Global Inductive Magnetosphere-Ionosphere-Thermosphere Coupling

Laundal, Karl M.; Skeidsvoll, Andreas S.; Popescu Braileanu, Beatrice; Hatch, Spencer M.; Olsen, Nils; Vanhamäki, Heikki

doi:10.5194/egusphere-2025-2051

Preprints

https://doi.org/10.5194/egusphere-2025-2051

Preprints

13 Jun 2025

| 13 Jun 2025

Global Inductive Magnetosphere-Ionosphere-Thermosphere Coupling

Karl M. Laundal, Andreas S. Skeidsvoll, Beatrice Popescu Braileanu, Spencer M. Hatch, Nils Olsen, and Heikki Vanhamäki

Abstract. The ionosphere forms the inner boundary of near-Earth space, where collisionless space plasma transitions into a partially ionized gas that interacts with the neutral atmosphere through collisions. Conventional models for magnetosphere-ionosphere (MI) coupling use an electric circuit framework, where an electric potential is calculated from the current continuity equation on a thin spherical shell that represents the ionosphere. This approach, founded in the E, j (electric field and current density) paradigm, contrasts with the approach used to study plasmas in other regions of cosmos, where the magnetic field B and plasma velocity v are treated as fundamental variables (the B, v paradigm). Since traditional MI coupling models also neglect induction by setting ∂B/∂t = 0, they omit the dynamic processes by which B evolves, leaving the global MI coupling process arguably poorly understood. To advance our understanding of MI coupling, we present a new global model of the 2D ionosphere that incorporates induction, with B as the primary variable. This model accommodates arbitrary ionospheric conductance, neutral wind patterns, and realistic main magnetic field geometries. Simulations reveal the complex nature of the induction process over a few seconds to several minutes. The induction timescales depend on the magnitudes and spatial scales of conductance, neutral wind, imposed magnetic field perturbations, and main magnetic field geometry. We simulate for the first time how low-latitude Sq currents and electric fields emerge through induction. Our model has the potential to replace existing MI coupling modules in magnetospheric simulation codes, offering both a truly global solution, and the inclusion of induction in the coupled system dynamics.

Received: 01 May 2025 – Discussion started: 13 Jun 2025

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10 Dec 2025

| Highlight paper

Global inductive magnetosphere-ionosphere- thermosphere coupling

Karl M. Laundal, Andreas S. Skeidsvoll, Beatrice Popescu Braileanu, Spencer M. Hatch, Nils Olsen, and Heikki Vanhamäki

Ann. Geophys., 43, 803–833, https://doi.org/10.5194/angeo-43-803-2025,https://doi.org/10.5194/angeo-43-803-2025, 2025

Short summary Editor-in-chief

Karl M. Laundal, Andreas S. Skeidsvoll, Beatrice Popescu Braileanu, Spencer M. Hatch, Nils Olsen, and Heikki Vanhamäki

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-2051', Arthur D. Richmond, 09 Jul 2025

This is an excellent description and analysis of magnetic induction effects on global ionospheric electrodynamics. It describes how the electroquasistatic assumption commonly used to model global electrodynamics can be avoided in order to examine the physical processes by which ionospheric electric fields and currents are established. A numerical model is developed to demonstrate and analyze the effects of induction. A surprising prediction of the modeling is that fully steady-state electrodynamic conditions within the ionosphere may require several minutes to establish, even without considering magnetospheric feedback, instead of tens of seconds that simple order-of-magnitude estimates typically predict. The article is properly placed in the context of prior work. Most of the limitations and potential future developments are well described.
A point requiring further clarification is the significance of height variations of winds, conductivities, and current densities within the ionosphere for the modeling. The mathematical development essentially ignores variations of these quantities with height, treating the quantities as existing only at a single height in an infinitesimally thin layer. The numerical modeling uses winds at 110 km from the Horizontal Wind Model and height-integrated conductivities. In reality winds and conductivities vary strongly with altitude in the lower ionosphere. Height integration of Equation (6) does not yield Equation (7) as the result. Instead, Equation (3) needs to be integrated in height and then solved for E in order to get something similar to Equation (7), except that the uxB term becomes terms involving height-averaged winds weighted by the Pedersen and Hall conductivities.
Another point requiring further clarification is the nature of winds responsible for Sq-like geomagnetic variations. The statement "Sq currents will only form if the winds imply an interhemispheric imbalance [of winds] at conjugate points" (Line 575) is incorrect. Winds at conjugate points can be balanced and still create a curl in uxB_0 that is balanced at conjugate points such that no interhemispheric magnetic tension is created, only a balanced change in magnetic pressure.
Minor comments
1. Add j_parallel to the right-hand side of (3).
2. Line 104: F can also be important at low altitudes, where E_parallel may be non-negligible.
3. In the caption for Figure 1 all the mathematical quantities should be defined.
4. Lines 136-140: The reason why the radial component of the current does not appear in (7) has nothing to do with high field-aligned electron mobility, but rather to the fact that current density appears in (6) and (7) only in the form jxb, and therefore excludes j_parallel.
5. Concerning notation, B is the total magnetic field in (2),(3),(6),(7), but is only the perturbation field starting at Line 151. Perhaps different symbols can be used.
6. Line 162: Is Equation (11) meant instead of Equation (10)?
7. Lines 294-295: It is not obvious that the deformation can be neglected if dB/dt is non-zero.
8. Lines 313-314 and Line 561: The force-free assumption applies only above the current layer, not within it. Currents can cross magnetic field lines everywhere in the current layer.

