The cause of the 100,000-year geomagnetic and climate cycles

Vogel, Koen

doi:https://doi.org/10.22541/essoar.174344800.02936683/v2

Preprints

https://doi.org/10.22541/essoar.174344800.02936683/v2

Preprints

26 May 2025

| 26 May 2025

The cause of the 100,000-year geomagnetic and climate cycles

Koen Vogel

Abstract. Paleotemperature and paleogeomagnetic data commonly exhibit a dominant 100,000-year cyclicity. Spectral and statistical analyses demonstrate that paleogeomagnetic intensity variations are strongly and significantly correlated to orbital inclination, obliquity and eccentricity oscillations. These orbital fluctuations vary the Earth-incident solar wind power, which is here shown to be the primary cause of geomagnetic fluctuations. The 100,000-year glacial-interglacial climate cyclicity is very likely controlled by similar orbital inclination forcings. The switch from 41,000-year glacial-interglacial cyclicity to 100,000-year cyclicity that occurred around the mid-Pleistocene Transition demonstrates that long-term climate cyclicity very likely varies due to orbital eccentricity modulating the relative strengths of orbital inclination and obliquity forcings.

Received: 18 Apr 2025 – Discussion started: 26 May 2025

Koen Vogel

Status: final response (author comments only)

RC1:
'Comment on egusphere-2025-1858', Anonymous Referee #1, 26 Jun 2025

The manuscript entitled "The cause of the 100,000-year geomagnetic and climate cycles" contains significant errors in data analysis, leading to incorrect conclusions. To date, there is no scientific report supporting the existence of a 100,000-year solar periodicity. The application of the Fourier transform is not appropriate for paleoclimatic or geomagnetic data, and the use of cross-coherence functions is also inadequate for this type of analysis. A time-frequency spectral analysis would be more suitable for non-stationary time series.
Although the author presents Maxwell’s equations, a solution exhibiting a 100,000-year periodicity is not derived from first principles. Moreover, available solar wind data spans only a few decades, and the longest observational solar record—the sunspot number—begins in 1610. Thus, there is no way to verify the existence of solar cycles on the scale of tens of thousands of years. Solar proxies such as cosmogenic isotopes typically reveal periodicities in the range of 1,000 to 3,000 years, not 100,000 years, implying a discrepancy of orders of magnitude.
Nevertheless, the manuscript raises an important question that could be of significant interest to both space weather research and geomagnetic field studies: how various indices of the geomagnetic field respond to solar parameters such as solar wind, irradiance, or other related variables. In this regard, the author could consider analyzing recent events, such as the geomagnetic storms of May 10, 2024, which triggered auroral displays at unusually low magnetic latitudes.
Based on the above considerations, this work cannot be accepted in its current form and is hereby rejected.

Citation: https://doi.org/10.5194/egusphere-2025-1858-RC1
- AC1:
  'Reply on RC1', Koen Vogel, 26 Jun 2025
  
  I appreciate your interest and comments. I believe you have some significant misunderstandings on the nature and conclusions of my work. I'll attempt to clarify the main items.
  "To date, there is no scientific report supporting the existence of a 100,000-year solar periodicity."
  My article does not claim there is. In fact I claim the exact opposite, and dedicate a number of paragraphs and reference a number of studies to demonstrate that such 100 ka solar cycles are unproven. My claim is that Earth's orbit around the sun causes the 100 ka periodicity, not that solar irradiation or solar wind energy varies significantly with time. The same applies to your comment "Moreover, available solar wind data spans only a few decades, and the longest observational solar record—the sunspot number—begins in 1610."
  "The application of the Fourier transform is not appropriate for paleoclimatic or geomagnetic data, and the use of cross-coherence functions is also inadequate for this type of analysis. A time-frequency spectral analysis would be more suitable for non-stationary time series." I mainly use the Fourier Transforms to validate the conclusions of previous studies, that is to support previous authors' conclusions about the significant or lack of significant energy at various spectra associated with the classic Milankovitch cycles. I can easily omit them if they offend, and just refer to the original peer-reviewed work. You refer to cross-coherence functions, but my analysis uses cross-correlation functions. There is a difference. Coherence measures the degree of linear dependency between two signals as a function of frequency, indicating how well one signal can be predicted from another at each frequency. Cross-correlation measures the similarity between two signals as a function of the displacement - in this case time - of one relative to the other. Correlation is therefore a time-domain measure, coherence is a frequency-domain measure derived from the cross-spectral density and the power spectral densities of the signals involved. As such my cross-correlations have statistical significance at the 99% level in the time domain, i.e. the periodicity domain. There is significant correlation over multiple orbital inclination and obliquity periods that must be therefore either due to orbital forcing influence or due to a confounding variable. I can't think of any confounding variable, and go to great lengths to demonstrate how the orbital forcings are explanatory.
  I do not understand your comment on non-stationarity. I refer you to "Laskar, J. Robutel, P. Joutel, F., et al., 2004: A long term numerical solution for the insolation quantities of the Earth, Astron. Astrophys., 428, 261-285. DOI: 10.1051/0004-6361:20041335" who calculate e.g. the obliquity time series I used. I use the 400ka-long Lasker calculated time series in the cross-correlations, which does not have any stationarity assumptions other than that gravitational constant is the same as it was 400 ka years ago.
  "Although the author presents Maxwell’s equations, a solution exhibiting a 100,000-year periodicity is not derived from first principles. " I also fail to understand the point being made here. The 100 ka periodicity stems from energy variations due to Earth's orbit, not the Maxwell equations. The Maxwell equations are used to remind readers that a time-variant electric field induces a magnetic field, and that a time-variant magnetic field induces an electric field, and that Earth-incident solar wind generates magnetic flux. This is completely uncontroversial. I refer you to Turner, J. , Winch, D., Ivers, D., Stening, R., 2007, Regular daily variations in satellite magnetic total intensity data. Annales Geophysicae, 25, 2167-2174. who demonstrate that the solar quiet solar wind causes significant magnetic flux at the top of the ionosphere.
  "the author could consider analyzing recent events, such as the geomagnetic storms of May 10, 2024, which triggered auroral displays at unusually low magnetic latitudes" I agree this is a fascinating topic, but you are ahead of me. I am working on a follow-up article which deals in more detail with the solar storm - geomagnetic field interactions, but I first need to get this article published as the next builds on it.
  
