LIVING

Living Rev. Solar Phys., 5, (2008), 3
http://www.livingreviews.org/lrsp-2008-3

RE VIE WS

in solar physics

A History of Solar Activity over Millennia
Ilya G. Usoskin
Sodankylä Geophysical Observatory (Oulu unit)
FIN-90014 University of Oulu, Finlandemail: ilya.usoskin@oulu.fi
http://cc.oulu.fi/~usoskin/Accepted on 5 September 2008
Published on 21 October 2008
(Revised on 22 April 2010)

Abstract
Presented here is a review of present knowledge of the long-term behavior of solar activity
on a multi-millennial timescale, as reconstructed using the indirect proxy method.
The concept of solar activity is discussed along with an overview of the special indices used
to quantify different aspects of variable solar activity, with special emphasis upon sunspot
number.
Over long timescales, quantitative information about past solar activity can only be obtained using a method based upon indirect proxy, such as the cosmogenic isotopes 14 C and
10
Be in natural stratified archives (e.g., tree rings or ice cores). We give an historical overview
of the development of the proxy-based method for past solar-activity reconstruction over millennia, as well as a description of the modern state. Special attention is paid to the verificationand cross-calibration of reconstructions. It is argued that this method of cosmogenic isotopes
makes a solid basis for studies of solar variability in the past on a long timescale (centuries tomillennia) during the Holocene.
A separate section is devoted to reconstructions of strong solar–energetic-particle (SEP)
events in the past, that suggest that the present-day average SEP flux is broadly consistent
with estimates on longer timescales, and that the occurrence of extra-strong events is unlikely.
Finally, the main features of the long-term evolution of solar magnetic activity, including
the statistics of grand minima and maxima occurrence, are summarized and their possible
implications, especially for solar/stellar dynamo theory, are discussed.

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22 April 2010: The review has been updated by an overview of recent relevant papers (19 newreferences), published between 2008 and March 2010, and their role in advancing the topic oflong-term solar activity.
Page 11: More recent references have been added.
Page 15: A recent reference has been added.
Page 15: Reference to Hathaway (2010) has been updated.
Page 16: A new evidence, based on a reconstructed sunspot butterfly diagram for the late
18th century, of the existence of the lost cycle has been discussed.
Page 17: A more extended discussion on the nature of random fluctuations in the solar dynamo
is added.
Page 22: A recent reference has been added.
Page 23: A recent reference has been added.
Page 23: A recent reference has been added.
Page 23: Recent data on paleomagnetic reconstruction of the dipole moment (K08) has been
added to Figure 3.
Page 25: References to the atmospheric cascade models have been updated.
Page 26: Reference to INTCAL09 has been added.
Page 27: A recent reference has been added.
Page 33: More recent references have been added.
Page 33: Uncertainties in the 10 Be production models are discussed.
Page 35: Applications of the use of short-living 7 Be cosmogenic isotope is discussed.
Page 36: New references have been added.
Page 41: A recent reference has been added.
Page 45: Comparison between the results based on 14 C and 10 Be data has been updated.
Page 49: References and discussion on the long-term memory in grand minima occurrence are
updated.
Page 51: North-south asymmetry is discussed in more details
Page 53: Discussion of the statistics of grand minima occurrence has been updated.
Page 55: A recent reference has been added.
Page 60: A recent reference has been added.

Contents
1 Introduction

7

2 Solar Activity: Concept and Observations
2.1 The concept of solar activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Indices of solar activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Direct solar indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Indirect indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Solar activity observations in the pre-telescopic epoch . . . . . . . . . . . . . . . .
2.3.1 Instrumental observations: Camera obscura . . . . . . . . . . . . . . . . . .
2.3.2 Naked-eye observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Mathematical/statistical extrapolations . . . . . . . . . . . . . . . . . . . .
2.4 The solar cycle and its variations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Quasi-periodicities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.2 Randomness vs. regularity . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.3 A note on solar activity predictions . . . . . . . . . . . . . . . . . . . . . . .
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9
9
9
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12
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14
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15
16
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3 The Proxy Method of Past Solar-Activity Reconstruction
3.1 The physical basis of the method . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Heliospheric modulation of cosmic rays . . . . . . . . . . . . . . . . . . . . .
3.1.2 Geomagnetic shielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Cosmic-ray–induced atmospheric cascade . . . . . . . . . . . . . . . . . . .
3.1.4 Transport and deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Radioisotope 14 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.2 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.3 Transport and deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.4 The Suess effect and nuclear bomb tests . . . . . . . . . . . . . . . . . . . .
3.2.5 The effect of the geomagnetic field . . . . . . . . . . . . . . . . . . . . . . .
3.3 Cosmogenic isotope 10 Be . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.4 Effect of the geomagnetic field . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Towards a quantitative physical model . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Regression models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Reconstruction of heliospheric parameters . . . . . . . . . . . . . . . . . . .
3.4.3 A link to sunspot numbers . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Solar activity reconstructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Verification of reconstructions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1 Comparison with direct data . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2 Meteorites and lunar rocks: A direct probe of the galactic cosmic-ray flux .
3.6.3 Comparison between isotopes . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

20
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25
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35
36
36
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45
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4 Variability of Solar Activity Over Millennia
4.1 The overall activity level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Quasi-periodicities and characteristic times . . . . . . . . . . . . . . . . . . . . . .
4.3 Grand minima of solar activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 The Maunder minimum . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.2 Grand minima on a multi-millennial timescale . . . . . . . . . . . . . . . . .
4.4 Grand maxima of solar activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 The modern episode of active sun . . . . . . . . . . . . . . . . . . . . . . . .
4.4.2 Grand maxima on a multi-millennial timescale . . . . . . . . . . . . . . . .
4.5 Related implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.1 Theoretical constrains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.2 Solar-terrestrial relations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.5.3 Other issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

47
47
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49
50
51
53
53
54
55
55
56
57
57

5 Solar Energetic Particles in the Past
5.1 Lunar and meteoritic rocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Nitrates in polar ice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58
59
60
63

6 Conclusions64

7 Acknowledgements

66

References

67

List of Tables
1
2
3

Approximate dates (in –BC/AD) of grand minima in reconstructed solar activity. .
Approximate dates (in –BC/AD) of grand maxima in the SN-L series. . . . . . . .
Estimates of 4𝜋 omni-directional integral (above 30 MeV) flux, F 30 in [cm2 s]–1 , ofsolar energetic particles, obtained from different sources. . . . . . . . . . . . . . . .

52
54
60

A History of Solar Activity over Millennia

17Introduction

The concept of the perfectness and constancy of the sun, postulated by Aristotle, was a strong belief
for centuries and an official doctrine of Christian and Muslim countries. However, as people had
noticed even before the time of Aristotle, some slight transient changes of the sun can be observed
even with the naked eye. Although scientists knew about the existence of “imperfect” spots on
the sun since the early 17th century, it was only in the 19th century that the scientific community
recognized that solar activity varies in the course of an 11-year solar cycle. Solar variability waslater found to have many different manifestations, including the fact that the “solar constant” (theamount of total incoming solar electromagnetic radiation in all wavelengths per unit area) is not a
constant. The sun appears much more complicated and active than a static hot plasma ball, witha great variety of nonstationary active processes going beyond the adiabatic equilibrium foreseenin the basic theory of sun-as-star. Such transient nonstationary (often eruptive) processes can bebroadly regarded as solar activity, in contrast to the so-called “quiet” 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.
The very fact of the existence of solar activity poses an enigma for solar physics, leading to thedevelopment of sophisticated models of an upper layer known as the convection zone and the solar
corona. The sun is the only star, which can be studied in great detail and thus can be considered
as a proxy for cool stars. Quite a number of dedicated ground-based and space-borne experiments
are being carried out to learn more about solar variability. The use of the sun as a paradigm
for cool stars, leads to a better understanding of the processes driving the broader population ofcool sun-like stars. Therefore, studying and modelling solar activity can increase the level of ourunderstanding of nature.
On the other hand, the study of variable solar activity is not of purely academic interest, as it
directly affects the terrestrial environment. Although changes in the sun are barely visible without the aid of precise scientific instruments, these changes have great impact on many aspectsof our lives. In particular, the heliosphere (a spatial region of about 100 astronomical units) ismainly controlled by the solar magnetic field. This leads to the modulation of galactic cosmic rays
(GCRs). Additionally, eruptive and transient phenomena in the sun/corona and in the interplanetary medium can lead to the acceleration of energetic particles with greatly enhanced flux. Suchprocesses can modify the radiation environment on Earth and need to be taken into account forplanning 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 in themagnetosphere and ionosphere, which may disturb radio-wave propagation and navigation-systemstability, 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 (see, e.g., the review
by Haigh, 2007).
It is important to study solar variability on different timescales. The primary basis for suchstudies is observational (or reconstructed) data. The sun’s activity is systematically explored indifferent ways (solar, heliospheric, interplanetary, magnetospheric, terrestrial), including groundbased and space-borne experiments and dedicated missions during the last few decades, thus covering 3 – 4 solar cycles. However, it should be noted that the modern epoch is characterized byunusually-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. Therefore, the behavior of solar activity in the past, before the era of direct
measurements, is of great importance for a variety of reasons. For example, it allows an improved
knowledge of the statistical behavior of the solar-dynamo process, which generates the cyclicallyvarying solar-magnetic field, making it possible to estimate the fractions of time the sun spends instates of very-low activity, what are called grand minima. Such studies require a long time series of

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8Ilya G. Usoskin

solar-activity data. The longest direct series of solar activity is the 400-year-long sunspot-number
series, which depicts the dramatic contrast between the (almost spotless) Maunder minimum andthe modern period of very high activity. Thanks to the recent development of precise technologies,
including accelerator mass spectrometry, solar activity can be reconstructed over multiple millennia from concentrations of cosmogenic isotopes 14 C and 10 Be in terrestrial archives. This allows
one to study the temporal evolution of solar magnetic activity, and thus of the solar dynamo, onmuch longer timescales than are available from direct measurements.
This paper gives an overview of the present status of our knowledge of long-term solar activity,
covering the Holocene (the last 11 millennia). A description of the concept of solar activity and a
discussion of observational methods and indices are presented in Section 2. The proxy method ofsolar-activity reconstruction is described in some detail in Section 3. Section 4 gives an overview
of what is known about past solar activity. The long-term averaged flux of solar energetic particles
is discussed in Section 5. Finally, conclusions are summarized in Section 6.

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A History of Solar Activity over Millennia

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Solar Activity: Concept and Observations

2.1

The concept of solar activity

The sun is known to be far from a static state, the so-called “quiet” sun described by simple
stellar-evolution theories, but instead goes through various nonstationary active processes. Such
nonstationary and nonequilibrium (often eruptive) processes can be broadly regarded as solar activity. Whereas the concept of solar activity is quite a common term nowadays, it is not 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. A variety ofindices quantifying solar activity have been proposed in order to represent different observables
and caused effects. Most of the indices are highly correlated to each other due to the dominant
11-year cycle, but may differ in fine details and/or long-term trends. The indices can be roughly
divided into physical indices (i.e., those representing real physical quantities measurable for thesun) and synthetic indices. In addition to the solar indices, indirect proxy data is often used toquantify solar activity via its presumably known effect on the magnetosphere or heliosphere. The
indices of solar activity that are often used for long-term studies are reviewed below.

2.2

Indices of solar activity

Solar (as well as other) indices can be divided into physical and synthetic according to the way they
are obtained/calculated. Physical indices quantify the directly-measurable values of a real physicalobservable, such as the radioflux, and thus have clear physical meaning. Physical indices quantify
physical features of different aspects of solar activity and their effects. Synthetic indices (the mostcommon being sunspot number) are calculated (or synthesized) using a special algorithm fromobserved (often not measurable in physical units) data or phenomena. Additionally, solar activity
indices can be either direct (i.e., directly relating to the sun) or indirect (relating to indirect effects
caused by solar activity), as discussed in subsequent Sections 2.2.1, 2.2.2.
2.2.1

Direct solar indices

The most commonly used index of solar activity is based on sunspot number. Sunspots are darkareas on the solar disc (of size up to tens of thousands of km, lifetime up to half-a-year), characterized by a strong magnetic field, which leads to a lower temperature (about 4000 K compared to5800 K in the photosphere) and observed darkening.
Sunspot number is a synthetic, rather than a physical, index, but it has still become quite
a useful parameter in quantifying the level of solar activity. This index presents the weighted
number of individual sunspots and/or sunspot groups, calculated in a prescribed manner from
simple visual solar observations. The use of the sunspot number makes it possible to combine
together thousands and thousands of regular and fragmentary solar observations made by earlier
professional and amateur astronomers. The technique, initially developed by Rudolf Wolf, yielded
the longest series of directly and regularly-observed scientific quantities. Therefore, it is common
to quantify solar magnetic activity via sunspot numbers. For details see the review on sunspot
numbers and solar cycles (Hathaway and Wilson, 2004; Hathaway, 2010).
Wolf sunspot number (WSN) series
The concept of the sunspot number was developed by Rudolf Wolf of the Zürich observatory inthe middle of the 19th century. The sunspot series, initiated by him, is called the Zürich or Wolf
sunspot number (WSN) series. The relative sunspot number Rz is defined as
𝑅𝑧 = 𝑘 (10 𝐺 + 𝑁 ) ,(1)

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10Ilya G. Usoskin

where 𝐺 is the number of sunspot groups, 𝑁 is the number of individual sunspots in all groups
visible on the solar disc and 𝑘 denotes the individual correction factor, which compensates fordifferences in observational techniques and instruments used by different observers, and is used tonormalize different observations to each other.
200

a)

R150
Z
100
50
0
1600
200

1650

1700

1750

-4

0

1800

1850

1900

1950

b)

R150
g
100
50
0
-12

-50

-10

MM

4

DM

8

12

16

20

Figure 1: Sunspot numbers since 1610. a) Monthly (since 1749) and yearly (1700 – 1749) Wolf sunspot
number series. b) Monthly group sunspot number series. The grey line presents the 11-year running mean
after the Maunder minimum. Standard (Zürich) cycle numbering as well as the Maunder minimum (MM)and Dalton minimum (DM) are shown in the lower panel.

The value of Rz (see Figure 1a) is calculated for each day using only one observation madeby the “primary” observer (judged as the most reliable observer during a given time) for the day.
The primary observers were Staudacher (1749 – 1787), Flaugergues (1788 – 1825), Schwabe (1826 –
1847), Wolf (1848 – 1893), Wolfer (1893 – 1928), Brunner (1929 – 1944), Waldmeier (1945 – 1980)
and Koeckelenbergh (since 1980). If observations by the primary observer are not available fora certain day, the secondary, tertiary, etc. observers are used (see the hierarchy of observers in
Waldmeier, 1961). The use of only one observer for each day aims to make Rz a homogeneous timeseries. As a drawback, such an approach ignores all other observations available for the day, whichconstitute a large fraction of the existing information. Moreover, possible errors of the primaryobserver cannot be caught or estimated. If no sunspot observations are available for some period,
the data gap is filled, without note in the final WSN series, using an interpolation between theavailable data and by employing some proxy data. The observational uncertainties in the monthly
Rz can be up to 25% (e.g., Vitinsky et al., 1986). The WSN series is based on observations
performed at the Zürich Observatory during 1849 – 1981 using almost the same technique. This partof the series is fairly stable and homogeneous. However, prior to that there have been many gaps inthe data that were interpolated. Therefore, the WSN series is a combination of direct observations
and interpolations for the period before 1849, leading to possible errors and inhomogeneities as
discussed, e.g, by Vitinsky et al. (1986); Wilson (1998); Letfus (1999). The quality of the Wolf
series before 1749 is rather poor and hardly reliable (Hoyt et al., 1994; Hoyt and Schatten, 1998;
Hathaway and Wilson, 2004).
Note that the sun has been routinely photographed since 1876 so that full information on daily

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A History of Solar Activity over Millennia

11

sunspot activity is available (the Greenwich series) with observational uncertainties being negligible
for the last 140 years.
The routine production of the WSN series was terminated in Zürich in 1982. Since then, thesunspot number series is routinely updated as the International sunspot number Ri , provided by
the Solar Influences Data Analysis Center in Belgium (Clette et al., 2007). The internationalsunspot number series is computed using the same definition (Equation 1) as WSN but it has asignificant distinction from the WSN; it is based not on a single primary solar observation for eachday but instead uses a weighted average of more than 20 approved observers.
In addition to the standard sunspot number Ri , there is also a series of hemispheric sunspot
numbers 𝑅N and 𝑅S , which account for spots only in the northern and southern solar hemispheres,
respectively (note that 𝑅𝑖 = 𝑅N + 𝑅S ). These series are used to study the N-S asymmetry of solar
activity (Temmer et al., 2002).
Group sunspot number (GSN) series
Since the WSN series is of lower quality before the 1850s and is hardly reliable before 1750, there
was a need to re-evaluate early sunspot data. This tremendous work has been done by Hoyt andSchatten (1998), who performed an extensive archive search and nearly doubled the amount oforiginal information compared to the Wolf series. They have produced a new series of sunspot
activity called the group sunspot numbers (GSN – see Figure 1b), including all available archival
records. The daily group sunspot number Rg is defined as follows:
𝑅𝑔 =12.08 ∑︁ ′𝑘𝑖 𝐺𝑖 ,𝑛𝑖(2)where 𝐺𝑖 is the number of sunspot groups recorded by the 𝑖-th observer, 𝑘 ′ is the observer’s
individual correction factor, 𝑛 is the number of observers for the particular day, and 12.08 is anormalization number scaling Rg to Rz values for the period of 1874 – 1976. Rg is more robust thanRz since it is based on more easily identified sunspot groups and does not include the number ofindividual spots. The GSN series includes not only one “primary” observation, but all available
observations, and covers the period since 1610, being, thus, 140 years longer than the original WSN
series. It is particularly interesting that the period of the Maunder minimum (1645 – 1715) was
surprisingly well covered with daily observations allowing for a detailed analysis of sunspot activity
during this grand minimum (see also Section 4.3). Systematic uncertainties of the Rg values are
estimated to be about 10% before 1640, less than 5% from 1640 – 1728 and from 1800 – 1849, 15 –20% from 1728 – 1799, and about 1% since 1849 (Hoyt and Schatten, 1998). The GSN series is morereliable and homogeneous than the WSN series before 1849. The two series are nearly identicalafter the 1870s (Hoyt and Schatten, 1998; Letfus, 1999; Hathaway and Wilson, 2004). However,the GSN series still contains some lacunas, uncertainties and possible inhomogeneities (see, e.g.,
Letfus, 2000; Usoskin et al., 2003a).
The search for other lost or missing records of past solar instrumental observations has not ended
even since the extensive work by Hoyt and Schatten. Archival searches still give new interestingfindings of forgotten sunspot observations, often outside major observatories – see a detailed review
book by Vaquero and Vázquez (2009) and original papers by Casas et al. (2006); Vaquero et al.
(2005, 2007); Arlt (2008, 2009). Interestingly, not only sunspot counts but also regular drawings,
forgotten for centuries, are being restored nowadays in dusty archives.
Other indices
An example of a synthetic index of solar activity is the flare index, representing solar flare activity(e.g., Özgüç et al., 2003; Kleczek, 1952). The flare index quantifies daily flare activity in thefollowing manner; it is computed as a product of the flare’s relative importance 𝐼 in the H𝛼 -range
and duration 𝑡, 𝑄 = 𝐼 𝑡, thus being a rough measure of the total energy emitted by the flare. The
daily flare index is produced by Bogazici University (Özgüç et al., 2003) and is available since 1936.

