component - Sun



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Solar irradiation


The Sun is a rotating magnetic star consisting of a hot plasma entangled with fluctuating magnetic fields. A vast amount of energy is continuously released from the Sun in the form of electromagnetic radiation as well as in the form of charged particles, called the solar wind. The latter is accelerated and ejected omni-directionally into interplanetary space. The region around the Sun filled with the solar wind and its imbedded magnetic field is known as the heliosphere. This magnetic field, called the heliospheric magnetic field (HMF), remains rooted on the Sun as it rotates, resulting in the formation of so-called Archimedean spiral, also referred to as the Parker spiral. Turbulent processes that occur on the surface of the Sun are characterized by cyclic variations e.g. in the number of sunspots. The direction of magnetic field also changes every ∼11 years resulting in polarity cycles of ∼22 years. The thin region where the magnetic polarity abruptly changes creates the heliospheric current sheet (HCS) that becomes increasingly wavy with growing solar activity. This waviness is caused by the fact that the magnetic axis of the Sun is tilted with respect to its rotational axis, forming an angle which is equal to the angle α with which the HCS is tilted. This angle is called the HCS tilt angle.

An average global warming of 0.6 ± 0.2°C has been measured along the 20th century. It has been in most part attributed to the anthropogenic influence on climate, in particular, burning fossil fuels which increases concentration of greenhouse gases in atmosphere (especially long-lived CO2). The current interest of the role of the Sun in climate change stems from the possibility that intrinsic variability of the solar irradiance may also play an active role in this temperature rise. Note that, it is variability and not the total irradiance which is important for climate change.

Simple correlations alone are not sufficient to settle the issue of whether the Sun really influences climate. Needed are mechanisms which could mediate such a connection. Basically, two solar quantities have the potential of having such an influence. One is the Sun's interplanetary magnetic field and the associated solar wind, the other is the Sun's irradiance.

The solar electromagnetic radiation that arrives to the Earth changes because of three main mechanisms:

Some of these mechanisms produce variations that are evident on time scales of thousands or even millions of years, but in particular the observed changes of the solar irradiance are occurring from minutes to decades.

Sun trivia (NASA)

General facts

Total Solar irradiance (TSI)

The total solar irradiance (TSI) is the value of the integrated solar energy flux over the entire spectrum arriving at the top of the terrestrial atmosphere at the mean Sun-Earth distance (the astronomical unit, AU). Mathematical calculations as well as satellite observations indicate an average value of 1367 ± 4 W/m2.

After distribution of the solar irradiance over the planetary atmosphere, the average solar radiation at the top of the atmosphere is 1/4 of this: 342 W/m2. The Earth's planetary albedo of 0.3 further reduces the incoming radiation to 239 W/m2. Upon entering the atmosphere solar irradiance wavelengths shorter than 300 nm are absorbed in the stratosphere and above.

We need to distinguish between solar spectral irradiance and total solar irradiance. The former is the irradiance at one wavelength or a set of wavelengths, while the latter is given by the integral over all wavelengths.

The spectrum of radiation incident at the top of the atmosphere resembles closely the curve of black body radiation at 5770 K, mainly for the visible and longer wavelengths. It has a maximum level near 500 nm and decreases to more than six orders of magnitude in the X-ray and radio spectral regions. Around 50% of the TSI is at visible and nearinfrared wavelengths from 400 to 800 nm, while between 300 and 10,000 nm occurs the 99% of the solar output.

Variability of the solar flux during the solar cycle, between the maximum and minimum, occurs mainly in the far ultraviolet and below 350 nm. It may exceed 5% up to 210 nm and reach 10–20% between 150 and 210 nm. In the far UV (FUV), it can reach, particularly in Lyman-Alpha, more than 100% over the cycle. The UV spectrum <350 nm does not reach the ground; it is completely absorbed by stratospheric ozone and oxygen and plays an important role in the stratosphere where it alters the local temperatures, pressures and the winds and, in fact, the conditions of propagation of atmospheric planetary waves that create a coupling between high and low levels of the atmosphere and affect the tropospheric circulation. The UV is only 1% of the total solar flux, but given its high variability, it represents in absolute 64% of the variability in the cycle.

Satellite measurements of the TSI started with NIMBUS-7 launched in November 1978 and have been carried out by their successors. From the satellite observations the following TSI variations and sources have been identified:

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Solar activity and its periodicities

The sun is the only star, which can be studied in great detail and thus can be considered as a proxy for cool stars. Numerous dedicated ground-based and space-borne experiments are being carried out to learn more about solar activity and its short- and long-term variability.

The Sun is a common star (G2V), one of those that we call dwarf stars. It belongs to the main sequence of stars, i.e., stars that still burn their hydrogen. The Sun started its life almost 4.6 billion years ago, has an age approximately equal to 1/3 of the life of the Universe and we expect it will live another 5 billion years or so. It is a second generation star, i.e., it is made out of a huge cloud with material that came partly from stars of the first generation, which died before the Sun was born.

The Sun rotates around its axis with an average period of approximately 25 days with respect to the position of the stars or 27 days as observed from the Earth, which moves around the Sun once per year.

The rotation axis makes an angle of 7.175° with the normal to the ecliptic plane which is the plane of the Earths trajectory around the Sun. The angular velocity of the Sun around its axis is differential, i.e., varies with latitude. It is faster near the equator and slower near the poles. The period is 24.56 days at the equator and increases to 35 days near the poles.

The extension of the solar atmosphere is the corona which expands radially in the interplanetary space and forms the solar wind. This differential rotation of the Sun plays a key role in the development and evolution of the magnetic field of the Sun. The rotational velocity varies also with the depth inside the Sun and height in the corona of the Sun.

Solar activity includes active transient and long-lived phenomena on the solar surface, such as spectacular solar flares, sunspots, prominences, coronal mass ejections (CMEs), etc.

Although changes in the sun are barely visible without the aid of precise scientific instruments, these changes have great impact on many aspects of our lives. In particular, the heliosphere (a spatial region of about 200 – 300 astronomical units across) is mainly controlled by the solar magnetic field which causes the modulation of galactic cosmic rays (GCRs). Additionally, eruptive and transient phenomena in the sun's corona and in the interplanetary medium can lead to sporadic acceleration of energetic particles with greatly enhanced flux. Such processes can modify the radiation environment on Earth and need to be taken into account for planning and maintaining space missions and even transpolar jet flights. Solar activity can cause, through coupling of solar wind and the Earth's magnetosphere, strong geomagnetic storms, which may disturb radio-wave propagation and navigation-system stability, or induce dangerous spurious currents in long pipes or power lines. Another important aspect is the link between solar-activity variations and the Earth's climate.

It should be noted that the modern epoch was characterized by unusually-high solar activity dominated by an 11-year cyclicity, and it is not straightforward to extrapolate present knowledge (especially empirical and semi-empirical relationships and models) to a longer timescale. The current cycle 24 indicates the return to the moderate level of solar activity, as manifested, e.g., via the extended and weak solar minimum in 2008 – 2009 and weak solar and heliospheric parameters.

The concept of solar activity

Although the concept of solar activity is quite a common term nowadays, it is neither straightforwardly interpreted nor unambiguously defined. For instance, solar-surface magnetic variability, eruption phenomena, coronal activity, radiation of the sun as a star or even interplanetary transients and geomagnetic disturbances can be related to the concept of solar activity. As a result, the concept of solar activity is quite broad and covers non-stationary and non-equilibrium (often eruptive) processes and their effects upon the terrestrial and heliospheric environment. Many indices are used to quantify different aspects of variable solar activity. Quantitative indices include direct (i.e., related directly to solar variability) and indirect (i.e., related to terrestrial and interplanetary effects caused by solar activity), they can be physical (measured) or synthetic (calculated).