  Citation: https://doi.org/10.5194/egusphere-2025-1858-AC1
  - AC2: 'Reply on AC1', Koen Vogel, 26 Jun 2025
    
    I'd like to add an appendix to my explanation, as I think it might help.
    Solar irradiation varies as a function of distance to the sun, R, and therefore decreases as a function of R³. Orbital eccentricity is the only orbital forcing that varies R_Earth, and even then only varies it very insignificantly, that is too small an impact to explain climate cycles, and impossible to explain geomagnetic cycles.
    The solar wind however oscillates around the solar equatorial plane, and therefore has its greatest energy density in this plane. It varies as a function of R²-R³. Earth's orbital inclination takes us in and out of denser solar wind areas of space every 100ka. I use the Maxwell equations to demonstrate that the solar wind deforms the geomagnetic field, generates magnetic flux and therefore transfers energy to it. Orbital inclination is therefore the only plausible 100 ka period orbital forcing.
    
    Citation: https://doi.org/10.5194/egusphere-2025-1858-AC2
    
    RC3: 'Reply on AC2', Anonymous Referee #1, 26 Jun 2025
    
    It's possible that I'm confused about the wordplay. But then I suggest the author withdraw the paper and rewrite it. It's not necessary, for example, to write Maxwell's equations if they aren't going to be used; it's sufficient to cite these equations. An appendix is also not necessary. But it's necessary for the author to focus on their objective. The use of the Fourier transform or the cross function is incorrect, and if they are used, the paper will again be rejected. It's not justifiable that other authors have used them and cited these works. This is incorrect. Again, this is my suggestion, and the Editor is the one who will decide the paper's status
    