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12Ilya G. Usoskin

A traditional physical index of solar activity is related to the radioflux of the sun in the wavelength range of 10.7 cm and is called the F10.7 index (e.g., Tapping and Charrois, 1994). This
index represents the flux (in solar flux units, 1 sfu = 10–22 Wm–2 Hz–1 ) of solar radio emission
at a centimetric wavelength. This emission is close to the peak of solar radio emission and is
produced as a result of the nonradiative heating of coronal plasma over active regions. It is a goodquantitative measure of the level of solar activity, which is not directly related to sunspots. Close
correlation between the F10.7 index and sunspot number indicates that the latter is a good index
of general solar activity, including coronal activity. The solar F10.7 cm record has been measured
continuously since 1947.
Another physical index is the coronal index (e.g., Rybanský et al., 2005), which is a measureof the irradiance of the sun as a star in the coronal green line. Computation of the coronalindex is based on observations of green corona intensities (Fe XIV emission line at 530.3 nm
wavelength) from coronal stations all over the world, the data being transformed to the Lomnický
Štit photometric scale. This index is considered a basic optical index of solar activity. A synthesized
homogeneous database of the Fe XIV 530.3 nm coronal-emission line intensities has existed since1943 and covers six solar cycles.
Often sunspot area is considered as a physical index representing solar activity (e.g., Baranyi
et al., 2001; Balmaceda et al., 2005). This index gives the total area of visible spots on the solar
disc in units of millionths of the sun’s visible hemisphere, corrected for apparent distortion due
to the curvature of the solar surface. The area of individual groups may vary between tens of
millionths (for small groups) up to several thousands of millionths for huge groups. This index
has a physical meaning related to the solar magnetic flux emerging at sunspots. Sunspot areas areavailable since 1874 in the Greenwich series obtained from daily photographic images of the sun.
In addition, some fragmentary data of sunspot areas, obtained from solar drawings, are available
for earlier periods (Vaquero et al., 2004; Arlt, 2008).
An important quantity is solar irradiance, total and spectral. Irradiance variations are physically related to solar magnetic variability (e.g., Solanki et al., 2000), and are often considered
manifestations of solar activity, which is of primary importance for solar-terrestrial relations.
Other physical indices include spectral sun-as-star observations, such as the CaII-K index (e.g.,
Donnelly et al., 1994; Foukal, 1996), the space-based MgII core-to-wing ratio as an index of solar
UVI (e.g., Donnelly et al., 1994; Viereck and Puga, 1999; Snow et al., 2005) and many others.
All the above indices are closely correlated to sunspot numbers on the solar-cycle scale, but
may depict quite different behavior on short or long timescales.
2.2.2

Indirect indices

Sometimes quantitative measures of solar-variability effects are also considered as indices of solar activity. These are related not to solar activity per se, but rather to its effect on different
environments. Accordingly, such indices are called indirect, and can be roughly divided into terrestrial/geomagnetic and heliospheric/interplanetary.
Geomagnetic indices quantify different effects of geomagnetic activity ultimately caused bysolar variability, mostly by variations of solar-wind properties and the interplanetary magnetic
field. For example, the aa-index, which provides a global index of magnetic activity relative toa quiet-day curve for a pair of antipodal magnetic observatories (in England and Australia), isavailable from 1868 (Mayaud, 1972). An extension of the geomagnetic series is available from the1840s using the Helsinki Ak(H) index (Nevanlinna, 2004a,b). A review of the geomagnetic effects
of solar activity can be found, e.g., in Pulkkinen (2007). It is noteworthy that geomagnetic indices,in particular low-latitude aurorae (Silverman, 2006), are associated with coronal/interplanetaryactivity (high-speed solar-wind streams, interplanetary transients, etc.) that may not be directly
related to the sunspot-cycle phase and amplitude, and therefore serve only as an approximate

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index of solar activity. One of the earliest instrumental geomagnetic indices is related to the daily
magnetic declination range, the range of diurnal variation of magnetic needle readings at a fixedlocation, and is available from the 1780s (Nevanlinna, 1995). However, this data exists as several
fragmentary sets, which are difficult to combine into a homogeneous data series.
Heliospheric indices are related to features of the solar wind or the interplanetary magnetic
field measured (or estimated) in the interplanetary space. For example, the time evolution of thetotal (or open) solar magnetic flux is extensively debated (e.g., Lockwood et al., 1999; Wang et al.,2005; Krivova et al., 2007).
A special case of heliospheric indices is related to the galactic cosmic-ray intensity recorded innatural 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 onlong timescales, as discussed in Section 3.

2.3

Solar activity observations in the pre-telescopic epoch

Instrumental solar data is based on regular observation (drawings or counting of spots) of the sunusing optical instruments, e.g., the telescope invented by Galileo in the early 17th century. Theseobservations have mostly been made by professional astronomers whose qualifications and scientificthoroughness were doubtless. They form the basis of the Group sunspot-number series (Hoyt andSchatten, 1998), which can be more-or-less reliably extended back to 1610 (see discussion in Section 2.2.1). However, some fragmentary records of qualitative solar and geomagnetic observations
exist even for earlier times, as discussed below (Sections 2.3.1 – 2.3.2).
2.3.1

Instrumental observations: Camera obscura

The invention of the telescope revolutionized astronomy. However, another solar astronomical
instrument, the camera obscura, also made it possible to provide relatively good solar images
and was still in use until the late 18th century. Small camera obscuras were known from earlytimes, and they have been used in major cathedrals to define the sun’s position (see the review by
Vaquero, 2007). The earliest known drawing of the solar disc was made by Frisius, who observed
the solar eclipse in 1544 using a camera obscura. That observation was performed during the Spörer
minimum and no spots were observed on the sun. The first known observation of a sunspot usinga camera obscura was done by Kepler in May 1607, who erroneously ascribed the spot on the sun
to a transit of Mercury. Although such observations were sparse and related to other phenomena(solar eclipses or transits of planets), there were also regular solar observations by camera obscura.
For example, about 300 pages of logs of solar observations made in the cathedral of San Petronio
in Bologna from 1655 – 1736 were published by Eustachio Manfredi in 1736 (see the full story in
Vaquero, 2007).
Therefore, observations and drawings made using camera obscura can be regarded as instrumental observations.
2.3.2

Naked-eye observations

Even before regular professional observations performed with the aid of specially-developed instruments (what we now regard as scientific observations) people were interested in unusual phenomena.
Several historical records exist based on naked-eye observations of transient phenomena on the sunor in the sky.
From even before the telescopic era, a large amount of evidence of spots being observed on
the solar disc can be traced back as far as to the middle of the 4th century BC (Theophrastus of
Athens). The earliest known drawing of sunspots is dated to December 8, 1128 AD as publishedin “The Chronicle of John of Worcester” (Willis and Stephenson, 2001). However, such evidence

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14Ilya G. Usoskinfrom occidental and Moslem sources is scarce and mostly related to observations of transits of inner
planets over the sun’s disc, probably because of the dominance of the dogma on the perfectnessof the sun’s body, which dates back to Aristotle’s doctrine (Bray and Loughhead, 1964). Oriental sources are much richer for naked-eye sunspot records, but that data is also fragmentary andirregular (see, e.g., Clark and Stephenson, 1978; Wittmann and Xu, 1987; Yau and Stephenson,1988). Spots on the sun are mentioned in official Chinese and Korean chronicles from 165 BC to1918 AD. While these chronicles are fairly reliable, the data is not straightforward to interpretsince it can be influenced by meteorological phenomena, e.g., dust loading in the atmosphere due
to dust storms (Willis et al., 1980) or volcanic eruptions (Scuderi, 1990) can facilitate sunspots observations. Direct comparison of Oriental naked-eye sunspot observations and European telescopic
data shows that naked-eye observations can serve only as a qualitative indicator of sunspot activity,
but can hardly be quantitatively interpreted (see, e.g., Willis et al., 1996, and references therein).
Moreover, as a modern experiment of naked-eye observations (Mossman, 1989) shows, Oriental
chronicles contain only a tiny (1 /200 – 1 /1000 ) fraction of the number of sunspots potentially visible
with the naked eye (Eddy et al., 1989). This indicates that records of sunspot observations in
the official chronicles were highly irregular (Eddy, 1983) and probably dependent on dominating
traditions during specific historical periods (Clark and Stephenson, 1978). Although naked-eye observations tend to qualitatively follow the general trend in solar activity according to a posteriori
information (e.g., Vaquero et al., 2002), extraction of any independent quantitative informationfrom these records seems impossible.
Visual observations of aurorae borealis at middle latitudes form another proxy for solar activity(e.g., Siscoe, 1980; Schove, 1983; Křivský, 1984; Silverman, 1992; Schröder, 1992; Lee et al., 2004;
Basurah, 2004). Fragmentary records of aurorae can be found in both occidental and oriental
sources since antiquity. The first known dated notation of an aurora is from March 12, 567 BC from
Babylon (Stephenson et al., 2004). Aurorae may appear at middle latitudes as a result of enhanced
geomagnetic activity due to transient interplanetary phenomena. Although auroral activity reflects
coronal and interplanetary features rather than magnetic fields on the solar surface, there is astrong correlation between long-term variations of sunspot numbers and the frequency of aurora
occurrences. Because of the phenomenon’s short duration and low brightness, the probabilityof seeing aurora is severely affected by other factors such as the weather, the Moon’s phase,season (night duration), etc. The fact that these observations were not systematic in early times(before the beginning of the 18th century) makes it difficult to produce a homogeneous data
set. Moreover, the geomagnetic latitude of the same geographical location may change quite
dramatically over centuries, due to the migration of the geomagnetic axis, which also affects theprobability of watching aurorae (Siscoe and Verosub, 1983; Oguti and Egeland, 1995). For example,
the geomagnetic latitude of Seoul (37.5° N 127° E), which is currently less than 30°, was about
40° a millennium ago (Kovaltsov and Usoskin, 2007). This dramatic change alone can explain theenhanced frequency of aurorae observations recorded in oriental chronicles.
2.3.3

Mathematical/statistical extrapolations

Due to the lack of reliable information regarding solar activity in the pre-instrumental era, it seems
natural to try to extend the sunspot series back in time, before 1610, by means of extrapolating its
statistical properties. Indeed, numerous attempts of this kind have been made even recently (e.g.,
Nagovitsyn, 1997; de Meyer, 1998; Rigozo et al., 2001). Such models aim to find the main featureof the actually-observed sunspot series, e.g., a modulated carrier frequency or a multi-harmonic
representation, which is then extrapolated backwards in time. The main disadvantage of thisapproach is that it is not a reconstruction based upon measured or observed quantities, but rather
a “post-diction” based on extrapolation. This method is often used for short-term predictions,but it can hardly be used for the reliable long-term reconstruction of solar activity. In particular,

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it assumes that the sunspot time series is stationary, i.e., a limited time realization contains full
information on its future and past. Clearly such models cannot include periods exceeding the timespan of observations upon which the extrapolation is based. Hence, the pre or post-diction becomesincreasingly unreliable with growing extrapolation time and its accuracy is hard to estimate.
Sometimes a combination of the above approaches is used, i.e., a fit of the mathematical model
to indirect qualitative proxy data. In such models a mathematical extrapolation of the sunspot
series is slightly tuned and fitted to some proxy data for earlier times. For example, Schove(1955, 1979) fitted the slightly variable but phase-locked carrier frequency (about 11 years) tofragmentary data from naked-eye sunspot observations and auroral sightings. The phase locking isachieved by assuming exactly nine solar cycles per calendar century. This series, known as Schoveseries, reflects qualitative long-term variations of the solar activity, including some grand minima,
but cannot pretend to be a quantitative representation in solar activity level. The Schove series
played an important historical role in the 1960s. In particular, a comparison of the Δ14 C datawith this series succeeded in convincing the scientific community that secular variations of 14 C intree rings have solar and not climatic origins (Stuiver, 1961). This formed a cornerstone of the
precise method of solar-activity reconstruction, which uses cosmogenic isotopes from terrestrial
archives. However, attempts to reconstruct the phase and amplitude of the 11-year cycle, using
this method, were unsuccessful. For example, Schove (1955) made predictions of forthcoming
solar cycles up to 2005, which failed. We note that all these works are not able to reproduce, forexample, the Maunder minimum (which cannot be represented as a result of the superpositionof different harmonic oscillations), yielding too high sunspot activity compared to that observed.
From the modern point of view, the Schove series can be regarded as archaic, but it is still in use insome studies. This approach has been modified using nonlinear relations and some related indices(Nagovitsyn, 1997, 2006), but its shortcomings are still limiting the reliability of reconstructions.

2.4

The solar cycle and its variations

2.4.1

Quasi-periodicities

The main feature of solar activity is its pronounced quasi-periodicity with a period of about
11 years, known as the Schwabe cycle. However, the cycle varies in both amplitude and duration.
The first observation of a possible regular variability in sunspot numbers was made by the Danish
astronomer Christian Horrebow in the 1770s on the basis of his sunspot observations from 1761 –
1769 (see details in Gleissberg, 1952; Vitinsky, 1965), but the results were forgotten. It took over
70 years before the amateur astronomer Schwabe announced in 1844 that sunspot activity varies
cyclically with a period of about 10 years. This cycle, called the 11-year or Schwabe cycle, is themost prominent variability in the sunspot-number series. It is recognized now as a fundamental
feature of solar activity originating from the solar-dynamo process. This 11-year cyclicity is prominent in many other parameters including solar, heliospheric, geomagnetic, space weather, climate
and others. The background for the 11-year Schwabe cycle is the 22-year Hale magnetic polarity
cycle. Hale found that the polarity of sunspot magnetic fields changes in both hemispheres whena new 11-year cycle starts (Hale et al., 1919). This 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 cycleis the modulo of the sign-alternating Hale cycle (e.g., Sonett, 1983; Bracewell, 1986; Kurths andRuzmaikin, 1990; de Meyer, 1998; Mininni et al., 2001). A detailed review of solar-cyclic variability
can be found in (Hathaway, 2010).
Sometimes the regular time evolution of solar activity is broken up by periods of greatly depressed activity called grand minima. The last grand minimum (and the only one covered bydirect solar observations) was the famous Maunder minimum from 1645 – 1715 (Eddy, 1976, 1983).
Other grand minima in the past, known from cosmogenic isotope data, include, e.g., the Spörer
minimum around 1450 – 1550 and the Wolf minimum around the 14th century (see the detailed

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16Ilya G. Usoskin

discussion in Section 4.3). Sometimes the Dalton minimum (ca. 1790 – 1820) is also considered to
be a grand minimum. However, sunspot activity was not completely suppressed and still showed
Schwabe cyclicity during the Dalton minimum. As suggested by Schüssler et al. (1997), this canbe a separate, intermediate state of the dynamo between the grand minimum and normal activity,
or an unsuccessful attempt of the sun to switch to the grand minimum state (Frick et al., 1997;
Sokoloff, 2004). This is observed as the phase catastrophe of solar-activity evolution (e.g., Vitinsky
et al., 1986; Kremliovsky, 1994). A peculiarity in the phase evolution of sunspot activity around1800 was also noted by Sonett (1983) who ascribed it to a possible error in Wolf sunspot data
and by Wilson (1988a), who reported on a possible misplacement of sunspot minima for cycles
4 – 6 in the WSN series. It has been also suggested that the phase catastrophe can be related toa tiny cycle, which might have been lost at the end of the 18th century because of very sparse
observations (Usoskin et al., 2001b, 2002a, 2003b; Zolotova and Ponyavin, 2007). We note that a
new independent evidence proving the existence of the lost cycle has been found recently in thereconstructed sunspot butterfly diagram for that period (Usoskin et al., 2009c). Another period
associated with a phase catastrophe is the period of sunspot-activity recovery after the Maunderminimum. The recovery of the 11-year cycle passed through the time of distorted phase evolution(Usoskin et al., 2001a) with the concurrent loss of the 88-year cycle phase (Feynman and Gabriel,1990).
The long-term change (trend) in the Schwabe cycle amplitude is known as the secular Gleissberg
cycle (Gleissberg, 1939). However, the Gleissberg cycle is not a cycle in the strict periodic sense
but rather a modulation of the cycle envelope with a varying timescale of 60 – 120 years (e.g.,
Gleissberg, 1971; Kuklin, 1976; Ogurtsov et al., 2002). This secular cycle has also been reported,using a spectral analysis of radiocarbon data as a proxy for solar activity (see Section 3), to exist
on long timescales (Feynman and Gabriel, 1990; Peristykh and Damon, 2003), but the question of
its phase locking and persistency/intermittency still remains open.
Longer (super-secular) cycles cannot be studied using direct solar observations, but several
such cycles have been found in cosmogenic isotope data. A cycle with a period of 205 – 210 years,
called the de Vries or Suess cycle in different sources, is a prominent feature, observed in varying
cosmogenic data (e.g., Suess, 1980; Sonett and Finney, 1990; Zhentao, 1990; Usoskin et al., 2004).
Sometimes variations with a characteristic time of 600 – 700 years or 1000 – 1200 years are discussed(e.g., Vitinsky et al., 1986; Sonett and Finney, 1990; Vasiliev and Dergachev, 2002), but they areintermittent and can hardly be regarded as a typical feature of solar activity. A 2000 – 2400-year
cycle is also noticeable in radiocarbon data series (see, e.g., Vitinsky et al., 1986; Damon and
Sonett, 1991; Vasiliev and Dergachev, 2002). However, the nonsolar origin of these super-secular
cycles (e.g., geomagnetic or climatic variability) cannot be excluded.
2.4.2

Randomness vs. regularity

The short-term (days - months) variability of sunspot numbers is greater than the observational
uncertainties indicating the presence of random fluctuations (noise). As typical for most real
signals, this noise is not uniform (white), but rather red or correlated noise (e.g., Ostryakov andUsoskin, 1990; Oliver and Ballester, 1996; Frick et al., 1997), namely, its variance depends on thelevel of the signal. While the existence of regularity and randomness in sunspot series is apparent,
their relationship is not clear (e.g., Wilson, 1994) – are they mutually independent or intrinsicallytied together? Moreover, the question of whether randomness in sunspot data is due to chaotic or
stochastic processes is still open.
Earlier it was common to describe sunspot activity as a multi-harmonic process with several
basic harmonics (e.g., Vitinsky, 1965; Sonett, 1983; Vitinsky et al., 1986) with an addition of
random noise, which plays no role in the solar-cycle evolution. However, it has been shown (e.g.,
Rozelot, 1994; Weiss and Tobias, 2000; Charbonneau, 2001; Mininni et al., 2002) that such an

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oversimplified approach depends on the chosen reference time interval and does not adequately
describe the long-term evolution of solar activity. A multi-harmonic representation is based on
an assumption of the stationarity of the benchmark series, but this assumption is broadly invalid
for solar activity (e.g., Kremliovsky, 1994; Sello, 2000; Polygiannakis et al., 2003). Moreover,a multi-harmonic representation cannot, for an apparent reason, be extrapolated to a timescalelarger than that covered by the benchmark series. The fact that purely mathematical/statisticalmodels cannot give good predictions of solar activity (as will be discussed later) implies that thenature of the solar cycle is not a multi-periodic or other purely deterministic process, but random(chaotic or stochastic) processes play an essential role in sunspot formation. Different numeric
tests, such as an analysis of the Lyapunov exponents (Ostriakov and Usoskin, 1990; Mundt et al.,
1991; Kremliovsky, 1995; Sello, 2000), Kolmogorov entropy (Carbonell et al., 1994; Sello, 2000) and
Hurst exponent (Ruzmaikin et al., 1994; Oliver and Ballester, 1998), confirm the chaotic/stochastic
nature of the solar-activity time evolution (see, e.g., the recent review by Panchev and Tsekov,
2007).