The most common and the longest available index of solar activity is the sunspot number, which is a synthetic index and is very useful for the quantitative representation of overall solar activity.

Sunspots are dark areas on the solar disc (of size up to tens of thousands of km with lifetime up to half-a-year), characterized by a strong magnetic field, which leads to a lower temperature (about 4000 K compared to 5800 K in the photosphere) and observed as darkening on the Sun's surface. The appearance of a large sunspot on the Sun temporarily decreases the irradiance of the Sun. However, during solar maximum the average facular brightening of 2 Wm-2 more than compensates the average sunspot darkening of 1 Wm-2. The record of the sunspots constitutes the longest time series of actual observations made by humans and sunspot number series is available for the period from 1610 AD, after the invention of the telescope. Solar activity in all its manifestations is dominated by quasi-periodicity with a period of about 11 years, known as the Schwabe cycle, which has, in fact, a variable length of 9 – 14 years for individual cycles. The amplitude of the Schwabe cycle varies greatly – from the almost spotless Maunder minimum to the very high cycle 19 (April 1954-October 1964; highest sunspot number 201.3 recorded in March 1958). The background for the 11-year Schwabe cycle is the 22-year Hale magnetic polarity cycle which relates to the reversal of the global magnetic field of the sun with the period of 22 years. It is often considered that the 11-year Schwabe cycle is the modulo of the sign-alternating Hale cycle.

The shape of the variation from minimum to maximum and to minimum again is usually very asymmetric. The average falling time is double than the rising time, like an asymmetric pulse, but there are several solar cycles with larger rising time than falling time. The rising time varies between 2.8 and 9 years, the falling time between 3.5 and 10.2 years. The sunspot number varies between almost zero to 250. The number of sunspots at the maxima varies between 49 and 250, while at the minimum from 0 to 12.

Numbering of the sunspot cycles started since 1755.

Solar cycles

Solar science (NASA image)

Forecasting solar activity

Solar activity contains essential chaotic/stochastic components, that lead to irregular variations and make the prediction of solar activity for a timescale exceeding one solar cycle impossible. Some models succeed in reasonable predictions of a forthcoming solar cycle, but they do not pretend to extend further in time. On the other hand, many claims of the solar activity forecast for 40 – 50 years ahead and even beyond. However, so far there is no evidence of any method giving a reasonable prediction of solar activity beyond single solar-cycle scale. Although several "predictions" of the general decline of the coming solar activity have been made recently, however, these are not true predictions but rather the acknowledge of the fact that the Modern Grand Maximum must end. Similar caution can be made about predictions of a Grand Minimum – a grand minimum should appear soon or later, but presently we are hardly able to predict its occurrence (Usoskin, 2013).

However, in her recent publication, Prof. Zharkova predicts reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

PREDICTION OF SOLAR ACTIVITY FROM SOLAR BACKGROUND MAGNETIC FIELD VARIATIONS IN CYCLES 21-23 Simon J. Shepherd, Sergei I. Zharkov, Valentina V. Zharkova The Astrophysical Journal 10/2014; 795(1):46. DOI:10.1088/0004-637X/795/1/46 · 6.28 Impact Factor (pdf available on-line).

A comprehensive spectral analysis of both the solar background magnetic field (SBMF) in cycles 21–23 and the sunspot magnetic field in cycle 23 reported in our recent paper showed the presence of two principal components (PCs) of SBMF having opposite polarity, e.g., originating in the northern and southern hemispheres, respectively. Over a duration of one solar cycle, both waves are found to travel with an increasing phase shift toward the northern hemisphere in odd cycles 21 and 23 and to the southern hemisphere in even cycle 22. These waves were linked to solar dynamo waves assumed to form in different layers of the solar interior. In this paper, for the first time, the PCs of SBMF in cycles 21–23 are analyzed with the symbolic regression technique using Hamiltonian principles, allowing us to uncover the underlying mathematical laws governing these complex waves in the SBMF presented by PCs and to extrapolate these PCs to cycles 24–26. The PCs predicted for cycle 24 very closely fit (with an accuracy better than 98%) the PCs derived from the SBMF observations in this cycle. This approach also predicts a strong reduction of the SBMF in cycles 25 and 26 and, thus, a reduction of the resulting solar activity. This decrease is accompanied by an increasing phase shift between the two predicted PCs (magnetic waves) in cycle 25 leading to their full separation into the opposite hemispheres in cycle 26. The variations of the modulus summary of the two PCs in SBMF reveals a remarkable resemblance to the average number of sunspots in cycles 21–24 and to predictions of reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

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Proxies of solar activity

A special case of heliospheric indices is related to the galactic cosmic-ray (GCR) intensity recorded in natural terrestrial archives. Since this indirect proxy is based on data recorded naturally throughout the ages and revealed now, it makes possible the reconstruction of solar activity changes on long timescales. For example, although the last grand minimum (Maunder minimum from 1645 – 1715) is the only one covered by direct solar observations (sometimes the Dalton minimum ca. 1790 – 1820 is also considered to be a grand minimum), other grand minima in the past were reconstructed from cosmogenic isotope data. They include, e.g., the Spörer minimum around 1450 – 1550 and the Wolf minimum around the 14th century. The first quantitative reconstructions of solar activity from cosmogenic proxy appeared in the early 2000s.

The most common proxy of solar activity is formed by the data on cosmogenic radionuclides (e.g., 10Be and 14C). Cosmic rays are the main source of cosmogenic nuclides in the atmosphere (excluding anthropogenic factors during the last decades) with the maximum production being in the upper troposphere/stratosphere. This process is also affected by changes in the geomagnetic field and climate. Cosmic rays' intensity is indirectly related to solar irradiance that reaches the Earth's atmosphere. Cosmic rays experience heliospheric modulation due to solar wind and the frozen-in solar magnetic field. The intensity of modulation depends on solar activity and, therefore, cosmic-ray flux and the ensuing cosmogenic isotope intensity depends inversely on solar activity. An important advantage of the cosmogenic data is that primary archiving is done naturally in a similar manner throughout the ages, and these archives are measured nowadays in laboratories using modern techniques. In contrast to fixed historical archival data (such as sunspot or auroral observations) this approach makes it possible to obtain homogeneous data sets of stable quality and to improve the quality of data with the invention of new methods (such as accelerator mass spectrometry). Cosmogenic isotope data is the main regular indicator of solar activity on the very long-term scale but it cannot resolve the details of individual solar cycles.

The most commonly used cosmogenic isotope is radiocarbon 14C. This radionuclide is an unstable isotope of carbon with a half-life of about 5,730 years. The main source of radioisotope 14C (except anthropogenic sources during the last decades) is cosmic rays in the atmosphere. It is produced as a result of the capture of a thermal neutron by atmospheric nitrogen 14N + 𝑛 → 14C + 𝑝.

The present day radiocarbon calibration curve, based on a dendrochronological scale, uninterruptedly covers the whole Holocene and provides a solid quantitative basis for studying solar activity variations on the multi-millennial time scale. The use of radiocarbon for earlier periods is limited by severe changes in global carbon cycle during the glacial and deglaciation epochs.

Also, cosmogenic 14C data cannot be easily used for the last century, primarily because of the extensive burning of fossil fuels. Since fossil fuels do not contain 14C, the produced CO2 dilutes the atmospheric 14CO2 concentration with respect to the pre-industrial epoch. This effect, known as the Suess effect. Moreover, while the cosmogenic production of 14C is roughly homogeneous over the globe and time, the use of fossil fuels is highly nonuniform both spatially (de-veloped countries, in the northern hemisphere) and temporarily (World Wars, Great Depression, industrialization, etc.). This makes it very difficult to perform an absolute normalization of the radiocarbon production to the direct measurements. Note that the atmospheric concentration of another carbon isotope 13C is partly affected by land use, which has also been modified during the last century. Another anthropogenic activity greatly disturbing the natural variability of 14C is related to the atmospheric nuclear bomb tests actively performed in the 1960s. On the other hand, such sources of momentary spot injections of radioactive tracers (including 14C) provide a good opportunity to verify and calibrate the exchange parameters for different carbon-cycle reservoirs and circulation models.