    Citation: https://doi.org/10.5194/egusphere-2025-1858-RC3
    
    AC4: 'Reply on RC3', Koen Vogel, 01 Sep 2025
    
    I personally do not see a problem with using FFT's to demonstrate discrete spectral energy peaks at certain key frequencies. I'm unaware of any guidelines Fourier might have given on FFT usage, but as I've mentioned above the figures are not key to the overall story. I can either replace them with (the more commonly used) spectral density plots or leave them out altogether. I prefer the FFT's because e.g. they demonstrate the dominant 75 ka paleogeomagnetic intensity frequency that features largely in the explanation of how the different orbital forcings combine to determine the G&V observed paleogeomagnetic intensity curve and its frequency content. I think its valid to point out that G&V did not make a mistake in determining that Obliquity signals are not apparent in their (Fig. 3) spectral density plot. My article points out that Obliquity combines with OI to produce the dominant 75 ka frequency (f=0.013), which might not be discernible from the 100 ka frequency (f=0.01) on a spectral density plot. . This is why the cross correlation functions are key to the explanation: the Obliquity signal is lurking in the paleogeomagnetic intensity data, and persists throughout the 3.5 cycles (145 ka) covered by the G&V data. The OI forcing however is dominant and masks the 41 ka signal on spectral density plots.
    Similarly, I can omit the Maxwell equations if the reviewer feels they are sufficiently known. I use them to remind readers that a temporally-variant magnetic field is always accompanied by an temporally-variant electric field and vice versa (Eqns 3 &4), plus there are no other known sources of magnetic energy other than electric currents (Eqn 2). I'm happy to leave them out if redundant. I hope readers ranging from astrophysicists to geophysicists - to whom they should be well-known - to geologists and climatologists - who may be less familiar - will have an interest in my work.
    On the use of cross (correlation or covariance) functions however I must respectfully disagree with the reviewer: their use is standard practice when determining cause and effect relationships in time series, as an effect must always lag the cause. I can take the analysis 1 step further and demonstrate Granger causality, but I thought such is redundant as the OI and Obliquity cross correlation functions show a visually obvious, statistically significant, multi-cycle correlation. The cross correlation (covariance) function investigates how much correlation (covariance) exists between two time series at different time lags, and whether such covariation is statistically significant. In the case of paleogeomagnetic intensity variations over the last 290 ka there is statistically significant covariation between Orbital Forcings (Orbital Inclination, Obliquity and Eccentricity) and paleogeomagnetic intensity variations over multiple cycles. That is, I can use the 200-300 ka OI, Obliquity and Eccentricity values to create a model based on their cross correlations to accurately predict geomagnetic intensity values between 0-100 ka. Or back in time to the rest of the Sint-800 curve (although doing so will run into some non-stationarity issues that have great potential to confuse). I can point out a covariation that is visually apparent in Fig. 5, but I would prefer to put the matter on a proper statistical / mathematical / scientific footing. The use of cross coherence functions, as was earlier suggested by the reviewer, is largely redundant, as such are mainly used to investigate similarities in time series frequencies. These have already been extensively investigated by numerous studies e.g. those mentioned in the Introduction. My title refers to the causes of a specific cycle frequency - 0.01, the 100 ka period - and does not question whether such exists or not, as other worker have sufficiently demonstrated that it does, and have determined (Zhou et al., 2023; SPECMAP) that geomagnetic intensity covaries with climate (Asian monsoon) cycles. This non-intuitive geomagnetic-climate covariation will require multiple steps to unravel. A first step is to determine what causes the paleogeomagnetic cyclicity.
    
    Citation: https://doi.org/10.5194/egusphere-2025-1858-AC4
  - RC2: 'Reply on AC1', Anonymous Referee #1, 26 Jun 2025
    
    I appreciate the correction. The author uses the cross-function instead of the coherence function. Although the coherence function is the cross function normalized, but, it doesn't change my suggestion. The editor is the one who will decide the paper's status.
    
    Citation: https://doi.org/10.5194/egusphere-2025-1858-RC2
    
    AC5: 'Reply on RC2', Koen Vogel, 01 Sep 2025
    
    I am required by the Editor to comment on this remark. Please see my answer to a different comment that I posted on 1 September
    
    Citation: https://doi.org/10.5194/egusphere-2025-1858-AC5
  - RC4: 'Reply on AC1', Anonymous Referee #1, 26 Jun 2025
    
    The author writes Maxwell's equations without using them, but he doesn't write the Fourier transform, nor does he cite Fourier. If the author analyzes this transform, you'll understand that Jean Baptiste Joseph Fourier very elegantly wrote the characteristics that signals must meet to be usable. Therefore, signals or data such as paleoclimate or geomagnetic data don't meet these requirements.
    
    Citation: https://doi.org/10.5194/egusphere-2025-1858-RC4
    
    AC3: 'Reply on RC4', Koen Vogel, 26 Jun 2025
    
    I agree a time-frequency spectral analysis would add value if I was trying to determine signal frequencies using a non-stationary time-series. But I'm doing something a lot simpler: I determine the co-variation between one peer-reviewed 400 ka time series, the Guyodo and Valet geomagnetic data, and another peer-reviewed 400 ka time-series, the Laskar orbital oscillations. The fact that the cross-correlations are excellent over multiple cycles, despite any non-stationarity of the orbital oscillations, strongly suggests that a cause-effect relationship exists between these independent variables. The fact that the orbital obliquity period varies a bit over the last 400 ka is immaterial: the peaks and troughs of the geomagnetic data covary with the peaks and troughs of the orbital oscillations, at a statistical significance of 99%. The last element of the proving the cause-effect relationship is: no credible alternative, i.e. no credible confounding variable. I cannot think of one, so my conclusion is that the orbital oscillations cause the geomagnetic oscillations.
    