It was suggested quite a while ago that the variability of the solar cycle may be a temporal
realization of a low-dimensional chaotic system (e.g., Ruzmaikin, 1981). This concept became
popular in the early 1990s, when many authors considered solar activity as an example of lowdimensional deterministic chaos, described by the strange attractor (e.g., Kurths and Ruzmaikin,
1990; Ostriakov and Usoskin, 1990; Morfill et al., 1991; Mundt et al., 1991; Rozelot, 1995; Salakhutdinova, 1999; Serre and Nesme-Ribes, 2000). Such a process naturally contains randomness, which
is an intrinsic feature of the system rather than an independent additive or multiplicative noise.
However, although this approach easily produces features seemingly similar to those of solar activity, quantitative parameters of the low-dimensional attractor have varied greatly as obtainedby different authors. Later it was realized that the analyzed data set was too short (Carbonell
et al., 1993, 1994), and the results were strongly dependent on the choice of filtering methods(Price et al., 1992). Developing this approach, Mininni et al. (2000, 2001) suggest that one consider sunspot activity as an example of a 2D Van der Pol relaxation oscillator with an intrinsic
stochastic component.

Such phenomenological or basic principles models, while succeeding in reproducing (to someextent) the observed features of solar-activity variability, do not provide insight into the nature of
regular and random components of solar variability. In this sense efforts to understand the natureof randomness in sunspot activity in the framework of dynamo theory are more advanced. Corresponding theoretical dynamo models have been developed (see reviews by Ossendrijver, 2003;
Charbonneau, 2005), which include stochastic processes (e.g., Weiss et al., 1984; Feynman andGabriel, 1990; Schmalz and Stix, 1991; Moss et al., 1992; Hoyng, 1993; Brooke and Moss, 1994;
Lawrence et al., 1995; Schmitt et al., 1996; Charbonneau and Dikpati, 2000; Brandenburg and
Sokoloff, 2002). For example, Feynman and Gabriel (1990) suggest that the transition from a
regular to a chaotic dynamo passes through bifurcation. Charbonneau and Dikpati (2000) studied stochastic fluctuations in a Babcock–Leighton dynamo model and succeeded in the qualitative
reproduction of the anti-correlation between cycle amplitude and length (Waldmeier rule). Their
model also predicts a phase-lock of the Schwabe cycle, i.e., that the 11-year cycle is an internal“clock” of the sun. Most often the idea of fluctuations is related to the 𝛼-effect, which is theresult of the electromotive force averaged over turbulent vortices, and thus can contain a fluctuating contribution (e.g., Hoyng, 1993; Ossendrijver et al., 1996; Brandenburg and Spiegel, 2008).
Note that a significant fluctuating component (with the amplitude more than 100% of the regularcomponent) is essential in all these model.

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2.4.3

Ilya G. Usoskin

A note on solar activity predictions

Randomness (see Section 2.4.2) in the SN series is directly related to the predictability of solar
activity. Forecasting solar activity has been a subject of intense study for many years (e.g., Yule,
1927; Newton, 1928; Gleissberg, 1948; Vitinsky, 1965) and has greatly intensified recently with ahundred journal articles being published before 2008 (see, e.g., the review by Kane, 2007) following
the boosting of space-technology development and increasing debates on solar-terrestrial relations.
All prediction methods can be generically divided into precursor and statistical techniques ortheir combinations (Hathaway et al., 1999). The precursor methods are usually based on phenomenological, but sometimes physical, links between the poloidal solar-magnetic field, estimated,e.g., from geomagnetic activity in the declining phase of the preceding cycle or in the minimum
time (e.g., Hathaway et al., 1999), with the toroidal field responsible for sunspot formation. Thesemethods usually yield better short-term predictions of a forthcoming cycle maximum than thestatistical methods, but cannot be applied to timescales longer than one solar cycle. Statistical methods, including a low-dimensional solar-attractor representation (Kurths and Ruzmaikin,1990), are based solely on the statistical properties of sunspot activity and may give a reasonable
result for short-term forecasting, but yield very poor results for long-term predictions (see reviewsby e.g., Conway, 1998; Hathaway et al., 1999; Li et al., 2001; Usoskin and Mursula, 2003; Kane,
2007) because of chaotic/stochastic behavior (see Section 2.4.2).
Some models, mostly based on precursor method, succeed in reasonable predictions of a forthcoming solar cycle (i.e., several years ahead), 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 have been made recently, often without sensible argumentation. However, so far there is noevidence of any method giving a reasonable prediction of solar activity beyond the solar-cycle scale(see, e.g., Section 2.3.3), probably because of the intrinsic limit of solar-activity predictability due
to its stochastic/chaotic nature (Kremliovsky, 1995). Accordingly, such attempts can be regarded
as speculative, unless they are verified by the actual behavior of solar activity. Note that even an
exact prediction of the amplitude of one solar cycle can be just a random coincidence and cannot
serve as a proof of the method’s veracity. Only a sequence of successful predictions can form abasis for confidence, which requires several decades.

2.5

Summary

In this section, the concept of solar activity and quantifying indices is discussed, as well as themain features of solar-activity temporal behavior.
The concept of solar activity is quite broad and covers nonstationary and nonequilibrium (often
eruptive) processes, in contrast to the “quiet” sun concept, 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 physicalor synthetic. While all indices depict the dominant 11-year cyclic variability, their relationships onother timescales (short scale or long-term trends) may vary to a great extent.
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 outside the grand minimum. The sunspot number series is available for the period from1610 AD, after the invention of the telescope, and covers, in particular, the Maunder minimumin the late 17th century. Fragmentary noninstrumental observations of the sun before 1610, while
giving a possible hint of relative changes in solar activity, cannot be interpreted in a quantitative
manner.
Solar activity in all its manifestations is dominated by the 11-year Schwabe cycle, which has,in fact, a variable length of 9 – 14 years for individual cycles. The amplitude of the Schwabe cycle

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varies greatly – from the almost spotless Maunder minimum to the very high cycle 19, possibly in
relation to the Gleissberg or secular cycle. Longer super-secular characteristic times can also befound in various proxies of solar activity, as discussed in Section 4.
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.

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3

The Proxy Method of Past Solar-Activity Reconstruction

In addition to direct solar observations, described in Section 2.2.1, there are also indirect solar
proxies, which are used to study solar activity in the pre-telescopic era. Unfortunately, we do nothave any reliable data that could give a direct index of solar variability before the beginning of
the sunspot-number series. Therefore, one must use indirect proxies, i.e., quantitative parameters,
which can be measured nowadays but represent different effects of solar magnetic activity in thepast. It is common to use, for this purpose, signatures of terrestrial indirect effects induced byvariable solar-magnetic activity, that is stored in natural archives. Such traceable signatures canbe related to nuclear (used in the cosmogenic-isotope method) or chemical (used in the nitrate
method – Section 5.2) effects caused by cosmic rays (CRs) in the Earth’s atmosphere, lunar rocks
or meteorites.
The most common proxy of solar activity is formed by the data on cosmogenic radionuclides(e.g., 10 Be and 14 C), which are produced by cosmic rays in the Earth’s atmosphere (e.g, Stuiverand Quay, 1980; Beer et al., 1990; Bard et al., 1997; Beer, 2000). Other cosmogenic nuclides,
which are used in geological and paleomagnetic dating, are less suitable for studies of solar activity(see e.g., Beer, 2000). 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. After a complicated transport in the atmosphere, the cosmogenic isotopes are stored in natural archives such as polar ice, trees, marine sediments, etc. This
process is also affected by changes in the geomagnetic field and climate. Cosmic rays experience
heliospheric modulation due to solar wind and the frozen-in solar magnetic field. The intensity ofmodulation 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, andthese archives are measured nowadays in laboratories using modern techniques. If necessary, allmeasurements can be repeated and improved, as has been done for some radiocarbon samples. In
contrast to fixed historical archival data (such as sunspot or auroral observations) this approachmakes it possible to obtain homogeneous data sets of stable quality and to improve the qualityof data with the invention of new methods (such as accelerator mass spectrometry). Cosmogenic
isotope data is the only regular indicator of solar activity on the very long-term scale but it cannot
always resolve the details of individual solar cycles. The redistribution of nuclides in terrestrial
reservoirs and archiving may be affected by local and global climate/circulation processes, whichare, to a large extent, unknown for the past. However, a combined study of different nuclides data,
whose responses to terrestrial effects are very different, may allow for disentangling external andterrestrial signals.

3.1

The physical basis of the method

3.1.1

Heliospheric modulation of cosmic rays

Before reaching the vicinity of Earth, galactic cosmic rays experience complicated transport in the
heliosphere that leads to modulation of their flux. Heliospheric transport of GCR is describedby Parker’s theory (Parker, 1965; Toptygin, 1985) and includes four basic processes: the diffusionof particles due to their scattering on magnetic inhomogeneities, the convection of particles byout-blowing solar wind, adiabatic energy losses in expanding solar wind, drifts of particles in themagnetic field, including the gradient-curvature drift in the regular heliospheric magnetic field, andthe drift along the heliospheric current sheet, which is a thin magnetic interface between the two
heliomagnetic hemispheres. Because of variable solar-magnetic activity, CR flux in the vicinity ofEarth is strongly modulated (see Figure 2). The most prominent feature in CR modulation is the
11-year cycle, which is in inverse relation to solar activity. The 11-year cycle in CR is delayed (fromLiving Reviews in Solar Physics
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A History of Solar Activity over Millennia

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a month up to two years) with respect to the sunspots (Usoskin et al., 1998). The time profile ofcosmic-ray flux, as measured by the longest-running neutron-monitor Climax, is shown in Figure 2(panel b) together with the sunspot numbers (panel a). Besides the inverse relation between them,some other features can also be noted. A 22-year cyclicity manifests itself in cosmic-ray modulation
through the alteration of sharp and flat maxima in cosmic-ray data, originated from the chargedependent drift mechanism. One may also note short-term fluctuations, which are not directly
related to sunspot numbers but are driven by interplanetary transients caused by solar eruptive
events, e.g., flares or CMEs. For the last 50 years of high and roughly-stable solar activity, no
trends have been observed in CR data; however, as will be discussed later, the overall level of CR
has changed significantly on the centurial-millennial timescales.

CR count rate (%)

Sunspot numbers

250

a)

200
150
100
50
0
1950

1960

1970

1980

1990

2000

b)

100
95
90
85
80
75
70
1950

1960

1970

1980

1990

2000

Years
Figure 2: Cyclic variations. Panel a: Time profiles of sunspot numbers; Panel b: Cosmic-ray flux as thecount rate of Climax neutron monitor (NM) (100% NM count rate corresponds to May 1965).

Full solution of the CR transport problems is a complicated task and requires sophisticated
3D time-dependent self-consistent modelling. However, the problem can be essentially simplified
for applications at a long-timescale. An assumption on the azimuthal symmetry (requires times
longer that the solar-rotation period) and quasi-steady changes reduces it to a 2D quasi-steadyproblem. Further assumption of the spherical symmetry of the heliosphere reduces the problem
to a 1D case. This approximation can be used only for rough estimates, since it neglects thedrift effect, but it is useful for long-term studies, when the heliospheric parameters cannot be
evaluated independently. Further, but still reasonable, assumptions (constant solar-wind speed,roughly power-law CR energy spectrum, slow spatial changes of the CR density) lead to the forcefield approximation (Gleeson and Axford, 1968), which can be solved analytically. The differential

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22Ilya G. Usoskinintensity 𝐽𝑖 of the cosmic-ray nuclei of type 𝑖 with kinetic energy 𝑇 at 1 AU is given in this case as
𝐽𝑖 (𝑇, 𝜑) = 𝐽LIS,𝑖 (𝑇 + Φ𝑖 )(𝑇 )(𝑇 + 2𝑇r ),(𝑇 + Φ)(𝑇 + Φ𝑖 + 2𝑇r )(3)where Φ𝑖 = (𝑍𝑖 𝑒/𝐴𝑖 )𝜑 for a cosmic nuclei of 𝑖-th type (charge and mass numbers are 𝑍𝑖 and𝐴𝑖 ), 𝑇 and 𝜑 are expressed in MeV/nucleon and in MV, respectively, 𝑇r = 938 MeV. 𝑇 is theCR particle’s kinetic energy, and 𝜑 is the modulation potential. The local interstellar spectrum(LIS) 𝐽LIS forms the boundary condition for the heliospheric transport problem. Since LIS is notmeasured directly, i.e., outside the heliosphere, it is not well known in the energy range affected by
CR modulation (below 100 GeV). Presently-used approximations for LIS (e.g., Garcia-Muñoz et al.,
1975; Burger et al., 2000; Webber and Higbie, 2003, 2009) agree with each other for energies above
20 GeV but may contain uncertainties of up to a factor of 1.5 around 1 GeV. These uncertainties inthe boundary conditions make the results of the modulation theory slightly model-dependent (seediscussion in Usoskin et al., 2005a) and require the LIS model to be explicitly cited. This approachgives results, which are at least dimensionally consistent with the full theory and can be used
for long-term studies1 (Usoskin et al., 2002b; Caballero-Lopez and Moraal, 2004). Differential CR
intensity is described by the only time-variable parameter, called the modulation potential 𝜑, which
is mathematically interpreted as the averaged rigidity (i.e., the particle’s momentum per unit ofcharge) loss of a CR particle in the heliosphere. However, it is only a formal spectral index whose
physical interpretation is not straightforward, especially on short timescales and during active
periods of the sun (Caballero-Lopez and Moraal, 2004). Despite its cloudy physical meaning, thisforce-field approach provides a very useful and simple single-parametric approximation for thedifferential spectrum of GCR, since the spectrum of different GCR species directly measured near
the Earth can be perfectly fitted by Equation 3 using only the parameter 𝜑 in a wide range ofsolar activity level (Usoskin et al., 2005a). Therefore, changes in the whole energy spectrum (inthe energy range from 100 MeV/nucleon to 100 GeV/nucleon) of cosmic rays due to the solar
modulation can be described by this single number within the framework of the adopted LIS. The
concept of modulation potential is a key concept for the method of solar-activity reconstruction
by cosmogenic isotope proxy.
3.1.2

Geomagnetic shielding

Cosmic rays are charged particles and therefore are affected by the Earth’s magnetic field. Thus thegeomagnetic field puts an additional shielding on the incoming flux of cosmic rays. The shielding
effect of the geomagnetic field is usually expressed in terms of the cutoff rigidity 𝑃c , which is theminimum rigidity a CR particle must posses (on average) in order to reach the ground at a given
location and time (Cooke et al., 1991). Neglecting such effects as the East-West asymmetry, which
is roughly averaged out for the isotropic particle flux, or nondipole magnetic momenta, which decay
rapidly with distance, one can come to a simple approximation, called the Störmer’s equation, that
describes the vertical geomagnetic cutoff rigidity 𝑃c :2

𝑃c ≈ 1.9 𝑀 (𝑅o /𝑅) cos4 𝜆𝐺 [GV] ,(4)

where 𝑀 is the geomagnetic dipole moment (in 1025 G cm3 ), 𝑅o is the Earth’s mean radius, 𝑅 isthe distance from the given location to the dipole center, and 𝜆𝐺 is the geomagnetic latitude. Thisapproximation provides a good compromise between simplicity and reality, especially when using
the eccentric dipole description of the geomagnetic field (Fraser-Smith, 1987). The eccentric dipole
has the same dipole moment and orientation as the centered dipole, but the dipole’s center and
1 Note that the famous work by Castagnoli and Lal (1980) contains an inconsistency in the force-field formula –see details in Usoskin et al. (2005a),

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A History of Solar Activity over Millennia

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consequently the poles, defined as crossings of the axis with the surface, are shifted with respect
to geographical ones.
The shielding effect is the strongest at the geomagnetic equator, where the present-day value of𝑃c may reach up to 17 GV in the region of India. There is almost no cutoff in the geomagnetic polar
regions (𝜆𝐺 ≥ 60∘ ). However, even in the latter case the atmospheric cutoff becomes important,i.e., particles must have rigidity above 0.5 GV in order to initiate the atmospheric cascade (seeSection 3.1.3).
The geomagnetic field is seemingly stable on the short-term scale, but it changes essentiallyon centurial-to-millennial timescales (e.g., Korte and Constable, 2006). Such past changes can beevaluated based on measurements of the residual magnetization of independently-dated samples.
These can be paleo (i.e., natural stratified archives such as lake or marine sediments or volcaniclava) or archaeological (e.g., clay bricks that preserve magnetization upon baking) samples. Most
paleo-magnetic data preserve not only the magnetic field intensity but also the direction of thelocal field, while archeo-magnetic samples provide information on the intensity only. Using a large
database of such samples, it is possible to reconstruct (under reasonable assumptions) the largescale magnetic field of the Earth. Data available provides good global coverage for the last 3
millennia, allowing for a reliable paleomagnetic reconstruction of the true dipole moment (DM) or
virtual dipole moment2 (VDM) and its orientation (the ArcheoInt collaboration – Genevey et al.,2008). Less precise, but still reliable reconstructions of the DM and its orientation are possible
for the last seven millennia (the CALS7K.2 model by Korte and Constable, 2005), however they
may slightly underestimate the dipole moment, especially in the earlier part of the period (Korte
and Constable, 2008). No reliable directional paleomagnetic reconstruction is presently possible
on a longer timescale, because of the spatial sparseness of the paleo/archeo-magnetic samples inthe earlier part of the Holocene. Therefore, only the virtual axial dipole moment3 (VADM) canbe estimated before ca. 5000 BC (Yang et al., 2000; Knudsen et al., 2008). Note that the strong
assumption of the coincidence of magnetic and geographical axes may lead to an overestimate of
the true dipole moment, if the magnetic axis is actually tilted. Accordingly, we assume that thetwo models of Y00 and CALS7K.2 bind the true dipole moment variations. These paleomagnetic
reconstructions are shown in Figure 3. All paleomagnetic models depict a similar long-term trend– an enhanced intensity during the period between 1500 BC and 500 AD and a significantly lower
field before that.
Changes in the dipole moment 𝑀 inversely modulate the flux of CR at Earth, with strong
effects in tropical regions and globally. The migration of the geomagnetic axis, which changes thegeomagnetic latitude 𝜆𝐺 of a given geographical location is also important; while not affecting the
global flux of CR, it can dramatically change the CR effect regionally, especially at middle andhigh latitude (Kovaltsov and Usoskin, 2007). These changes affect the flux of CR impinging on the
Earth’s atmosphere both locally and globally and must be taken into account when reconstructing
solar activity from terrestrial proxy data (Usoskin et al., 2008). Accounting for these effects is quite
straightforward provided the geomagnetic changes in the past are known independently, e.g., fromarcheo and paleo-magnetic studies. However, because of progressively increasing uncertainties of
paleomagnetic reconstructions back in time, it presently forms the main difficulty for the proxymethod on the long-term scale (Snowball and Muscheler, 2007), especially in the early part of the
Holocene. On the other hand, the geomagnetic field variations are relatively well known for thelast few millennia (Genevey et al., 2008; Korte and Constable, 2008).

2 The concept of VDM assumes that the geomagnetic dipole is centered at the planet’s center and its axis isaligned with the true magnetic axis.
3 The concept of VADM assumes that the centered geomagnetic dipole is always aligned with the geographicalaxis.

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Ilya G. Usoskin

142

Dipole moment (10 Am )

24

22

12
10

Y00
HBI
K05
A08
K08

8
6
4
-5000

-4000

-3000

-2000

-1000

0

1000

2000

Years (-BC/AD)
Figure 3: Geomagnetic field intensity over millennia: VADM compilation by Yang et al. (2000, – Y00
curve with 1𝜎 statistical errors of the sample distribution); dipole moment according to Hongre et al. (1998,– HBI red dots) since 800 AD, dipole moment according to CALS7K.2 model (Korte and Constable, 2005,– K05 magenta curve with 1𝜎 error band) as well as a recent ArcheoInt compilations of VADM/VDM(Genevey et al., 2008, – A08 azure diamonds) and (Knudsen et al., 2008, – K08 blue stars).

