No, Solar Variations Can’t Account for the Current Global Warming Trend. Here’s Why:

In part I of this series on the sun and Earth’s climate, I covered the characteristics of the sun’s 11 and 22 year cycles, the observed laws which describe the behavior of the sunspot cycle, how proxy data is used to reconstruct a record of solar cycles of the past, Grand Solar Maxima and Minima, the relationship between Total Solar Irradiance (TSI) and the sunspot cycle, and the relevance of these factors to earth’s climate system. In part II, I went over the structure of the sun, and some of the characteristics of each layer, which laid the groundwork for part III, in which I explained the solar dynamo: the physical mechanism underlying solar cycles, which I expanded upon in part IV, in which I talked about some common approaches to solar dynamo modeling, including Mean Field Theory. This installment covers how all of that relates to climate change and the current warming trend.

Solar Cycles and Earth’s Climate

The sun is responsible for nearly all of the energy entering our climate system, so it should come as no surprise that variations in Total Solar Irradiance throughout solar cycles do indeed affect Earth’s climate (Eddy 1977, Bond 2001, Solanki 2002, de Jager 2008). Knowing this, it’s natural to wonder whether solar variations are to blame for the current global warming trend. There’s nothing irrational about wondering “hey, you know that gigantic fusion reactor fireball thing in the sky? What if that thing has something to do with global warming and climate change?” I want to emphasize that this is by no means a crazy or unreasonable question to ask. It’s just that with the current warming we’re not just looking at cyclical oscillations or subtle fluctuations; we’re looking at a clear trend (NOAA 2016, Anderson et al 2013, Hansen et al 2010). And changes in solar activity are simply not sufficient to explain that rate and magnitude of the current trend (Frohlich 1998, Meehl et al 2004, Wild 2007, Lean and Rind 2008, Duffy 2009, Gray et al 2010, Kopp 2011).

It has been estimated that climate forcings attributable to solar variability have not contributed more than 30% of the global warming from 1970 – 1999 (Solanki 2003). To add insult to injury, 15 of the 16 hottest years on the instrumental record have occurred since the turn of the millennium, and more recent analyses have found that the solar activity and global temperature trends have been moving in opposite directions in recent cycles (Lockwood and Frohlich 2007 and 2008, Lockwood 2009). Moreover, researchers have found that the warming trend becomes even clearer after correcting for El Niños and volcanic and solar forcings (Foster 2011).

That’s right! Solar activity has actually declined in the last decade, and this last cycle (solar cycle 24) has been well below average amplitude (Jiang 2015, Pesnell 2016). So if changes in solar activity were the principle determinant of the recent changes, we should expect to be experiencing cooling: not warming. So this is also ruled out as a principle cause of late 20th century and early 21st century global warming and resultant climate change. Look at how solar forcings stack up against the observed temperature curve from Meehl et al 2004.

Image 3: c/o Meehl 2004

Firstly, if greenhouse gases are primarily responsible, we should expect to see little change in the amount of solar energy entering the earth’s atmosphere, but a decrease in the amount leaving. Contrastingly, if the sun is primarily responsible, we should expect to see an increase both in the energy entering earth’s atmosphere and the amount leaving. Since the mid-late 1970s, we’ve been able to measure this with satellites.

Lo and behold! It turns out that the rate of energy coming in from the sun has changed very little, while the rate at which energy leaves the earth has decreased significantly (Harries 2001, Griggs and Harries 2007, Philipona 2004, Leroy 2008, Worden 2008, Huang et al 2010). This is the proverbial smoking gun evidence that recent climate change is not due to changes in solar forcing, but rather to the greenhouse effect.

Secondly, if the warming effects were attributable primarily to the sun, then we should be seeing a very different distribution of temperatures than what we are actually observing. Specifically, warming due to solar forcing should be most prominent during the daytime and during the summer months, because these are the times during which the sun is most intensely bombarding the earth.

However, what we observe instead is that night time and winter temperatures are increasing faster than would be the case if the sun was chiefly responsible for the trend (Alexander et al 2006, Caesar et al 2006). This distribution cannot be explained by natural variability, but is consistent with the predictions of the greenhouse effect explanation (Brown 2008). The energy is entering the climate system during the day when the sun is shining, and is getting trapped by greenhouse gases, which slows down the rate at which that energy can escape the earth’s atmosphere. Alexander et al in particular found that over 70% of the land area sampled showed a significant increase in the occurrence of warm nights annual from 1951 – 2003, and a corresponding decrease in the occurrence of cold nights (Alexander et al 2006). So, here we have multiple lines of smoking gun evidence unanimously converging on the conclusion that current climate change cannot be blamed on changes in solar activity.

Could a Grand Minimum Mitigate 21st Century Global Warming?

Okay, so we know that variations in Total Solar Irradiance can’t account for the current warming trend, but what if we just lucked out and entered a new Grand Solar Minimum? How likely is it that it would stop or reverse the trend, and make the last few decades of climate science research and undesirable predictions seem like much ado about nothing? This possibility has been investigated in several papers as well. Although the predictions vary slightly insofar as the precise amounts by which TSI and temperatures would be reduced, they all arrive at reductions in TSI of no greater than a few watts per square meter, a slowing of ascending temperatures by no more than 0.1 – 0.3 °C, and therefore imply that a 21st Century Grand Minimum would (at most) slightly slow global warming down temporarily without actually stopping it (Wigley et al 1990, Feulner and Rahmstorf 2010, Jones et al 2012, Meehl et al 2013, Anet et al 2013, Maycock et al 2015). One might reason that any delay in the warming trend would be better than nothing, because it might buy some time for the innovation and implementation of mitigation and/or coping strategies, and I would not be compelled to argue against that, but the current weight of the evidence suggests that it would be of only marginal help at best.


In summary, solar cycles can affect earth’s weather and climate, both on decadal scales in correspondence with the 11 year sunspot cycle, as well as longer term amplitude changes associated with grand solar maxima and minima.

The prevailing scientific theory for the mechanism underlying these cycles is the solar dynamo, which explains the associated magnetic field oscillations in terms of a branch of physics called magnetohydronamics. It accounts for the observed sunspot butterfly diagrams, Sporer’s Law, Joy’s Law, and Hale’s Polarity Law, and explains the 11 and 22 year cycle periods. Mean Field theory is one of the ways in which stellar astrophysicists simplify solar dynamo model calculations, but it has its limitations.

Multiple lines of evidence suggest the current warming trend on earth is not caused by an increase in solar activity. We know from satellite data that there has been no substantial increase in the amount of solar energy (TSI) entering earth’s climate system, but less of it has been making it back out into space. Moreover, winter and night time warming has increased rapidly, which is consistent with the greenhouse effect explanation, but not with the solar forcing explanation.

Additionally, if a 21st Century Grand Solar Minimum were to occur, it would most-likely have a noticeable but small slowing effect on Global Warming and the resultant Climate Change.

What we humans should do about this is not a strictly scientific question, because it depends not only on model predictions but also on normative issues, personal values, and cost-benefit analyses of different potential solution strategies (both technological and political). However, what we do know with VERY high confidence is that global warming and climate change are happening, and that the sun is not to blame for it.


Related Articles:


Alexander, L. V., Zhang, X., Peterson, T. C., Caesar, J., Gleason, B., Klein Tank, A. M. G., … & Tagipour, A. (2006). Global observed changes in daily climate extremes of temperature and precipitation. Journal of Geophysical Research: Atmospheres111(D5).

Anderson, D. M., Mauk, E. M., Wahl, E. R., Morrill, C., Wagner, A. J., Easterling, D., & Rutishauser, T. (2013). Global warming in an independent record of the past 130 years. Geophysical Research Letters40(1), 189-193.

Anet, J. G., Rozanov, E. V., Muthers, S., Peter, T., Brönnimann, S., Arfeuille, F., … & Schmutz, W. K. (2013). Impact of a potential 21st century “grand solar minimum” on surface temperatures and stratospheric ozone. Geophysical Research Letters40(16), 4420-4425.

Bond, G., Kromer, B., Beer, J., Muscheler, R., Evans, M. N., Showers, W., … & Bonani, G. (2001). Persistent solar influence on North Atlantic climate during the Holocene. Science294(5549), 2130-2136.

Brown, S. J., Caesar, J., & Ferro, C. A. (2008). Global changes in extreme daily temperature since 1950. Journal of Geophysical Research: Atmospheres113(D5).

Caesar, J., Alexander, L., & Vose, R. (2006). Large‐scale changes in observed daily maximum and minimum temperatures: Creation and analysis of a new gridded data set. Journal of Geophysical Research: Atmospheres111(D5).

Cox, P. M., Betts, R. A., Jones, C. D., Spall, S. A., & Totterdell, I. J. (2000). Acceleration of global warming due to carbon-cycle feedbacks in a coupled climate model. Nature408(6809), 184-187.

De Jager, C. (2008). Solar activity and its influence on climate. Neth. J. Geosci. Geologie En Mijnbouw87, 207-213.

Duffy, P. B., Santer, B. D., & Wigley, T. M. (2009). Solar variability does not explain late-20th-century warming. Physics Today62(1), 48.

Eddy, J. A. (1977). Climate and the changing sun. Climatic Change1(2), 173-190.

Feulner, G., & Rahmstorf, S. (2010). On the effect of a new grand minimum of solar activity on the future climate on Earth. Geophysical Research Letters37(5).

Foster, G., & Rahmstorf, S. (2011). Global temperature evolution 1979 – 2010. Environmental Research Letters6(4), 044022.

Frohlich, C., & Lean, J. (1998). The Sun’s total irradiance: Cycles, trends and related climate change uncertainties since 1976. Geophys. Res. Lett25(23), 4377-4380.

Gray, L. J., Beer, J., Geller, M., Haigh, J. D., Lockwood, M., Matthes, K., … & Luterbacher, J. (2010). Solar influences on climate. Reviews of Geophysics48(4).

Griggs, J. A., & Harries, J. E. (2007). Comparison of spectrally resolved outgoing longwave radiation over the tropical Pacific between 1970 and 2003 using IRIS, IMG, and AIRS. Journal of climate20(15), 3982-4001.

Hansen, J., Ruedy, R., Sato, M., & Lo, K. (2010). Global surface temperature change. Reviews of Geophysics48(4).

Harries, J. E., Brindley, H. E., Sagoo, P. J., & Bantges, R. J. (2001). Increases in greenhouse forcing inferred from the outgoing longwave radiation spectra of the Earth in 1970 and 1997. Nature410(6826), 355-357.

Huang, Y., Leroy, S., Gero, P. J., Dykema, J., & Anderson, J. (2010). Separation of longwave climate feedbacks from spectral observations. Journal of Geophysical Research: Atmospheres115(D7).