    Citation: https://doi.org/10.5194/egusphere-2025-1858-AC3
- AC7:
  'Reply on RC1', Koen Vogel, 08 Sep 2025
  Before finalizing, I’d like to sum up the first reviewer’s comments and my reply. After eliminating some misunderstandings, the reviewer’s main remaining objection centers on the methodology, namely the use of a Fourier transform in Figure 3 & 7, as well as the use of cross correlation functions to determine causality in Figures 4 & 7.
  The Fourier Transform is a discrete representation of the paleogeomagnetic intensity data in the frequency domain. Its use is recommended practice for time series analysis in the geosciences:
  Gossel & Laehne, 2013, Applications of time series analysis in geosciences: an overview of methods and sample applications. Hydrol. Earth Syst. Sci. Discuss., 10, 12793–12827
  
  so I still do not understand the reviewer’s objection to its use. I use the Fourier transform in Fig. 3 to demonstrate two things:
  To compare with G&V’s spectral density analysis, which shows a very similar result, namely no peak at obliquity frequency, a large peak around 0.01 (100 ka) frequency
  
  A dominant peak at 0.013 (75 ka) that is indiscernible from the 0.01 peak in G&V’s spectral density plot (their Fig. 3). This dominant 75 ka peak is the result of the combination of eccentricity, obliquity and orbital inclination forcing (described in my text).
  
  Plotting this in a spectral plot (my Fig. 3) shows the two discrete large peak frequencies much clearer than a spectral density plot. If for whatever reason my Fig. 3 is objectionable, I can use a workaround using autocorrelation functions and published literature, but such would diminish clarity in my opinion.
  
  The use of cross-correlation functions to demonstrate causality between time series is similarly standard practice, e.g. :
  Rehfeld, Kira & 𝙼𝚊𝚛𝚠𝚊𝚗, 𝙽𝚘𝚛𝚋𝚎𝚛𝚝 & Heitzig, Jobst & Kurths, Juergen. (2011). Comparison of correlation analysis techniques for irregularly sampled time series. Nonlinear Processes in Geophysics. 18. 389–404. 10.5194/npg-18-389-2011.
  
  The goal of such analysis is ideally to find a cause with time lag = 0. While OI is the dominant forcing, and the cause of the 100 ka paleogeomagnetic intensity cyclicity, it is the combination of eccentricity, obliquity and OI forcing that causes the dominant 75 ka periodicity. I explain this in the text.
  
  In short: I think my methodology is fairly standard and robust.
  
  Citation: https://doi.org/10.5194/egusphere-2025-1858-AC7
RC5:
'Comment on egusphere-2025-1858', Anonymous Referee #2, 24 Aug 2025

Study by Koen investigates 100ka cycles seen in paleomagnetic intensity and glacial-interglacial climate changes, and it argues that orbital inclination is the main cause of this periodicity. Using data such are Sint-800 (first 290ka) and SPECMAP, the author show links between paleomagnetic intensity and orbital factors (inclination, obliquity and eccentricity). He further suggests that solar wind, controlled by orbital inclination, is the main cause of geomagnetic variations.
While the paper is well written and is an interesting read, the correlations found in this study are not convincing and some physical concepts are misinterpreted. Many of the claims, e.g. P4L70-71, P4L73 (... almost cerntanly caused by the OI forcing), P5L91-92 need some proof.
1. Please use longer datasets for the paleomagnetism. 290ka is not sufficient to investigate periods of 100ka. PISO-1500 would be a better choice as it covers 1.5Ma. The correlations with orbital parameters would be far more convincing if longer time periods are covered.
2. Solar wind explanation. The solar wind at 1 astronomical unit is essentially radial and nearly isotropic, it is not concentrated in the solar equatorial plane. Therefore, the Earth's small inclination changes would have negligible effect on the total intercepted solar wind energy. What matters far more are coronal mass ejections and the high speed solar wind streams.
3. Solar wind and changes in paleomagnetism. The paper claims that magnetic flux at the magnetopause must pass through the mantle before reaching the core; mantle is low conductivity, so it cannot regenerate the flux. Therefore, solar wind deformation of the field lines at the magnetopause somehow couples into the outer core. This is flawed - magnetopause currents are external, not internal. Internal field is the mag field generated by the geodynamo in the outer core, and external is induced by solar wind. The magnetic perturbations from the solar wind are generated outside the Earth, in the magnetosphere and ionosphere. These fields can be observed at the Earth's surface, but they are not transmitted through the mantle into the core as flux. Mantle is a poor conductor of the current and it protects the outer core from the direct penetration of the solar wind mag field. Magnetic variations from the magnetosphere could in theory induce small secondary currents in the mantle, but they are shallow and do not significantly affect the geodynamo. The opposite is true: The geomagnetic field shapes the magnetopause and drives how solar wind couples to Earth - solar wind produces external geomag variations which we can measure at the Earth's surface.