The cosmogenic isotope 10Be is useful for long-term studies of solar activity because of its long halflife of around 1.5 × 106 years. Its concentration is usually measured in stratified ice cores allowing for independent dating. Because of its long life, the beryllium concentration is difficult to measure by the decay rate. Accordingly, the 10Be/9Be ratio needs to be precisely measured at an accuracy better than 10-13. This can be done using AMS (Accelerator Mass Spectrometry) technique, which makes the measurements complicated and expensive.

The isotope 10Be is produced as a result of spallation of atmospheric nitrogen and oxygen by the nucleonic component of the cosmic-ray–induced atmospheric cascade. Maximum production occurs at an altitude of 10 – 15 km. Most of the global 10Be is produced in the stratosphere (55 – 70%) and the rest in the troposphere.

After production, the 10Be isotope becomes attached to atmospheric aerosols and follows their fate. In addition, it may be removed from the lower troposphere by wet deposition (rain and snow). Therefore, the measured 10Be concentration (flux) in polar ice is modulated not only by production but also by climate/precipitation effects. However, comparison between Greenland and Antarctic 10Be series and between 10Be and 14C data suggests that the beryllium data mostly depicts production variations (i.e., solar signal) on top of which some meteorological effects can be superposed.

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Isotope comparisons

As an indirect test of the solar-activity reconstruction, one can compare different isotopes. Recently, Usoskin et al. (2009) studied the dominance of the solar signal in different cosmogenic isotope data on different time scales. They compared the expected 10Be variations computed from 14C-based reconstruction of cosmic ray intensity with the actually measured 10Be abundance at the sites and found that:

Thus, comparison of the results obtained from different sources implies that the variations of cosmogenic nuclides on the long-term scale (centuries to millennia) during the Holocene are primarily defined by the solar modulation of CR.

Grand minima

A very particular type of solar activity is the grand minimum, when solar activity is greatly reduced. The most famous is the Maunder minimum in the late 17th century. Grand minima are believed to correspond to a special state of the dynamo and its very existence poses a challenge for the solar-dynamo theory. Dynamo models do not agree on how often such episodes occur in the sun's history and whether their appearance is regular or random.

The Maunder minimum is a representative of grand minima in solar activity, when sunspots have almost completely vanished from the solar surface, while the solar wind kept blowing, although at a reduced pace. The "formal" duration of the minimum is 1645 – 1715, while its deep phase with the absence of apparent sunspot cyclic activity is often considered as 1645 – 1700, with the low, but very clear, solar cycle of 1700 – 1712 being ascribed to a recovery or transition phase. The Maunder minimum was amazingly well covered (more than 95% of days) by direct sunspot observations. On the other hand, sunspots appeared rarely (during ∼ 2% of the days) and seemingly sporadically, without an indication of the 11-year cycle.

The 11-year Schwabe cycle started dominating solar activity after 1700. Recovery of sunspot activity from the deep minimum to normal activity was gradual, passing through a period of nearly-linear amplification of the 11-year cycle. Although the Maunder minimum is the only one with available direct sunspot observations, its predecessor, the Spörer minimum from 1450 – 1550, is covered by precise bi-annual measurements of 14C.

It appears that the minima are generally of two distinct types: short minima of duration 50 – 80 years (called Maunder-type) and longer minima collectively called Spörer-like minima. A total of 27 grand minima were identified in the quantitative solar-activity reconstruction of the last 11,000 years. The cumulative duration of the grand minima is about 1,900 years, indicating that the sun in its present evolutionary stage spends ∼ 1/6 (17%) of its time in a quiet state, corresponding to grand minima.

Herrera et al. (2015) suggest that the solar activity grand minima periodicity is of 120 years and tha this periodicity could possibly be one of the principal periodicities of the magnetic solar activity. The negative (positive) 120-year phase coincides with the grand minima (maxima) of the 11-year periodicity (see also, Shepherd et al. 2014 for hypthesis about possible physical mechanism).

Grand maxima

In the last decades we were living in a period of a very active sun with a level of activity that is unprecedentedly high for the last few centuries covered by direct solar observation. The sunspot number was growing rapidly between 1900 and 1940, with more than a doubling average group sunspot number, and has remained at that high level until recently. Note that growth comes mostly from raising the cycle maximum amplitude, while sunspot activity always returns to a very low level around solar cycle minima. While the average group sunspot number for the period 1750 – 1900 was 35 ± 9 (39 ± 6, if the Dalton minimum in 1797 – 1828 is not counted), it stands high at the level of 75 ± 3 for 1950 – 2000. Therefore, the modern active sun episode, which started in the 1940s, can be regarded as the modern grand maximum of solar activity, as opposed to a grand minimum. As first shown by Usoskin et al. (2003) and Solanki et al. (2004), such high activity episodes are quite rare.

The high activity episode known as the Modern grand maximum is over and after the very weak solar minimum in 2008 – 2009, solar activity returned to its normal moderate level, or perhaps even to a low-activity stage, comparable to the Dalton minimum in the turn of 18 – 19th centuries.

While it is broadly agreed that the modern active sun episode was a special phenomenon, the question of how (a)typical such upward bumps are from "normal" activity is a topic of hot debate as the definition of grand maxima is less robust than thst of grand minima.

The question of how often grand maxima occur and how strong they are, cannot be studied using the 400-year-long series of direct observations. An increase in solar activity around 1200 AD, also related to the Medieval temperature optimum, is sometimes qualitatively regarded as a grand maximum, but its magnitude is lower than the modern maximum.

Re-analysis of cosmogenic isotope records by Usoskin suggests that an increase of solar activity comparable with the modern episode might have taken place around 2000 BC, i.e., around 4 millennia ago. This result is confirmed by the most recent composite reconstruction by Steinhilber et al. (2012).

A total of 19 grand maxima have been identified for the last 11,400 years with a total duration of around 1,030 years, suggesting that the sun spends around 10% of its time in an active state. A statistical analysis of grand-maxima–occurrence time suggests that they do not follow long-term cyclic variations, but like grand minima, are defined by stochastic/chaotic processes. The duration of grand maxima has a smooth distribution, which nearly exponentially decreases towards longer intervals. Most of the reconstructed grand maxima (about 75%) were not longer than 50 years, and only four grand minima (including the modern one) have been longer than 70 years. Modern grand maximum has ceased after solar cycle 23 and the probability of the Sun entering the next active episode soon is very low.

The beginning and maximum of the 23rd solar cycle appeared to be quite typical compared to previous recent cycles. Sunspot maxima reached ∼170 in 2000 and the smoothed maximum was ∼120. Then the sunspot number dropped well below what was expected, with sunspot minimum stretching through 2006, 2007, 2008, 2009, and only beginning to rise in 2010.

Characteristics of solar cycle 23 (Hady AA.):

We are now far enough into solar cycle 24 to tell it will be a weak solar cycle.

In conclusion, according to most recent reconstructions, the sun has spent about 70% of its time during the Holocene, which is ongoing, in a normal state characterized by medium solar activity. About 15 – 20% of the time the sun has experienced a grand minimum, while 10 – 15% of the time has been taken up by periods of very high activity.