Jiang, J., Cameron, R. H., & Schuessler, M. (2015). The cause of the weak solar cycle 24. The Astrophysical Journal Letters808(1), L28.

Jones, G. S., Lockwood, M., & Stott, P. A. (2012). What influence will future solar activity changes over the 21st century have on projected global near‐surface temperature changes?. Journal of Geophysical Research: Atmospheres117(D5).

Karl, T. R., & Trenberth, K. E. (2003). Modern global climate change. science302(5651), 1719-1723.

Kopp, G., & Lean, J. L. (2011). A new, lower value of total solar irradiance: Evidence and climate significance. Geophysical Research Letters38(1).

Lean, J. L., & Rind, D. H. (2008). How natural and anthropogenic influences alter global and regional surface temperatures: 1889 to 2006. Geophysical Research Letters35(18).

Leroy, S., Anderson, J., Dykema, J., & Goody, R. (2008). Testing climate models using thermal infrared spectra. Journal of Climate21(9), 1863-1875.

Liverman, D. (2007). From uncertain to unequivocal. Environment: Science and policy for sustainable development49(8), 28-32.

Lockwood, M., & Fröhlich, C. (2007, October). Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 463, No. 2086, pp. 2447-2460). The Royal Society.

Lockwood, M., & Fröhlich, C. (2008, June). Recent oppositely directed trends in solar climate forcings and the global mean surface air temperature. II. Different reconstructions of the total solar irradiance variation and dependence on response time scale. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (Vol. 464, No. 2094, pp. 1367-1385). The Royal Society.

Lockwood, M. (2009, December). Solar change and climate: an update in the light of the current exceptional solar minimum. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (p. rspa20090519). The Royal Society.

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Maycock, A. C., Ineson, S., Gray, L. J., Scaife, A. A., Anstey, J. A., Lockwood, M., … & Osprey, S. M. (2015). Possible impacts of a future grand solar minimum on climate: Stratospheric and global circulation changes. Journal of Geophysical Research: Atmospheres120(18), 9043-9058.

Meehl, G. A., Washington, W. M., Ammann, C. M., Arblaster, J. M., Wigley, T. M. L., & Tebaldi, C. (2004). Combinations of natural and anthropogenic forcings in twentieth-century climate. Journal of Climate17(19), 3721-3727.

Meehl, G. A., Arblaster, J. M., & Marsh, D. R. (2013). Could a future “Grand Solar Minimum” like the Maunder Minimum stop global warming?. Geophysical Research Letters40(9), 1789-1793.

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Philipona, R., Dürr, B., Marty, C., Ohmura, A., & Wild, M. (2004). Radiative forcing‐measured at Earth’s surface‐corroborate the increasing greenhouse effect. Geophysical Research Letters31(3).

Solanki, S. K. (2002). Solar variability and climate change: is there a link?. Astronomy & Geophysics43(5), 5-9.

Solanki, S. K., & Krivova, N. A. (2003). Can solar variability explain global warming since 1970?. Journal of Geophysical Research: Space Physics108(A5).

Wigley, T. M., Kelly, P. M., Eddy, J. A., Berger, A., & Renfrew, A. C. (1990). Holocene Climatic Change, 14C Wiggles and Variations in Solar Irradiance [and Discussion]. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences330(1615), 547-560.

Wild, M., Ohmura, A., & Makowski, K. (2007). Impact of global dimming and brightening on global warming. Geophysical Research Letters34(4).

Worden, H. M., Bowman, K. W., Worden, J. R., Eldering, A., & Beer, R. (2008). Satellite measurements of the clear-sky greenhouse effect from tropospheric ozone. Nature Geoscience1(5), 305-308.

Image Credits:

Image 3:

Meehl, G. A., Washington, W. M., Ammann, C. M., Arblaster, J. M., Wigley, T. M. L., & Tebaldi, C. (2004). Combinations of natural and anthropogenic forcings in twentieth-century climate. Journal of Climate17(19), 3721-3727.

Images 1 and 2:

Myhre, G., D. Shindell, F.-M. Bréon, W. Collins, J. Fuglestvedt, J. Huang, D. Koch, J.-F. Lamarque, D. Lee, B. Mendoza, T. Nakajima, A. Robock, G. Stephens, T. Takemura and H. Zhang, 2013: Anthropogenic and Natural Radiative Forcing. In: Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change [Stocker, T.F., D. Qin, G.-K. Plattner, M. Tignor, S.K. Allen, J. Boschung, A. Nauels, Y. Xia, V. Bex and P.M. Midgley (eds.)]. Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA, pp. 659–740, doi:10.1017/ CBO9781107415324.018.

Image 4:

Thoughtscapism and Making Sense of Climate Science Denial

coronal mass ejection c/o NASA

Mean Field Theory and Solar Dynamo Modeling

In a recent post, I talked about the characteristics of the sun’s 11 and 22 year cycles, the observed laws which describe the behavior of the sunspot cycle, how proxy data is used to reconstruct a record of solar cycles of the past, Grand Solar Maxima and Minima, the relationship between Total Solar Irradiance (TSI) and the sunspot cycle, and the relevance of these factors to earth’s climate system. In a follow up post, I went over the structure of the sun, and some of the characteristics of each layer, which laid the groundwork for my last post, in which I explained the solar dynamo: the physical mechanism underlying solar cycles.

Before elaborating on the sun’s role in climate change in the installment following this one, I’ll be going over an approach called “Mean Field Theory” in this installment, which dynamo theorists and other scientists sometimes use to make the modelling of certain systems more manageable. As was the case with part III, this may be a bit more technical than most of my subscribers are accustomed to, but I think the small subset of readers with the tools to digest it will appreciate it. And to be perfectly blunt, writing this was not just about my subscribers. I wanted to do it. It was an excuse for me to dig more deeply into something that has been going on in modern stellar astrophysics that I thought was interesting. The fact that it happened to be tangentially related to my series on climate science was a mere convenience. Anyone wanting to avoid the math and/or to cut to the chase with respect to the effects of solar cycles on climate change might want to skip ahead to part V, or perhaps just read only the text portions of this post. However, for those who don’t mind a little bit of math, I present to you the following:

Mean Field Theory

One approach by which scientists and mathematicians can simplify the models describing large complex systems stochastic effects is called Mean Field Theory (Schrinner 2005). This involves subsuming multiple complicated interactions between different parts of a system into a single averaged effect. In this way, multi-body problems, (which are notoriously difficult to solve even with numerical approximation methods with supercomputers), can be reduced to simpler single body problems. For instance, the velocity field u and magnetic field B could each be broken up into two separate terms: A mean term (u0 and B0 respectively), and a fluctuating term (u’ and B’ respectively), whereby the mean terms are taken as averages over time and/or space depending on what is appropriate to the system being modeled.

In other words, u = u0 + u’ and B = B0 + B’, where (by definition) the average velocity <u> = u0, the average magnetic field <B> = B0, because u0 and B0 are the mean field terms, and the average of the fluctuating terms <B’> and <u’> are both equal to zero by definition. The angled brackets simply denote a suitable average of the term they enclose (again taken over time and/or space as deemed appropriate by the scientist or mathematician). The reason the fluctuating terms average out to zero is because the mean field terms are defined as the average of the entire field, so by definition, the only way that can be true is if the fluctuating terms average out to zero.

Using the vector calculus identity × ( × B) = ∇(∇·B) + 2B, and the fact that ·B = 0 by Gauss’s Law for magnetic fields, the induction equation, ∂B/∂t  = × (u × B − η × B) from the previous section can also be expressed as ∂B/∂t = η2B + × (u × B), where 2B is called the Laplacian operator of the magnetic field B.

Plugging in our mean field equations u and B into this form of the induction equation:

∂B0/∂t + ∂B’/∂t = η2B0 + η2B’+

× (u0× B0) + × (u0 × B’) +

× (u’ × B0) + × (u’ × B’)

Now we take the average of both sides:

∂<B0>/∂t + ∂<B’>/∂t = η2<B0> + η2 <B’> + 

× <u0× B0> + × <u0 × B’> +

× <u’ × B0> + × <u’ × B’>

However, we’ve already know that <B0> = B0, <u0> = u0, and <u’> = < B’> = 0, so this can be simplified:

∂B0/∂t = η2B0 + × <u0× B0> + × <u’ × B’>.

The × <u’ × B’> is typically then replaced with a term × ε, where ε is called the mean electromotive force (Radler 2007). This yields the Mean Field Induction Equation:

∂B0/∂t = η2B0 + × <u0× B0 + ε>

Although many details of the theory are still being worked out, models based on the solar dynamo mechanism are consistent with the periodicity of the solar cycle, Hale’s law (the opposing magnetic polarity of sunspots above and below the solar equator and the alternation of polarity in successive 11 year cycles), as well as both Sporer’s and Joy’s laws (the apparent migration of sunspots towards the equator as a cycle progresses, as well as their tilt), which together produce the observed sunspot butterfly diagrams I talked about here.

Some models can even simulate variations in amplitude from one cycle to the next, but the precise manner in which Grand Solar Maxima and Minima emerge is still being worked out. Consequently, our models’ ability to reliably and accurately forecast them is currently still limited. Methods have been developed for estimating sunspot number and solar activity of a cycle’s solar maxima from observations of the poloidal field strength of the preceding cycle’s solar minima (Schatten 1978, Svalgaard 2005). In addition to only providing information on the solar maxima immediately after the minima being measured, this approach is also limited by the fact that our poloidal field measurements only go back a few cycles, and because the poloidal magnetic fields during solar minima are difficult to measure reliably, because they are weak and have radial as well as meridional components.

Other researchers have focused on kinematic flux transport solar dynamo models which, in addition to differential rotation, include the effects of meridional flow in the convective envelope, whereby the poloidal magnetic field is regenerated by the decay of the bipolar magnetically active regions subsequent to their emergence at the solar surface (Dikpati 1999, Dikpati 2006, Choudhuri 2007). Active regions are the high magnetic flux regions at which sunspots emerge.

Image  by Andres Munoz-Jaramillo (check out his fantastic presentations on

This meridional flow sets the period of the cycle, the strength of the poloidal field, and the amplitude of the solar maximum of the subsequent cycle. However, estimates of meridional flow velocities prior to 1996 are highly uncertain (Hathaway 1996). All of these models have been criticized by peers of their proponents. A concise summary of the blow by blow can be viewed here.

As for Grand Solar Maxima and Minima, no comprehensive theory has yet emerged on how they arise and decay, let alone a scientific consensus. However, certain constraints have been identified. There is evidence that the dynamo cycle does continue in some modified form during Maunder-type minima periods. The idea is that the dynamo enters Grand Maxima and Minima by way of chaotic and/or stochastic processes. In the case of Grand Maxima, the dynamo also exits that state via stochastic processes. In the case of Grand Minima, on the other hand, the dynamo then gets “trapped” in this state, but eventually gets out of it via deterministic internal processes (Usoskin 2007). It is also thought that the polarity of the sun’s toroidal magnetic field may lose its equatorial anti-symmetry during such minima, and instead become symmetric (Beer, Tobias and Weiss 1998).