Citation: https://doi.org/10.5194/egusphere-2025-1858-RC5
- AC6:
  'Reply on RC5', Koen Vogel, 02 Sep 2025
  Thank you for your time and effort. Your summary of my article is accurate. I see this article as a first step towards clarifying the 100 ka climate cycle, as well as better explaining the causes of geomagnetic variations such as magnetic reversals. Your comments indicate that a few of my arguments have failed to convince you of some key conclusions. I will address these individually below and rewrite the article to better clarify these issues once all final comments are in. Note that I have included some pictures in the attached pdf file, as I unfortunately was not able to add them in line. Where I mention e.g. "Picture 1" I suggest you go to the attached PDF file, or just download and read from it.
  “… the correlations found in this study are not convincing and some physical concepts are misinterpreted. Many of the claims, e.g. P4L70-71, P4L73 (... almost cerntanly caused by the OI forcing), P5L91-92 need some proof.”
  This comment goes to the heart of the paper, so I will try to make my reasoning clearer. I start by presenting the cross-correlations between OI, Obliquity and Eccentricity. These correlations are among the very best and clearest I’ve ever seen between time series, and I am therefore unclear whether these are the correlations you find unconvincing. The statistically significant, multi-cycle Obliquity and OI correlations indicate orbital forcings almost certainly – directly or indirectly - play a role in determining geomagnetic intensity variations. The blue dashed lines on the graphs indicate the 95% significance level, but the correlations are also significant at the 99% level (not shown on the graphs): there is therefore a <1% chance that the observed multi-cycle correlations are due to random chance. Especially convincing to me is that all orbital forcings show a good, significant correlation, because such builds confidence all three good correlations together happen by random chance is one in a million. I rule out sampling errors playing a significant role: the Laskar, 2004 and G&V curves are peer-reviewed, and therefore taken “as is”. Which leaves the question of a lurking variable, that is some parameter X that also varies with all 3 orbital forcing frequencies (41, 100, 400 ka) as well as paleogeomagnetic intensity. But if such were the case than variable X is almost certainly orbitally-forced, indicating that paleogeomagnetic intensity variations indirectly are too, via intermediate parameter X. Therefore: the paleogeomagnetic variations are almost certainly directly or indirectly caused by OI, Obliquity, and Eccentricity variations. The fact that both commonly found orbital forcing signatures (Obliquity and Eccentricity) are clearly influential almost certainly means that the dominant 100 ka period is also caused by an orbital forcing. The fact that orbital inclination is the only orbital forcing to have a 100 ka period, coupled to its statistically significant cross correlation, means that the 100 ka period is almost certainly caused by OI-forcing. The rest of the article deals with the physical processes underlying OI forcing.
  Orbital forcings therefore play a leading role in determining paleogeomagnetic intensity variations, so the next paragraphs deal with the plausible energy sources, which need to be large enough to influence/alter a geodynamo requiring 3.6-10 TW [Merrill et al., 1998; Verhoogen, 1980]. Ruling out cosmic forcings (evidently too small) leads to the conclusion that solar energy must be the orbital forcing source. Solar irradiation energy however can be ruled out: even if the G&V curve had a dominant 41 ka (Obliquity) period, one would be hard-pressed to imagine a process that converts solar irradiation energy – that doesn’t penetrate through Earth’s crust – into a large, geomagnetic power source that can vary geomagnetic intensity. But solar irradiation can additionally be ruled out as it insignificantly varies with orbital inclination (Viera), and therefore cannot explain the dominant 100 ka period. Fortunately, solar wind energy is more plausible:
  Orbitally-forced. OI variations demonstrably cause large solar wind intensity variations (see your point below)
  
  Interacts with the geomagnetic field (compresses and extends it on a daily basis) and therefore transfers energy to it.
  
  Has the right magnitude, i.e. 5 TW, and can be shown to vary between ~2 TW (OI = 3º) to ~ 10 TW (OI=0º), thereby fully bracketing the range estimated to power a geodynamo [Merrill et al., 1998; Verhoogen, 1980]
  