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TSI and Earth's climate

Earth desiquilibrium

According to Kleiton, There are two major sources that generate free abiotic energy on Earth. The first source is solar radiation reaching the system boundary (top of the Earth's atmosphere). Incident solar radiation is associated with spatial and temporal variations that maintain temperature gradients that are the main driver for climate system processes. The total free energy generated from this source includes the generation of potential free energy associated with motion of air, water vapour and aerosols in the atmosphere, oceans and river flow, the chemical free energy generated by evaporation and desalination of sea water, the electric free energy generated by thunderstorms and so on. All of these are fuelled by uneven heating and cooling, resulting in vertical and horizontal gradients in density and pressure.

The second source is associated with the depletion of the initial conditions of the planet at formation, in the form of secular cooling of the interior, heating by radioactive decay and crystallization of the core. The differential heating results in a similar sequence of free energy generation that results in plate tectonics, uplift of continental crust and generation of geochemical free energy at the surface.

A total of about 180,000 terawatts (terawatt is equal to one trillion (1012) watts) of solar power reaches Earth's surface. Absorption of solar radiation at the surface and cooling by emission of radiation aloft generates a vertical gradient in heating that can be converted into free energy. Using a mean surface heating of 170Wm−2 and typical temperatures of 288 and 255 K, Kleidon estimates that free energy generation from this vertical gradient is less than 5000TW (note that much of this power is used for vertical mixing and transport and is likely to contribute relatively little to large-scale cycling and transport). Owing to the planet's geometry and rotation, absorption of incident solar radiation results in horizontal gradients. Using a mean difference in solar radiation of about 40 per cent between the tropics and the poles yields an upper limit of about 900TW. The temporal variation of heating in time yields an additional power of about 170TW at maximum efficiency, so that the total power generated from radiative heating gradients is of the order of 6000TW.

Incident solar radiation contains wavelengths that can be used to generate short-lived chemical free energy when visible or ultraviolet radiation is absorbed by electronic absorption or photodissociation. Photosynthesis is able to generate longer lasting free energy using complex photochemistry that prevents rapid dissipation. Using typical values for global gross primary productivity and typical free energy content of carbohydrates yields a generation rate of chemical free energy of about 215TW.

Present-day free energy consumption by human activity in the form of industrial activity and human appropriated net primary productivity is of the order of 50TW (estimates vary) and therefore constitutes a considerable term in the free energy budget of the planet.

TSI variations and climate

The solar activity change affects the climate through several physical processes: for one thing, the total radiation, particularly that in the ultraviolet range, varies with solar activity. When many sunspots are visible, the Sun is somewhat brighter than in "quiet" times and radiates considerably more in the ultraviolet. Solar UV mainly affects the stratosphere by creating and destructing ozone (in different parts of the atmosphere and at different wavelengths of radiation) and causing temperature changes. Effects of these changes on the underlying troposphere, where we live, depend on stratosphere-troposphere interactions. These interactions involve large-scale dynamical climate patterns. On the other hand, the cosmic ray intensity entering the Earth's atmosphere varies opposite to the solar activity, since the cosmic ray particles are deflected by the Sub's magnetic field to a greater or lesser degree. With increased solar activity (and stronger magnetic fields), the cosmic ray intensity decreases, and with it the amount of cloud coverage, resulting in a rise of temperatures on Earth. Conversely, a reduction in solar activity produces lower temperatures.

Correlations between solar activity and climate, often arising from its common cycle, are ubiquitous in the past 10,000 years, especially in drought and rainfall. Although the great volume and fidelity of the empirical evidence may suggest a prominent solar impact on global climate, the global response is typically an order of magnitude smaller than the strongest site-specific (regional) Sun–climate linkages (with increases of as much as 1°C during the solar cycle).

Several attempts have been made to estimate the impact of TSI changes on global climate in general and on temperatures in particular. Lean et al. (1995) reconstructed total irradiance from 1610 to the present. For the TSI variations they used two components: an 11-year cycle plus a slowly varying background related with the amplitude of the group sunspot cycle. For the temperature record they use the decadal averages of North Hemisphere (NH) temperature anomalies. The authors concluded that from 1610 to 1800 there is a high correlation between both series (r = 0.86). They indicate that from 1860 to the present half of the observed surface warming is attributable to direct solar forcing, but 65% of this warming has occurred since 1970 and solar forcing can account for less than a third of this. Solanki and Krivova (2003) have used a TSI irradiance reconstruction for 1856–1999 taking into account the composite solar irradiance of Willson (1997) and Fröhlich & Lean (1998); for the extended irradiance record back in time they used as long-term component both the length and the amplitude of the solar cycle. Also they work with global and north hemisphere surface temperatures. The 11-year running means show a good correlation of r = 0.83 and r = 0.97 for the global and NH temperatures respectively for the years before 1970. They point out that the contribution of total solar irradiance before 1970 is substantial but after 1970 is at most 30% coinciding with Lean et al. (1995).

Several calculations with energy balance models (e.g., Crowley, 2000) and three-dimensional coupled ocean-atmosphere models (e.g., Cubasch and Voss, 2000) indicate that relatively small solar irradiance changes could cause changes of surface temperature of the order of several tenths of C°. Simulations follow the temperature reconstruction between 1700 and 1800, however, during the 18th century the temperature reconstruction and the simulation tend to behave diffrently: during the last 100 years, the simulations have linear increasing trends of 0.17– 0.19 K, while the observed one is 0.6, which means that TSI is contributing moderately to the observed warming.

A recent model by Shindell et al. (2001) examined the climate response to TSI changes between the late 17th century and the late 18thh century. They used a version of the general circulation model which included a parameterization of the response of the complete stratospheric ozone to TSI. They worked with the Lean et al. (1995) irradiance and temperature reconstruction. Global changes of 0.3–0.4 °C were obtained coinciding with temperature reconstructions. However, regional temperature changes as large as 1–2 °C in the NH winter are obtained. The 20th century simulations show that TSI together with ozone variations and climate feedbacks change the temperature by 0.19 °C, almost a third of the warming trend.

The broad conclusion reached from the studies mentioned above is that before 1970 although reproducing well the observed temperature, the TSI variations cannot account for all the temperature changes, and that after 1970 its influence has conspicuously descended. Even more, as the TSI cannot account for all temperature changes other sources of solar variability and/or sources different from solar variability must be present. Besides the TSI changes, two more mechanism have been proposed for the Sun-climate relations: variations in the UV, and the solar wind flux and energetic particles.

Solar UV irradiance has been used as a forcing because this radiation is absorbed by the stratospheric ozone raising the temperature there. Warming of the lower stratosphere produces stronger winds, and penetration of these winds into the troposphere alters the Hadley circulation which then affects the equator-to-pole energy transport and the lower atmosphere temperature (Haigh, 1999; Shindell et al., 1999). The models show the observed 11-year variation in the stratosphere but the amplitude of the simulated changes is still too small compared to the observations. Also, Foukal (2002) compared his reconstructed UV solar irradiance with global temperature along 1915–1999, finding a poor correlation of r = 0.46. This result suggests that the interaction of UV irradiance and climate could be indirect.

Simulations that take the greenhouse gases as prescribed according to observations but without the influence of the Sun simulate a linear trend of 0.43 K for the 20th century. When taking both, the greenhouse gases increase and the TSI according to Hoyt and Schatten (1993), the linear trend is of 0.6 K, which is very close to observations (Paeth et al., 1999); however, the aerosol cooling effect, neglected in the model, should lower the temperature below the 0.6 K.

Studies such as that of Crowley (2000) for the last millennia forced an energy balance model with TSI from Lean et al. (1995), indices of volcanism and changes in greenhouse gases. Explosive volcanic eruptions emit sulphur rich volatiles; these gases result in sulphuric acid aerosols being produced in the stratosphere, such aerosols are known to reduce solar radiation at the surface as they increase the atmospheric albedo. The authors found that for this time span the combination of the TSI and volcanism before 1850 reproduces between the 41% and 64% of the total temperature variations. They also point out to the unusual increase in temperature in the late 20th century compared with the last 1000 years. Finally, at most 25% of the temperature increase in the late 20th century is due to natural variability, the remaining augment is consistent with the increase in greenhouse gases.