Citation: https://doi.org/10.5194/egusphere-2025-2051-RC1
- AC1: 'Reply on RC1', Karl M. Laundal, 17 Oct 2025
  
  We thank the reviewers for their careful reading and valuable feedback, which helped strengthen the manuscript. A detailed response, along with a version of the manuscript with all our proposed changes highlighted, is attached.
  
  Citation: https://doi.org/10.5194/egusphere-2025-2051-AC1
RC2:
'Comment on egusphere-2025-2051', Stephan C. Buchert, 11 Jul 2025

The authors skillfully condense into the paper a relatively large amount of work and impressive progress on modeling the thermosphere-ionosphere-magnetosphere. I have only a few minor comments in parts of section 5 "Discussion"
"Sq currents will only form if the winds imply an interhemispheric imbalance [of winds] at conjugate points" (Line 575) is a bit vague about what interhemispheric (im)balance means, but essentially correct, in my opinion. It is the uxB term (integrated over the dynamo region in the 2D model) which' mismatch at conjugate points forms Sq. In order to balance, i.e. suppress Sq completely, the neutral wind vectors would need to compensate also for any conjugate assymmetries of the magnetic field, including asymmetric magnitudes |B_N| and |B_S|. This is implied by the statement "2) if u × B0 at conjugate points imply different electric fields, ... " in lines 570-572. I'm not sure whether this is relevant for Art Richmond's comment on the issue in his review.
Regarding altitude dependence of the neutral wind, rather of the uxB term within the ionosphere (in each hemisphere), an imbalance would form intra-ionosphere current systems, i.e current loops closing within different layers. I'm not aware of any experimental evidence of such currents which is probably owing to the absence of satellite data from the lower-middle thermosphere-ionosphere. According to Fukushima's theorem the effects would be almost undetectable both below/on the ground as well as above in low Earth orbits. A future 3D version of the B,v model presented here could demonstrate the existence of such currents/magnetic tensions between thermospheric layers in the presence of horizontal neutral wind with vertical gradients. This is meant as a contribution to the discussion, not necessarily a suggestion for additions to the paper, which might rather focus on describing what has been achieved so far.
Lines 579-580, "In steady state the electric field is such that no further deformation happens, as the j × B force and momentum transfer due to collisions with neutrals counterbalance each other.": The jxB force and momentum transfer by collisions are different views of the same forcing, the former in the B,v paradigm, the latter in E,j. They do not counterbalance. jxB (or collisional transfer in E,j) rather is counterbalanced by the inertia of the atmosphere. Thus strictly only a quasi-steady state is reached, with generally long atmospheric time scales. Rapid changes as mentioned in lines 494-500 would so be able to excite atmospheric acoustic/gravity waves, probably of relatively low amplitudes, Parker's (1996) long paper includes an example calculation of the neutral atmosphere forcing by magnetic stress (i.e. closure of FACs). This has been studied/simulated within the E,j paradigm modeling the frictional forcing of magnetosphere ion convection, for example, one simulated effect has been described as "flywheel" (Deng et al.., JGR< 1991). But an inductive treatment has advantages. I suggest to briefly mention the potential to couple dynamic models of the atmosphere with an inductive Magnetosphere-Ionosphere-Thermosphere (B,v) description in a conceptually relatively straight forward manner (i.e. propagate forward in time du/dt = ... + jxB and dB/dt = -(∇ x E(u, B)), Faraday with GOL, equation (2)). The treatment of the inductive Magnetosphere-Ionosphere-Thermosphere would so become more analogue to that of the Earth core and relatively recently also Ocean dynamos.
Section "Conclusions", especially paragraph lines "677-683°: The high-latitude field-aligned currents are described as being prescribed and an input into the coupled Magnetosphere-Ionosphere-Thermosphere model of this work. I would suggest to mention (at this paragraph and/or elsewhere in the paper) that the neutral wind in the dynamo region is the other 2nd input to the 2D model. Here it is prescribed using the HWM by Drob et al. (2017). In reality the neutral wind varies with time. Precise and spatially sufficiently dense magnetic measurements on the ground and in space at mid-latitudes would so carry information on neutral wind differences at magnetically conjugate points.