Truly fantastic long term predictive power for solar cycles probably won’t be achieved until poloidal magnetic field generation is better understood, which will likely include improvements in flux transport models, and a more complete characterization of the statistical properties of bipolar magnetic regions (BMRs). For a comprehensive overview of the current state of Solar Dynamo Models and their predictive strengths and limitations, see Charbonneau 2010.

In the next installment, I’ll explain how all of this relates to climate change on earth, and address the elephant in the room: “are solar variations responsible for the current global warming trend?”

Related Articles:


Beer, J., Tobias, S., & Weiss, N. (1998). An active Sun throughout the Maunder minimum. Solar Physics181(1), 237-249.

Charbonneau, P. (2010). Dynamo models of the solar cycle. Living Reviews in Solar Physics7(1), 1-91.

Choudhuri, A. R., Chatterjee, P., & Jiang, J. (2007). Predicting solar cycle 24 with a solar dynamo model. Physical review letters98(13), 131103-131103.

Coriolis, G. G. (1835). Théorie mathématique des effets du jeu de billard. Carilian-Goeury.

Dikpati, M., & Charbonneau, P. (1999). A Babcock-Leighton flux transport dynamo with solar-like differential rotation. The Astrophysical Journal518(1), 508.

Dikpati, M., De Toma, G., & Gilman, P. A. (2006). Predicting the strength of solar cycle 24 using a flux‐transport dynamo‐based tool. Geophysical research letters33(5).

Hathaway, D. H. (1996). Doppler measurements of the sun’s meridional flow. The Astrophysical Journal460, 1027.

Rädler, K. H., & Rheinhardt, M. (2007). Mean-field electrodynamics: critical analysis of various analytical approaches to the mean electromotive force. Geophysical & Astro Fluid Dynamics101(2), 117-154.

Schatten, K. H., Scherrer, P. H., Svalgaard, L., & Wilcox, J. M. (1978). Using dynamo theory to predict the sunspot number during solar cycle 21. Geophysical Research Letters5(5), 411-414.

Schrinner, M., Rädler, K. H., Schmitt, D., Rheinhardt, M., & Christensen, U. (2005). Mean‐field view on rotating magnetoconvection and a geodynamo model. Astronomische Nachrichten326(3‐4), 245-249.

Svalgaard, L., Cliver, E. W., & Kamide, Y. (2005). Sunspot cycle 24: Smallest cycle in 100 years?. GEOPHYSICAL RESEARCH LETTERS32, L01104.

Usoskin, I. G., Solanki, S. K., & Kovaltsov, G. A. (2007). Grand minima and maxima of solar activity: new observational constraints. Astronomy & Astrophysics471(1), 301-309.

The Solar Dynamo: The Physical Basis of the Solar Cycle and the Sun’s Magnetic Field

In my previous article, I laid out some basics about the sun’s structure and physical characteristics in order to set up the groundwork upon which I could then explain the physical mechanism which underlies the solar cycles I talked about in the article prior to that one. I understand that this is a bit more technical than most readers may be accustomed to, which is why I’ve included a simplified “tl; dr” version before delving deeper.

Solar Dynamo Theory

The leading scientific explanation for the mechanism by which these solar cycles emerge is the solar dynamo theory. It arises from an area of physics called magnetohydrodynamics, which is the field which studies the magnetic properties of electrically conducting fluids, and is covered in most university textbooks on plasma physics. So how does it work?

The tl; dr version is as follows: the convective zone of the sun is a plasma (ionized gas), and it moves around via turbulent convection currents. The flow of these charged particles generates electric currents. Those electric currents generate magnetic fields (via Ampere’s law). In turn, when those magnetic fields change, they induce electric currents (Faraday’s law). In this manner, the dynamo is self-reinforcing, and permits the continual generation of magnetic dipole fields over time. An analogy that helps some people is to think of the magnetic field loops as being like rubber bands. And the convection currents stretch and twist the magnetic field lines. Just as how stretching and twisting rubber bands will increase their tension, the stretching and twisting of magnetic field lines can make the field stronger at certain points and/or change the field’s direction. If this twisting and stretching is done in a particular way (i.e. in the manner which occurs in our sun), it produces a cycle of changing magnetic fields which corresponds to the 11 and 22 year solar cycles.

However, this is an extremely over-simplified version of what the theory entails. There constraints on what sort of velocity fields will produce the observed effects. Namely, the flow must be turbulent like a pot of boiling water (rather than like a stream or faucet). The flow must be three dimensional. That means that the flow must have components in the radial direction, along the meridians (north and south), and along the latitudinal lines (also referred to as the azimuthal direction). And the flow must be roughly helical (Seehafer 1996).

Another critical requirement is differential rotation. In other words, the angular velocities at which the different parts of the sun rotate vary both with radius and with latitude (Schou 1998). The rotation rate at the solar equator, for example, is faster than the rotation at the poles. This is possible for the sun because it is composed primarily of plasma rather than a solid like the Earth. In the convective zone, differential rotation is primarily a function of latitude, and varies only weakly with depth, while the tachocline exhibits a strong radial shear (Howe 2009). The reason for these requirements is that the motions of the plasma must be capable of converting a meridional (poloidal) magnetic field into an azimuthal (toroidal) magnetic field, and vice versa.

The Omega Effect

Basically, if we begin with a meridional magnetic field, the differential rotation of the sun twists and coils this field around the sun, which results in an azimuthal magnetic field. This phenomenon of converting a meridional magnetic field into an azimuthal one is called the Omega effect. Its relevance to the observed solar cycle is that the twisting of the magnetic flux strands in the azimuthal (toroidal) direction in shallow depths and low latitudes create concentrated magnetic “ropes,” which are brought to the surface via magnetic buoyancy to produce the bipolar magnetic fields associated with sunspots and other related activity of the solar cycle (Parker 1955, Babcock 1961).

The Alpha Effect

Contrastingly, the Alpha effect converts an azimuthal (toroidal) magnetic field into a meridional (poloidal) field. The precise mechanism by which this occurs is still not fully understood as of this writing, but it has to do with the interaction between the velocity field of the plasma, the rotation of the sun, the toroidal magnetic field, and the Coriolis Effect acting on rising flux tubes.

From a qualitative standpoint, suppose we have a sphere of hot plasma rotating at an angular velocity ω. Suppose also that the fluid convects, and that certain localized pockets are hotter than the surrounding fluid, and thus move radially outward at velocity u. Additionally, suppose the presence of a toroidal magnetic field which gets partially dragged by the motion of the fluid. Since the sphere is rotating, each of those pockets of fluid is acted on by the Coriolis force ω x u, and therefore twists as it moves upwards and expands. Consequently, the magnetic field lines twist as well. Since the signs of both the Coriolis force and the toroidal magnetic field are reversed in the northern versus the southern hemisphere, this results in small scale magnetic field loops of the same polarity in both hemispheres (Coriolis 1835). The idea then is that these small scale loops of magnetic flux gradually coalesce as a result of magnetic diffusivity, which therefore generates a large scale poloidal magnetic field (Parker 1955).

The Omega Effect and the Alpha Effect. Image by E. F. Dajka

In this manner, a poloidal magnetic field generates a toroidal magnetic field, which in turn regenerates the poloidal magnetic field, and so on and so forth. The poloidal fields predominate during solar minima, while the toroidal fields generate the sunspots and other activity associated with solar maxima. The cycle repeats with an approximately 11 year period, and the associated magnetic fields alternate polarity from one cycle to the next, thus producing the observed 22 year solar cycle. I should reiterate that there are other hypotheses than what I’ve described here, and unlike the Omega effect, which is better understood, no clear scientific consensus has yet emerged on the precise mechanism of the alpha effect. In recent years, a lot of focus has been placed on variants of what’s known as the Babcock-Leighton (BL) mechanism, which is described here.

The Fundamental Equations of Magnetohydrodynamics and the Solar Dynamo

Warning!! Vector partial differential equations ahead!

The mathematically faint of heart may want to scroll past this section!

The physics involved in the dynamo are described by the equations of magnetohydrodynamics (MHD), which derive primarily from classical electromagnetism, but also from fluid mechanics to some extent, because hot plasmas share certain dynamical behaviors with liquids. The relevant equations include the following:

E = J/σ − u × B,

where E represents the electric field, J is the electric current density (charge per unit time per unit area), u is the velocity of a fluid element of the plasma, B represents the magnetic field, and σ is the conductivity of the plasma (J can also be expressed as J = nqvd, where q = the charge of a given particle, n = the number of said particles present, and vd is the average “drift” velocity of the particles).

This actually derives from Ohm’s law. You may be more familiar with Ohm’s law in its common form V = IR, where V is voltage (or electric potential difference), I is the electric current, and R is the resistance. But this is just veiled form of a more fundamental form of the Ohm’s law equation. The current I can also be expressed as I = J·A (the dot product of the current density with area element), and the resistance R can be expressed as a property called the resistivity ρ of the conductor (in this case the plasma) times the length element L of a charged particle’s path divided by the path’s cross sectional area element A, (R = ρL/A).

Thus V = IR becomes V = J·A(ρL/|A|) = JρL. But the resistivity term ρ of a given medium is also the reciprocal of a quantity called its conductivity (denoted as 1/ρ = σ), and the dot product of J·A is just the product of their magnitudes, thus giving us V = JL/σ, or alternatively, J = σV/L. But in many conductive mediums, this term scales linearly with the electric field, and can be expressed as J = σE. However, that’s in a reference frame co-moving with the fluid element. From a fixed reference frame (assuming non-relativistic velocities), and with an external magnetic field B, an additional term must be added to account for the Lorentz force on the moving charges, and the equation becomes J = σ(E + u x B), where u is the velocity of the fluid element, and x is not a multiplication sign, but rather what’s called a cross-product operator.

Dividing both sides by σ, and subtracting u x B from both sides yields the aforementioned E = J/σ − u × B equation.

Another important equation in the magnetohydrodynamics of the solar dynamo is the pre-Maxwellian form of Ampere’s Law:

× B = μ0J,

where μ0 is the magnetic permeability constant, and × B operator represents what’s called the curl of the magnetic field B.

Finally, there’s Faraday’s Law, one form of which is × E = – ∂B/∂t, which is basically saying that the curl of the electric field is equal to the negative of the rate of change of the magnetic field with time.

But we already have another expression for E = J/σ − u × B.