One of most recent and very convincing analyses of TSI-global temperature relationships is represented by Stauning P in Journal of Atmospheric and Solar-Terrestrial Physics (2011, Solar activity-climate relations: a different approach). The study shows clearly that the changes in terrestrial temperatures are related to sources different from solar activity after ~1986. Before 1986, based on analyses of data series for the years 1850-1985 it is demonstrated that, apart from interval of positive deviation followed by a similar negative excursion in Earth's temperatures between ~1923 and 1965, there is strong correlation between solar activity and terrestrial temperature delayed by 3 years. Authors focused on the interval from 1850 to present based on the series of monthly average sunspot numbers provided back to 1749 (sunspot no. 0) and through 2010 (cycle 24). Since 1986 the more recent sunspot and temperature deviate strongly from their past trends of approx. correspondence: the cycle-average temperatures shoot up while the sunspot numbers continue decreasing.

Solar periodicities and global climate

Although only the 11- and 22-year solar periodicities (Schwabe and Hale cycle, respectively) can be observed in instrumental-meteorological records, other solar cycles are known, e.g. at ~90 years (Gleissberg), ~208 years (DeVries cycle, a.k.a. Suess cycle), ~1000 years (Eddy cycle), and ~2300 years (Hallstatt cycle). Of these the DeVries cycle is very prominent during the Holocene. This particular frequency has been identified in essentially all long-term proxy records of solar activity using a variety of spectral techniques, record lengths, and detrending approaches. The well-known, grand solar minima during the second millenium AD, in particular the Oort, the Wolf, the Sporer, and the Maunder minima, closely correspond to minima of the 208-year oscillation.

Many studies were devoted to researching these periodicities and isolating solar fingeprints over the past millenia using various proxies. Most studies agree on temporal phase relationships between solar forcing and climatic response. Radiative energy is absorbed by oceans and land surfaces and in the lower troposphere by water vapor and by CO2. Hence, a direct link between TSI and tropospheric temperature can be established and the attenuation of the radiative forcing may lead to a lagged temperature and precipitation response. The thermal inertia of the ocean and the land surface are prominent candidated for decadal scale lagged responses of the climate system to solar forcing. The estimated lag period ranges from 0 to 70 years with 10-30 year period being accepted by most studies.

DeVries cycles (~208 years)

Breitenmoser P et al. Solar and volcanic fingerprints in tree-ring chronologies over the past 2000 years. Palaeogeography, Palaeoclimatology, Palaeoecology 313–314 (2012) pp. 127–139.

Breitenmoser P et al. (2012) showed that "volcano free" temperature records show significant periodicities near the DeVries periodicity during the entire past 1500 years. For example, the well-known, grand solar minima during the second millenium AD, in particular the Oort, the Wolf, the Sporer, and the Maunder minima, closely correspond to minima of the 208-year oscillation.

This ~200 year pacing cannot only be found in solar activity reconstructions but has also been identified in a range of climate proxies from different archives such as glacier variations, monsoon intensity changes, and other climate-linked processes. Breitenmoser P et al. (2012) demonstrated existence of this periodicity using tree-rings as a proxy. They examined centennial-scale climate variability during the past approx. two millenia (AD 553-1979) usung reconstructions of the solar and volcanic forcing, as well as the climate response derived from 17 high quality tree chronologies. Reconstructions from trees have advantages over other proxies, including their 1) wide spatial distribution, ii) annual resolution, iii) calendar-exact dating, and iv) high climate sensitivity making them one of the most important archives for reconstructing past climates, especially temperature and hydrological regimes. Note that analysis using tree data is biased towards the warm season when tree-growth processes are most active and temperature is significantly influenced by solar radiation and local/regional climate processes.

Cross-correlation analysis reveals that eight time series, the leading temperature principal component, and the second principal component fo the precipitation subset correlate significantly with TSI, but there are considerable differences in the phase relationships. Moreover, analysis of the 180-230 year band pass-filtered series indicates that the climate response to any assumed solar 208-year pacing has, at best, regional characteristics and considerable temporal phase shifts. Nevertheless, the results from Principal Component Analysis (PCA) sugest a relationship between TSI and the dominant modes of temperature/precipitation in thei frequency range. The climate response is found to lag the solar forcing by +10 years on average, which conforms to our physical understanding of solar-temperature links. However, individual negative phase shifts occur, demonstrating the uncertainty of the data and method.

Analysis performed over the common time interval with respect to key years during the grand solar minima centered at AD 662, 897, 1028, 1282, 1458, 1698, and 1817 shows significan climatic responses near year t+6, i.e. the climate follows the Sun with a lag of 6 years, for temperature and t+13 years for precipitation, implying generally cooler and drier conditions, respectively. Analysis of the drought series, on the other hand, does not contain clear evidence of a Sun-drought linkage at multidecadal-to-centennial time scales.

Besides solar forcing, volcanism is considered to be one of the primary agents for global, decadal-scale climate variability during the pre-industrial era and, hence, also needs consideration. The general pattern of low volcanic activity during Medieval Climate Anomaly (MCA) and high activity during the Little Ice Age has been described in numerous studies. Tree-ring analysis of all temperature time series using volcanic key years during and before LIA (period between the mid 13th and 19th century) shoed that the temperature response to medium and large volcanic activity was more distinct during the LIA, with particularly the years around 1452/59 and 1809/15 having a profound negative impact on summer temperatures, even at the decadal scale.

Gleissberg cycles (~90 years)

Ruzmaikin A, Faynman J. The Earth's climate at minima of centennial Gleissberg Cycles. Advances in Space Research Advances in Space Research, Volume 56, Issue 8, p. 1590-1599 (2015)

The Earth's global temperature trend leveled off to a plateau, called the hiatus, at the beginning of the 21st century. One of the potential contributors to this climate chnage could be extended, deep minimum of solar activity associated with the low solar irradiance. This minimum has been identified by numerous studies. Investigations of solar variabilty have shown that there are low-frequency variations of the 11-year sunspot cycle amplitude with 50 and 90-100 years collectively referred as Gleissberg Cycles. The 90-100-year Gleissberg variation has been studied extensively and called the Centennial Gleissberg Cycle (CGC).

Ruzmaikin & Faynman investigated response of the Earth's global land temperature to the solar input variability on the centennial time scale. They showed that the land temperature represents well the whole Earth's global temperature.

An updated annual record of the Earth's land surface temperature has been generated by the Berkley Earth Project (Rohde et al., Geoinfor Geostat: An Overview 2013, 1:1. "A New Estimate of the Average Earth Surface Land Temperature Spanning 1753 to 2011" - pdf is available on-line). It uses a large sample of the ground stations and spans the time period 1753-2011. This temperature record represents to a combination of volcanic activity, TSI and anthropogenic CO2 forcings.

Estimates of the decreases in the land temperature from CGC maxima to minima, i.e., for about a half of century, are approx. 0.35°C, 0.25°C and 0.15°C for the 19th, 20th and 21st century minima correspondingly. According to the IPCC (2013) the Earth's global temperature warmed roughly by 0.85°C from 1880 to 2012, i.e., with the rate of 0.07°C per decade. These estimates show that the CGC forced cooling for 2 decades from 1980 to the beginning of the 21st century, enhanced with the volcano effect 0.02-0.07°C, Pinatubo - Santer et. al. 2014), may be sufficient for the reduction of the global warming that led to the current climate hiatus.

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How might the Sun and climate evolve in future decades?