Citation: https://doi.org/10.5194/egusphere-2025-2051-RC2
- AC2: 'Reply on RC2', Karl M. Laundal, 17 Oct 2025
  
  We thank the reviewers for their careful reading and valuable feedback, which helped strengthen the manuscript. Please see the comment posted in response to Art Richmond for a detailed response to both reviewers, along with a version of the manuscript with all our proposed changes highlighted.
  
  Citation: https://doi.org/10.5194/egusphere-2025-2051-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-2051', Arthur D. Richmond, 09 Jul 2025

This is an excellent description and analysis of magnetic induction effects on global ionospheric electrodynamics. It describes how the electroquasistatic assumption commonly used to model global electrodynamics can be avoided in order to examine the physical processes by which ionospheric electric fields and currents are established. A numerical model is developed to demonstrate and analyze the effects of induction. A surprising prediction of the modeling is that fully steady-state electrodynamic conditions within the ionosphere may require several minutes to establish, even without considering magnetospheric feedback, instead of tens of seconds that simple order-of-magnitude estimates typically predict. The article is properly placed in the context of prior work. Most of the limitations and potential future developments are well described.
A point requiring further clarification is the significance of height variations of winds, conductivities, and current densities within the ionosphere for the modeling. The mathematical development essentially ignores variations of these quantities with height, treating the quantities as existing only at a single height in an infinitesimally thin layer. The numerical modeling uses winds at 110 km from the Horizontal Wind Model and height-integrated conductivities. In reality winds and conductivities vary strongly with altitude in the lower ionosphere. Height integration of Equation (6) does not yield Equation (7) as the result. Instead, Equation (3) needs to be integrated in height and then solved for E in order to get something similar to Equation (7), except that the uxB term becomes terms involving height-averaged winds weighted by the Pedersen and Hall conductivities.
Another point requiring further clarification is the nature of winds responsible for Sq-like geomagnetic variations. The statement "Sq currents will only form if the winds imply an interhemispheric imbalance [of winds] at conjugate points" (Line 575) is incorrect. Winds at conjugate points can be balanced and still create a curl in uxB_0 that is balanced at conjugate points such that no interhemispheric magnetic tension is created, only a balanced change in magnetic pressure.
Minor comments
1. Add j_parallel to the right-hand side of (3).
2. Line 104: F can also be important at low altitudes, where E_parallel may be non-negligible.
3. In the caption for Figure 1 all the mathematical quantities should be defined.
4. Lines 136-140: The reason why the radial component of the current does not appear in (7) has nothing to do with high field-aligned electron mobility, but rather to the fact that current density appears in (6) and (7) only in the form jxb, and therefore excludes j_parallel.
5. Concerning notation, B is the total magnetic field in (2),(3),(6),(7), but is only the perturbation field starting at Line 151. Perhaps different symbols can be used.
6. Line 162: Is Equation (11) meant instead of Equation (10)?
7. Lines 294-295: It is not obvious that the deformation can be neglected if dB/dt is non-zero.
8. Lines 313-314 and Line 561: The force-free assumption applies only above the current layer, not within it. Currents can cross magnetic field lines everywhere in the current layer.

Citation: https://doi.org/10.5194/egusphere-2025-2051-RC1
- AC1: 'Reply on RC1', Karl M. Laundal, 17 Oct 2025
  
  We thank the reviewers for their careful reading and valuable feedback, which helped strengthen the manuscript. A detailed response, along with a version of the manuscript with all our proposed changes highlighted, is attached.
  
  Citation: https://doi.org/10.5194/egusphere-2025-2051-AC1
RC2:
'Comment on egusphere-2025-2051', Stephan C. Buchert, 11 Jul 2025