3.1.3

Cosmic-ray–induced atmospheric cascade

When an energetic CR particle enters the atmosphere, it first moves straight in the upper layers,
suffering mostly from ionization energy losses that lead to the ionization of the ambient rarefied
air. However, after traversing some amount of matter (the nuclear interaction mean-free path ison the order of 100 g/cm2 for a proton in the air) the CR particle may collide with a nucleus
in the atmosphere, producing a number of secondaries. These secondaries have their own fatein the atmosphere, in particular they may suffer further collisions and interactions forming an
atmospheric cascade (e.g., Dorman, 2004). Because of the thickness of the Earth’s atmosphere(1033 g/cm2 at sea level) the number of subsequent interactions can be large, leading to a fullydeveloped cascade (also called an air shower) consisting of secondary rather than primary particles.
Three main components can be separated in the cascade:• The “hadronic” nucleonic component is formed by the products of nuclear collisions of primary cosmic rays and their secondaries with the atmospheric nuclei, and consists mostly ofsuperthermal protons and neutrons.
• The “soft” or electromagnetic component consists of electrons, positrons and photons.
• The “hard” or muon component consists mostly of muons; pions are short lived and decay
almost immediately upon production, feeding muons and the “soft” component.
The development of the cascade depends mostly on the amount of matter traversed and isusually linked to residual atmospheric depth rather than to the actual altitude, that may varydepending on the exact atmospheric density profile.
Cosmogenic isotopes are a by-product of the hadronic branch of the cascade (details are given
below). Accordingly, in order to evaluate cosmic-ray flux from the cosmogenic isotope data, one
needs to know the physics of cascade development. Several models have been developed for thiscascade, in particular its hadronic branch with emphasis on the generation of cosmogenic isotope

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A History of Solar Activity over Millennia

25

production. The first models were simplified quasi-analytical (e.g., Lingenfelter, 1963; O’Brien
and Burke, 1973) or semi-empirical models (e.g., Castagnoli and Lal, 1980). With the fast advanceof computing facilities it became possible to exploit the best numerical method suitable for suchproblems – Monte-Carlo (e.g., Masarik and Beer, 1999, 2009; Webber and Higbie, 2003; Webber
et al., 2007; Usoskin and Kovaltsov, 2008; Kovaltsov and Usoskin, 2010). The fact that models,
based on different independent Monte-Carlo packages, namely, a general GEANT tool and a specific
CORSIKA code, yield similar results provides additional verification of the approach.
3.1.4

Transport and deposition

A scheme for the transport and redistribution of the two most useful cosmogenic isotopes, 14 C
and 10 Be, is shown in Figure 4. After a more-or-less similar production, the two isotopes follow
quite different fates, as discussed in detail in Sections 3.2.3 and 3.3.3. Therefore, expected terrestrial effects are quite different for the isotopes and comparing them with each other can help in
disentangling solar and climatic effects (see Section 3.6.3).

Cosmic Rays

helio
modulation

Cosmic Rays

geomagnetic

AtmosphereStratosphere 
ClimateBiosphere
14

C

Ocean
mixed layer
Ocean
deep layers

Troposphere

Geosphere
10

Be

Figure 4: Schematic representation of 14 C (left) and 10 Be (right) production chains. The flux of cosmic
rays impinging on the Earth is affected by both heliospheric modulation and geomagnetic field changes.
The climate may affect the redistribution of the isotopes between different reservoirs. Dashed line denotes
a possible influence of solar activity on climate.

3.2

Radioisotope 14 C

The most commonly used cosmogenic
is radiocarbon 14 C. This radionuclide is an unstable(︀ isotope)︀isotope of carbon with a half-life 𝑇1/2 of about 5730 years. Since the radiocarbon method is
extensively used in other science disciplines where accurate dating is a key issue (e.g., archeology,
paleoclimatology, quaternary geology), it was developed primarily for this task. The solar-activity–
reconstruction method, based on radiocarbon data, was initially developed as a by-product of thedating techniques used in archeology and Quaternary geology, in an effort to improve the quality

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26

Ilya G. Usoskinof the dating by means of better information on the 14 C variable source function. The present-day
radiocarbon calibration curve, based on a dendrochronological scale, uninterruptedly covers thewhole Holocene (and extending to 26,000 BP) and provides a solid quantitative basis for studying
solar activity variations on the multi-millennial time scale.
3.2.1

Measurements

Radiocarbon is usually measured in tree rings, which allows an absolute dating of the samples bymeans of dendrochronology. Using a complicated technique, the 14 C activity4 𝐴 is measured in an
independently dated sample, which is then corrected for age as(︂)︂
0.693 𝑡𝐴* = 𝐴 · exp
,
(5)
𝑇1/2
where 𝑡 and 𝑇1/2 are the age of the sample and the half-life of the isotope, respectively. Then therelative deviation from the standard activity 𝐴𝑜 of oxalic acid (the National Bureau of Standards)
is calculated:)︂(︂ *𝐴 − 𝐴𝑜· 1000.
(6)
𝛿 14 C =𝐴𝑜
After correction for the carbon isotope fractionating (account for the 13 C isotope) of the sample,
the radiocarbon value of Δ14 C is calculated (see details in Stuiver and Pollach, 1977).
Δ14 C = 𝛿 14 C − (2 · 𝛿 13 C + 50) · (1 + 𝛿 14 C/1000),(7)

where 𝛿 13 C is the per mille deviation of the 13 C content in the sample from that in the standard
belemnite sample calculated similarly to Equation 6. The value of Δ14 C (measured in per mille h)is further used as the index of radiocarbon relative activity. The series of Δ14 C for the Holocene
is presented in Figure 5A as published by the INTCAL04 (which is an update of the INTCAL98
series – Stuiver et al., 1998) collaboration of 21 dating laboratories as a result of systematic precise
measurements of dated samples from around the world (Reimer et al., 2004). The most recent
INTCAL09 data-set is available at http://www.radiocarbon.org/IntCal09.htm.
A potentially interesting approach has been made by Lal et al. (2005), who measured theamount of 14 C directly produced by CR in polar ice. Although this method is free of the carboncycle influence, the first results, while being in general agreement with other methods, are notprecise.
3.2.2

Production

The main source of radioisotope 14 C (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 byatmospheric nitrogen14
N + 𝑛 → 14 C + 𝑝.
(8)
Neutrons are always present in the atmosphere as a product of the cosmic-ray–induced cascade(see Section 3.1.3) but their flux varies in time along with the modulation of cosmic-ray flux. This
provides continuous source of the isotope in the atmosphere, while the sinks are isotope decay andtransport into other reservoirs as described below (the carbon cycle).
4 Isotope’s activity quantifies its decay rate and is usually given in terms of disintegrations per minute per gramof carbon.

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A History of Solar Activity over Millennia

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14

C prod. rate (at/cm2 /sec)∆ 14C (per mille)

200
150
100
50
0
-50
2.5

2

1.5

1

0.5
-10000

-8000

-6000

-4000

-2000

0

2000

Years (AD/BC)

Figure 5: Radiocarbon series for the Holocene. Upper panel: Measured content of Δ14 C in tree rings by
INTCAL-98/04 collaboration (Stuiver et al., 1998; Reimer et al., 2004). The long-term trend is caused by
the geomagnetic field variations and the slow response of the oceans. Lower panel: Production rate of 14 C
in the atmosphere, reconstructed from the measured Δ14 C (Usoskin and Kromer, 2005).

The connection between the cosmogenic-isotope–production rate, 𝑄, at a given location (quantified via the geomagnetic latitude 𝜆G ) and the cosmic-ray flux is given by∫︁ ∞𝑄=
𝑆(𝑃, 𝜑) 𝑌 (𝑃 ) 𝑑𝑃 ,(9)𝑃c (𝜆G )where 𝑃c is the local cosmic-ray–rigidity cutoff (see Section 3.1.2), 𝑆(𝑃, 𝜑) is the differential energy
spectrum of CR (see Section 3.1.1) and 𝑌 (𝑃 ) is the differential yield function of cosmogenic isotope
production (Castagnoli and Lal, 1980; Masarik and Beer, 1999, 2009). Because of the global natureof the carbon cycle and its long attenuation time, the radiocarbon is globally mixed before thefinal deposition, and Equation 9 should be integrated over the globe. The yield function 𝑌 (𝑃 )of the 14 C production is shown in Figure 6A together with those for 10 Be (see Section 3.3.2) andfor a ground-based neutron monitor (NM), which is the main instrument for studying cosmic-ray
variability during the modern epoch. One can see that the yield function increases with the energyof CR. On the other hand, the energy spectrum of CR decreases with energy. Accordingly, thedifferential production rate (i.e., the product of the yield function and the spectrum, 𝐹 = 𝑌 · 𝑆 –the integrand of Equation 9), shown in Figure 6B, is more informative. The differential production
rate reflects the sensitivity to cosmic rays, and the total production rate is simply an integral of 𝐹
over energy above the geomagnetic threshold. One can see that the sensitivity of 14 C to CR peaks
at a few GeV and is quite close to that of a neutron monitor (Beer, 2000).
Thanks to the development of atmospheric cascade models (Section 3.1.3), there are numericalmodels that allow one to compute the radiocarbon production rate as a function of the modulation
potential 𝜑 and the geomagnetic dipole moment 𝑀 . The overall production of 14 C is shown in
Figure 7.
The production rate of radiocarbon, 𝑄14 C , can vary as affected by different factors (see, e.g.,

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28

Ilya G. Usoskin

Arb. units

1

A)

0.1

10Be, polar
10Be, global
14C, global
Polar NM
GCR spectrum

0.01

Diff. production rate (arb. units)

1E-3
0.1

1

Energy (GeV)

10

100

B)

100

10

1

0.1
0.1

1

Energy (GeV)

10

100

Figure 6: Differential production rate for cosmogenic isotopes and ground-based neutron monitors as afunction of cosmic-ray energy. Panel A): Yield functions of the globally averaged and polar 10 Be production(Webber and Higbie, 2003), global 14 C production (Castagnoli and Lal, 1980), polar neutron monitor (Clemand Dorman, 2000) as well as the energy spectrum of galactic cosmic protons for medium modulation(𝜑 = 550 MV). Panel B): The differential production rate for global and polar 10 Be production, global 14 C
production, and polar neutron monitor.

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A History of Solar Activity over Millennia

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Damon and Sonett, 1991):• Variations of the cosmic-ray flux on a geological timescale due to the changing galactic
background (e.g., a nearby supernova explosion or crossing the dense galactic arm).
• Secular-to-millennial variations are caused by the slowly-changing geomagnetic field. This is
an important component of the variability, which needs to be independently evaluated from
paleo and archeo-magnetic studies.
• Modulation of cosmic rays in the heliosphere by solar magnetic activity. This variation is theprimary aim of the present method.
• Short-term variability of CR on a daily scale (suppression due to interplanetary transients orenhancement due to solar energetic-particle events) cannot be resolved in radiocarbon data.

14

2

C production rate (at/cm /sec)

2.5

2.0

1.5

1.0

11

0

10
9

500

φ (MV)

8

25

7

1000
6

M

(10

G

12
3

cm

)

14

Figure 7: Globally-averaged production rate of C as a function of the modulation potential 𝜑 andgeomagnetic dipole moment 𝑀 , computed using the yield function by Castagnoli and Lal (1980), LIS by
Burger et al. (2000) and cosmic-ray–modulation model by Usoskin et al. (2005a). Another often usedmodel (Masarik and Beer, 1999) yields a similar result.

Therefore, the production rate of 14 C in the atmosphere can be modelled for a given time
(namely, the modulation potential and geomagnetic dipole moment) and location. The global
production rate 𝑄 is then obtained as a result of global averaging.
There is still a small unresolved discrepancy in the absolute value of the modeled 14 C production
rate. Different models yield the global-average production rate of 1.75 – 2.3 atoms cm–2 s–1 (see,e.g., O’Brien, 1979; Masarik and Beer, 1999; Goslar, 2001; Usoskin et al., 2006b, and references
therein), which is consistent with a direct estimate of the radiocarbon reservoir, based on analysesof the specific 14 C activity on the ground, 1.76 – 2.0 (Suess, 1965; Damon et al., 1978; O’Brien,1979). On the other hand, the steady-state production calculated from the 14 C inventory inthe carbon-cycle model (see Section 3.2.3) typically yields 1.6 – 1.7 atoms cm–2 s–1 for the preindustrial period (e.g., Goslar, 2001, and references therein). Thus, results obtained from the

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30

Ilya G. Usoskincarbon cycle models and production models agree only marginally in the absolute values, andthis needs further detailed studies. In 14 C-based reconstructions, the pre-industrial steady-state
production is commonly used.
3.2.3

Transport and deposition

Upon production cosmogenic radiocarbon gets quickly oxidized to carbon dioxide CO2 and takes
part in the regular carbon cycle of interrelated systems: atmosphere-biosphere-ocean (Figure 4).
Because of the long residence time, radiocarbon becomes globally mixed in the atmosphere andinvolved in an exchange with the ocean. It is common to distinguish between an upper layer ofthe ocean, which can directly exchange CO2 with the air and deeper layers. The measured Δ14 C
comes from the biosphere (trees), which receives radiocarbon from the atmosphere. Therefore, theprocesses involved in the carbon cycle are quite complicated. The carbon cycle is usually describedusing a box model (Oeschger et al., 1974; Siegenthaler et al., 1980), where it is represented byfluxes between different carbon reservoirs and mixing within the ocean reservoir(s), as shown in
Figure 8. Production and radioactive decay are also included in box models. Free parameters
in a typical box model are the 14 C production rate 𝑄, the air-sea exchange rate (expressed asturnover rate 𝜅), and the vertical–eddy-diffusion coefficient 𝐾, which quantifies ocean ventilation.
Starting from the original representation (Oeschger et al., 1974), a variety of box models havebeen developed, which take into account subdivisions of the ocean reservoir and direct exchange
between the deep ocean and the atmosphere at high latitudes. More complex models, including a
diffusive approach, are able to simulate more realistic scenarios, but they require knowledge of alarge number of model parameters. These parameters can be evaluated for the present time using
the bomb test – studying the transport and distribution of the radiocarbon produced during theatmospheric nuclear tests. However, for long-term studies, only the production rate is consideredvariable, while the gas-exchange rate and ocean mixing are kept constant. Under such assumptions,
there is no sense in subdividing reservoirs or processes, and a simple carbon box model is sufficient.

Figure 8: A 12-box model of the carbon cycle (Broeker and Peng, 1986; Siegenthaler et al., 1980).The
number on each individual box is the steady-state Δ14 C of this particular reservoir expressed in per mil.
(After Bard et al., 1997)

Using the carbon cycle model and assuming that all its parameters are constant in time, one canevaluate the production rate 𝑄 from the measured Δ14 C data. This assumption is well validated

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A History of Solar Activity over Millennia

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for the the Holocene (Damon et al., 1978; Stuiver et al., 1991) as there is no evidence of considerable
oceanic change or other natural variability of the carbon cycle (Gerber et al., 2002), and accordingly
all variations of Δ14 C predominantly reflect the production rate. This is supported by the strong
similarity of the fluctuations of the 10 Be data in polar ice cores (Section 3.3) compared to 14 C,
despite their completely different geochemical fate (Bard et al., 1997). However, the changes in the
carbon cycle during the last glaciation and deglaciation were dramatic, especially regarding ocean
ventilation; this and the lack of independent information about the carbon cycle parameters, makeit hardly possible to qualitatively estimate solar activity from 14 C before the Holocene.
First attempts to extract information on production-rate variations from measured Δ14 C werebased on simple frequency separations of the signals. All slow changes were ascribed to climaticand geomagnetic variations, while short-term fluctuations were believed to be of solar origin. Thiswas done by removing the long-term trend from the Δ14 C series and claiming the residual as
being a series of solar variability (e.g., Peristykh and Damon, 2003). This oversimplified approach
was natural at earlier times, before the development of carbon cycle models, but later it was
replaced by the inversion of the carbon cycle (i.e., the reconstruction of the production rate fromthe measured 14 C concentration). Although mathematically this problem can be solved correctly
as a system of linear differential equations, the presence of fluctuating noise with large magnitude
makes it not straightforward, since the time derivative cannot be reliably identified. One traditional
approach (e.g., Stuiver and Quay, 1980) is based on an iterative procedure, first assuming a constantproduction rate, and then fitting the calculated Δ14 C variations to the actual measurements using
a feedback scheme. A concurrent approach based on the presentation of the carbon cycle as a
Fourier filter (Usoskin and Kromer, 2005) produces similar results. The production rate 𝑄14 C
for the Holocene is shown in Figure 5 and depicts both short-term fluctuations as well as slower
variations, mostly due to geomagnetic field changes (see Section 3.2.5).
3.2.4

The Suess effect and nuclear bomb tests

Unfortunately, cosmogenic 14 C data cannot be easily used for the last century, primarily becauseof the extensive burning of fossil fuels. Since fossil fuels do not contain 14 C, the produced CO2
dilutes the atmospheric 14 CO2 concentration with respect to the pre-industrial epoch. Therefore,
the measured Δ14 C cannot be straightforwardly translated into the production rate 𝑄 after thelate 19th century, and a special correction for fossil fuel burning is needed. This effect, known
as the Suess effect (e.g., Suess, 1955) can be up to −25h in Δ14 C in 1950 (Tans et al., 1979),
which is an order of magnitude larger than the amplitude of the 11-year cycle of a few per mil.
Moreover, while the cosmogenic production of 14 C is roughly homogeneous over the globe andtime, the use of fossil fuels is highly nonuniform (e.g., de Jong and Mook, 1982) both spatially(developed countries, in the northern hemisphere) and temporarily (World Wars, Great Depression,industrialization, etc.). This makes it very difficult to perform an absolute normalization of theradiocarbon production to the direct measurements. Sophisticated numerical models (e.g., Sabine
et al., 2004; Mikaloff Fletcher et al., 2006) aim to account for the Suess effect and make good
progress. However, the results obtained indicate that the determination of the Suess effect does not
yet reach the accuracy required for the precise modelling and reconstruction of the 14 C production
for the industrial epoch. As noted by Matsumoto et al. (2004), “. . . Not all is well with the current
generation of ocean carbon cycle models. At the same time, this highlights the danger in simply
using the available models to represent state-of-the-art modeling without considering the credibilityof each model.” Note that the atmospheric concentration of another carbon isotope 13 C is partly
affected by land use, which has also been modified during the last century.
Another anthropogenic activity greatly disturbing the natural variability of 14 C is related to theatmospheric nuclear bomb tests actively performed in the 1960s. For example, the radiocarbon
concentration nearly doubled in the early 1960s in the northern hemisphere after nuclear tests

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32Ilya G. Usoskin

performed by the USSR and the USA in 1961 (Damon et al., 1978). On one hand, such sourcesof momentary spot injections of radioactive tracers (including 14 C) provide a good opportunity toverify and calibrate the exchange parameters for different carbon -cycle reservoirs and circulation
models (e.g., Bard et al., 1987; Sweeney et al., 2007). Thus, the present-day carbon cycle is moreor-less known. On the other hand, the extensive additional production of isotopes during nuclear
tests makes it hardly possible to use the 14 C as a proxy for solar activity after the 1950s (Joos,
1994).
These anthropogenic effects do not allow one to make a straightforward link between preindustrial data and direct experiments performed during more recent decades. Therefore, thequestion of the absolute normalization of 14 C model is still open (see, e.g., the discussion in
Solanki et al., 2004, 2005; Muscheler et al., 2005).
3.2.5

The effect of the geomagnetic field

As discussed in Section 3.1.2, knowledge of geomagnetic shielding is an important aspect of the cosmogenic isotope method. Since radiocarbon is globally mixed in the atmosphere before deposition,
its production is affected by changes in the geomagnetic dipole moment 𝑀 , while magnetic-axis
migration plays hardly any role in 14 C data.
The crucial role of paleomagnetic reconstructions has long been known (e.g., Elsasser et al.,1956; Kigoshi and Hasegawa, 1966). Many earlier corrections for possible geomagnetic-field changes
were performed by detrending the measured Δ14 C abundance or production rate 𝑄 (Stuiver andQuay, 1980; Voss et al., 1996; Peristykh and Damon, 2003), under the assumption that geomagnetic
and solar signals can be disentangled in the frequency domain. Accordingly, the temporal seriesof either measured Δ14 C or its production rate 𝑄 is decomposed into the slow changing trend andfaster oscillations. The trend is supposed to be entirely due to geomagnetic changes, while theoscillations are ascribed to solar variability. Such a method, however, obliterates all information
on possible long-term variations of solar activity. Simplified empirical correction factors werealso often used (e.g., Stuiver and Quay, 1980; Stuiver et al., 1991). The modern approach isbased on a physics-based model (e.g., Solanki et al., 2004; Vonmoos et al., 2006) and allows thequantitative reconstruction of solar activity, explicitly using independent reconstructions of thegeomagnetic field. In this case the major source of errors in solar activity reconstructions is related
to uncertainties in the paleomagnetic data (Snowball and Muscheler, 2007). These errors are
insignificant for the last millennium (Usoskin et al., 2006a), but become increasingly important forearlier times.