By dividing both sides of our × B = μ0J equation by μ0 to get J = × B/μ0, and then substituting that for J into our Ampere’s Law equation E = J/σ − u × B, we get E = ( × B)/(μ0σ) – u × B.

We can then substitute into our Faraday’s Law equation × E = – ∂B/∂t, in which case we get

× [( × B)/(μ0σ) – u × B] = – ∂B/∂t.

Rearranging this, we get the following:

∂B/∂t  = × (u × B − η × B),

where η = 1/(μ0σ) is the magnetic diffusivity term.

This is the MHD induction equation. The first term on the right side of the MHD induction equation represents the induction via the flow of electrically charged constituents across the magnetic field, while the second term expresses Ohmic dissipation of the current systems supporting that magnetic field. The relative importance of these two terms is measured by what’s called a magnetic Reynold’s number: Rm = u0L/η, where u0 and L are characteristic values for the flow velocity and length scale of the system respectively. For solar dynamo action, where L is on the order of the solar radius, Rm is invariably much greater than 1. Ergo, the Ohmic dissipation is highly inefficient on this scale, and therefore maintaining a solar magnetic field against diffusion is no problem.  

And now for something unrelated…

In the next installment, I’ll briefly go over an approach called Mean Field Theory, which astrophysicists and other scientists sometimes use to simplify their mathematical models of large complex systems.

Related Articles:


Babcock, H. W. (1961). The Topology of the Sun’s Magnetic Field and the 22-YEAR Cycle. The Astrophysical Journal133, 572.

Coriolis, G. G. (1835). Théorie mathématique des effets du jeu de billard. Carilian-Goeury.

Howe, R. (2009). Solar interior rotation and its variation. Living Reviews in Solar Physics6(1), 1-75.

Parker, E. N. (1955). Hydromagnetic dynamo models. The Astrophysical Journal122, 293.

Parker, E. N. (1955). The Formation of Sunspots from the Solar Toroidal Field. The astrophysical journal121, 491.

Schou, J., Antia, H. M., Basu, S., Bogart, R. S., Bush, R. I., Chitre, S. M., … & Gough, D. O. (1998). Helioseismic studies of differential rotation in the solar envelope by the solar oscillations investigation using the Michelson Doppler Imager. The Astrophysical Journal505(1), 390.

Seehafer, N. (1996). Nature of the α effect in magnetohydrodynamics. Physical Review E53(1), 1283.

The Structure and Properties of the Sun

In my most recent post, I discussed the characteristics of the sun’s 11 and 22 year cycles, the observed laws which describe the behavior of the sunspot cycle, how proxy data is used to reconstruct a record of solar cycles of the past, Grand Solar Maxima and Minima, the relationship between Total Solar Irradiance (TSI) and the sunspot cycle, and the relevance of these factors to earth’s climate system. Before elaborating on the sun’s role in climate change, I’d like to take a look at the mechanism in terms of which the magnetic cycles underlying these solar cycles actually arises, but in order to do that, it’s necessary to first go over some basics:

The Structure of the Sun

The Core: The core of the sun is where pressures and temperatures are high enough to facilitate the nuclear fusion reactions which power the sun (Eddington 1920). The sun is so hot that there are few (if any) actual atoms of hydrogen and helium gas (Bethe 1939). They exist in a plasma state; the gases are ionized and cohabit with free electrons. So protons are being collided and fused into helium nuclei in what’s known as the proton-proton chain (PPO Chain), which is the dominant fusion process in stars of masses comparable to (or less than) the sun. In the PPO chain, two protons fuse and release a neutrino. The resulting diproton either decays back into hydrogen via proton emission, or undergoes beta decay (emitting a positron), which turns one of the protons into a neutron, thus yielding deuterium. The deuterium then reacts with another proton, producing 3He and a gamma ray. Two 3He from two separate implementations of this process then fuse to produce 4He plus two protons (Salpeter 1952).

Image by UCAR: Randy Russell (Windows of the Universe project)

This region comprises about the first 0.2 of the solar radius, and exhibits temperatures on the order of 14 – 15 million Kelvin.

The Radiative Zone: From about 0.2 – 0.7 solar radii from the center is the radiative zone. The nuclear fusion reactions in the core produce radiation which gets reiteratively absorbed and reemitted by various particles in this zone in a random zig-zag pattern. It can take hundreds of thousands of years for photons in this region to reach the surface in this manner. This succession of absorptions and reemissions also results in the photons which escape into the convective zone being of longer wavelength and lower energy than the gamma ray photons that were initially emitted from the nuclear fusion reactions in the core. The temperatures here are still on the order of a few million Kelvin.

The Layers of the Sun. (Image by Kelvinsong).

The Tachocline: The interface layer at the boundary separating the radiative zone and convective zone is called the Tachocline. The radiative and convective zones obey different rotational laws, and the advection of angular momentum in the Tachocline (which acts as a transition layer between them) is controlled by horizontal turbulence (Spiegel 1992). Changes in fluid flow velocities across this layer can twist magnetic field lines.

The Convective Zone: This zone runs from about 0.7 solar radii up to the sun’s surface (the Photosphere). As the name implies, heat pockets convect through the ionized gas in this region towards the surface in a manner similar to a boiling pot of water. The convective zone is just cool enough that many of the heavier ions are able to retain at least some of their electrons, which means that the material in the convective zone is more opaque, and thus it’s harder for radiation to get through it. Consequently, a lot of heat gets trapped in this zone, which causes the material to “boil” (or convect). As we’ll see soon enough, this property is important in making possible the solar dynamo mechanism that underlies the solar cycle. The temperature gradient of the convection zone ranges from around 2 million Kelvin near the tachocline to roughly 6,000 Kelvin at the sun’s surface.

The Photosphere: This is the sun’s visible surface layer. The photosphere includes features such as the following:

Sunspots: these are dark regions representing high magnetic flux, and are associated with changes in polarity of the sun’s magnetic field (Hale 1908). I’ve already covered some of the properties of sunspots, the sunspot cycle, and how sunspot abundance can be used as a proxy for Total Solar Irradiance (TSI) in a recent post here, and will cover the mechanism underlying the sunspot cycle when I elucidate the Solar Dynamo  in a follow-up post.

Sunspot c/o NASA

Faculae: these are bright regions which are also highly magnetized, but whose magnetic fields are concentrated in considerably smaller bundles than in sunspots (Richardson 1933). During solar maxima, when abundant dark sunspots are blocking the emission of heat and light, these bright regions overpower the darkening effect of the sunspots, thus resulting in the net increase in luminosity that we observe during solar maxima (Spruit 1982).

Faculae c/o NASA

Granules: these are the tops of convection cells which cover nearly the entire photosphere in ever-changing grain-like patterns (Langley 1874). The bright center bulges of the granules are regions where the plasma is rising to the surface, whereas the darker boundaries around them are where the plasma is cooler and sinking back down.

Granules: Image by Goran Scharmer and Mats G. Löfdahl

Supergranules c/o NASA

And supergranules: these are huge polygonal convective cells which are larger and last longer than granules, and are outlined by the chromospheric network. They have an average diameter of about 13,000 – 32,000 km and last an average of about 20 hrs (Simon 1964, Hagenaar 1997).

Additionally, the photosphere is also where solar flares originate. For more on solar flares, check out this article from

The Chromosphere: This is an approximately 2,000 km layer of gas residing above the photosphere, in which temperatures run from around 6,000 – 25,000 K (Vernazza 1976, Carlsson 1994). As a consequence, hydrogen in this layer emits light of a reddish color in a process called H-alpha emission (Michard 1958). The electrons of a particular atom can only occupy certain specific allowed energy states. They are quantized. These states correspond to specific principle quantum numbers, n = 1, n = 2, n = 3 etc… When an electron drops from one allowed energy state to a lower level, it emits a photon whose wavelength (and thus color) corresponds to the difference in energy between those two allowed states. Contrastingly, only a photon corresponding to the exact energy difference between two states can be absorbed by the electron to push it up to the higher energy state. In the limited case of hydrogen-like atoms, the relationship is described by the Rydberg formula, which is as follows:

1/λ = RZ2(1/nf2 – 1/ni2),

where λ is the wavelength of the photon emitted or absorbed, Z is the atomic number of the hydrogen-like atom in question (1 in this case), R is the Rydberg constant (approximately 1.097*10^7 m-1 in S.I. units), ni is the quantum number of the electron’s initial state, and nf is the quantum number of its final state. H-alpha emission occurs when an electron of a hydrogen atom drops from its third lowest allowed energy level (ni = 3) to its second lowest (nf = 2). ). If you plug in these values, you get that λ = 656 nm, which is in the red light range.

This transition is part of what’s called the Balmer series, which consists of all the allowed transitions between ni ≥ 3 and nf = 2 (Bohr 1913).

Other chromospheric features include the chromospheric network, which is a web-like pattern outlining supergranule cells, which results from bundles of magnetic field lines concentrated in the supergranules (Hagenaar 1997). Spicules are jet like eruptions of hot gas which protrude from the chromospheric network thousands of kilometers above the chromosphere and into the corona. Filaments and prominences are huge plumes of gas suspended as loops above the sun by magnetic fields, which underlie many solar flares (Kiepenheuer 1951, Menzel 1960). Plage, which are also associated with concentrations of magnetic field lines, appear as bright spots surrounding sunspots (Leighton 1959).

The Transition Region: This thin region resides between the cooler chromosphere and the much hotter corona. For this reason, temperatures rapidly increase with radial distance outward, ranging from 25,000 K around the boundary of the chromosphere to about 10^6 K out near the corona (Peter 2001).

The Corona: This aura of plasma is the sun’s outer atmosphere. It reaches temperatures far greater than at the sun’s surface (on the order of 1 – 3.5 million degrees Celsius). The reasons for these extreme temperatures comprise a long standing puzzle in solar astrophysics known as the Coronal Heating Problem, which is beyond the scope of this brief outline. That said, these extreme temperatures result in jets of plasma at speeds of up to 400 km/s (Brueckner 1983). Consequently, some of this ionized gas overcomes the sun’s gravitational pull, escapes, and subsequently cools down (Hundhausen 1970). This is the solar wind (Brueckner 1983). Incidentally, there is evidence that the sun’s rotation rate was greater in the past, and that the solar wind is responsible for its subsequent loss of angular momentum (Durney 1977). The corona is also the region from which Coronal Mass Ejections (CME) emerge. As the name implies, these can involve the ejection of billions of tons of plasma as a result of the reconnection of opposite ends of complicated magnetic field loops in the corona, and often accompany strong solar flares and filament eruptions. Not all solar flares and filament eruptions result in a CME though. Solar flares typically involve the expulsion of long radio wave radiation all the way up the EM spectrum through visible light (or even gamma rays), as well as protons and electrons, the latter of which can result in x-ray emissions via bremsstrahlung radiation (Arnoldy 1968). Charged particles in flares are accelerated by a combination of electric fields and magnetohydrodynamic waves (Miller 1997). You can read more about CME events here, here and here and solar flares here and here.