  “1. Please use longer datasets for the paleomagnetism. 290ka is not sufficient to investigate periods of 100ka. PISO-1500 would be a better choice as it covers 1.5Ma. The correlations with orbital parameters would be far more convincing if longer time periods are covered.”
  I agree that an analysis over a longer period offers several advantages, but disagree 290 ka is insufficient. Going back longer than 800 ka suffers from numerous serious drawbacks, e.g. including the Brunhes–Matuyama magnetic reversal (780 ka) as well as including the period prior to the mid-Pleistocene transition after which the dominant climate (and geomagnetic) period shifted from 41 ka (Obliquity) to 100 ka (see PISO-1500; Channell, 2009, Fig. 3).
  [Picture 1
  In addition, OI shows significant non-stationarity going back to 800 ka (see picture), while Eccentricity decreases to a minimum around 400 ka, all of which add significant complexity to the conclusions, without impacting the overall picture. Note that my article’s conclusions are consistent with PISO-1500: cycle-average OI reaches a minimum around 780 ka, indicating the OC was consistently receiving higher amounts of solar wind energy around this time, indicating the OC was (over) heating, indicating the paleogeomagnetic intensity was reaching a local minimum (see below from Channell, 2009), thereby creating the correct environment for the Brunhes–Matuyama magnetic reversal. But all this is far beyond the scope of the article: the article needs to walk before future articles can run.
  [Picture 2
  In addition Quinn et al.’s OI curve only extends back for 800 ka, but over this interval the multi-cycle cross correlation is good and significant.
  [Picture 3
  Additionally, G&V used a separate ∂18O paleotemperature proxy reference curve to normalize (age and value shift) the intervals older than 300 ka, which possibly makes comparisons of the post-300 ka to the pre-300 ka inappropriate (for now). Age uncertainty increases substantially for periods older than 40 ka, and for the less-documented MIS stages older than MIS 8. I therefore prefer the selected 290 ka period, as its correlations are statistically significant, and the subtle interplay between the orbital forcings readily explained, without overloading the reader with additional complexity.
  “2. Solar wind explanation. The solar wind at 1 astronomical unit is essentially radial and nearly isotropic, it is not concentrated in the solar equatorial plane. Therefore, the Earth's small inclination changes would have negligible effect on the total intercepted solar wind energy. What matters far more are coronal mass ejections and the high speed solar wind streams.”
  I haven’t been able to find any studies on Earth-incident solar wind variations during yearly, 11-year solar cycle or orbital time scales. The ones that deal with solar wind variations over the heliosphere invariably focus on its impact on something else of interest e.g. climate (Dessler, 1974; Herman & Goldberg, 1978) or the extent of the heliosphere, e.g.
  Richardson, J. D., 2001, The solar wind: Probing the heliosphere with multiple spacecraft. In: The Outer Heliosphere: The Next Frontiers, Edited by K. Scherer, Horst Fichtner, Hans Jörg Fahr, and Eckart Marsch COSPAR Colloquiua Series, 11. Amsterdam: Pergamon Press, 2001., p.301
  The solar wind model I employed was created from Richardson (2001), whose Fig. 1 deals with SW speed, density and pressure variations at 1 AU:
  [Picture 4
  Note I added the red line over the Voyager data as its line is very faint (I have a B&W copy of the COSPAR book) and I presume the graph was originally in color. Richardson concludes: “From solar minimum to solar maximum the latitudinal gradients of density and speed reverse so that at solar maximum speeds are higher near the solar equator, but solar cycle changes in the dynamic pressure occur at all solar latitudes. … During solar minimum, the speed and density decrease rapidly away from the solar equator. … The slow speed region is narrow enough that Earth's 7.25ºinclination produces significant speed effects.” Note Richardson projects the Voyager and Ulysses data back to 1 AU in order to compare the different datasets. Richardson claims that “At solar minimum, low speeds and high densities are found only near the equator in a band with half-width of order 10º with a several degree transition region to the fast, low density wind which persists up to high latitudes”, implying that Earth’s Orbital inclination of 6º-9º relative to the solar equator (OI to the Invariable Plane of 0 – 3º) keeps it within the near equator band, simplifying things. The graph above shows that around the solar maximum (1992-1994) the solar wind Pressure (i.e. its energy) is roughly isotropic at 1 AU, but that during the solar minimum (1994-1998) that followed the IMP8 satellite (i.e. Earth) shows a higher solar wind pressure than the higher solar latitude Voyager or Ulysses. This is mainly due to the higher density of the SW in the solar equatorial plane. During the solar minimum Earth’s SW density fluctuates between ~8 and ~12, with the higher value occurring when Earth passes through the solar equatorial plane (solar latitude 0º) and the lower values occurring when Earth’s orbit reaches the higher (7.25ºN and S) solar latitudes.
  
  Using the work-energy principle Earth-incident solar wind power, Us, can be calculated as:
  [Eqn 1
  
  where (assumed values between brackets) R_M is the magnetosphere radius (12 Earth radii), ⍴ the mass density of the solar wind, Vs the solar wind velocity (500 km/s), B_IMF the strength of the interplanetary magnetic field (10 nT), and µ₀ the vacuum magnetic permeability (1.26 10^-6 H/m). Note that the second term between the round brackets, the incident magnetic energy of the IMF, is commonly ignored as its size is much smaller than the first term, which represents the solar wind momentum energy. When Earth is at 7.25º solar latitude a SW density of 8.10^-21 kg.m^-3 results in a power of 6.4 TW. When passing through the solar equatorial plane however this increases to 9.6 TW (⍴ = 12.10^-21 kg.m^-3). When Voyager left the 10º band around 1994 its observed SW density dropped to about 6.10^-21 kg.m^-3 , so at high OI values of ~3º (9º angle to the solar equator) the solar wind power is on the order of 2.5 TW. In a nutshell: when OI is low (OI = ~0º ) the average Earth-incident SW power is significantly higher than when OI = ~3º
  