The solar cycle variation of 0.1% observed in TSI in the last 20 years corresponds to changes of 0.24 W/m2 in the low atmosphere. Models of secular TSI variations indicate changes from 0.24% to 0.30% (e.g., Lean et al., 1995, 1997) corresponding to 0.5–0.75 W/m2, with an extreme value during the deepest phase of the Maunder minimum of 1.23% decrease corresponding to 2.9 W/m2 (Mendoza, 1997). Then the solar forcing has been most of the time small compared with estimates of the anthropogenic forcing by greenhouse gases of 2.4 W/m2 during the 20th century.

Predictions of the strength of activity of future solar cycles have large uncertainties. Forecasting solar irradiance is even more difficult, requiring additional knowledge of the partitioning of magnetic flux into sunspots (which decrease irradiance) and faculae (which increase it). This partitioning may not be linear for all solar activity levels - for example, it has been suggested that high activity might produce saturation of total solar irradiance.

Initial predictions of solar cycle 24 indicated that its maximum activity might exceed that of cycle 23 but observations have shown that cycle 24's amplitude was moderate to low relative to the historical sunspot record. Possibility exists that the Sun may be entering an extended period of low activity, countering anthropogenic global warming.

Long-range forecasts project global temperature increases in the range 1.5–4°C by the end of the 21st century, in response to a continuing anthropogenic influence. In the immediate future, natural influences, including by the varying Sun, will likely alter Earth's surface temperature sufficiently to amplify or mitigate this expected global warming trend.

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Earth's orbital variations and insolation changes over milennia

The discovery of glacial ages in the 19th century triggered the first scientific questions on the evolution of climate through time, and thus corresponds to the dawn of paleoclimatology. Since then, scientists have attempted to reconstruct past climatic changes and to understand their physical basis.

Two main theories of glacial ages were forged it 19th century: the astronomical theory and the changing concentration of atmospheric carbon dioxide.

Currently, 3 major drivers are concidered that explain glacial-interglacial quasi-cyclicity:

Here, we will examine current opinions on how Earth's orbital variations cause climate cyclicity through changes in insolation and major climate feedbacks.

The first astronomical theory of glacial ages was formulated by Joseph Adhémar in 1842. Today, best explanations of Earth's astronomical climate forcing are built upon theory developed in the 1930s by Serbian astrophysicist and mathematician Milutin Milankovitch.

Milankovitch demonstrated that summer melting is much more critical for the Arctic ice mass balance than winter snow accumulation, and his theory is therefore based on effect of orbital variations on summer insolation in high latitudes of Northern Hemisphere. Milankovitch also computed explicitly a third astronomical parameter relevant for the insolation at the top of the atmosphere: the obliquity of the Earth's axis, which corresponds to its tilt with respect to the orbital plane. This sets the basis of the current astronomical theory of climate.

Unraveling orbital-scale processes is difficult because, in Laurent Labeyrie's words, "everything is correlated to everything". One way of searching for cause and effect is to study terminations, but this strategy is problematic for several reasons and one of them being that each deglaciation represents just a single realization of a range of possible sequences of events, and thus no termination is "typical".

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Eccentricity of the Earth's orbit

The Earth's orbit is a slowly changing ellipse. It is characterized by a size parameter, the semimajor axis, traditionally represented by a, and by a shape parameter, the eccentricity e. The perturbations induced by the other planets are not affecting the size of the ellipse, but only its shape and its orientation. On the one hand, the perturbations become significant only on very long time scales. On the other hand, the computation of orbital parameters, and among them eccentricity, is possible only for periods of time not too remote in the past or in the future. The errors are increasing exponentially through time and a precise computation beyond about 20 or 30 millions of years is not possible,which is in fact quite short compared to the age of the Earth. Beyond this duration, changes in eccentricity are still similar (with identical pseudoperiodicities near 100,000 and 400,000 years) but it becomes impossible to ascertain if, for instance, 600 millions years ago eccentricity was at a minimum or at a maximum. In other words, the phase of oscillations becomes unpredictable.

Today, eccentricity reaches 0.0167, but it changed between values close to zero and values close to 0.06, with pseudoperiodicities of about 100,000 and 400,000 years.

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Axial parameters: obliquity and precession

Beyond orbital parameters, we also need to account for the orientation of the Earth's axis with respect to the orbital plane, or ecliptic. This is given by two axial parameters, the obliquity, which represents the tilt of the Earth's axis compared to the ecliptic, and the precession of the equinoxes, which relates to its absolute position with respect to the stars. In contrast to orbital parameters like eccentricity, which depends only on point mechanics, the axial parameters (obliquity and precession) also depend on the Earth's shape. This introduces additional uncertainties and potential errors. The characteristic duration beyond which predictions for axial parameters become impossible is therefore probably shorter that for eccentricity, and difficulties arise already after several millions of years. In particular, the shape of the Earth changes slightly throughout a glacial cycle with huge ice masses being accumulated at high northern latitudes. Similarly, internal mantle convection in the Earth may also redistribute masses within the Earth in ways than cannot be accounted for in astronomical computations. As a result, the phase of obliquity and precession are uncertain in the remote past and future.

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Obliquity (tilt)


The first axial cycle involves slight variations in the orbital tilt or obliquity of the Earth's axis in relation to it's orbital plane. Increases in tilt expose more of the polar regions to sun rays during the summer and less during the winter, enhancing seasonal extremes. Decreases in tilt lead to colder polar summers. Varying between 22.1° and 24.5° from vertical, the obliquity cycle runs over a peak to peak period of 41,000 years.

Today, obliquity is e = 23°27', which defines the latitude of polar circles (67°33' north and south) and tropics (23°27' north and south). This value oscillates between extremes of 21.9° and 24.5° , with a pseudoperiodicity of about 41,000 years. Change in obliquity modifies the extent of these polar and tropical geographic domains.

If the global mean radiation received by the Earth is unchanged, its geographic distribution depends on obliquity. More precisely, the annual mean solar radiation received at the top of the atmosphere in a given location depends mostly of obliquity (and slightly of eccentricity through its global effect). An increase in obliquity translates into an increase of the solar radiation received at high latitudes, and a decrease in the tropics. The current decrease in obliquity, at a pace of about 0.46 arcsecond per year, induces a shift of the tropics by about 14.4 m each year.

Obliquity changes from 21.98° to 24.58° represents a 4% increase, i.e., more than 50 Wm-2 during summer sostice at the pole. In contrast to the precessional effects, the effect of obliquity on insolation is symmetrical with respect to the equator i.e. climatic changes associated with obliquity changes are synchronous in both hemispheres.

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The precession of equinoxes is known since the Antiquity. This "third motion of the Earth" corresponds to a slow drift of the polar axis with respect to the fixed stars with a periodicity of 25,765 years. It is necessary to distinguish the precession of equinoxes and the climatic precession because the absolute orientation of the Earth's axis with respect to stars is not relevant for climate. However, when this axis is oriented in a certain way, the same is true for the equatorial plane of the Earth. Equinoxes are precisely defined by the intersection of the equatorial plane and the orbital plane. The precession of equinoxes corresponds therefore to a drift of this line with respect to the stars in the zodiac, thus its name. The perihelion is also moving with respect to the stars, according to the "precession of the perihelion". The combination of these two motions defines the climatic precession, noted as the angle between the vernal point and the perihelion. If the vernal point moves around the sky in about 25,700 years, the perihelion does so in 112,000 years. These motions being in opposite directions, they combine into a mean climatic precessional cycle of 21,000 years.

Today, the Sun is in the Fish constellation (Pisces) at the March equinox, thus defining what astronomers are calling the vernal point. It was in the Ram (Aries) during Greek times and in the Bull (Taurus) during the Egyptian epoch. The vernal point and the location of seasons on the Earth orbit thus moves together with the precession of equinoxes. The orbit being elliptic, seasons in each hemisphere will then occur at changing distances from the Sun and have different duration, depending on their situations compared to perihelion and aphelion. Thus, the precessional forcing is antisymetrical with respect to hemispheres. When summer and winter solstices line up at the extremes of the ellipse, the effect is toward a cooler earth.