Any one of these layers and properties I’ve described here could be elaborated upon in greater detail, but this should be sufficient for the purpose of seguing into an explanation of the solar dynamo: the physical mechanism in terms of which solar cycles arise, which will be the topic of my next installment of this series.

Related Articles:


Arnoldy, R. L., Kane, S. R., & Winckler, J. R. (1968). Energetic solar flare X-rays observed by satellite and their correlation with solar radio and energetic particle emission. The Astrophysical Journal151, 711.

Bethe, H. A. (1939). Energy production in stars. Physical Review55(5), 434.

Bohr, N. (1913). The spectra of helium and hydrogen. Nature92, 231-232.

Brueckner, G. E., & Bartoe, J. D. (1983). Observations of high-energy jets in the corona above the quiet sun, the heating of the corona, and the acceleration of the solar wind. The Astrophysical Journal272, 329-348.

Carlsson, M., & Stein, R. F. (1995). DOES A NONMAGNETIC SOLAR CHROMOSPHERE EXIST?. The Astrophysical Journal440, L29-L32.

Durney, B. R., & Latour, J. (1977). On the angular momentum loss of late-type stars. Geophysical & Astrophysical Fluid Dynamics9(1), 241-255.

Eddington, A. S. (1920). The internal constitution of the stars. The Scientific Monthly, 297-303.

Hagenaar, H. J., & Schrijver, C. J. (1997). The distribution of cell sizes of the solar chromospheric network. The Astrophysical Journal481(2), 988.

Hale, G. E. (1908). On the probable existence of a magnetic field in sun-spots. The astrophysical journal28, 315.

Hundhausen, A. J. (1970). Composition and dynamics of the solar wind plasma. Reviews of Geophysics8(4), 729-811.

Kiepenheuer, K. O. (1951). The Nature of Solar Prominences. Publications of the Astronomical Society of the Pacific63, 161.

Langley, S. P. (1874). On the structure of the solar photosphere. Monthly Notices of the Royal Astronomical Society34, 255.

Leighton, R. B. (1959). Observations of Solar Magnetic Fields in Plage Regions. The Astrophysical Journal130, 366.

Menzel, D. H., & Wolbach, J. G. (1960). On the Fine Structure of Solar Prominences. The Astronomical Journal65, 54.

Michard, R. (1958). INTERPRETATION OF THE H* alpha/SPECTRUM OF THE CHROMOSPHERE. Compt. rend.247.

Miller, J. A., Cargill, P. J., Emslie, A. G., Holman, G. D., Dennis, B. R., LaRosa, T. N., … & Tsuneta, S. (1997). Critical issues for understanding particle acceleration in impulsive solar flares. Journal of Geophysical Research: Space Physics102(A7), 14631-14659.

Peter, H. (2001). On the nature of the transition region from the chromosphere to the corona of the Sun. Astronomy & Astrophysics374(3), 1108-1120.

Richardson, R. S. (1933). A Photometric Study of Sun-Spots and Faculae. Publications of the Astronomical Society of the Pacific45(266), 195-198.

Salpeter, E. E. (1952). Nuclear reactions in the stars. I. Proton-proton chain. Physical Review88(3), 547.

Simon, G. W., & Leighton, R. B. (1964). Velocity Fields in the Solar Atmosphere. III. Large-Scale Motions, the Chromospheric Network, and Magnetic Fields. The Astrophysical Journal140, 1120.

Spiegel, E. A., & Zahn, J. P. (1992). The solar tachocline. Astronomy and Astrophysics265, 106-114.

Spruit, H. C. (1982). The flow of heat near a starspot. Astronomy and Astrophysics108, 356-360.

Vernazza, J. E., Avrett, E. H., & Loeser, R. U. D. O. L. F. (1976). Structure of the solar chromosphere. II-The underlying photosphere and temperature-minimum region. The Astrophysical Journal Supplement Series30, 1-60.

Image Credits:

Layers of the Sun by Kelvinsong (Own work) [CC BY-SA 3.0 (], via Wikimedia Commons

Granules by Goran Scharmer/Mats G. Löfdahl of the Institute for Solar Physics at the Royal Swedish Academy of Sciences. 

Proton-Proton chain Image by UCAR: Randy Russell (Windows of the Universe project)

Sunspots, Faculae, and Supergranules by NASA

The Sun and Earth’s Climate: The Solar Cycle and the Maunder Minimum

The Solar Cycle

The Sun goes through an approximately 11 year periodic solar cycle (Gnevyshev 1967). This cycle includes variations in solar irradiation, the amount of ejected materials, solar flares and sunspot activity. Total Solar Irradiance (TSI) is measured in power per unit area (energy per unit time per unit area), and is of particular importance in that it represents the total incoming energy driving the climate system.

Since we’ve only had direct satellite measurements of TSI since the mid-late 1970s, estimates of solar output for earlier times were (and are) based on one or more proxies. Sunspot observations are one such proxy. Sunspot abundance correlates strongly with TSI, so they can thus be used as a proxy for solar maxima and minima. Astronomers have recorded telescopic sunspot observations since the early 1600s, and there is evidence of naked eye observations dating much further back (Stephenson 1990). In addition to noticing that the number of sunspots oscillated in 11 year cycles, astronomers also noticed that sunspots would first appear in pairs or groups at about 30 – 35 degrees both North and South of the solar equator, and the mean latitudes of subsequently appearing spots would tend to migrate towards the solar equator as the cycle progressed, a phenomenon referred to as Spörer’s Law (Carrington 1858, Carrington 1863, Spörer 1879).

Closely related to this is Joy’s Law, which is the observation that the spots tend to be “tilted,” in the sense that the leading spots tend to be closer to the solar equator than the following spots, and that the magnitude of the slope of that tilt increases with latitude (Hale et al 1919, Wang 1989, d’Silva 1992, Tian 2001). These sunspots emerge in regions of bipolar magnetic field lines, whereby the typical pair of North-South sunspot counterparts are of opposite polarity of one another (Hale 1915). When the observed patterns of emergence of these sunspots are plotted over time, they give rise to what are referred to as butterfly diagrams.

Sunspot Butterfly Diagrams c/o NASA

In the early 20th century, G.E. Hale observed the Zeeman splitting of spectral lines from sunlight, which suggested the existence of magnetic field lines at the solar surface (Hale 1908). Subsequently, Hale and other astronomers deduced that sunspots were regions of particularly strong magnetic fields, and that their dark appearance was due to them being cooler than their surroundings (about 3,700 K, as opposed to about 5,700 K for their surroundings). They also figured out that, when polarity is taken into account, the 11 year sunspot cycle was really part of a 2*11 = 22 year cycle, whereby the polarity of the magnetic fields of the sunspots in the second half of the 22 year cycle was the reverse of their polarity in the first half (Hale 1924). This is called Hale’s Polarity Law. Since periods of maximum and minimum sunspot activity correspond to solar maxima and minima, they make for excellent proxies for variables such as Total Solar Irradiance.

Through the use of dendroclimatological (tree ring) and other proxy data, scientists have put together sunspot and solar activity reconstructions stretching back over 11,000 years (Solanki 2004, Beer 2000, Usoskin 2006). This is possible because the flux of high energy cosmic rays entering earth’s atmosphere is modulated by solar magnetic activity (particularly the solar wind)(Stuiver 1980, Beer 2000). These particles are responsible for the production of certain radio isotopes, such as 14C and 10Be, whose respective abundances are anti-correlated with solar magnetic activity. The former is preserved in tree rings, while the latter is preserved in ice caps (Beer 2000, Bard 1997, Stuiver 1980). Here are some data sets for your perusal.

Grand Solar Maxima and Minima

It’s important to note that not all solar cycles are equal. Solar maxima and minima can vary in amplitude from one solar cycle to the next, and in some cases extended Grand Solar Maxima and Minima can arise (Gleissberg 1939). Additionally, stronger cycles tend to rise more quickly and peak earlier than weaker cycles: a phenomenon known as the Waldmeier effect (Waldmeier 1941, Karak and Choudhuri 2011), though not all measures of solar activity exhibit this effect (Dikpati et al 2008, Cameron and Schussler 2008). The occurrences of grand solar maxima and minima are driven in part by stochastic and/or chaotic processes that result from the complicated action of the solar dynamo: the physical mechanism underlying solar cycles (Charbonneau 2000), which I will attempt to elucidate soon enough.

The Maunder Minimum

The Maunder Minimum, which took place in middle of a roughly 550 year period known as the Little Ice Age, was an example of a Grand Solar Minimum (Eddy 1976). More specifically, the Maunder Minimum refers to an extended period of very low sunspot activity spanning from about 1645 – 1715. As a point of reference, this period coincided almost exactly with the reign of the French monarch, Louis XIV (known to his subjects as “The Sun King”), whom you may remember reading about in history class. He had the longest reign of any king in all of European history (1643 – 1715), and is often presented as the quintessential example of a European Absolute Monarch. In science, this period also saw the publication of Newton’s Principia, Robert Hooke’s discovery of the cell as the fundamental biological unit, Newton and Leibniz’s co-discovery of calculus, and the discovery of Boyle’s law for ideal gases. During this period, very few sunspots were observed. One might assume that this was due to a lapse in vigilance on the part of European astronomers, but that was not the case. There really was significantly less sunspot activity than usual during the Maunder Minimum (Ribes et al 1993), hence why it is often given as a recent example of a Grand Solar Minimum. Perhaps unsurprisingly, the Earth was slightly cooler during this time (Guinan 2002).

Average Sunspot numbers during the Maunder Minimum (c/o NASA)

So, what causes grand solar minima and maxima? For that matter, what causes the maxima and minima of the usual 11 year solar cycle? Why do these cycles exist? In order to unpack the concepts underlying the mechanism by which changes in the sun’s magnetic field produce these solar cycles (called the solar dynamo), it is necessary to give a brief overview of the structure of the sun, and the characteristics of its different layers. I’ll cover that in part II.

Related Articles:


Bard, E., Raisbeck, G. M., Yiou, F., & Jouzel, J. (1997). Solar modulation of cosmogenic nuclide production over the last millennium: comparison between 14C and 10Be records. Earth and Planetary Science Letters3(150), 453-462.

Beer, J. (2000). Long-term indirect indices of solar variability. Space Science Reviews94(1-2), 53-66.

Cameron, R., & Schüssler, M. (2008). A robust correlation between growth rate and amplitude of solar cycles: consequences for prediction methods. The Astrophysical Journal685(2), 1291.