3.3

Cosmogenic isotope 10 Be

3.3.1

Measurements

The cosmogenic isotope 10 Be 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 measureby the decay rate (Beer, 2000). Accordingly, the 10 Be/9 Be ratio needs to be precisely measured
at an accuracy better than 10–13 . This can be done using AMS (Accelerator Mass Spectrometry)technique, which make the measurements complicated and expensive. Correction for the decay isstraightforward and does not include isotope fractionating. From the measured samples, first the10
Be concentration is defined, usually in units of 104 atoms/g. Sometimes, a correction for thesnow precipitation amount is considered leading to the observable 10 Be flux, which is the numberof atoms per cm2 per second.
There exist different 10 Be series suitable for studies of long-term solar activity, coming from ice
cores in Greenland and Antarctica. They have been obtained from different cores with different

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resolutions, and include data from Milcent, Greenland (Beer et al., 1983), Camp Century, Greenland (Beer et al., 1988), Dye 3, Greenland (Beer et al., 1990), Dome Concordia and South Pole,
Antarctica (Raisbeck et al., 1990), GRIP, Greenland (Yiou et al., 1997), GISP2, Greenland (Finkel
and Nishiizumi, 1997), Dome Fuji, Antarctica (Horiuchi et al., 2007, 2008). We note that data on
10
Be in other archives, e.g., lake sediments, is usually more complicated to interpret because of thepotential influence of the climate (Horiuchi et al., 1999; Belmaker et al., 2008).
Details of the 10 Be series and their comparison with each other can be found in Beer (2000);Muscheler et al. (2007).
3.3.2

Production

The isotope 10 Be is produced as a result of spallation of atmospheric nitrogen and oxygen (carbon
is less abundant by far in the atmosphere and makes a negligible contribution) by the nucleoniccomponent of the cosmic-ray–induced atmospheric cascade (Section 3.1.3). The cross section (afew mb) of the spallation reactions is almost independent of the energy of impacting particles andhas a threshold of about 15 MeV. Thus, the production of 10 Be is defined solely by the multiplicityof the nucleonic component, which increases with the energy of primary cosmic rays (see Figure 6).
Maximum production occurs at an altitude of 10 – 15 km due to a balance between the totalenergy of the cascade (which increases with altitude) and the number of secondaries (decreasing
with altitude). Most of the global 10 Be is produced in the stratosphere (55 – 70%) and the restin the troposphere (Lal and Peters, 1967; Masarik and Beer, 1999, 2009; Usoskin and Kovaltsov,
2008; Kovaltsov and Usoskin, 2010).
Computation of 10 Be isotope production is straightforward, provided a model of the atmospheric cascade is available. The first consistent model was developed by D. Lal et al. (Bhandari
et al., 1966; Lal and Peters, 1967; Lal and Suess, 1968), using an empirical approach based on fitting
simplified model calculations to measurements of the isotope concentrations and “star” (inelastic
nuclear collisions) formations in the atmosphere. Next was an analytical model by O’Brien (1979),
who solved the problem of the GCR-induced cascade in the atmosphere using an analytical stationary approximation in the form of the Boltzmann equation, which has also been normalized per“star” formation. Those models were based on calculating the rate of inelastic collisions or “stars”
and then applying the mean spallation yield per “star”. A new step in the modelling of isotope
production was made by Masarik and Beer (1999), who performed a full Monte-Carlo simulation ofa GCR-initiated cascade in the atmosphere and used cross sections of spallation reactions directly
instead of the average “star” efficiency. A recent model by Webber and Higbie (2003) and Webber et al. (2007) is also based on a full Monte-Carlo simulation of the atmospheric cascade, using
improved cross sections. The global production rate of 10 Be is about 0.02 – 0.03 atoms cm–2 s–1(Masarik and Beer, 1999; Webber et al., 2007; Kovaltsov and Usoskin, 2010), which is lower thanthat for 14 C by two orders of magnitude (about 2 atoms cm–2 s–1 ; see Section 3.2.2). The yieldfunction of 10 Be production is shown in Figure 6A and the differential production rate in Figure 6B.
One can see that the peak of 10 Be sensitivity, especially in polar regions, is shifted towards lower
energies (below 1 GeV) compared with both 14 C and neutron monitor sensitivities. This implies
that the 10 Be isotope is relatively more sensitive to less energetic CR and is, therefore, more affected by solar energetic particles (Usoskin et al., 2006b). There is discrepancy of a factor of 1.5
between different production models of 10 Be production that needs to be resolved. Comparison ofmodel computations with direct beryllium production experiments (Usoskin and Kovaltsov, 2008;
Kovaltsov and Usoskin, 2010), and also the results of modelling of the short-living 7 Be isotope(Usoskin et al., 2009a) suggest that some numerical models (Masarik and Beer, 1999; Webber andHigbie, 2003; Webber et al., 2007) tend to underestimate the production.
Although the production of 10 Be can be more or less precisely modelled, a simple normalization“surface”, similar to that shown in Figure 7 for 14 C, is not easy to produce because of partial mixing

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34Ilya G. Usoskinin the atmosphere (see Section 3.3.3). Simplified models, assuming either only global (e.g., Beer,
2000) or polar production (Bard et al., 1997; Usoskin et al., 2004), have been used until recently.
However, it has been recognized that a more realistic model of the limited atmospheric mixing
should be used. Without detailed knowledge of 10 Be transport in the atmosphere, it is impossible
to relate the quantitatively-measured concentration to the production (as done for 14 C using thecarbon cycle), and one has to assume that the measured abundance is proportional (with an
unknown coefficient) to the production rate in a specific geographical region (see Section 3.3.3).
3.3.3

Transport

After production, the 10 Be isotope has a seemingly simple (Figure 4) but difficult-to-accountfor fate in the atmosphere. Its atmospheric residence time depends on scavenging, stratospheretroposphere exchange and inter-tropospheric mixing (e.g., McHargue and Damon, 1991). Soon
after production, the 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).
The mean residence time of the aerosol-bound radionuclide in the atmosphere is quite different
for the troposphere, being a few weeks, and stratosphere, where it is one to two years (Raisbeck
et al., 1981). Accordingly, 10 Be produced in the troposphere is deposited mostly locally, i.e., in thepolar regions, while stratospheric 10 Be can be partly or totally mixed. In addition, because of theseasonal (usually Spring) intrusion of stratospheric air into the troposphere at mid-latitudes, there
is an additional contribution of stratospheric 10 Be. Therefore, the measured 10 Be concentration (orflux) in polar ice is modulated not only by production but also by climate/precipitation effects (e.g.,
Steig et al., 1996; Bard et al., 1997). This led Lal (1987) to the extreme conclusion that variationsof polar 10 Be reflect a meteorological, rather than solar, signal. However, comparison between
Greenland and Antarctic 10 Be series and between 10 Be and 14 C data (e.g., Bard et al., 1997;
Horiuchi et al., 2008) suggests that the beryllium data mostly depicts production variations (i.e.,
solar signal) on top of which some meteorological effects can be superposed (see also Section 3.6.3).
Since both assumptions of the global and purely-local polar production of 10 Be archived inpolar ice are over-simplified, several attempts have been made to overcome this problem. For
instance, McCracken (2004) proposed several simple mathematical models of partial atmosphericmixing (without division in the troposphere and stratosphere) and compared them with observed
data. From this semi-empirical approach McCracken concluded that M2 (full mixing above 60°
latitude and a limited mixing between 40° and 60° latitude) is a reasonable model for Antarctica.
Vonmoos et al. (2006) assumed that the production of 10 Be recorded in Greenland is related to theentire hemisphere in the stratosphere (i.e, global stratospheric mixing) but is limited to latitudes
above 40° latitude in the troposphere (partial tropospheric mixing). This approach uses either
semi-empirical or indirect arguments in choosing the unknown degree of mixing.
Recent efforts in employing modern atmospheric 3D circulation models for simulations of 10 Be
transport and deposition, including realistic air-mass transport and dry-vs-wet deposition (Field
et al., 2006; Heikkilä et al., 2007), look more promising. An example of 10 Be deposition computedon the world grid using the NASA GISS model (Field et al., 2006) is shown in Figure 9. Precisionof the models allows one to distinguish local effects, e.g., for Greenland (Heikkilä et al., 2007). A
simulation performed by combining a detailed 10 Be-production model with an air-dynamics model
can result in an absolute model relating production and deposition of the radionuclide. We may
expect this breakthrough to occur in the near future. The validity and usefulness of this approachhas been recently demonstrated by (Usoskin et al., 2009a), who directly modeled production (using
the CRAC model – Usoskin and Kovaltsov, 2008) and transport (using the GISS ModelE – Kochet al., 2006) of a short beryllium living isotope 7 Be and showed that this such a combined model
is able to correctly reproduce absolute level and temporal variations of the 7 Be concentration
measured in near ground air around the globe. Keeping in mind the similarity between production

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A History of Solar Activity over Millennia

35

and transport of the two beryllium isotopes, 7 Be and 10 Be, this serves as support for the advanced
modelling of 10 Be transport.

Figure 9: Wet (panel a) and dry (panel b) deposition of 10 Be, computed using the NASA GISS model(Field et al., 2006) for a fixed sea-surface temperature.

3.3.4

Effect of the geomagnetic field

In order to properly account for geomagnetic changes (Section 3.1.2), one needs to know the effective region in which the radionuclide is produced before being stored in the archive analyzed. For
instance, if the concentration of 10 Be measured in polar ice reflects mainly the isotope’s productionin the polar atmosphere (as, e.g., assumed by Usoskin et al., 2003c), no strong geomagnetic signal
is expected to be observed, since the geographical poles are mostly related to high geomagnetic
latitudes. On the other hand, assuming global mixing of atmospheric 10 Be before deposition inpolar ice (e.g., Masarik and Beer, 1999), one expects that only changes in the geomagnetic dipole
moment affect will the signal. However, because of partial mixing, which can be different in the

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36Ilya G. Usoskinstratosphere and troposphere, taking into account migration and displacement of the geomagnetic
dipole axis may be essential for a reliable reconstruction of solar variability from 10 Be data (McCracken, 2004). Therefore, only a full combination of the transport and production models, thelatter explicitly including geomagnetic effects estimated from paleomagnetic reconstructions, canadequately account for geomagnetic changes and separate the solar signal. These will form the next
generation of physics-based models for the cosmogenic-isotope proxy method. We note that paleomagnetic data should ideally not only provide the dipole moment (VADM or VDM) but should
also provide estimates of the geomagnetic axis attitude and displacement of the dipole center.

3.4

Towards a quantitative physical model

Several methods have been developed historically to convert measured cosmogenic-isotope data intoa solar activity index, ranging from very simple regressions to physics-based models. A new stepin long-term solar-activity reconstruction has been made recently, which is the development of theproxy method in which physics-based models are used, instead of a phenomenological regression,
to link SN with cosmogenic-isotope production (Usoskin et al., 2003c, 2007; Solanki et al., 2004;
Vonmoos et al., 2006; Muscheler et al., 2007; Steinhilber et al., 2008). Due to recent theoreticaldevelopments, it is now possible to construct a chain of physical models to simulate the entire
relationship between solar activity and cosmogenic data.
The physics-based reconstruction of solar activity (in terms of sunspot numbers) from cosmogenic proxy data includes several steps:• Computation of the isotope’s production rate in the atmosphere from the measured concentration in the archive (Sections 3.2.2 and 3.3.2);• Computation, considering independently-known secular geomagnetic changes (see Section 3.2.5)
and a model of the CR-induced atmospheric cascade, of the GCR spectrum parameter quantified via the modulation potential 𝜑 (Section 3.4.2), some reconstructions being terminatedat this point;• Computation of a heliospheric index, whether of the open solar magnetic flux or of the average
HMF intensity at the Earth’s orbit (Section 3.4.2)• Computation of a solar index (sunspot number series), corresponding to the above-derived
heliospheric parameter (Section 3.4.3).
Presently, all these steps can be completed using appropriate models. Although the uncertainties of the models may be considerable, the models allow a full basic quantitative reconstruction ofsolar activity in the past. However, much needs to be done, both theoretically and experimentally,
to obtain an improved reconstruction.
3.4.1

Regression models

Mathematical regression is the most apparent and often used (even recently) method of solaractivity reconstruction from proxy data (see, e.g., Stuiver and Quay, 1980; Ogurtsov, 2004). The
reconstruction of solar activity is performed in two consecutive steps. First, a phenomenologicalregression (either linear or nonlinear) is built between proxy data set and a direct solar-activity
index for the available “training” period (e.g., since 1750 for WSN or since 1610 for GSN). Then thisregression is extended backwards to evaluate SN from the proxy data. The main shortcoming of
the regression method is that it depends on the time resolution and choice of the “training” period.
The former is illustrated by Figure 10, which shows the scatter plot of the 10 Be concentration vs.
GSN for the annual and 11-year smoothed data.

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A History of Solar Activity over Millennia

150

Annual data

37

a)

150

11-y
Regression, annual
Regression, 11y

11-y data

b)

100

GSN

100

50

50

0

0
0.5

1 10

4

Be (10 at/g)

1.5

0.5

1 10

Be (104 at/g)

1.5

Figure 10: Scatter plot of smoothed group sunspot numbers vs. (2-year delayed) 10 Be concentration. a)
Annual (connected small dots) and 11-year averaged (big open dots) values. b) Best-fit linear regressions
between the annual (dashed line) and 11-year averaged values (solid line). The dots are the same as inpanel (a). (After Usoskin and Kovaltsov, 2004).

One can see that the slope of the 10 Be-vs-GSN relation (about –500 g/atom) within individual
cycles is significantly different from the slope of the long-term relation (about –100 g/atom, i.e.,
individual cycles do not lie on the line of the 11-year averaged cycles. Therefore, a formal regression
built using the annual data for 1610 – 1985 yields a much stronger GSN-vs-10 Be dependence thanfor the cycle-averaged data (see Figure 10b), leading to a potentially-erroneous evaluation of thesunspot number from the 10 Be proxy data.
It is equally dangerous to evaluate other solar/heliospheric/terrestrial indices from sunspot
numbers, by extrapolating an empirical relation obtained for the last few decades back in time. Thisis because the last few decades (after the 1950s), which are well covered by direct observations ofsolar, terrestrial and heliospheric parameters, correspond to a very high level of solar activity. Aftera steep rise in activity level between the late 19th and mid 20th centuries, the activity remained ata roughly constant high level, being totally dominated by the 11-year cycle without an indication of
long-term trends. Accordingly, all empirical relations built based on data for this period are focusedon the 11-year variability and can overlook possible long-term trends (Mursula et al., 2003). This
may affect all regression-based reconstructions, whose results cannot be independently (directly or
indirectly) tested. In particular, this may be related to solar irradiance reconstructions, which areoften based on regression-like models, built and verified using data for the last three solar cycles,
when there was no strong trend in solar activity.
As an example let us consider an attempt (Belov et al., 2006) to reconstruct cosmic-ray intensity
since 1610 from sunspot numbers using a (nonlinear) regression. The regression between the
count rate of a neutron monitor and sunspot numbers, established for the last 30 years, yields anagreement at a 95% level for the period 1976 – 2003. Based on that, Belov et al. (2006) extrapolated
the regression back in time to produce a reconstruction of cosmic-ray intensity (quantified in NM
count rate) to 1560 (see Figure 11). One can see that there is no notable long-term trend in thereconstruction, and the fact that all CR maxima essentially lie at the same level, from the Maunderminimum to modern times, is noteworthy. It would be difficult to dispute such a result if there
was no direct test for CR levels in the past. Independent reconstructions based on cosmogenic
isotopes or theoretical considerations (e.g., Usoskin et al., 2002b; Scherer et al., 2004; Scherer andFichtner, 2004) provide clear evidence that cosmic-ray intensity was essentially higher during theMaunder minimum than nowadays. This example shows how easy it is to overlook an essential
feature in a reconstruction based on a regression extrapolated far beyond the period it is based

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38Ilya G. Usoskin

on. Fortunately, for this particular case we do have independent information that can prevent us
from making big errors. In many other cases, however, such information does not exist (e.g., fortotal or spectral solar irradiance), and those who make such unverifiable reconstructions should be
careful about the validity of their models beyond the range of the established relations.

Figure 11: An unsuccessful attempt at the reconstruction of cosmic-ray intensity in the past usinga regression with sunspot numbers (After Belov et al., 2006). Dots represent the observed cosmic-ray
intensity since 1951. Note the absence of a long-term trend.

3.4.2

Reconstruction of heliospheric parameters

The modulation potential 𝜑 (see Section 3.1.1) is most directly related to cosmogenic isotope
production in the atmosphere. It is a parameter describing the spectrum of galactic cosmic rays(see the definition and full description of this index in Usoskin et al., 2005a) and is sometimes used
as a stand-alone index of solar (or, actually, heliospheric) activity. We note that, provided theisotope production rate 𝑄 is estimated and geomagnetic changes can be properly accounted for, it
is straightforward to obtain a time series of the modulation potential, using, e.g., the relation shownin Figure 7. Several reconstructions of modulation potential for the last few centuries are shown in
Figure 12. While being quite consistent in the relative changes, they differ in the absolute level andfine details. Reconstructions of solar activity often end at this point, representing solar activity by
the modulation potential, as some authors (e.g., Beer et al., 2003; Vonmoos et al., 2006; Muscheler
et al., 2007) believe that further steps (see Section 3.4.3) may introduce additional uncertainties.
However, since 𝜑 is a heliospheric, rather than solar, index, the same uncertainties remain whenusing it as an index of solar activity. Moreover, the modulation potential is a model-dependent
quantity (see discussion in Section 3.1.1) and therefore does not provide an unambiguous measureof heliospheric activity. In addition, the modulation potential is not a physical index but rather
a formal fitting parameter to describe the GCR spectrum near Earth (Usoskin et al., 2005a) and,thus, does not seem to be a universal solar-activity index.
Modulation of GCR in the heliosphere (see Section 3.1.1) is mostly defined by the turbulent
heliospheric magnetic field (HMF), which ultimately originates from the sun and is thus related tosolar activity. It has been shown, using a theoretical model of the heliospheric transport of cosmic
rays (e.g., Usoskin et al., 2002b), that on the long-term scale (beyond the 11-year solar cycle) themodulation potential 𝜑 is closely related to the open solar magnetic flux F o , which is a physicalquantity describing the solar magnetic variability (e.g., Solanki et al., 2000; Krivova et al., 2007).
Sometimes, instead of the open magnetic flux, the mean HMF intensity at Earth orbit, B, isused as a heliospheric index (Caballero-Lopez and Moraal, 2004; McCracken, 2007). Note that B is

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A History of Solar Activity over Millennia

φ (MV)1000

NM
SN (U02)
14C(S04)
14C(M05)
14C(M07)

A)

500

0
1500
1000

φ (MV)

39

1600

1700

1800

1900

2000

B)

NM
SN(U02)
10Be-A(U03)10Be-A(MC04)

500

0
1500

1600

1700

1800

1900

2000

Years
Figure 12: Several reconstructions of the decade-averaged modulation potential 𝜑 for the last few centuries: from sunspot numbers (SN(U02) – Usoskin et al., 2002b), from 14 C data (14C(S04), 14C(M05),
14C(M07) – Solanki et al., 2004; Muscheler et al., 2005, 2007, respectively), from Antarctic 10 Be data
(10Be(U03), 10Be(MC04) – Usoskin et al., 2003c; McCracken et al., 2004, respectively). The thick black
NM curve is based on direct cosmic-ray measurements by neutron monitors since 1951 (Usoskin et al.,2005a) and ionization chambers since 1936 (McCracken and Beer, 2007).