Orbital precession provides a range of incremental insolation "boosts" aligned to every season and month of the year. This synthesis accepts Milankovitch's choice of northern hemisphere summer as the critical forcing season but further specifies mid- July as the critical month. This choice makes physical sense because July is the time of greatest extent of snowfree land and these low-albedo land surfaces will most effectively absorb the extra increment of solar radiation provided by precession during July.

The initial suggestion by Milankovitch (1949) was that glacial-interglacial cycles were regulated by summer insolation at about 65°N; this was because he reasoned that for an ice sheet to expand additional ice had to survive each successive summer. The focus on the Northern Hemisphere is because the capacity for ice growth is much less in the Southern Hemisphere due to its smaller landmasses combined with the fact that Antarctica is already close to its ice storage limit. The conventional view of glaciation is that low summer insolation in the temperate North Hemisphere allows ice to survive the summer and thus build-up on the northern continents. As snow and ice accumulate the ambient environment is modified. This is primarily by an increase in albedo that reduces the absorption of incident solar radiation, and thus suppresses local temperatures. The cooling promotes the accumulation of more snow and ice and thus a further modification of the ambient environment, causing the so-called 'ice albedo' feedback. Other climate feedbacks such as changes in atmospheric circulation, surface and deep water circulation and the reduction in atmospheric greenhouse gases then play a role in driving the climate into a glacial period (e.g., Berger, 1988; Li et al., 1998; Ruddiman, 2004; Brovkin et al., 2012). These feedbacks then operate in reverse when summer insolation starts to increase (Brovkin et al., 2012; Shakun et al., 2012).

Holocene climate

Steffen W et al. Ambio. 2011 Nov; 40(7): 739–761.

Astronomical forcing: Quaternary Climatic Change

Over the past 2.6 Myr, the Earth acquired the combination of physical characteristics (e.g., shape and disposition of continents and mountain belts, ocean circulation systems, atmospheric gas content, and major vegetation biomes) that we can observe today, and which differ markedly from those of earlier eras. Quaternary Period is composed of the Pleistocene and the Holocene.

Throughout the mast million years, as demostrated by proxy data, successive glaciation-deglaciation cycles have occurred with a dominant quasi-periodicity of 100K over which quasi-cycles of about 41 and 21 K are superimposed. The astronomical theory of paleoclimates aims to explain the recurrence of these cycles. The last one followed the Eemian interglacial centered about 125 K BP to the present-day Holocene interglacial which peaked around 6 K BP, and includes the last glacial maximum (LGM) which occurred at 21 K BP. During LGM, huge land-based ice sheets, reaching approximately 2-3 km in thickness covered northern parts of the Northern Hemisphere (NH). Sea level was lower by at least 115 m and the global average surface-air temperature was 5°C below present. Carbon dioxide (CO2) levels was about 200 ppm (compare with 280 ppm befor Industrial Revolution and almost 400 ppm today).

To compute astronomical forcing of insolation the most current practice is to use the insolation at a given summer day (Milankovitch used a seasonal averaged value). The standard forcing is therefore the daily insolation WD taken at 65.8°N at the summer solstice. But insolations averaged over longer periods of time may still be useful.

Concerning Milankovitch's theory, it is worth insisting on the point that the central object of interest is not "climate", i.e. the temperature over different regions of the Earth, but the ice-sheets, and more precisely ice-sheets in high northern latitudes for the Quaternary period. It can be said that Milankovitch's theory is clearly not a theory of "climate", but a theory of ice-sheets. In contrast to the geochemical theory which states that CO2 and global climate are driving ice sheet changes, the hypothesis of Milankovitch is just the opposite: ice-sheets are driving global climatic changes over the Quaternary, in particular through their large albedo effect. This mechanism is largely confirmed by LGM (Last Glacial Maximum) simulations with state-of-the-art models, since the ice sheets are responsible for a half of the LGM cooling. But the Milankovitch theory does not account for other possible climatic features, like abrupt changes, CO2 variations or any other mechanisms that are now recognized climatically relevant. It is therefore not entirely surprising that its predictions of a quasi-linear, mainly obliquity driven oscillation, is not corresponding exactly to observations. Indeed, climatic changes might, in turn, also have an impact on ice sheets. For instance, it is now a classical result from general circulation models that CO2 accounts for almost the other half of the LGM cooling.

In particular, 3 aspects of evolution of ice-sheet cyclical responses remain unexplained by astronomical forcing alone:

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Evolution of ice sheet responses: "41-K world" and "100-K world"

Ice sheets of substantial size did not exist on North America and Eurasia prior to 2.7 million years ago. After that time, moderate-sized ice sheets grew and melted primarily at a 41-K cycle until 900K BP (starting with Marine Oxygen Isotope Stage 22 (MIS 22)), when ice sheets began to fluctuate at a period near 100K (Ruddiman 2003, 2006). This progression is widely ascribed to a slow cooling trend evident in climatic proxies over the last several million years (Mix et al., 1995). Because ice ablation is an exponential function of warm-season temperature, a relatively small polar cooling could have significantly diminished summer ablation and allowed increased ice accumulation.

Raymo (1997) proposed a mechanism to explain the appearance of the 100,000-year ice-volume signal near 0.9 Myr ago. She suggested that just prior to that time temperatures at high northern latitudes were cold enough to let ice sheets grow at many 41,000-year and 23,000-year insolation minima, but were still warm enough to melt all of that ice during the next insolation maximum. As a result, ice sheets grew and melted only at those periods (Raymo et al. 1989). Near 0.9Myr, she proposed that northern hemisphere temperature cooled to a threshold that allowed some ice to persist through weak insolation maxima and reach a larger size.

Even though eccentricity has little direct impact on insolation (less than 0.15% of the amplitude of those at precession), it has a large indirect impact on climate through its modulation of orbital precession. Many recent attempts to explain the 100-K cycle have called on non-linear internal transformations linked to eccentricity. With external forcing, internal resonance, and free oscillations apparently eliminated, the most widely accepted explanation is that some kind of internal reaction within the climate system transforms incoming changes in solar radiation at the tilt and precession cycles into a 100- K response. Such an internal transformation requires some kind of preferred sensitivity within the climate system to tilt and/or precession forcing. In this sense, these internal responses are termed 'non-linear', rather than the linear (one-for-one) Milankovitch responses.

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The Early Middle Pleistocene Transition (EMPT) is the term used to describe the prolongation and intensification of glacial-interglacial climate cycles that initiated after 0.9Myr. During the transition glacial-interglacial cycles shift from lasting 41,000 years to an average of 100,000 years. The structure of these glacial-interglacial cycles shifts from smooth to more abrupt 'saw-toothed' like transitions. Despite eccentricity having by far the weakest influence on insolation received at the Earth's surface of any of the orbital parameters; it is often assumed to be the primary driver of the post-EMPT 100,000 years climate cycles because of the similarity in duration. The traditional solution to this is to call for a highly nonlinear response by the global climate system to eccentricity. Raymo (1997) noted that terminations are 'quantum' in nature: they tend to occur near every fourth or fifth precession maximum, at intervals that vary from 90K to 115K and average 100K. Others argue that post-EMPT deglaciations occurred every second or third obliquity cycle. Maslin et al. suggest that though phase-locking between orbital forcing and global ice volume may occur the chaotic nature of the climate system response means the relationship is not consistent through the last 900,000 years.