Carrington, R. C. (1858). On the distribution of the solar spots in latitudes since the beginning of the year 1854, with a map. Monthly Notices of the Royal Astronomical Society19, 1-3.

Carrington, R. C. (1863). Observations of the spots on the sun: from November 9, 1853, to March 24, 1861, made at Redhill. Williams and Norgate.

Charbonneau, P., & Dikpati, M. (2000). Stochastic fluctuations in a Babcock-Leighton model of the solar cycle. The Astrophysical Journal543(2), 1027.

Dikpati, M., Gilman, P. A., & De Toma, G. (2008). The waldmeier effect: an artifact of the definition of wolf sunspot number?. The Astrophysical Journal Letters673(1), L99.

D’Silva, S. (1992). Joy’s Law and Limits on the Magnetic Field Strength at the Bottom of the Convection Zone. In The Solar Cycle (Vol. 27, p. 168).

Eddy, J. A. (1976). The Maunder Minimum. Science192, 1189-1202.

Gleissberg, W. (1939). A long-periodic fluctuation of the sun-spot numbers. The Observatory62, 158-159.

Gnevyshev, M. N. (1967). On the 11-years cycle of solar activity. Solar Physics1(1), 107-120.

Guinan, E. F., & Ribas, I. (2002). Our changing Sun: the role of solar nuclear evolution and magnetic activity on Earth’s atmosphere and climate. In The evolving Sun and its influence on planetary environments (Vol. 269, p. 85).

Hale, G. E. (1908). On the probable existence of a magnetic field in sun-spots. The astrophysical journal28, 315.

Hale, G. E. (1915). The Direction of Rotation of Sun-Spot Vortices. Proceedings of the National Academy of Sciences1(6), 382-384.

Hale, G. E., Ellerman, F., Nicholson, S. B., & Joy, A. H. (1919). The magnetic polarity of sun-spots. The Astrophysical Journal49, 153.

Hale, G. E. (1924). Sun-spots as magnets and the periodic reversal of their polarity. Nature113, 105-112.

Karak, B. B., & Choudhuri, A. R. (2011). The Waldmeier effect and the flux transport solar dynamo. Monthly Notices of the Royal Astronomical Society410(3), 1503-1512.

Ribes, J. C., & Nesme-Ribes, E. (1993). The solar sunspot cycle in the Maunder minimum AD1645 to AD1715. Astronomy and Astrophysics276, 549.

Solanki, S. K., Usoskin, I. G., Kromer, B., Schüssler, M., & Beer, J. (2004). Unusual activity of the Sun during recent decades compared to the previous 11,000 years. Nature431(7012), 1084-1087.

Spörer, F. W. (1879). Beobachtung der Sonnenflecken etc. Astronomische Nachrichten96, 23.

Stephenson, F. R. (1990). Historical evidence concerning the sun: interpretation of sunspot records during the telescopic and pretelescopic eras. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences330(1615), 499-512.

Stuiver, M., & Quay, P. D. (1980). Changes in atmospheric carbon-14 attributed to a variable sun. Science207(4426), 11-19.

Tian, L., Bao, S., Zhang, H., & Wang, H. (2001). Relationship in sign between tilt and twist in active region magnetic fields. Astronomy & Astrophysics374(1), 294-300.

Usoskin, I. G., Solanki, S. K., & Korte, M. (2006). Solar activity reconstructed over the last 7000 years: The influence of geomagnetic field changes. Geophysical Research Letters33.

Waldmeier, M. (1941). Ergebnisse und probleme der sonnenforschung, von dr. M. Waldmeier… MIT 102 figuren. Leipzig, Becker & Erler kom.-ges., 1941.1.

Wang, Y. M., & Sheeley Jr, N. R. (1989). Average properties of bipolar magnetic regions during sunspot cycle 21. Solar physics124(1), 81-100.


The Ultimate Environmental Cataclysm: Asteroid and Comet Impacts and their Effects on Climate

The Cretaceous-Tertiary (K-T boundary) extinction ~66 million years ago is perhaps the most famous extinction event in Earth’s history. It featured a massive asteroid impact which led to the extinction of an estimated 76% of all fossilizable species, and marked the end of the ~170 million+ year reign of the dinosaurs (Pope 1998). Initially regarded as a radical proposition, this is the Alvarez hypothesis, after Luis Alvarez, the lead scientist of the team that discovered the first of multiple lines of smoking gun evidence for the impact of an asteroid ~10 km across under Chicxulub on the coast of the Yucatan Peninsula right around the time of the K-T boundary (Alvarez 1979, Smit 1981, Smit 1980, Bohor 1984, Bohor 1987, Bourgeois 1988 & Hildebrand 1991).


An artist’s interpretation of a hypothetical asteroid impact. Sources: Here and here.

In addition to the famous K-T extinction, which is also sometimes referred to in the literature as the Cretaceous-Paleogene (or K-Pg boundary) extinction, I also mentioned that one or more meteoroid impact may have been one of several contributing factors of Earth’s worst mass extinction event of all time: the Permian extinction. So, such impacts may have affected life on Earth on more than one occasion, but in precisely what ways can such impact events affect the climate? First of all, let’s clarify the difference between an asteroid, comet, bolide, meteoroid or meteorite:

The degree to which an asteroid impact affects the climate depends on its size and mass. It’s estimated that an impact which releases a million megatons of energy (representing an asteroid roughly 2 km in diameter) would produce about 10^16 kg of ejecta, which is approximately on par with an M9 Super Volcano (Morrison 2006). That’s near the upper limit of what is considered possible. In terms of energy, such an impact would also be on par with an earthquake of magnitude 10, which is beyond the range considered to be possible (Morrison 2006). This would likely also be accompanied by a subsequent tsunami as well as wild fires due to thermal radiation. Insofar as climatological effects, an impact in this range would have significant global effects on the ozone (ostensibly destroying it), and would produce enough stratospheric dust and sulfates to induce global cooling (Toon 1997, & Pierazzo 1998).

The Chicxlub K-T boundary event in particular may have also indirectly triggered global warming effects by releasing large amounts of carbon monoxide (CO) (Kawarigi 2009). Although only a weak greenhouse gas, CO tends to react with hydroxyl (OH) radicals in the atmosphere. This reduces their abundance. The OH radicals normally help limit the lifetime of stronger greenhouse gases like methane, so the idea is that CO released by the K-T boundary impact event may have led to global warming by reducing atmospheric OH radical concentrations, thus increasing greenhouse gases by extending their lifetime.

So as you can see, some of these effects can sometimes work in opposition to one another, and it’s not always obvious which effects will “win out” in either the short term or the long term for a particular impact. In this example, the resultant warming effects may have potentially been compounded by the 0.8 million years of Deccan Traps basalt eruptions overlapping the K-T boundary, and were ultimately more than offset by the acute sulfate aerosol cooling effects (Keller 2008, & Pope 1997).

The impact event is believed to have caused so-called Impact Winter effects for a few decades; these consisted of darkness and cooling from ash, debris and sulfate aerosols, which thus inhibited photosynthesis for up to a year (Vellekoop 2014, Schulte 2010, Ohno 2014, Pope 1998). It also likely led to acid rain and ocean acidification (Schulte 2010, & Ohno 2014)  There is evidence of a relatively fast post-climatic recovery (Pierazzo 2003), but insofar as 76% of fossilizable species on Earth were concerned, the damage was already done.

I should mention that this is just the most well-known scientific hypothesis for the primary cause of the K – T boundary extinction. There are alternative hypotheses regarding the causes of the extinction itself, such as the aforementioned Deccan Traps (Keller 2008), the Multiple Impact Hypothesis, the Maastrichtian Sea Regression hypothesis (li 1998), and research which proposes combinations of two or more of these factors (Peterson 2016). But the fact that the Chicxlub Impact occurred is not a matter of serious contention. The evidence for it is about as close to a proverbial smoking gun as one could expect to get in science. These alternatives don’t contradict that. Rather, they merely posit that the impact was not the sole and/or primary cause of the mass extinction, which is not germane to my focus here, which has been on using the Chicxlub event as an example of how such impacts can affect Earth’s climate.

That said, it should go without saying that the current climate change we are experiencing is not attributable to meteorite and asteroid impacts. Their climatic effects are proportional to their magnitude, but we track them, and the big ones are far too conspicuous to go unnoticed.

Oh, and in case the prospect of a massive impact has anyone alarmed, just realize that potential impact threats are closely monitored, so we’d most-likely know well ahead of time (at least for the larger ones). For smaller ones, which might not be detected until weeks or days before impact, there is also ATLAS: the Asteroid Terrestrial – impact Last Alert System. Of course knowing in advance is only as useful as our best impact avoidance and/or evacuation protocols. But hey! The really big impacts are even less frequent than Super Volcanoes. There are plenty of more probable calamities to worry about than having one’s home city vaporized by an asteroid impact.

Besides, mass extinctions are 100% natural! And nobody ever said that the Universe was nothing but sunshine and rainbows, right?

Okay, so maybe some people have alluded to that, but oh well. She was wrong.

  • Credible hulk


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The Climatological effects of Volcanic Eruptions: The End Permian Extinction, the Toba Super-Volcano, and the Volcanic Explosivity Index

Volcanic eruptions can have both short-term and long term effects on Earth’s climate. In the short term, they release large quantities of ash and sulfur dioxide (SO2) into the stratosphere, which quickly gets blown all around the globe. The sulfur dioxide subsequently reacts to form droplets of sulfuric acid (H2SO4), which then condense into fine aerosols. These aerosols reflect sunlight back into space, thereby cooling the troposphere below. These effects can last for 1 – 3 years. In the long term, they can increase atmospheric concentrations of CO2 which can lead to global warming via the greenhouse effect over long periods of heightened volcanic activity

For years it was thought that the volcanic ash was primarily responsible for cooling effects by blocking sunlight. However, it was later discovered that its effects are short-lived, and that the total amount of sulfur-rich gases released in an eruption was a more important determinant of an eruption’s global cooling effects.

Cooling from Volcanic Sulfide Aerosols (source).

Cooling from Volcanic Sulfide Aerosols (source).

In rare cases of exceptionally large “Super Volcano” eruptions, there is evidence that the ash can contribute significantly to climate change – largely through changes in the surface albedo of the affected area, but these are estimated to occur only about once every 50,000 years on average. It’s worth noting however that eruptions of that magnitude still occur roughly twice as frequently as asteroid, comet, or meteoroid impacts with comparable climate effects (diameter ≥1 km). The Toba eruption of about 74,000 years ago in Sumatra, Indonesia was perhaps the greatest Super Volcano eruption of human pre-history. Some estimates posit that its initial 3 – 5 degree Celsius cooling effect may have triggered the first couple of centuries of a nearly 1,000 year cooling period. There is even a hypothesis that the Toba eruption may have been largely responsible for an apparent genetic bottleneck in human evolution around that time, but other research disputes the extent to which Toba could have been to blame for that.