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40Ilya G. Usoskinlinearly related to F o assuming constant solar-wind speed, which is valid on long-term scales. An
example of HMF reconstruction for the last 600 years is shown in Figure 13. In addition, the countrate of a “pseudo” neutron monitor (i.e., a count rate of a neutron monitor if it was operated in
the past) is considered as a solar/heliospheric index (e.g., Beer, 2000; McCracken and Beer, 2007).
10.0

HELIOMAGNETIC FIELD (nT)

9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
1400

1500

1600

1700
YEAR

1800

1900

2000

Figure 13: An example of reconstruction of the heliospheric magnetic field at Earth orbit for the last
600 years from 10 Be data (McCracken, 2007).

3.4.3

A link to sunspot numbers

The open solar magnetic flux F o described above is related to the solar surface magnetic phenomena such as sunspots or faculae. Modern physics-based models allow one to calculate the open
solar magnetic flux from data of solar observation, in particular sunspots (Solanki et al., 2000,
2002; Krivova et al., 2007). Besides the solar active regions, the model includes ephemeral regions.
Although this model is based on physical principals, it contains one adjustable parameter, thedecay time of the open flux, which cannot be measured or theoretically calculated and has to befound by means of fitting the model to data. This free parameter has been determined by requiring
the model output to reproduce the best available data sets for the last 30 years with the help of agenetic algorithm. Inversion of the model, i.e., the computation of sunspot numbers for given F ovalues is formally a straightforward solution of a system of linear differential equations, however,the presence of noise in the real data makes it only possible in a numerical-statistical way (see, e.g.,
Usoskin et al., 2004, 2007). By inverting this model one can compute the sunspot-number seriescorresponding to the reconstructed open flux, thus forging the final link in a chain quantitatively
connecting solar activity to the measured cosmogenic isotope abundance. A sunspot-number series
reconstructed for the Holocene using 14 C isotope data is shown in Figure 14. While the definition of
the grand minima (Section 4.3) is virtually insensitive to the uncertainties of paleomagnetic data,
the definition of grand maxima depends on the paleomagnetic model used (Usoskin et al., 2007).
Since the Y00 paleomagnetic model forms an upper bound for the true geomagnetic strength (Section 3.1.2), the corresponding solar-activity reconstructions may underestimate the solar-activity

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A History of Solar Activity over Millennia

41level. Accordingly, the grand maxima defined using the Y00 model are robust and can be regarded
as “maximum maximorum” (see Section 4.4).

Sunspot number

100
K05
Y00

50

0
-8000

-6000

-4000

-2000

0

2000

Years (-BC/AD)
Figure 14: Long-term sunspot-number reconstruction from 14 C data (after Usoskin et al., 2007). All data
are decade averages. Solid (denoted as ‘Y00’) and grey (‘K05’) curves are based on the paleo-geomagnetic
reconstructions of Yang et al. (2000) and Korte and Constable (2005), respectively. Observed group sunspot
numbers (Hoyt and Schatten, 1998) are shown after 1610.

3.5

Solar activity reconstructions

Detailed computational models of cosmogenic isotope production in the atmosphere (e.g., Masarik
and Beer, 1999) have opened up a new possibility for long-term solar-activity reconstruction (e.g.,Beer, 2000). The first quantitative reconstructions of solar activity from cosmogenic proxy appeared in the early 2000s based on 10 Be deposited in polar ice (Beer et al., 2003; Usoskin et al.,2003c).
Beer et al. (2003) reconstructed the modulation potential on a multi-millennial timescale using
the model computations by Masarik and Beer (1999) and the 10 Be data from the GISP2 corein Greenland. This result has been extended, even including the 14 C data set, and presently
covers the whole Holocene (Vonmoos et al., 2006; Steinhilber et al., 2008). Usoskin et al. (2003c)
presented the reconstruction of sunspot activity over the last millennium, based on 10 Be datafrom both Greenland and Antarctica, using a physics-based model described in detail in Usoskin
et al. (2004). This result reproduces the four known grand minima of solar activity – Maunder,Spörer, Wolf and Oort minima (see Section 4.3). Later Solanki et al. (2004) reconstructed 10year–averaged sunspot numbers from the 14 C content in tree rings throughout the Holocene andestimated its uncertainties (see Figure 15). This result was disputed by Muscheler et al. (2005),
whose concurrent model, however, rested on an erroneous normalization, as argued in Solanki et al.
(2005). The reconstruction of Solanki et al. (2004) has been recently updated by Usoskin et al.
(2006a), using a newer paleomagnetic reconstruction by Korte and Constable (2005), and was laterslightly revised (Usoskin et al., 2007), considering an updated model of the solar open magnetic
flux by Krivova et al. (2007). Reconstruction of the HMF from 10 Be data has been performed
by Caballero-Lopez and Moraal (2004), using a model of CR modulation in the heliosphere and a

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42Ilya G. Usoskin10

Be production model by Webber and Higbie (2003). Recently it was revised (McCracken, 2007)
to present a detailed reconstruction of HMF intensity since 1428.
The obtained results are discussed in Section 4.

GSN
10Be
14C

Sunspot number

80
60
40
20
0
-20
800

1000

1200

1400

1600

1800

2000

Years
Figure 15: 10-year averaged sunspot numbers: Actual group sunspot numbers (thick grey line) and thereconstructions based on 10 Be (thin curve, Usoskin et al., 2003c) and on 14 C (thick curve with error bars,
Solanki et al., 2004). The horizontal dotted line depicts the high activity threshold.

3.6

Verification of reconstructions

Because of the diversity of the methods and results of solar-activity reconstruction, it is vitally
important to verify them. Even though a full verification is not possible, there are different meansof indirect or partial verification, as discussed below. Several solar-activity reconstructions on themillennium timescale, which differ from each other to some degree and are based on terrestrial
cosmogenic isotope data, have been published recently by various groups. Also, they may sufferfrom systematic effects. Therefore, there is a need for an independent method to verify/calibratethese results in order to provide a reliable quantitative estimate of the level of solar activity in thepast, prior to the era of direct observations.
3.6.1

Comparison with direct data

The most direct verification of solar-activity reconstruction is a comparison with the actual GSN
data for the last few centuries. However, regression-based models (see Section 3.4.1) cannot be
tested in this way, since it would require a long set of independent direct data outside the “training”
interval. It is usual to include all available data into the “training” period to increase the statisticsof the regression, which rules out the possibility of testing the model. On the other hand, sucha comparison to the actual GSN since 1610 can be regarded as a direct test for a physics-basedmodel since it does not include phenomenological links over the same time interval. The period of
the last four centuries is pretty good for testing purposes since it includes the whole range of solar
activity levels from the nearly spotless Maunder minimum to the modern period of a very activesun. As an example, a comparison between the measured GSN and the 14 C-based (Solanki et al.,2004) and 10 Be-based (Usoskin et al., 2003c) reconstructions is shown in Figure 15. The agreement

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A History of Solar Activity over Millennia

43

between the actual and reconstructed sunspot numbers is quite good, the correlation coefficientfor the 14 C-based series is r = 0.93 with the RMS deviation between the two series being six forthe period of 1610 – 1900 (Solanki et al., 2004). We want to stress that this reconstruction is fully
physics based and does not include any fitting to the whole GSN data series; thus this comparison
verifies the approach in both absolute level and relative variations. The agreement between GSN
and 10 Be-based reconstructions (Usoskin et al., 2003c) is also good (r = 0.78, RMS = 10 for
1700 – 1985). In this case, however, the comparison can only test the relative variation becauseof the unknown proportionality coefficient between the measured concentration of 10 Be and the
production rate (Section 3.3.3), which is fitted to match the overall level of the reconstructed solar
activity. One can see that the reconstructed sunspot series generally follows the real GSN series,
depicting the same main features, namely, the Maunder minimum, the tiny Dalton minimum, aslight decrease of activity around 1900 (known as the modern minimum) as well as a steep risein the first half of the 20th century. Note, however, that individual 11-year cycles are poorly
resolved in these reconstructions. This validates the reliability of the physics-based reconstructionof sunspot numbers.
Models focused on the reconstruction of heliospheric parameters (HMF or the modulation
potential 𝜑) cannot be verified in this manner since no heliospheric data exists before the 1950s.
Comparison to direct cosmic-ray data after the 1950s (or, with caveats, after the 1930s – McCracken
and Beer, 2007) is less conclusive, since the latter are of shorter length and correspond to a periodof high solar activity, leading to larger uncertainties during grand minima.
3.6.2

Meteorites and lunar rocks: A direct probe of the galactic cosmic-ray flux

Another more-or-less direct test of solar/heliospheric activity in the past comes from cosmogenic
isotopes measured in lunar rock or meteorites. Cosmogenic isotopes, produced in meteoritic or
lunar rocks during their exposure to CR in interplanetary space, provide a direct measure of cosmicray flux. Uncertainties due to imprecisely known terrestrial processes, including the geomagnetic
shielding and redistribution process, are naturally avoided in this case, since the nuclides are
directly produced by cosmic rays in the body, where they remain until they are measured, without
any transport or redistribution. The activity of a cosmogenic isotope in meteorite/lunar rock
represents an integral of the balance between the isotope’s production and decay, thus representing
the time-integrated CR flux over a period determined by the mean life of the radioisotope. The
results of different analyses of measurements of cosmogenic isotopes in meteoritic and lunar rocks
show that the average GCR flux remained roughly constant – within 10% over the last million years
and within a factor of 1.5 for longer periods of up to 109 years (e.g., Vogt et al., 1990; Grieder,
2001).
By means of measuring the abundance of relatively short-lived cosmogenic isotopes in meteorites, which fell through the ages, one can evaluate the variability of the CR flux, since theproduction of cosmogenic isotopes ceases after the fall of the meteorite. A nearly ideal isotope
for studying centurial-scale variability is 44 Ti with a half-life of 59.2 ± 0.6 yr (a lifetime of about
85 years). The isotope is produced in nuclear interactions of energetic CR with nuclei of iron andnickel in the body of a meteorite (Bonino et al., 1995; Taricco et al., 2006). Because of its mean
life, 44 Ti is relatively insensitive to variations in cosmic-ray flux on decade (11-year Schwabe cycle)
or shorter timescales, but is very sensitive to the level of CR flux and its variations on a centurial
scale. Using a full model of 44 Ti production in a stony meteorite (Michel and Neumann, 1998) anddata on the measured activity of cosmogenic isotope 44 Ti in meteorites, which fell during the past
235 years (Taricco et al., 2006), Usoskin et al. (2006c) tested, in a straightforward manner, several
recent reconstructions of heliospheric activity after the Maunder minimum. First, the expected44
Ti activity has been calculated from the reconstructed series of the modulation potential, andthen compared with the results of actual measurements (see Figure 16). It has been shown that

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44Ilya G. Usoskin

44

Ti data can distinguish between various reconstructions of past solar activity, allowing unrealistic models to be ruled out. Presently, the Torino group (Taricco et al., 2008) is working hard on
improving the quality of 44 Ti measurements in meteorites, reducing the error bars in Figure 16,
which will allow for more precise estimates in the near future.
Because of the long life time of the 44 Ti nuclide (about 85 years), this method does not allow
for the reconstruction of solar/heliospheric activity, but it serves as a direct way to test existing
reconstructions independently. Most of the reconstructions appear consistent with the measured
44
Ti activity in meteorites, including the last decades, thus validating their veracity. The only
apparently-inconsistent model is the one by Muscheler et al. (2005), which is based on erroneous
normalization (as discussed in Solanki et al., 2005). In particular, the 44 Ti data confirms significant
secular variations of the solar magnetic flux during the last century (cf. Lockwood et al., 1999;
Solanki et al., 2000; Wang et al., 2005).

10

SN(U02)14C(S04)
14C(M05-M)
14C(M07)

A)

9
8

44

Ti activity (dpm/kg Fe+Ni)

7
6
5
4
1600

10

1700

1800

1900

2000

1800

1900

2000

B)

9
8
7
6
5
4
1600

SN(U02)
10Be-A(U03)10Be-A(MC04)
1700

Years
Figure 16: Immediate 44 Ti activity in stony meteorites as a function of time of fall. Dots with error bars
correspond to measured values (Taricco et al., 2006). Curves correspond to the theoretically expected 44 Ti
activity, computed using the method of Usoskin et al. (2006c) and different reconstructions of 𝜑 shown in
Figure 12.

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3.6.3

45

Comparison between isotopes

As an indirect test of the solar-activity reconstruction, one can compare different isotopes. The
idea behind this test is that two isotopes, 14 C and 10 Be, have essentially different terrestrial fates,
so that only the production signal, namely, solar modulation of cosmic rays, can be regarded ascommon in the two series. Processes of transport/deposition are completely different (moreover,the 14 C series is obtained as an average of the world-wide–distributed samples). The effect ofchanging geomagnetic fields is also different (although not completely) for the two isotopes, sinceradiocarbon is globally mixed, while 10 Be is only partly mixed before being stored in an archive.
Even comparison between data of the same 10 Be isotope, but measured in far-spaced ice cores(e.g., Greenland and Antarctica), may help in separating climatic and extraterrestrial factors,
since meteorology in the two opposite polar areas is quite different.
The first thorough consistent comparison between 10 Be and 14 C records for the last millennium was performed by Bard et al. (1997). They assumed that the measured 10 Be concentrationin Antarctica is directly related to CR variations. Accordingly, 14 C production was considered
as proportional to 10 Be data. Then, applying a 12-box carbon-cycle model, Bard et al. (1997)
computed the expected Δ14 C synthetic record. Finally, these 10 Be-based Δ14 C variations werecompared with the actual measurements of Δ14 C in tree rings, which depicted a close agreementin the profile of temporal variation (coefficient of linear correlation r = 0.81 with exact phasing).
Despite some fine discrepancies, which can indicate periods of climatic influence, that result has
clearly proven the dominance of solar modulation of cosmogenic nuclide production variations during the last millennium. This conclusion has been confirmed (e.g., Usoskin et al., 2003c; Muscheler
et al., 2007) in the sense that quantitative solar-activity reconstructions, based on 10 Be and 14 C
data series for the last millennium, yield very similar results, which differ only in small details.
However, a longer comparison over the entire Holocene timescale suggests that, while centennial
variations of solar activity reconstructed from the two isotopes are very close to each other, there
might be a discrepancy in the very long-term trend (Vonmoos et al., 2006; Muscheler et al., 2007),
whose nature is not clear (climate changes, geomagnetic effects or model uncertainties).
Recently, Usoskin et al. (2009b) studied frequency ranges in which the solar signal dominatesin different cosmogenic isotope data. They compared the expected 10 Be variations computed from14
C-based reconstruction of cosmic ray intensity with the actually measured 10 Be abundance at thesites and found that: (1) There is good agreement between the 14 C and 10 Be data sets, on different
timescales and at different locations, confirming the existence of a common solar signal in bothisotope data; (2) The 10 Be data are driven by the solar signal on timescales from about centennial
to millennial time scales; (3) The synchronization is lost on short (< 100 years) timescales, either
due to local climate or chronological uncertainties (Delaygue and Bard, 2010) but the solar signal
becomes important even at short scales during periods of Grand minima of solar activity, (4) Thereis an indication of a possible systematic uncertainty in the early Holocene (cf., Vonmoos et al.,2006), likely due to a not-perfectly-stable thermohaline circulation. Overall, both 14 C- and 10 Bebased records are consistent with each other over a wide range of timescales and time intervals.
Thus, comparison of the results obtained from different sources implies that the variationsof cosmogenic nuclides on the long-term scale (centuries to millennia) during the Holocene are
primarily defined by the solar modulation of CR.

3.7

Summary

In this section, a proxy method of past–solar-activity reconstruction is described in detail.
This method is based on the use of indirect proxies of solar activity, i.e., quantitative parameters,
which can be measured now, but represent signatures, stored in natural archives, of the different
effects of solar magnetic activity in the past. Such traceable signatures can be related to nuclear
or chemical effects caused by cosmic rays in the Earth’s atmosphere, lunar rocks or meteorites.

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Ilya G. Usoskin

This approach allows one to obtain homogeneous data sets with stable quality and to improve thequality of data when new measurement techniques become available. It provides the only possible
regular indicator of solar activity on a very long-term scale.
The most common proxy of solar activity is formed by data of the cosmogenic radionuclides,
10
Be and 14 C, produced by cosmic rays in the Earth’s atmosphere. After a complicated transport
in the atmosphere, these cosmogenic isotopes are stored in natural archives such as polar ice, trees,marine sediments, from where they can now be measured. This process is also affected by changes
in the geomagnetic field and the climate.
Radioisotope 14 C, measured in independently-dated tree rings, forms a very useful proxy forlong-term solar-activity variability. It participates in the complicated carbon cycle, which smoothes
out spatial and short-term variability of isotope production. For the Holocene period, with its stableclimate, it provides a useful tool for studying solar activity in the past. Existing models allow thequantitative conversion between the measured relative abundance of 14 C and the production ratein the atmosphere. The use of radiocarbon for earlier periods, the glacial and deglaciation epochs,
is limited by severe climate and ocean ventilation changes. Radiocarbon data cannot be used after
the end of the 19th century because of the Suess effect and atmospheric nuclear tests.
Another solar activity proxy is the cosmogenic 10 Be isotope measured in stratified polar ice
cores. Atmospheric transport of 10 Be is relatively straightforward, but its details are as of yet
unresolved, leading to the lack of a reliable quantitative model relating the measured isotope
concentration in ice to the atmospheric production. Presently, it is common to assume that the
production rate is proportional, with an unknown coefficient, to the measured concentration. However, a newly-developed generation of models, which include 3D atmospheric-circulation models,
will hopefully solve this problem soon.
Modern physics-based models make it possible to build a chain, which quantitatively connects
isotope production rate and sunspot activity, including subsequently the GCR flux quantified via
the modulation potential, the heliospheric index, quantified via the open solar magnetic flux orthe average HMF intensity at the Earth’s orbit, and finally the sunspot-number series. Presently,
all these steps can be made using appropriate models allowing for a full basic quantitative reconstruction of solar activity in the past. The main uncertainties in the solar-activity reconstruction
arise from paleo-magnetic models and the overall normalization.
An independent verification of the reconstructions, including direct comparison with sunspot
numbers, cosmogenic isotopes in meteorites and the comparison of different models with eachother, confirms their veracity in both relative variations and absolute level. It also implies thatthe variations in cosmogenic nuclides on the long-term scale (centuries to millennia) during the
Holocene are primarily defined by the solar modulation of CR.

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447

Variability of Solar Activity Over Millennia

Several reconstructions of solar activity on multi-millennial timescales have been performed recently
using physics-based models (see Section 3) from measurements of 14 C in tree rings and 10 Be inpolar ice. The validity of these models for the last few centuries was discussed in Section 3.6.
In this section we discuss the temporal variability of thus-reconstructed solar activity on a longer
scale.