  “3. Solar wind and changes in paleomagnetism. The paper claims that magnetic flux at the magnetopause must pass through the mantle before reaching the core; mantle is low conductivity, so it cannot regenerate the flux. Therefore, solar wind deformation of the field lines at the magnetopause somehow couples into the outer core. This is flawed - magnetopause currents are external, not internal. Internal field is the mag field generated by the geodynamo in the outer core, and external is induced by solar wind. The magnetic perturbations from the solar wind are generated outside the Earth, in the magnetosphere and ionosphere. These fields can be observed at the Earth's surface, but they are not transmitted through the mantle into the core as flux. Mantle is a poor conductor of the current and it protects the outer core from the direct penetration of the solar wind mag field. Magnetic variations from the magnetosphere could in theory induce small secondary currents in the mantle, but they are shallow and do not significantly affect the geodynamo. The opposite is true: The geomagnetic field shapes the magnetopause and drives how solar wind couples to Earth - solar wind produces external geomag variations which we can measure at the Earth's surface.”
  I understand the general gist of this comment, but feel it may be due to a confusion over jargon.
  [Picture 5
  after Turner, J. , Winch, D., Ivers, D., Stening, R., 2007, Regular daily variations in satellite magnetic total intensity data. Annales Geophysicae, 25, 2167-2174.)
  The above pictures represent the magnetic daily variations above the ionosphere during a low activity (Solar Quiet) period. These geomagnetic variations are caused by the solar wind’s charged particle deflection by the geomagnetic field via the Lorentz force: geomagnetic energy is converted to particle kinetic energy, thus locally lowering the geomagnetic field strength in the solar direction. The particles’ kinetic energy is transferred to the magnetosphere as magnetic flux. Magnetic flux is defined as the surface integral of the normal component of the magnetic field, so locations where the field lines penetrate the Earth’s surface at a high angle, that is the high-latitude region “sweet spots” where inclination > 70° (blue and red blobs above) experience greater EM flux variations than the equatorial regions (inclination ≈ 0°). On a schematic: any movement of the geomagnetic field lines (𝛛B/𝛛t) represents the magnetic flux energy that is transferred. A small part of this flux energy is absorbed by the ionosphere and induces currents that attempt to undo (Lenz law) the magnetic flux variations, but what’s measured at Earth’s surface is a combination of the two.
  [Picture 6
  The ionospheric currents cannot completely “undo” the magnetic flux variations, as is evidenced by the above picture: the solar wind “pushes” the magnetic field lines, in this case the NMP away from the solar direction, causing magnetic flux at high latitudes. The induced ionospheric currents/fields cause (small) diminishment of the solar wind generated magnetic flux, but cannot completely cancel it (efficiency < 100%). Solar wind generated magnetic flux therefore enters solid Earth, where it is commonly assumed it is quickly absorbed by Earth’s Mantle, based on commonly assumed skin depth models. E.g. Banerdt, 2014, on deep EM probing of planets:
  "The effective penetration depth for EM waves is a strong function of frequency and resistivity. The EM skin depth (in meters) is given by d 1⁄4 500/s1⁄2f 1⁄2, where s is the conductivity (S/m) and f is the frequency (Hz)."
  Ott, 2009 and Schelkunoff, 1943, who formulate more complex skin depth models whereby conductivity is a function of frequency, but even Banerdt agrees that low frequencies on the order of 10^-5 Hz, i.e. the EM wave pulse generated by the solar wind, can be used to image the Lower Mantle. That is to say even under Banerdt’s overly conservative skin depth model, some solar wind generated magnetic flux makes it to the outer core, thereby establishing a route for solar wind generated EM flux to reach the OC.
  
  I explain most of this in the text, but in summary Ott indicates magnetic flux absorption is a function of shield conductivity (σ_r) and shield magnetic permeability (μ_r), both which vary as a function of frequency, and that assuming a static conductivity model and constant magnetic permeability – as Banerdt does - are inappropriate simplifications when determining the Mantle’s absorption of electromagnetic waves with frequencies below 1 kHz, as the electromagnetic properties of Earth's layers - μ_r and σ_r - vary greatly with frequency [Ott, 2009; Schelkunoff, 1943]. Ott claims experimental data suggest that absorption by non-magnetic shields is relatively insignificant for frequencies below 1 kHz (see graph from Ott below).
  