Eruptions are rated on a scale called the Volcanic Explosivity Index (VEI) from 0 – 8 based on the resultant volume of ash and debris (tephra) and cloud height, as well as on subsequent developments of this index based on the mass of magma from an eruption (magnitude). Scales based the rate of mass ejection (intensity), and the area covered by lava (destructiveness). All of these are logarithmic scales (pg. 263 – 269).

Particularly explosive eruptions with high levels of halogen emissions may also exacerbate ozone depletion, possibly via interactions with human emitted Chlorofluorocarbons (CFCs).


Take for instance the following reaction of chlorine and ozone:

CFCl3 + UV photon ==> CFCl2 + Cl
Cl + O3 ==> ClO + O2
ClO + O ==> Cl + O2

This leaves another chlorine atom free to react with another ozone molecule

Cl + O3 ==> ClO + O2
ClO + O ==> Cl + O2

And so on and so forth. This can occur thousands of times.

Stratospheric ozone protects life on earth from damage from harmful UV radiation.

Although possible mechanisms have been proposed by which ozone depletion might indirectly affect the climate by suppressing terrestrial carbon sinks in the carbon cycle, its effects on the climate are not well understood, and usually take a back seat to concerns over the deleterious effects of the resultant influx of UV radiation on human, plant and animal health. Although subordinate to CFCs emitted by humans, volcanoes can have some effect on the ozone too.

In the long term, extended periods of heightened volcanic activity can also result in warming via the greenhouse effect. For instance, about a million years of severe volcanism spanned the Permian-Triassic boundary in what is referred to as the Siberian Traps. This released large quantities of CO2 and methane into the atmosphere and led to significant warming about 250 million years ago (albeit likely preceded with short term cooling effects from the aforementioned sulfate aerosols). These were flood basalt eruptions in which ferromagnetic lava of relatively low viscosity covered as much as 1.3*10^6 km^2 in Northern Pangea.

Artist’s rendering of the landscape during end-Permian extinction. Image: Jose-Luis Olivares/MIT

This is suspected to have been a major contributing factor to the worst mass extinction in Earth’s history: The End Permian Extinction: known colloquially as The Great Dying. The End Permian event is estimated to have included the extinction of up to 96% of marine species and 70% of terrestrial vertebrates (though estimates vary).

I should mention that volcanism and subsequent warming via the greenhouse effect were likely not the sole determinants of the Permian extinction event: there is also evidence that these events triggered the eruption and burning of coal deposits, and of possibly one or more asteroid (or large comet) impacts, and possibly even a contribution from a methane producing genus of archaea.

However, tremendous volcanism and global warming almost certainly played key roles in the End Permian extinction as well. As the authors of this study put it:

“When the end-Permian extinction is compared with other short-lived events such as the end-Triassic and end-Cretaceous extinctions and the PETM, we see in common, a short-lived perturbation of the carbon cycle followed by a rise in atmospheric pCO2 and temperature, evidence for ocean acidification, anoxia, and rapid extinction (10s of thousands of years) (485657).”


In my articles on plate tectonics and continental drift (here and here), I used the Rodinia Supercontinent and Snowball Earth hypothesis as an example of how continental drift could dramatically affect climate. I did not, however, discuss how that extreme glaciation is thought to have come to an end. Well, models suggest that atmospheric greenhouse gas concentrations would have needed to get extremely high to break out of such a glaciation. Global glaciation would entail that that the carbonate and silicate rock weathering reactions (which I discussed in the continental drift articles) would not have been able to sequester atmospheric CO2, so CO2 from volcanic eruptions should have been allowed to accumulate unmitigated in the atmosphere over millions of years, which could explain how the Earth warmed enough to end the glaciation period.

Knowing this, it’s not unreasonable to wonder whether GHG emissions from volcanoes could be contributing to current global warming. However, we track volcanic activity closely, and it turns out that volcanic CO2 contributions since 1750 have been at least 100 times smaller than the contributions by human’s burning fossil fuels. This fact runs contrary to the common climate myth that states that a single volcanic eruption releases more CO2 than humans have emitted throughout all of history. The myth attempts to portray anthropogenic contributions as a drop in the bucket compared to volcanic CO2 emissions. In actuality, the opposite is the case. If anything, volcanic activity may have even slowed down warming from 2008 – 2011 via sulfuric acid aerosol forcing.


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Milankovitch Cycles and Climate: Part III – Putting it All Together

In parts I and II, we looked at axial obliquity, axial precession, apsidal precession, orbital eccentricity and orbital inclination, and how their cycles can affect the climate. In this installment of the series, we’ll look briefly at how these cycles look when combined, and then discuss one of the most prominent unsolved problems raised by the theory: The 100,000 Year problem.

Putting it all together

Putting it all together

Notice that the peaks and valleys in temperature are roughly periodic, and that with the possible exception of apsidal precession, there are slight fluctuations in the periods and amplitudes of these orbital cycles. One reason for this has to do with fluctuations in solar output, but another likely reason has to do with the very causes of these orbital cycles themselves: namely, these cycles are driven by mutual gravitational perturbations between the Earth, Sun, Moon, and to a lesser extent, Jupiter and the other planets in the solar system (Borisenkov 1985, Spiegel 2010) .

These are what are referred to in physics as “n-body problems.” Isaac Newton recognized early on that some such orbital fluctuations would have to occur, but it turns out that n-body problems cannot be solved analytically for systems of n ≥ 3 (Heggie 2005). That means the resultant systems of differential equations has to be solved using what are called numerical methods, rather than being solved for a set of analytic functions describing the precise trajectories of each body in the system over time. As a result, the actual precise paths that celestial bodies take and the variations in their tilt and precession can be more complex than just a fixed elliptical path. To add insult to injury, these problems become even more complicated in General Relativity than in classical Newtonian Celestial Mechanics.

Milankovitch Cycle/Insolation animation c/o Cal Tech

Milankovitch Cycle/Insolation animation c/o Caltech

I want to also emphasize the fact that even though Milankovitch first proposed his ideas nearly a century ago, this is still an area of active research. There are still unsolved questions about how these cycles combine to help produce the glaciation data we see in the paleo-climatological records. For instance, there’s what is known as The 100,000 Year Problem. This refers to the fact that during the past million years, glacial-interglacial periods have occurred on roughly a 100,000 year cycle, which has been difficult to reconcile with the fact that the insolation changes due to the 100,000 year orbital eccentricity cycle are very small. The effect appears to exceed the magnitude of the cause.

There is no shortage of plausible hypotheses, each with their respective strengths and weaknesses, but as of yet there’s still no unified theory that explains how precisely the cycles all work together to produce the observed pattern of glacial and interglacial periods.

For instance, researchers such as Muller et al have hypothesized that orbital inclination may be more important in producing the observed 100kyr glaciation cycle than the other cycles (Muller 1997). The only physical mechanism thus far proposed for this is the possibility that different inclinations of the orbital plane may correspond to different densities of meteoroid and dust accretion. Such a change could alter stratospheric concentrations of dust and aerosols, which would change the amount of sunlight reflected back into space. So far there’s no evidence for sufficiently different amounts of accretion at different orbital inclinations for this to be the case, but it’s a testable hypothesis whose strengths and weaknesses are outlined by the lead author here (Muller 1995).

Other researchers have been able to reproduce the 100,000 year cycles in models involving the non-linear phase locking of interactions between the known orbital forcings and internal oscillations in the climate system (Tziperman et al 1997). The basic idea behind the non-linear phase locking models is that axial obliquity and/or precession may act as pacemakers for the glaciation cycle in a manner that is distinct from models based on mere amplifications of the effects of the eccentricity cycle.

The minutia of the actual physical mechanisms involved in the non-linear phase locking models is left quite vague. No definite conclusion is attempted regarding whether the dominant cycle is obliquity, precession or both; the models work just as well with CO2 changes driving glaciation in synchrony with the orbital cycles as they do with the orbital cycles driving them with CO2 changes merely amplifying the signal. But that’s because the goal with that paper was merely to figure out whether such models could reproduce the cycle. The same lead author (Tziperman) has also co-authored work that explored a sea ice triggering mechanism for glaciation (Gildor 2000).

Others have even argued that the last 800,000 or so of climate records extends insufficiently far back to establish that the apparent 100,000 year glaciation cycle and its relationship to the eccentricity cycle are even statistically significant (Wunsch 2004).

This is not the only unresolved problem related to Milankovitch cycles. In addition to the 100k year problem, there’s also a similar 400k year problem, which exists because a strong variation in the eccentricity cycle doesn’t appear to correspond to an extra strong 400k period climatological cycle.

Then there’s also what’s called the “Stage 5” Problem: aka the Causality Problem (Oppo et al 2001). This refers to the fact that the penultimate interglacial period (corresponding to Marine Oxygen-Isotopic Stage 5) appears to have occurred about 10k years prior to the forcing hypothesized to have caused it. Another issue is what’s called the Split Peak Problem, which refers to the fact that eccentricity cycles have cleanly resolved variations at both 95k and 125k years which don’t appear to translate into two cleanly resolved peaks in insolation (Zachos et al 2001).  Instead, what’s observed is a single peak on a roughly 100k frequency.

So, as you can see, determining the precise manner in which the combinations of these cycles affect global climate is no easy task, and we still don’t know everything.

That said, what we DO know is that these cycles are not sufficient to explain the rate of the current warming. For one, they occur over much longer periods of time than the current trend (on the order of tens or hundreds of thousands of years versus a couple hundred years).

Moreover, Earth’s Orbital Eccentricity is nearly circular, and both Axial Obliquity and Axial Precession are currently changing in opposition to the warming trend; Axial Obliquity is getting smaller: not larger, which means if anything that we in the Northern Hemisphere should be cooling (or at least not warming). Similarly, precession is changing such that it should be moderating the warming, but it’s not. If anything, other variables (i.e. human activities) may be delaying the next glacial period (Berger 2002). So, even though we don’t know everything about how Milankovitch cycles affect the climate, we do know that they can’t explain the current warming trend.


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Photo Credits:

Incredio –, CC BY-SA 3.0,


Milankovitch Cycles and Climate: Part II – Orbital Eccentricity, Apsidal Precession and Orbital Inclination

In part I, we looked at some of the ways in which changes in axial obliquity and precession can affect the climate. In this article, we’ll look at orbital eccentricity, apsidal precession and orbital inclination, and some of their climatological consequences.