The authors skillfully condense into the paper a relatively large amount of work and impressive progress on modeling the thermosphere-ionosphere-magnetosphere. I have only a few minor comments in parts of section 5 "Discussion"
"Sq currents will only form if the winds imply an interhemispheric imbalance [of winds] at conjugate points" (Line 575) is a bit vague about what interhemispheric (im)balance means, but essentially correct, in my opinion. It is the uxB term (integrated over the dynamo region in the 2D model) which' mismatch at conjugate points forms Sq. In order to balance, i.e. suppress Sq completely, the neutral wind vectors would need to compensate also for any conjugate assymmetries of the magnetic field, including asymmetric magnitudes |B_N| and |B_S|. This is implied by the statement "2) if u × B0 at conjugate points imply different electric fields, ... " in lines 570-572. I'm not sure whether this is relevant for Art Richmond's comment on the issue in his review.
Regarding altitude dependence of the neutral wind, rather of the uxB term within the ionosphere (in each hemisphere), an imbalance would form intra-ionosphere current systems, i.e current loops closing within different layers. I'm not aware of any experimental evidence of such currents which is probably owing to the absence of satellite data from the lower-middle thermosphere-ionosphere. According to Fukushima's theorem the effects would be almost undetectable both below/on the ground as well as above in low Earth orbits. A future 3D version of the B,v model presented here could demonstrate the existence of such currents/magnetic tensions between thermospheric layers in the presence of horizontal neutral wind with vertical gradients. This is meant as a contribution to the discussion, not necessarily a suggestion for additions to the paper, which might rather focus on describing what has been achieved so far.
Lines 579-580, "In steady state the electric field is such that no further deformation happens, as the j × B force and momentum transfer due to collisions with neutrals counterbalance each other.": The jxB force and momentum transfer by collisions are different views of the same forcing, the former in the B,v paradigm, the latter in E,j. They do not counterbalance. jxB (or collisional transfer in E,j) rather is counterbalanced by the inertia of the atmosphere. Thus strictly only a quasi-steady state is reached, with generally long atmospheric time scales. Rapid changes as mentioned in lines 494-500 would so be able to excite atmospheric acoustic/gravity waves, probably of relatively low amplitudes, Parker's (1996) long paper includes an example calculation of the neutral atmosphere forcing by magnetic stress (i.e. closure of FACs). This has been studied/simulated within the E,j paradigm modeling the frictional forcing of magnetosphere ion convection, for example, one simulated effect has been described as "flywheel" (Deng et al.., JGR< 1991). But an inductive treatment has advantages. I suggest to briefly mention the potential to couple dynamic models of the atmosphere with an inductive Magnetosphere-Ionosphere-Thermosphere (B,v) description in a conceptually relatively straight forward manner (i.e. propagate forward in time du/dt = ... + jxB and dB/dt = -(∇ x E(u, B)), Faraday with GOL, equation (2)). The treatment of the inductive Magnetosphere-Ionosphere-Thermosphere would so become more analogue to that of the Earth core and relatively recently also Ocean dynamos.
Section "Conclusions", especially paragraph lines "677-683°: The high-latitude field-aligned currents are described as being prescribed and an input into the coupled Magnetosphere-Ionosphere-Thermosphere model of this work. I would suggest to mention (at this paragraph and/or elsewhere in the paper) that the neutral wind in the dynamo region is the other 2nd input to the 2D model. Here it is prescribed using the HWM by Drob et al. (2017). In reality the neutral wind varies with time. Precise and spatially sufficiently dense magnetic measurements on the ground and in space at mid-latitudes would so carry information on neutral wind differences at magnetically conjugate points.

Citation: https://doi.org/10.5194/egusphere-2025-2051-RC2
- AC2: 'Reply on RC2', Karl M. Laundal, 17 Oct 2025
  
  We thank the reviewers for their careful reading and valuable feedback, which helped strengthen the manuscript. Please see the comment posted in response to Art Richmond for a detailed response to both reviewers, along with a version of the manuscript with all our proposed changes highlighted.
  
  Citation: https://doi.org/10.5194/egusphere-2025-2051-AC2

Peer review completion

AR – Author's response | RR – Referee report | ED – Editor decision | EF – Editorial file upload

ED: Publish subject to minor revisions (review by editor) (30 Oct 2025) by Dalia Buresova

AR by Karl M. Laundal on behalf of the Authors (01 Nov 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (03 Nov 2025) by Dalia Buresova

AR by Karl M. Laundal on behalf of the Authors (05 Nov 2025)

Journal article(s) based on this preprint

10 Dec 2025

| Highlight paper

Global inductive magnetosphere-ionosphere- thermosphere coupling

Karl M. Laundal, Andreas S. Skeidsvoll, Beatrice Popescu Braileanu, Spencer M. Hatch, Nils Olsen, and Heikki Vanhamäki

Ann. Geophys., 43, 803–833, https://doi.org/10.5194/angeo-43-803-2025,https://doi.org/10.5194/angeo-43-803-2025, 2025

Short summary Editor-in-chief

Karl M. Laundal, Andreas S. Skeidsvoll, Beatrice Popescu Braileanu, Spencer M. Hatch, Nils Olsen, and Heikki Vanhamäki

Model code and software

PynaMIT Andreas Skeidsvoll and Karl M. Laundal https://github.com/DynaMIT-uib/PynaMIT

Karl M. Laundal, Andreas S. Skeidsvoll, Beatrice Popescu Braileanu, Spencer M. Hatch, Nils Olsen, and Heikki Vanhamäki

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The ionosphere is where Earth’s atmosphere overlaps with a gas of charged particles in space. There, collisions with neutral air and electromagnetic forces driven by the solar wind control plasma motion. We created a global model that includes magnetic induction, explaining how electric currents and fields are altered, offering a more accurate view of atmosphere–space coupling than conventional models based on electric circuits.


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