Prevailing view is that eccentricity is a pace-maker of glacial-interglacial cycles since ~900K BP. For tens of thousands of years after each termination, sequences of large insolation maxima occur at the precession cycle, promote ablation, and tend to keep the system in an interglacial state. When eccentricity later decreases (as in MIS 4 and 3), the insolation maxima at the precession cycle weaken, removing a major source of forcing toward interglacial conditions. As larger ice sheets begin to grow, the absence of strong insolation maxima at the precession period allows more ice growth until the next termination. In this way, eccentricity also paces transitions into glacial conditions.

Evolution of ice sheet response: 400-K problem

413 K is the other periodicity of eccentricity, which is absent from reconstructed ice sheet responses.

The northern (Arctic) margins of the ice sheets impose a fundamental constraint on the interglacial extreme of ice sheet behavior. When insolation forcing is sufficiently strong, all of the ice along the Arctic margin disappears. When all North American and Eurasian ice melts, the only ice sheet left is the small and less vulnerable ice on Greenland. At this point in a deglaciation, the rate of loss of northern ice slows drastically or stops. In effect, the loss of all vulnerable northern ice is a form of signal truncation. Because of this truncation, northern ice volume cannot react further to insolation forcing during extreme interglaciations and cannot register extra-large 413-K melting events. Thus, marine δ18O signals would not be expected to show extreme minima during large 413-K insolation maxima.

A different constraint on the maximum size of ice sheets comes into play when large ice sheets expand to lower latitudes. In the global-mean climate of the last million years, even the most favorable orbital configuration cannot shift the equilibrium line far enough south to produce snow/ice accumulation at low altitudes in the subtropics. Somewhere in the middle latitudes, ablation stops ice growth even when orbital configurations are highly favorable.

A second factor also helps to constrain ice growth within any single tilt or precession cycle: the orbital configurations that favor snow accumulation give way to unfavorable (or less-favorable) configurations within half of an orbital cycle (11K or 20K), too little time for a full equilibrium ice volume response to occur. When the orbital configurations begin to favor ice melting, the southern margins of the ice sheets become vulnerable to increasing ablation. As a result, large ice sheets are naturally constrained from registering a full response to 413-K extremes of insolation forcing by precession. Ruddiman notes the '400-K problem' may be less of a problem than has been thought because ice-volume fluctuations are naturally constrained by geographic limits in the north and climate-system factors in the south.

Possible origin of post-EMPT "saw-tooth" terminations' profile

With an upturn in summer insolation in the North the ice sheet start to melt, this causes sea level to rise. The ice sheets adjacent to the coasts are undercut by rising sea levels accelerating their collapse, which in turns raises sea level. This sea-level feedback mechanism can be extremely rapid. This rapid deglaciation that has been postulated causes the saw-tooth climate signal, that is characteristic of glacialeinterglacial cycles post-EMPR. However, this is a simplification, because though 80% of the ice sheet volume melts during this short period of time the remaining 20% or about 25 m of global sea level does not fully disappear until 5000 years later (Woodroffe and Webster, 2014), producing a kink in the rapid deglaciation curve.

Despite the pronounced change in Earth system response shown in palaeoclimatic records across the EMPT, the frequency and amplitude characteristics of the orbital parameters do not vary (Berger and Loutre, 1991; Berger et al., 1999). This indicates that the cause of change in response at the EMPT is internal rather than external to the global climate system.

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The last 10,000 years: anomalous trends in CH4, CO2 and ice volume (Ruddiman)

Orbital-scale phase relationships between insolation, ice volume, and greenhouse gases can be traced into the last 15,000 years Mid-July orbital precession reached a maximum value near 11,000 years ago, and obliquity reached a maximum near 10,000 years ago. Eccentricity reached a maximum 13,500 years ago.

For orbital precession, with ice volume lagging 4500 years behind insolation, ice sheets should have reached a minimum 6500 years ago and then begun to grow. For obliquity, the 6500-year ice-volume lag behind insolation forcing should have produced ice-sheet growth after 3500 years ago. The deglacial portion of the observed ice-volume trend appears to be in reasonable agreement with these predictions. The European ice sheet had melted by about 10,000 years ago, and North American ice by 6000 years ago. But no accumulation of global ice has occurred in the last several millennia, and this disagrees with the predictions based on long-term trends.

At the precession cycle, both the CH4 and CO2 concentrations should have reached peaks near 11,000 years ago and then steadily declined until today. At the obliquity cycle, the CO2 decrease should have begun near 3500 years ago, the time ice sheets should have begun to grow. The observed greenhouse-gas trends initially match these expected patterns, but then they diverge. CH4 reached a peak near 11,000 years ago and then decreased by 100 ppb until 5000 years ago, but then it began a totally unpredicted rise (of 100 ppb) prior to the industrial era. The CO2 signal reached a peak after 11,000 years ago and slowly fell until 8000 years ago (Indermuhle et al., 1999), but then it also began an unpredicted increase of 20–25 ppm. In summary, the observed greenhouse-gas trends match those predicted from longer-term orbital relationships prior to 8000–5000 years ago, but then begin anomalous rises. And northern hemisphere ice sheets that should have begun to grow several thousand years ago failed to appear, even though decreasing summer insolation in the northern hemisphere favored ice growth. These anomalous responses point to an obvious connection: whatever caused greenhouse gases to begin their "anomalous" rises countered the insolation trends and stopped the ice sheets from growing. Ruddiman and Thomson (2001) noted that the two proposed natural explanations of the CH4 rise since 5000 years ago (greater CH4 input from tropical wetlands or boreal peat-lands) can be rejected based on other evidence. They concluded that human activities must be responsible for the anomalous methane production. Human populations had begun to increase as a result of the discovery of agriculture 12,000 years ago, and tending of livestock and cultivation of rice had begun between 8000 and 6500 years ago. Although the number of humans on Earth 5000 years ago was still very small relative to today's population, methane emissions were an unavoidable product of daily activity such as tending livestock (which generate CH4 by waste and gastric emissions), human waste, biomass burning, and (especially) irrigation for rice, which began 5000 years ago.

Ruddiman proposed an anthropogenic origin for the CO2 rise since 8000 years ago. Evidence summarized by Roberts (1998) shows that humans began to cut forests for agriculture in Europe just as the anomalous CO2 increase began. By 2000 years ago, complex agricultural practices had replaced natural forests in large areas of southern and western Europe, India, and eastern China. Early deforestation in these regions is more than large enough to account for the observed increase in CO2 since 8000 years ago. Ruddiman estimated the full amplitude of the anthropogenic inputs at 250 ppb for CH4 and 40 ppm for CO2. These estimates incorporated both the observed increases of these greenhouse gases as well as the amount by which the concentrations should have decreased during the last several thousand years but did not.

These anthropogenic anomalies would produce a radiatively forced warming of about 0.8C° globally for a global climatic sensitivity to a CO2 doubling of 2.5°C. With positive albedo feedback at high latitudes, the warming should be about 2.5 times larger, or 2°C. Based on energy-balance modeling, Williams (1978) reported that broad areas of high terrain in northeast Canada were within 1°C to 2°C of the glaciation limit during the Little Ice Age. Without the early anthropogenic warming of 2°C, large parts of northeast Canada would have been cold enough for an ice sheet to grow. In summary, human additions of greenhouse gases to the atmosphere since 8000 to 5000 years ago have been large enough to stop a glaciation that would have been produced by natural trends of falling summer insolation and decreasing greenhouse-gas concentrations.

Also see: the community of climatologists predicts a progressive global warming [IPCC Fourth Assessment Report—Climate Change, 2007. The Scientific Basis. Cambridge University Press, Cambridge] that will not be interrupted by a glacial inception for the next 50 ka [Berger and Loutre, 2002. An exceptionally long Interglacial ahead? Science 297, 1287–1288] and [Müller U, Pross J, 2007. Lesson from the past: present insolation minimum holds potential for glacial inception.].

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