Orbital Eccentricity: This refers how elliptical earth’s orbital path is. The greater the eccentricity of a planet’s orbital path, the less circle-like and more elliptical (oval-like) it is. An ellipse has an eccentricity greater than or equal to zero, but less than one. An eccentricity value of e = 0 corresponds to a perfect circle, whereas e = 1 corresponds to a parabola, and e > 1 corresponds to a hyperbola. At higher eccentricity values (albeit less than one), there is a greater discrepancy between a planet’s perihelion and aphelion: a planet’s nearest and furthest points from the Sun during its orbit.

Earth’s orbital eccentricity changes over cycles of about 100,000 and 413,000 years or so due to the gravitational influence of massive planets such as Jupiter and Saturn. During these cycles, earth’s orbital eccentricity varies between about e = 0 (perfectly circular) to about e = 0.06.

Orbital Eccentricity

Orbital Eccentricity

Orbital eccentricity is the only Milankovitch cycle that affects total annual insolation on the earth: the total amount of solar energy per unit area reaching the earth, and it does so by a factor of 1/(1- e2 )1/2 for a given solar irradiance (Spiegel 2010). That means that while eccentricity (e) varies between 0 and 0.06, insolation should vary between a factor of 1/(1-(0)2)1/2 = 1 and a factor of 1/(1- (0.06)2 )1/2 = 1.0018 for a given solar output. Currently, Earth’s eccentricity is approximately e = 0.017, which works out to 1/(1-(0.017)2)1/2 = 1.00014. So the variation in insolation isn’t very significant. However, that doesn’t mean that these cycles don’t have a significant effect on climate. At greater eccentricity values, the seasons occurring while Earth is closer to the aphelion are of longer duration than the ones occurring while the Earth is closer to the perihelion.

Additionally, the regional and seasonal climatological effects of changes in axial obliquity and precession are more pronounced during periods of greater orbital eccentricity than when Earth’s orbit is circular (or nearly circular). This is because greater eccentricity values correspond to greater differences between the closest point to the sun (perihelion) and furthest point (aphelion) in Earth’s orbital path. In turn, those greater differences between the perihelion and aphelion can either amplify or moderate the discrepancies in seasonal insolation caused by axial tilt and precession. A hemisphere tilted towards the sun at the perihelion and away from the sun at the aphelion would have its summers and winters slightly reinforced, while a hemisphere tilted away from the sun at the perihelion and towards the sun at the aphelion would experience a slight moderating effect on its summers and winters.

Apsidal precession: The theory of Milankovitch cycles also predicts that the orientation of earth’s entire elliptical orbital path rotates in cycles of 21,000 years. That is to say that the location of the perihelion in Earth’s orbit changes over thousands of years (Greenberg 1981). The following graphic should clarify what is meant by this:

Apsidal Precession and the Seasons.

Apsidal Precession and the Seasons.

There is some evidence to suggest that these changes in the orientation of the perihelion work together in combination with the axial precession cycle to affect temporal and geographical insolation and precipitation patterns (Merlis 2013). In other words, it affects where and when higher and lower local levels of sunshine and rain occur.

Orbital Inclination: Although the planets and asteroids follow elliptical orbits in accordance with Kepler’s first law, they don’t all orbit in precisely the same plane. Their orbital planes are often inclined with respect to one another, and their angles of inclination can change slightly over time. The Earth’s orbital plane is also called the Plane of the Ecliptic (or simply the ecliptic).

By Lasunncty (talk). (Lasunncty (talk)) [CC-BY-SA-3.0 ( or GFDL (], via Wikimedia Commons

Orbital Inclination.

The orbital inclination angles of planets, asteroids and other celestial objects are usually computed with respect to Earth’s ecliptic, and thus the Earth’s inclination with respect to its own ecliptic would therefore be zero by definition, but this is primarily for purposes of convenience. The inclination of the ecliptic changes over time on a cycle of approximately 70,000 years. This is known as Precession of the Ecliptic. Milankovitch did not study this cycle, but I’ve included it anyway for the sake of completeness. Additionally, its climatological effects are still a matter of scientific debate. Earlier calculations suggested that its effect on insolation would be negligible (Berger 1976), but other researchers have postulated that it may play a role in the explanation of one of the hitherto unsolved problems raised by the theory of Milankovitch cycles (Muller 1995). In fact, Muller et al even went as far as to argue that when the inclination is computed with respect to the Invariable Plane of the solar system: the plane through the solar system’s barycenter (center of mass) and perpendicular to its angular momentum vector (approximately the orbital plane of Jupiter), rather than with respect to Earth’s 1850 orbital plane, the cycle works out to closer to 100,000 years rather than the traditionally accepted 70,000 years (Muller 1995).

The relevance of this claim will become clearer in part III when we discuss how these cycles combine together to affect climate, and when we take a look at one of the most prominent unsolved questions raised by the theory.


Berger, A. L. (1976). Obliquity and precession for the last 5 000 000 years.Astronomy and Astrophysics51, 127-135.

Greenberg, R. (1981). Apsidal precession of orbits about an oblate planet.The Astronomical Journal86, 912-914.

Merlis, T. M., Schneider, T., Bordoni, S., & Eisenman, I. (2013). The tropical precipitation response to orbital precession. Journal of Climate26(6), 2010-2021.

Muller, R. A., & MacDonald, G. J. (1995). Glacial cycles and orbital inclination. Nature377(6545), 107-108.

Spiegel, D. S., Raymond, S. N., Dressing, C. D., Scharf, C. A., & Mitchell, J. L. (2010). Generalized Milankovitch cycles and long-term climatic habitability.The Astrophysical Journal, 721(2), 1308.

Photo Credits:

Orbital Eccentricity: By NASA, Mysid – Vectorized by Mysid in Inkscape from NASA image at, Public Domain,

Apsidal Precession and the Seasons:  By Krishnavedala (Own work) [CC BY-SA 3.0 (], via Wikimedia Commons.

Orbital Inclination: By Lasunncty (talk). (Lasunncty (talk)) [CC-BY-SA-3.0 ( or GFDL (], via Wikimedia Commons

Milankovitch Cycles and Climate: Part I – Axial Tilt and Precession

The theory of Milankovitch cycles is named after Serbian astronomer and geophysicist, Milutin Milanković, who in the 1920s postulated three cyclical movement patterns related to Earth’s orbit and rotation and their resultant effects on the Earth’s climate. These cycles include axial tilt (obliquity), elliptical eccentricity, and axial precession. In aggregate, these cycles contribute to profound long term changes in earth’s climate via orbital forcing.

Axial Obliquity: The Earth’s rotational axis is always tilted slightly; currently, its axis is about 23.4 degrees from the vertical. Alternatively, you could say that its equatorial plane is tilted about 23.4 degrees relative to its orbital plane. This tilt is responsible for Earth’s seasons. During the Northern Hemisphere (NH) summer, Earth is further away from the Sun than it is during the NH winter due to its slightly elliptical orbit, yet it receives more sunlight because it’s tilted towards the Sun. During this same time period, the Southern Hemisphere (SH) is tilted away from the Sun, which is why NH summer coincides with SH Winter and vice versa. Contrastingly, during the NH winter, the Earth is closer to the Sun, yet receives less sunlight because it’s tilted away from it. During that same period, the SH is tilted towards the Sun, and is thus experiencing summer.

However, that axial tilt slowly varies between about 22.1 degrees and 24.5 degrees over long quasi-periodic cycles of roughly 41,000 years. The last maximum is estimated to have occurred around 8,700 BCE, and the next minimum should occur roughly around the year 11,800 CE. A more exaggerated tilt corresponds to more severe seasons: warmer summers and colder winters. As you may have guessed, less exaggerated tilt corresponds to milder seasons: cooler summers and warmer winters. The latter phases can lead to increased glaciation. This is because cooler summers mean less ice loss per year, and warmer winters mean more precipitation (rain or snow) to build up ice sheets. Now, you might be wondering why exaggerated tilt wouldn’t build ice sheets with its extra cold winters, but remember that the freezing point of water at 1 ATM of pressure is still going to be 0 degrees Celsius. Reaching negative 50 degrees C in the winter isn’t likely to facilitate much greater glaciation than reaching negative 10 degrees C, and those extra cold winters would involve less precipitation. To add insult to injury, the extra hot summers would melt greater portions of the existing ice each year. That’s why smaller axial tilt values are thought to correspond to increased glaciation and larger tilt values to deglaciation. Moreover, greater surface areas of ice cover can function to resist warming via the ice-albedo feedback (or snow-albedo feedback), which I mentioned briefly in my article on how continental drift affects climate (here and here).

Axial Tilt (photo credit).

Axial Tilt (photo credit).

Axial Precession: At any given obliquity, the direction of the earth’s rotational axis can “wobble” around the vertical in its own cycles (called precession) even while maintaining a more or less constant angle between the rotational axis and the vertical. This is caused by gravitational influences on the earth from the sun and moon. It takes roughly just under 26,000 years for the earth to complete an entire cycle of precession. Estimates differ from different sources, in part due to the fact that the rate of precession is not constant. This is also the reason earth’s axis points either towards Polaris or Vega as the “North Star” roughly every 13,000 years.

Axial Precession.

Axial Precession.

In the contrasting case (i.e. precession in the opposite phase of its current configuration), NH Winters would occur when Earth was furthest away from the sun and summers would occur when it was closest. That would mean extra hot summers, and thus more glacial melting. It would also mean extra cold winters, but those colder winters also correspond to less precipitation. That’s why our current precession should be more conducive to building the NH ice sheets, but the opposite is occurring due to reasons we’ll delve into soon enough. Again, loss of ice also means less help from the ice-albedo feedback effect, which could otherwise help resist further warming. Although axial precession does not affect total annual insolation, it can have a profound effect on where and when that solar energy is distributed, and consequently on the formation or disintegration of ice sheets. Right now, the northern hemisphere is closer to the sun in the NH Winter and further away in the NH Summer. This makes NH Summers less hot and NH Winters less cold than would be the case if Earth were in the opposite phase in its precession cycle. Presumably, the warmer NH Winters should be conducive to more precipitation (snow fall), which would contribute to glaciation, whereas the moderate summers would be conducive to less glacial melting than if the precession were in the opposite configuration from its current phase.

Keep in mind that the magnitude of these seasonal effects also depends on how eccentric our orbit is around the sun, and neither obliquity nor precession affects the total amount of energy coming in from the sun. Their immediate warming or cooling effects are only regional, but regional warming can lead to global warming by altering ocean circulation patterns, redistributing heat throughout the oceans, and consequently causing the oceans to release stored CO2, by decreasing its solubility, which can drive additional warming via the greenhouse effect.

In part II, we’ll look at three other orbital cycles: orbital eccentricity, apsidal precession and orbital inclination. After that, we’ll look at their combined effects on climate in part III, and then discuss the limitations of our current knowledge by examining some unsolved problems regarding the relationship between these cycles and Earth’s glaciation cycles.


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