4.1

The overall activity level

Here we consider the 14 C-based decade reconstruction of sunspot numbers (shown in Figure 17).
It is identical to that shown in Figure 14, but includes also a Gleissberg 1-2-2-2-1 filter in orderto suppress noise and short-term fluctuations. This series forms the basis for the forthcoming
analysis, while differences related to the use of other reconstructions are discussed.
First, we analyze the distribution of the occurrence frequency of sunspot-number values. The
histogram for sunspot-number distribution (for the series shown in Figure 17) is shown in Figure 18.
The over-decades filtered sunspot numbers range between 0 and 95. The bulk of the distribution
can be roughly approximated by a normal Gaussian distribution with a mean of 31 and standard
deviation of 𝜎 = 30. However, there are apparent excesses both at very low (SN < 10) and high(SN > 70) sunspot numbers. These excesses are very unlikely to be a result of random fluctuations
or noise in the data and, as argued in Section 4.3, correspond to special states of the solar dynamo,
namely, the grand minima and grand maxima. It is important that the entire distribution is moreor-less consistent with the directly-observed sunspot series after 1610, suggesting that the lattercan serve as a representative sample for sunspot-activity statistics, including a grand minimum(the Maunder minimum) and the modern maximum.

4.2

Quasi-periodicities and characteristic times

In order to discuss spectral features of long-term solar-activity dynamics, we show in Figure 19
a wavelet spectral decomposition of the sunspot number reconstruction throughout the Holocene
shown in Figure 17. The left-hand panels show the conventional wavelet decomposition in the timefrequency domain, while the right-hand panels depict the global spectrum, namely, an integral over
the time domain, which is comparable to a Fourier spectrum. The peak in the global spectrum atabout an 80-year period corresponds to the Gleissberg periodicity, known from a simple Fourier
analysis of the Δ14 C series (Peristykh and Damon, 2003). The peak at an approximately 150 year
period does not correspond to a persistent periodicity, but is formed by a few time intervals(mostly 6000 – 4000 BC) and can be related to another “branch” of the secular cycle, according to
Ogurtsov et al. (2002). The de Vries/Suess cycle, with a period of about 210 years, is prominent in
the global spectrum, but it is intermittent and tends to become strong with around 2400 clustering
time (Usoskin and Kovaltsov, 2004). Another variation with a period of around 350 years can beobserved after 6000 BC. Variations with a characteristic time of 600 – 700 years are intermittent
and can be hardly regarded as a typical feature of solar activity. Of special interest is the 2000 –2400 year Hallstatt cycle (see, e.g., Vitinsky et al., 1986; Damon and Sonett, 1991; Vasiliev andDergachev, 2002), which is relatively stable and mostly manifests itself as a modulation of long-term
solar activity, leading to the clustering of grand minima (Usoskin et al., 2007).
On the other hand, an analysis of the occurrence of grand minima (see Section 4.3) shows
no clear periodicity except for a marginal 2400 year clustering, implying that the occurrenceof grand minima and maxima is not a result of long-term cyclic variability but is defined bystochastic/chaotic processes.

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Ilya G. Usoskin

Sunspot number

80

60

40

20

0
-10000

-9000

-8000

-3000

-2000

-7000

-6000

-5000

-4000

-1000

0

1000

2000

Sunspot number

80

60

40

20

0
-4000

Years (-BC/AD)

Figure 17: Sunspot activity (over decades, smoothed with a 12221 filter) throughout the Holocene,reconstructed from 14 C by Usoskin et al. (2007) using geomagnetic data by Yang et al. (2000). Blue andred areas denote grand minima and maxima, respectively.

Min

Max

Number per bin

100

10

1

0

20

40

60

80

<Sunspot number>
Figure 18: Histogram of sunspot-number distribution for the series shown in Figure 17. Hatched areas
correspond to directly-observed sunspots after 1610. The curve represents the best fit normal distribution.

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A History of Solar Activity over Millennia

49

5000
4000
Period (years)

3000
2000

1000

500

Period (years)-10000

-8000

-6000
-4000
Time (year)

-2000

1000
Power

500

500

400

400

300

300

200

200

100

100
-10000

-8000

-6000
-4000
Time (year)

-2000

100

1000
Power

Figure 19: Wavelet (Morlet basis) spectrum of the sunspot-number reconstruction shown in Figure 17.
Left and right-hand panels depict 2D and global wavelet spectra, respectively. Upper and lower panels
correspond to period ranges of 500 – 5000 years and 80 – 500 years, respectively. Dark/light shading denotes
high/low power.

4.3

Grand minima of solar activity

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, which is discussed below insome detail (for a detailed review see the book by Soon and Yaskell, 2003). Grand minima are
believed to correspond to a special state of the dynamo (Sokoloff, 2004; Miyahara et al., 2006b),
and its very existence poses a challenge for the solar-dynamo theory. It is noteworthy that dynamo
models do not agree on how often such episodes occur in the sun’s history and whether theirappearance is regular or random. For example, the commonly used mean-field dynamo yields
a fairly-regular 11-year cycle (Charbonneau, 2005), while dynamo models including a stochastic
driver predict the intermittency of solar magnetic activity (Choudhuri, 1992; Schüssler et al., 1994;
Schmitt et al., 1996; Ossendrijver, 2000; Weiss and Tobias, 2000; Mininni et al., 2001; Charbonneau,2001). Most of the models predict purely random occurrence of the grand minima, without any
intrinsic long-term memory (Moss et al., 2008). Although cosmogenic isotope data suggest theexistence of such memory (Usoskin et al., 2007), statistics is not enough to distinguish between
the two cases (Usoskin et al., 2009d).

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4.3.1

Ilya G. Usoskin

The Maunder minimum

The Maunder minimum is a representative of grand minima in solar activity (e.g., Eddy, 1976),
when sunspots have almost completely vanished from the solar surface, while the solar wind kept
blowing, although at a reduced pace (Cliver et al., 1998; Usoskin et al., 2001a). There is someuncertainty in the definition of its duration; the “formal” duration is 1645 – 1715 (Eddy, 1976),
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 ortransition phase (Usoskin et al., 2000). The Maunder minimum was amazingly well covered (morethan 95% of days) by direct sunspot observations (Hoyt and Schatten, 1996), especially in its latephase (Ribes and Nesme-Ribes, 1993). On the other hand, sunspots appeared rarely (during ∼ 2%of the days) and seemingly sporadically, without an indication of the 11-year cycle (Usoskin andMursula, 2003). This makes it almost impossible to apply standard methods of time-series analysis
to sunspot data during the Maunder minimum (e.g., Frick et al., 1997)). Therefore, special methods
such as the distribution of spotless days vs. days with sunspots (e.g., Harvey and White, 1999) oran analysis of sparsely-occurring events (Usoskin et al., 2000) should be applied in this case. Using
these methods, Usoskin et al. (2001a) have shown that sunspot occurrence during the Maunderminimum was gathered into two large clusters (1652 – 1662 and 1672 – 1689), with the mass centersof these clusters being in 1658 and 1679 – 1680. Together with the sunspot maxima before (1640)
and after (1705) the deep Maunder minimum, this implies a dominant 22-year periodicity insunspot activity throughout the Maunder minimum (Mursula et al., 2001), with a subdominant
11-year cycle emerging towards the end of the Maunder minimum (Ribes and Nesme-Ribes, 1993;
Mendoza, 1997; Usoskin et al., 2000) and becoming dominant again after 1700. Similar behavior ofa dominant 22-year cycle and a weak subdominant Schwabe cycle during the Maunder minimum
has been found in other indirect solar proxy data: auroral occurrence (Křivský and Pejml, 1988;
Schlamminger, 1990; Silverman, 1992) and 14 C data (Stuiver and Braziunas, 1993; Kocharov et al.,
1995; Peristykh and Damon, 1998; Miyahara et al., 2006b). This is in general agreement with theconcept of “immersion” of 11-year cycles during the Maunder minimum (Vitinsky et al., 1986, andreferences therein). This concept means that full cycles cannot be resolved and sunspot activity
only appears as pulses around cycle-maximum times.
The time behavior of sunspot activity during the Maunder minimum yields the following generalscenario (Vitinsky et al., 1986; Ribes and Nesme-Ribes, 1993; Sokoloff and Nesme-Ribes, 1994;
Usoskin et al., 2000, 2001a; Miyahara et al., 2006b). Transition from the normal high activity
to the deep minimum was sudden (within a few years) without any apparent precursor. A 22year cycle was dominant in sunspot occurrence during the deep minimum (1645 – 1700), with thesubdominant 11-year cycle, which became visible only in the late phase of the Maunder minimum.
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 ofnearly-linear amplification of the 11-year cycle. It is interesting to note that such a qualitative
evolution of a grand minimum is consistent with predictions of the stochastically-forced returnmap (Charbonneau, 2001).
Although the Maunder minimum is the only one with available direct sunspot observations, itspredecessor, the Spörer minimum from 1450 – 1550, is covered by precise bi-annual measurementsof 14 C (Miyahara et al., 2006a). An analysis of this data (Miyahara et al., 2006a,b) reveals asimilar pattern with the dominant 22-year cycle and suppressed 11-year cycle, thus supporting theidea that the above general scenario may be typical for a grand minimum.
A very important feature of sunspot activity during the Maunder minimum was its strong
north-south asymmetry, as sunspots were only observed in the southern solar hemisphere during
the end of the Maunder minimum (Ribes and Nesme-Ribes, 1993; Sokoloff and Nesme-Ribes, 1994).
This observational fact has led to intensive theoretical efforts to explain a significant asymmetry

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A History of Solar Activity over Millennia

51of the sun’s surface magnetic field in the framework of the dynamo concept (see the review by
Sokoloff, 2004, and references therein). Note that a recent discovery (Arlt, 2008, 2009) of theStaudacher’s original drawings of sunspots in late 18th century shows that similarly asymmetricsunspot occurrence existed also in the beginning of the Dalton minimum in 1790s (Usoskin et al.,2009c). However, the northern hemisphere dominated at that period contrary to the situation
during the Maunder minimum.
4.3.2

Grand minima on a multi-millennial timescale

The presence of grand minima in solar activity on the long-term scale has been mentioned numerously (e.g., Eddy, 1977a; Usoskin et al., 2003c; Solanki et al., 2004), using the radioisotope 14 C
data in tree rings. For example, Eddy (1977b) identified major excursions in the detrended 14 C
record as grand minima and maxima of solar activity and presented a list of six grand minima andfive grand maxima for the last 5000 years (see Table 1). Stuiver and Braziunas (1989) and Stuiver
et al. (1991) also studied grand minima as systematic excesses of the high-pass filtered 14 C dataand suggested 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. Using
the same method of identifying grand minima as significant peaks in high-pass filtered Δ14 C series,
Voss et al. (1996) provided a list of 29 such events for the past 8000 years. A similar analysis ofbumps in the 14 C production rate was presented recently by Goslar (2003). However, such studies
retained a qualitative element, since they are based on high-pass–filtered 14 C data and thus implicitly assume that 14 C variability can be divided into short-term solar variations and long-termchanges attributed solely to the slowly-changing geomagnetic field. This method ignores any possible long-term changes in solar activity on timescales longer than 500 years (Voss et al., 1996).
The modern approach, based on physics-based modelling (Section 3), allows for the quantitative
reconstruction of the solar activity level in the past, and thus, for a more realistic definition of theperiods of grand minima or maxima.
A list of 27 grand minima, identified in the quantitative solar-activity reconstruction of thelast 11,000 years, shown in Figure 17, is presented in Table 1 (after Usoskin et al., 2007). The
cumulative duration of the grand minima is about 1900 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.
Note that the definition of grand minima is quite robust.
The question of whether the occurrence of grand minima in solar activity is a regular or chaotic
process is important for understanding the solar-dynamo machine. Even a simple deterministic
numerical dynamo model can produce events comparable with grand minima (Brandenburg et al.,1989). Such models can also simulate a sequence of grand minima occurrences, which are irregularand seemingly chaotic (e.g., Jennings and Weiss, 1991; Tobias et al., 1995; Covas et al., 1998).
The presence of long-term dynamics in the dynamo process is often explained in terms of the
𝛼-effect, which, being a result of the electromotive force averaged over turbulent vortices, cancontain a fluctuating part (e.g., Hoyng, 1993; Ossendrijver et al., 1996) leading to irregularly
occurring grand minima (e.g., Brandenburg and Spiegel, 2008). All these models predict thatthe occurrence of grand minima is a purely random “memoryless” Poisson-like process, with theprobability of a grand minimum occurring being constant at any given time. This unambiguously
leads to the exponential shape of the waiting-time distribution (waiting time is the time interval
between subsequent events) for grand minima.
Usoskin et al. (2007) performed a statistical analysis of grand minima occurrence time (Table 1)
and concluded that their occurrence is not a result of long-term cyclic variations, but is definedby stochastic/chaotic processes. Moreover, waiting-time distribution deviates significantly fromthe exponential law. This implies that the event occurrence is still random, but the probability
is nonuniform in time and depends on the previous history. In the time series it is observed as a

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52Ilya G. Usoskin

Table 1: Approximate dates (in –BC/AD) of grand minima in reconstructed solar activity.

No.

centerdurationcomment

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27

1680
1470
1305
1040
685
–360
–765
–1390
–2860
–3335
–3500
–3625
–3940
–4225
–4325
–5260
–5460
–5620
–5710
–5985
–6215
–6400
–7035
–7305
–7515
–8215
–9165

80
160
70
60
70
60
90
40
60
70
40
50
60
30
50
140
60
40
20
30
30
80
50
30
150
110
150

MaunderSpörer
Wolf
a, d)
b, d)
a, b, c, d)a, b, c, d)b, d)a, c, d)a, b, c, d)a, b, c, d)a, b, d)a, c, d)c, d)a, c, d)a, b, d)
c, d)
d)
c, d)
a, c, d)c, d, e)a, c, d, e)a, c, d)c, d)a, c, d)d)d)a) According to Stuiver and Quay (1980); Stuiver and Braziunas (1989).
b) According to Eddy (1977a,b).
c) According to Goslar (2003).
d) According to Usoskin et al. (2007).
e) Exact duration is uncertain.

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A History of Solar Activity over Millennia

53

tendency of the events to cluster together with a relatively-short waiting time, while the clusters
are separated by long event-free intervals (cf. Section 4.2). Such behavior can be interpreted indifferent ways, e.g., self-organized criticality or processes related to accumulation and release ofenergy. This poses a strong observational constraint on theoretical models aiming to explain thelong-term evolution of solar activity (Section 4.5.1). However, as discussed by Moss et al. (2008)
and (Usoskin et al., 2009d), the observed feature can be an artefact of the small statistics (only 27
grand minima are identified during the Holocene), making this result only indicative and waiting
for a more detailed investigation.
A histogram of the duration of grand minima from Table 1 is shown in Figure 20. The mean
duration is 70 year but the distribution is bimodal. The minima tend to be either of a short(30 – 90 years) duration similar to the Maunder minimum, or rather long (> 100 years), similar to
the Spörer minimum, in agreement with earlier conclusions (Stuiver and Braziunas, 1989). Thissuggests that grand minima correspond to a special state of the dynamo. Once falling into a grandminimum as a result of a stochastic/chaotic, but non-Poisson process, the dynamo is “trapped” inthis state and its behavior is driven by deterministic intrinsic features.

Number per bin

6

4

2

0
50

100

150

Duration (Years)

Figure 20: Histogram of the duration of grand minima from Table 1.

4.4

Grand maxima of solar activity

4.4.1

The modern episode of active sun

We have been presently living in a period of very high sun activity with a level of activity that isunprecedentedly 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 groupsunspot number, and has remained at that high level until recently (see Figure 1). Note thatgrowth comes entirely 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 forthe 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 since 1950. Therefore the modern active sun episode, whichstarted in the 1940s, can be regarded as the modern grand maximum of solar activity, as opposed
to a grand minimum (Wilson, 1988b).
Is such high solar activity typical or is it something extraordinary? While it is broadly agreed
that the present active sun episode is a special phenomenon, the question of how (a)typical such
upward bumps are from “normal” activity is a topic of hot debate.

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4.4.2

Ilya G. Usoskin

Grand maxima on a multi-millennial timescale

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 grandmaximum (Wilson, 1988b; de Meyer, 1998), but its magnitude is lower than the modern maximum(Usoskin et al., 2003c). Accordingly, it was not included in a list of grand maxima by Eddy
(1977a,b).
Table 2: Approximate dates (in –BC/AD) of grand maxima in the SN-L series. (after Usoskin et al.,2007).

No.

centerduration

†

1960
–445
–1790
–2070
–2240
–2520
–3145
–6125
–6530
–6740
–6865
–7215
–7660
–7780
–7850
–8030
–8350
–8915
–9375

80
40
20
40
20
20
30
20
20
100
50
30
80
20
20
50
70
190
130

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
†

Center and duration of the modern maximum are preliminary since it is still ongoing.

A quantitative analysis is only possible using proxy data, especially cosmogenic isotope records.
Using a physics-based analysis of solar-activity series reconstructed from 10 Be data from polar(Greenland and Antarctica) archives, Usoskin et al. (2003c, 2004) stated that the modern maximum
is unique in the last millennium. Then, using a similar analysis of the 14 C calibrated series, Solanki
et al. (2004) found that the modern activity burst is not unique, but a very rare event, with theprevious burst occurring about 8 millennia ago. An update (Usoskin et al., 2006a) of this result,using a more precise paleo-magnetic reconstruction by Korte and Constable (2005) since 5000 BC,
suggests that an increase of solar activity comparable with the modern episode might have takenplace around 2000 BC, i.e., around 4 millennia ago. The result by Solanki et al. (2004) has beendisputed by Muscheler et al. (2005) who claimed that equally high (or even higher) solar-activity
bursts occurred several times during the last millennium, circa 1200 AD, 1600 AD and at the endof the 19th century. We note that the latter claimed peak (ca. 1860) is not confirmed by direct
solar or geomagnetic data. However, as argued by Solanki et al. (2005), the level of solar activity
reconstructed by Muscheler et al. (2005) was overestimated because of an erroneous normalization
to the data of ground-based ionization chambers (see also McCracken and Beer, 2007). This

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A History of Solar Activity over Millennia

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indicates that the definition of grand maxima is less robust than grand minima and is sensitive toother parameters such as geomagnetic field data or overall normalization.
Keeping possible uncertainties in mind, let us consider a list of the largest grand maxima(the 50 year smoothed sunspot number stably exceeding 50), identified for the last 11,400 years
using 14 C data, as shown in Table 2 (after Usoskin et al., 2007). A total of 19 grand maxima
have been identified with a total duration of around 1030 years, suggesting that the sun spends
around 10% of its time in an active state. A statistical analysis of grand-maxima–occurrence timesuggests that they do not follow long-term cyclic variations, but like grand minima, are definedby stochastic/chaotic processes. The distribution of the waiting time between consecutive grandmaxima is not as clear as that for grand minima, but also hints at a deviation from exponential law.
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. This suggest that the probability of the modern active-sun episode continuing is low5
(cf. Solanki et al., 2004; Abreu et al., 2008).