  [Picture 7
  
  A final point I would like to make is that in the solar quiet pictures above, you can see the geomagnetic field energy that was consumed by the solar wind incidence to the west of Mexico at 20:30 UT has been resupplied by 04:30, that is to say some energy source resupplied the magnetic flux energy and restored the geomagnetic field back to its normal, undeformed values. This restorative geomagnetic flux energy must have been generated in the outer core by the geodynamo and have travelled upwards through the Mantle. If restorative flux energy can travel up through the Mantle to the Magnetopause the solar wind generated flux energy can travel down through the Mantle to the OC. Physical theory and observations therefore overwhelmingly point to the fact that non-magnetic shields such as the Mantle do not absorb significant amounts of low frequency EM energy.
  
  Citation: https://doi.org/10.5194/egusphere-2025-1858-AC6
- AC8: 'Reply on RC5', Koen Vogel, 09 Sep 2025
  
  Before finalizing, I’d like to sum up the second reviewer’s comments and my reply.
  The reviewer’s comments are mainly technical in nature, and to a large extent support the consensus view on such matters as skin depth and solar wind – magnetosphere interactions. My article makes the case that the consensus view is occasionally mistaken
  I believe I have demonstrated that paleogeomagnetic intensity cross-correlates significantly with orbital inclination, obliquity and eccentricity, i.e. these orbital forcings can be used to partially explain paleogeomagnetic intensity variance, as well as build a predictive model. One periodicity match, e.g. 100 ka, can be a fluke, but when all 3 orbital forcings show significant cross-correlation it strongly suggests an orbitally forced external geomagnetic power source is at work. The reviewer feels such terms as “almost certainly” are an overstatement, so I’ll need to better justify such conclusions. Using a longer period (1.5 Ma) does not help, statistically, as these cross-correlations require time series with (weak) stationarity, and orbital inclination demonstrably isn’t over the last 800 ka (see my reply), but is over the 290 ka interval.
  The geomagnetic field is commonly thought to be generated by an Earth-internal geodynamo, whereby ferromagnetic convection cells convert thermal and mechanical energy to magnetic energy via induced electric currents. But a fairly recent review of 155 geodynamo models determined that the basic morphological properties of the geomagnetic field - relative axial dipole power, equatorial symmetry, zonality, and flux concentration - can only be reproduced under input parameters that are “remote from Earth's core values” (Christensen et al. 2010), that is the reviewed models can only produce Earth-like geometries using input parameters such as Core Ekman, magnetic Prandtl and Reynolds numbers, that are orders of magnitude different from realistic values.
  Ulrich R. Christensen, Julien Aubert, Gauthier Hulot, Conditions for Earth-like geodynamo models, Earth and Planetary Science Letters, Volume 296, Issues 3–4, 2010, Pages 487-496,
  ISSN 0012-821X, https://doi.org/10.1016/j.epsl.2010.06.009.
  So there is far too little internal energy available to explain the normal geomagnetic field strength, let alone explain how large intensity variations can occur over geologically short time periods or vary them cyclically with 100 ka or 41 ka periodicities. An orbitally-forced external energy source solves these problems nicely. Any orbital forcing very likely implicates solar energy. Solar irradiation can be ruled out. Solar wind energy has the right magnitude (~5 TW), and co-varies with orbital inclination, obliquity, and eccentricity. It demonstrably exchanges energy with the magnetosphere, consuming magnetic energy during its charged particle deflection. As stated by reviewer ” The geomagnetic field shapes the magnetopause and drives how solar wind couples to Earth - solar wind produces external geomag variations which we can measure at the Earth's surface.”, which means the solar wind-consumed energy must be replenished by the field generated in the outer core, which means magnetic flux must travel from the outer core, through the mantle to the magnetopause on a daily basis, which contradicts the claim that similar magnitude and frequency solar wind generated magnetic flux cannot travel down to the core. Even under Banerdt’s (see my comments) overly conservative skin depth model some magnetic flux reaches the core, indicating my theory is plausible, although some quibbling over the magnitude of flux energy reaching the outer core is possible: my article claims most of the energy reaches the core, traditional skin depth models indicate some fraction reaches the core. I believe solar wind energy is the only plausible orbitally-forced, 5 TW magnitude source transferring power to the geomagnetic field solution, and explaining the G&V observed paleogeomagnetic intensity fluctuations.
  
  Citation: https://doi.org/10.5194/egusphere-2025-1858-AC8

Koen Vogel

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Short summary

Earth's geologically recent past was characterised by a number of cold, glacial periods that came and went every 100,000 years. Earth's magnetic field similarly shows a 100,000 year cyclicity. This 100,000 year cyclicty is very likely caused by Earth's orbital movements relative to the solar equator, whereby Earth intercepts more solar wind energy during periods within the 100,000 cycles when Earth is closer to the solar equatorial plane.


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