Aug 2023
Review of "F-region drift current distribution by X wave ionospheric heating" by Li et al..
This paper is a theoretical and numerical study of drift current model in the ionosphere by incorporating the ohmic heating model and the MHD momentum equation. The authors found that the ionospheric currents are mainly driven by a diamagnetic drift effect due to the ionospheric heating. The intensity of the ionospheric currents tended to decrease with an increase of the propagation direction angle of X wave. The main reason is that the effective conductivity becomes small for the large propagation angle. This result is clear and interesting, and I recommend that this paper should be published for Ann. Geophys. journal after some minor revisions. The revision points are shown below.
1. Line 55: The authors assume that the magnetic field inclination is 90 degrees for the calculation of X-wave heating. However, the magnetic field line has an inclination that is different from 90 degrees except for the magnetic pole. The authors should explain the validity of this assumption in this paper.
2. Equation (9): Please replace ERP with one character. In this case, the reader may regard ERP as ExRxP.
3. Line 91: ...the electric force should be ...The electric force...
4. Lines 105-107: Please include the references for each model. Further, the authors should show the version of the IGRF model used in this study. Please spell out IGRF.
Citation: https://doi.org/10.5194/egusphere-2023-610-RC2 -
AC4: 'Reply on RC2', yaung li, 12 Aug 2023
We are grateful to the reviewer for making time to review our manuscript. The comments are valuable and helpful for revising and improving our paper, We have studied the comments carefully and have made corrections which we hope meet with approval. Below are your comments and our responses and modifications
This paper is a theoretical and numerical study of drift current model in the ionosphere by incorporating the ohmic heating model and the MHD momentum equation. The authors found that the ionospheric currents are mainly driven by a diamagnetic drift effect due to the ionospheric heating. The intensity of the ionospheric currents tended to decrease with an increase of the propagation direction angle of X wave. The main reason is that the effective conductivity becomes small for the large propagation angle. This result is clear and interesting, and I recommend that this paper should be published for Ann. Geophys. journal after some minor revisions. The revision points are shown below.
Re: Your acknowledgment of our work is an excellent incentive for us to keep going.
1. Line 55: The authors assume that the magnetic field inclination is 90 degrees for the calculation of X-wave heating. However, the magnetic field line has an inclination that is different from 90 degrees except for the magnetic pole. The authors should explain the validity of this assumption in this paper.
Re: There are two reasons why we assume a magnetic inclination angle of 90°.
First, the location we chose for our study is HAARP. A query reveals that the magnetic inclination of the place is 75°, which is relatively close to the magnetic inclination of the magnetic pole. Therefore, the magnetic inclination angle always defaults to 90° in previous studies, and this paper adopts the previous literature setting.
Second, it can be found that the current (or effective conductivity) depends mainly on the angle between the magnetic inclination and the launching angle; the effect of the initial value is not so significant. Therefore, to simplify the calculation, we simplify the magnetic inclination to 90 °
2. Equation (9): Please replace ERP with one character. In this case, the reader may regard ERP as ExRxP.
Re: ERP is the effective radiated power of the transmitter. To avoid ambiguity, we rewrite ERP in Eq. 9 as PER
3. Line 91: ...the electric force should be ...The electric force...
Re: Thank you for your comments on; we have made corrections in the manuscript.
4. Lines 105-107: Please include the references for each model. Further, the authors should show the version of the IGRF model used in this study. Please spell out IGRF.
Re: According to the comments, the section was rewritten as follows. “Background data were acquired at HAARP on 2 October 2011. The ionospheric and atmospheric background profiles are given by the International Reference Ionosphere (IRI-2016)(Bilitza et al., 2022) model and the neutral atmosphere model (MSIS)(Picone et al., 2002), as well as geomagnetic field data from the International Geomagnetic Reference Field(IGRF-11) model(Geomagnetism et al., 2010)”.
The references:
Bilitza, D., Pezzopane, M., Truhlik, V., Altadill, D., Reinisch, B. W., and Pignalberi, A.: The International Reference Ionosphere Model: A Review and Description of an Ionospheric Benchmark, Reviews of Geophysics, 60, e2022RG000792, https://doi.org/10.1029/2022RG000792, 2022.
Picone, J. M., Hedin, A. E., Drob, D. P., and Aikin, A. C.: NRLMSISE-00 empirical model of the atmosphere: Statistical comparisons and scientific issues, Journal of Geophysical Research: Space Physics, 107, SIA 15-11-SIA 15-16, https://doi.org/10.1029/2002JA009430, 2002.
Geomagnetism, I. A. o., Aeronomy.: International Geomagnetic Reference Field: the eleventh generation, Geophysical Journal International, 183, 1216-1230, https://doi.org/10.1111/j.1365-246X.2010.04804.x, 2010.
Thanks again for your comment.
Citation: https://doi.org/10.5194/egusphere-2023-610-AC4
-
AC4: 'Reply on RC2', yaung li, 12 Aug 2023
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Yong Li
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Chengxun Yuan
Ce Li
Zhongxiang Zhou
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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