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.

Matthews, H. D., Graham, T. L., Keverian, S., Lamontagne, C., Seto, D., & Smith, T. J. (2014). National contributions to observed global warming. Environmental Research Letters9(1), 014010.

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.

Min, S. K., Zhang, X., Zwiers, F. W., & Hegerl, G. C. (2011). Human contribution to more-intense precipitation extremes. Nature470(7334), 378-381.

NOAA National Centers for Environmental Information, State of the Climate: Global Analysis for Annual 2015, published online January 2016, retrieved on January 8, 2017 from

NOAA National Centers for Environmental information, Climate at a Glance: Global Time Series, published December 2016, retrieved on January 8, 2017 from

Pesnell, W. D. (2016). Predictions of Solar Cycle 24: How are we doing?. Space Weather14(1), 10-21.

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

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 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.