4.5

Related implications

Reconstructions of long-term solar activity have different implications in related areas of science.
The results, discussed in this overview, can be used in such diverse research disciplines as theoreticalastrophysics, solar-terrestrial studies, paleo-climatology, and even archeology and geology. We will
not discuss all possible implications of long-term solar activity in great detail but only briefly
mention them here.
4.5.1

Theoretical constrains

The basic principles of the occurrence of the 11-year Schwabe cycle are more-or-less understoodin terms of the solar dynamo, which acts, in its classical form (e.g., Parker, 1955), as follows.
Differential rotation Ω produces a toroidal magnetic field from a poloidal one, while the “𝛼-effect”
associated with the helicity of the velocity field produces a poloidal magnetic field from a toroidal
one. This classical model results in a periodic process in the form of propagation of a toroidal
field pattern in the latitudinal direction (the “butterfly diagram”). As evident from observation,
the solar cycle is far from being a strictly periodic phenomenon, with essential variations in thecycle length and especially in the amplitude, varying dramatically between nearly spotless grandminima and very large values during grand maxima. The mere fact of such great variability, known
from sunspot data, forced solar physicists to develop dynamo models further. Simple deterministic
numerical dynamo models, developed on the basis of Parker’s migratory dynamo, can simulate
events, which are seemingly comparable with grand minima/maxima occurrence (e.g., Brandenburg
et al., 1989). However, since variations in the solar-activity level, as deduced from cosmogenic
isotopes, appear essentially nonperiodic and irregular, appropriate models have been developed
to reproduce irregularly-occurring grand minima (e.g., Jennings and Weiss, 1991; Tobias et al.,
1995; Covas et al., 1998). Models, including an ad hoc stochastic driver (Choudhuri, 1992; Schmitt
et al., 1996; Ossendrijver, 2000; Weiss and Tobias, 2000; Mininni et al., 2001; Charbonneau, 2001;
Charbonneau et al., 2004), are able to reproduce the great variability and intermittency found in
the solar cycle (see the review by Charbonneau, 2005). A recent statistical result of grand minima
occurrence (Usoskin et al., 2007) shows disagreement between observational data, depicting a
degree of self-organization or “memory”, and the above dynamo model, which predicts a pure
Poisson occurrence rate for grand minima (see Section 4.3). This poses a new constraint on the
dynamo theory, responsible for long-term solar-activity variations.
5 This is not a prediction of future solar activity, but only a statistical estimate.

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56Ilya G. Usoskin

In general, the following additional constraints can be posed on dynamo models aiming todescribe the long-term (during the past 11,000 years) evolution of solar magnetic activity.
• The sun spends about 3 /4 of its time at moderate magnetic-activity levels, about 1 /6 of its
time in a grand minimum and about 1 /5 – 1 /10 in a grand maximum. Modern solar activity
corresponds to a grand maximum.
• Occurrence of grand minima and maxima is not a result of long-term cyclic variations but isdefined by stochastic/chaotic processes.
• Observed statistics of the occurrence of grand minima and maxima display deviation from a“memory-less” Poisson-like process, but tend to either cluster events together or produce longevent-free periods. This can be interpreted in different ways, such as self-organized criticality(de Carvalho and Prado, 2000, e.g.,), a time-dependent Poisson process (e.g., Wheatland,2003), or some memory in the driving process (e.g., Mega et al., 2003).
• Grand minima tend to be of two different types: short minima of Maunder type and longminima of Spörer type. This suggests that a grand minimum is a special state of the dynamo.
• Duration of grand maxima resemble a random Possion-like process, in contrast to grandminima.
4.5.2

Solar-terrestrial relations

The sun ultimately defines the climate on Earth supplying it with energy via radiation received by
the terrestrial system, but the role of solar variability in climate variations is far from being clear.
Solar variability can affect the Earth’s environment and climate in different ways (see, e.g., a review
by Haigh, 2007). Variability of total solar irradiance (TSI) measured during recent decades is known
to be too small to explain observed climate variations (e.g., Foukal et al., 2006; Fröhlich, 2006).
On the other hand, there are other ways solar variability may affect the climate, e.g., an unknown
long-term trend in TSI (Solanki and Krivova, 2004; Wang et al., 2005) or a terrestrial amplifierof spectral irradiance variations (Shindell et al., 1999). Alternatively, an indirect mechanism also
driven by solar activity, such as ionization of the atmosphere by CR (Usoskin and Kovaltsov,
2006) or the global terrestrial current system (Tinsley and Zhou, 2006) can modify atmosphericproperties, in particular cloud cover (Ney, 1959; Svensmark, 1998). Even a small change in cloud
cover modifies the transparency/absorption/reflectance of the atmosphere and affects the amountof absorbed solar radiation, even without changes in the solar irradiance. Since the CR flux atEarth is modulated not only by solar activity, but also by the slowly changing geomagnetic field,
the two CR modulation mechanisms are independent and act on different timescales, thus giving
one the opportunity to study the CR effect on Earth separately from solar irradiance (de Jager
and Usoskin, 2006; Usoskin et al., 2005b).
Accordingly, improved knowledge of the solar driver’s variability may help in disentangling
various effects in the very complicated system that is the terrestrial climate (e.g., de Jager, 2005;
Versteegh, 2005). It is of particular importance to know the driving forces in the pre-industrial
era, when all climate changes were natural. Knowledge of the natural variability can lead to an
improved understanding of anthropogenic effects upon the Earth’s climate.
Studies of the long-term solar-terrestrial terrestrial are mostly phenomenological, lacking aclear quantitative physical mechanism. Even phenomenological and empirical studies suffer fromlarge uncertainties, related to the quantitative interpretation of proxy data, temporal and spatial
resolution (Versteegh, 2005). Therefore, more precise knowledge of past solar activity, especiallysince it is accompanied by continuous efforts of the paleo-climatic community on improving climatic
data sets, is crucial for improved understanding of the natural (including solar) variability of theterrestrial environment.

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4.5.3

57

Other issues

The proxy method of solar-activity reconstruction, based on cosmogenic isotopes, was developed
from the radiocarbon dating method, when it was recognized that the production rate of 14 C is
not constant and may vary in time due to solar variability and geomagnetic field changes. Neglectof these effects can lead to inaccurate radiocarbon (or more generally, cosmogenic nuclide) dating,which is a key for, e.g., archeology and Quaternary geology. Thus, knowledge of past solar activity
and geomagnetic changes allows for the improvement of the quality of calibration curves, such as
the IntCal (Stuiver et al., 1998; Reimer et al., 2004) for radiocarbon, eventually leading to more
precise dating.
Long-term variations in the geomagnetic field are often evaluated using cosmogenic isotope
data. Knowledge of source variability due to solar modulation is important for better results.

4.6

Summary

In this section, solar activity on a longer scale is discussed, based on recent reconstructions.
According to these 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 thetime the sun has experienced a grand minimum, while 10 – 15% of the time has been taken up by
periods of very high activity.
One of the main features of long-term solar activity is its irregular behavior, which cannot
be described by a combination of quasi-periodic processes as it includes an essentially random
component.
Grand minima, whose typical representative is the Maunder minimum of the late 17th century,
are typical solar phenomena. A total of 27 grand minima have been identified in reconstructionsof the Holocene period. Their occurrence suggests that they appear not periodically, but rather
as the result of a chaotic process within clusters separated by 2000 – 2500 years. Grand minima
tend to be of two distinct types: short (Maunder-like) and longer (Spörer-like). The appearanceof grand minima can be reproduced by modern stochastic-driven dynamo models to some extent,
but some problems still remain to be resolved.
The modern level of solar activity (after the 1940s) is very high, corresponding to a grandmaximum, which are typical but rare and irregularly-spaced events in solar behavior. The durationof grand maxima resembles a random Possion-like process, in contrast to grand minima.
These observational features of the long-term behavior of solar activity have important implications, especially for the development of theoretical solar-dynamo models and for solar-terrestrial
studies.

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58

5

Ilya G. Usoskin

Solar Energetic Particles in the Past

In addition to galactic cosmic rays, which are always present in the Earth’s vicinity, sometimes
sporadic solar energetic particle (SEP) events with a greatly enhanced flux of less energetic particles
in the interplanetary medium also occur (e.g., Klecker et al., 2006). Strong SEP events mostly
originate from CME-related shocks propagating in the solar corona and interplanetary medium,that lead to effective bulk acceleration of charged particles (e.g., Cane and Lario, 2006). Althoughthese particles are significantly less energetic than GCRs, they can occasionally be accelerated toan energy reaching up to several GeV, which is enough to initiate the atmospheric cascade. Peakintensity of SEP flux can be very high, up to 104 particles (with energy > 30 MeV) per cm2 persecond. In fact, the long-term average flux (or fluence) of SEP is mostly defined by rare major
events, which occur one to two times per solar cycle, with only minor contributions from a large
number of weak events (Shea and Smart, 1990, 2002). As an example, energy spectra of GCR and
SEP are shown in Figure 21 for the day of January 20, 2005, when an extreme SEP event took
place. Such SEPs dominate the low-energy section of cosmic rays (below hundreds of MeV of aparticle’s kinetic energy), which is crucial for the radiation environment, and play an importantrole in solar-terrestrial relations. For many reasons it is important to know the variations of SEPs
on long-term scales.
10

10

9

10

2

Daily fluence (cm s sr GeV)

-1

8

10

7

10

6

10

5

10

4

10

3

10

2

10

1

10

0

10

0.01

0.1

1

10

100

Energy (GeV)

Figure 21: Daily fluence of solar energetic particles (dashed curve) and galactic cosmic rays for the dayof January 20, 2005. Open circles represent space-borne measurements (Mewaldt, 2006).

It is not straightforward to evaluate the average SEP flux even for the modern instrumental
epoch of direct space-borne measurements (e.g., Mewaldt et al., 2007). For example, estimates
for the average flux of SEPs with an energy above 30 MeV (called F 30 henceforth) for individual
cycles may vary by an order of magnitude, from 8 cm–2 s–1 for cycle 21 up to 60 cm–2 s–1 forcycle 19 (Smart and Shea, 2002). Moreover, estimates of the SEP flux were quite uncertain during
the earlier years of space-borne measurements because of two effects, which are hard to account for(e.g., Reeves et al., 1992; Tylka et al., 1997). One is related to the very high flux intensities of SEPs
during the peak phase of events, when a detector can be saturated because of the dead-time effect(the maximum trigger rate of the detector is exceeded). The other is related to events with highenergy solar particles, which can penetrate into the detector through the walls of the collimatoror the detector, leading to an enhanced effective acceptance cone with respect to the “expected”

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A History of Solar Activity over Millennia

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one. Since the SEP fluence is defined by major events, these effects may lead to an underestimateof the average flux of SEPs. The modern generation of detectors are better suited for measuringhigh fluxes. The average F 30 flux for the last five solar cycles (1954 – 2006) is estimated at about
35 cm–2 s–1 (Smart and Shea, 2002; Shea et al., 2006).
The method of cosmogenic isotopes in terrestrial archives does not allow quantitative estimatesof SEP events because of atmospheric and geomagnetic rigidity/energy cutoffs, which are too highfor less energetic particles of solar/interplanetary origin. While the SEP effect is negligible in 14 C
records, the 10 Be record may contain information on extreme SEP events in the past (Usoskin et al.,2006b). In particular, an additional SEP-related enhancement of the 10 Be signal can appear aroundsome solar activity maxima leading to an intermittent 5.5-year quasi-periodicity (McCracken et al.,2002). However, such peaks can be studied only a posteriori, i.e., for known SEP events (e.g., theCarrington flare), which can be associated with strong peaks in 10 Be, but the relation is not
one-to-one. Therefore, SEP events cannot be unambiguously identified from the 10 Be data.
Since energy spectra of the two populations of cosmic rays are significantly different (very softfor SEP and much harder for GCR), they can be separated by their energy. Accordingly, for earlier
times, when direct measurements were not possible, one needs a natural spectrometer in order todistinguish between cosmic particles of solar and galactic origin. Such a spectrometer should be
able to naturally separate lower and higher energy components of the cosmic-ray spectrum and“record” them in different archives. Fortunately, there are such natural spectrometers, which allow
us to study not only galactic cosmic rays but also solar energetic particle flux in the past.

5.1

Lunar and meteoritic rocks

One spectrometer that is able to separate cosmic rays is lunar (or meteoritic) rocks.
90
80

14

C (dpm/kg)

70
60
50
40
30
20
0

5

10

15

2

depth (g/cm )Figure 22: Measured (dots) and calculated (curves) 14 C activity in a lunar sample 68815 (Jull et al.,1998). The big diamond implies contamination of a thin surface layer by 14 C implanted from solar wind.
The dotted curve represents the expected production due to GCR, while the solid curve is the best fit
SEP+GCR model production.

Figure 22 depicts an example of 14 C measured in a lunar sample (Jull et al., 1998). The dottedline shows the expected production of radiocarbon by GCR. The production increases with depth
due to the development of a nucleonic cascade in the matter, initiated by energetic GCR particles,
similar to the atmospheric cascade. Less energetic particles of solar origin produce the isotope only
in upper layers of the rock, since their low energy does not allow them to initiate a cascade. On
the other hand, thanks to their high flux in the lower energy range, the production of 14 C in the

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60

Ilya G. Usoskin

upper layers is much higher than that from GCR. Thus, by first measuring the isotope activity indeep layers one can evaluate the average GCR flux, and then the measured excess in the upper
level yields an estimate for the SEP flux in both integral intensity and spectral shape. The result
is based on model computations and therefore is slightly model dependent but makes it possible
to give a robust estimate of the GCR and SEP in the past.
A disadvantage of this approach is that lunar samples are not stratified and do not allow for
temporal separation. The measured isotope activity is a balance between production and decay
and, therefore, represents the production (and the ensuing flux) integrated over the life-time of theisotope before the sample has been measured. However, using different isotopes with different life
times, one can evaluate the cosmic-ray flux integrated over different timescales.
Estimates of the average SEP flux F 30 on different timescales, as obtained from various isotopes
measured in lunar samples, are collected in Table 3. The average F 30 flux for the last five solar
cycles (1954 – 2006) is consistent with the average flux estimated in the past for longer timescales
from 103 to 107 years (cf. Reedy, 2002).
Table 3: Estimates of 4𝜋 omni-directional integral (above 30 MeV) flux, F 30 in [cm2 s]–1 , of solar energetic
particles, obtained from different sources.

†

Timescale

MethodSourceReference

F 30 (cm–2 s–1 )1954 – 2006
500 yrs
104 yrs
105 yrs
105 yrs
5 × 105 yrs
106 yrs
106 yrs
106 yrs
106 yrs2 × 106 yrs
5 × 106 yrs
2 × 106 yrs

measurements
nitrates
14
C
41
Ca
41
Ca
36
Cl
26
Al
10
Be, 26 Al
10Be, 26 Al
10Be, 26 Al
10Be, 26 Al
53
Mn
21
Ne, 22 Ne, 38 Ar

space-borne
polar ice
lunar rock
lunar rock
lunar rock
lunar rock
lunar rock
lunar rock
lunar rock
lunar rock
lunar rock
lunar rock
lunar rock

Smart and Shea (2002)
McCracken et al. (2001b)
Jull et al. (1998)
Klein et al. (1990)
Fink et al. (1998)
Nishiizumi et al. (1995)
Kohl et al. (1978)
Michel et al. (1996)
Nishiizumi et al. (1995)
Fink et al. (1998)
Nishizumi et al. (1997)
Kohl et al. (1978)
Rao et al. (1994)

∼ 35†
24†
42
28
56
26
25
24
26
32
∼ 35
25
22

Lower bound.

5.2

Nitrates in polar ice

Another natural spectrometer is the Earth’s atmosphere, where the penetration depth of cosmic
rays depends on their energy. As an illustration, Figure 23 shows ionization due to cosmic rays in
the polar atmosphere. One can see that ionization due to GCR is present in the entire atmospherewith a minor solar-cycle variation (Bazilevskaya et al., 2008). The ionization effect of a SEP eventis minor in the troposphere even for the extreme event of January 20, 2005. On the other hand, theionization rate is greatly enhanced (by orders of magnitude) in the polar stratosphere during strong
SEP events (Bütikofer et al., 2008). Although such enhanced stratospheric ionization cannot bedirectly recorded in natural archives to be measured later, there is an indirect way to restore thehistory of extreme SEP events in the past.
Cosmic-ray–induced ionization can lead to essential chemical changes in the polar stratospherewith enhanced production of “odd nitrogens” NOy (e.g., N, NO, NO2 , NO3 , 2N2 O5 , BrONO2 ,Living Reviews in Solar Physics
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A History of Solar Activity over Millennia

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7

-1

-1

CRII (ion pairs g s )

10

6

10

5

10

GCR, max
GCR, min
SCR, Jan. 20, 2005

4

10

3

10

0

5

10

15

20

25

30

35

Altitude (km)Figure 23: Altitude profile of the cosmic-ray–induced ionization (CRII) rate in the polar atmosphere,
computed using the model by Usoskin and Kovaltsov (2006). Dashed and dotted curves depict the average
CRII for solar maxima and minima, respectively. The solid curve denotes the average CRII due to solar
energetic particles for the day of January 20, 2005.

ClONO2 , HO2 NO2 , and HNO3 ) (see, e.g., Jackman et al., 1990, 1993; Vitt et al., 2000). Due
to ionization of the ambient air and subsequent dissociation of O2 and N2 , energetic particles
precipitating into the atmosphere facilitate formation of the odd nitrogen. The abundance of odd
nitrogen dramatically responds to variations in the SEP flux on the background of a smooth 11-yr
cycle due to GCR variations (Thomas et al., 2007). Odd nitrogen is long-lived during the polarnight, and some species, such as nitric acid HNO3 , can be effectively transported down and finallystored in polar snow/ice. By measuring such chemical species in a stratified polar-ice archive,
one can obtain a record of the physical-chemical conditions of the polar atmosphere (Zeller et al.,
1986; Zeller and Dreschhoff, 1995). Under some basic reasonable assumptions (stable atmosphericproperties, no mixing in snow, etc.), the abundance of compounds, related to the stratospheric5chemistry such as nitrate ions (NO−3 ), provides a unique and long-term (potentially up to 10 years)
record of the radiation environment and climate in polar atmosphere. The concentration of nitrates
has been measured in polar ice from both the Southern (South Pole, e.g., Dreschhoff and Zeller,1990) and Northern (Greenland, e.g., Zeller and Dreschhoff, 1995; Dreschhoff and Zeller, 1998)
polar caps. The Greenland series of ultra-high resolution (better than 30 equispaced samples peryear) provides a unique record in which (groups of) individual strong SEP events can be identified
for as far back as 1562.
The nitrate abundance measured in polar ice depicts a clear seasonal cycle with a peak during
the local summer because of increased snow sublimation under sunlight (Zeller et al., 1986). Moreover, the nitrate series contains clear time stamps of major volcano eruptions, which are apparent
in the measured signal. Altogether it provides a solid basis for absolute dating of the samples
with a time resolution within one year (McCracken et al., 2001b). Thus, the nitrate concentration
in well-dated polar-ice cores provides a unique opportunity to evaluate the flux of SEP in thepast, before instrumental observations. High time resolution allows the separating of (groups of)individual SEP events, such as the famous Carrington event in September 1859 (Shea et al., 2006;
Thomas et al., 2007). It has been suggested that nitrate enhancements caused by strong SEP
events can be reliably distinguished both from the relatively slow and shallow variations of galactic
cosmic rays and from meteorologically-derived nitrate peaks.

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Figure 24: Cumulative probability of a large solar energetic particle event to occur (after McCracken
et al., 2001b). The black histogram, extrapolated from the blue line corresponds to the directly observed
SEP events (Reedy, 1996). Arrows (extrapolated from the brown line) depict an upper limit obtained fromthe analysis of lunar rock (see Table 3) assuming that the entire fluence has been produced within a few
extreme events. Diamonds represent the result derived from the nitrate data for 1561 – 1950 (McCracken
et al., 2001b).

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The first studies based on the correlation between peaks of nitrate concentration and measuresof solar activity were qualitative and aimed to search for periods of active/quiet sun (e.g., Zeller
et al., 1986; Dreschhoff and Zeller, 1998) or even for a supernova event (Dreschhoff and Laird, 2006).
Later, the method was explored more fully (McCracken et al., 2001a,b), which made it possible toidentify large SEP events since 1560 and evaluate their fluence (see Table 1 in McCracken et al.,2001b). Only events with F 30 fluence exceeding 109 particles per cm2 , which is estimated as a
threshold for the nitrate signal, are identified in this way. This analysis leads to a statisticalestimate of the occurrence frequency of large SEP events (Figure 24). Thus-obtained statistics
of SEP-event occurrence complements directly observed data and that reconstructed from lunar
samples, indicating a kind of break in the distribution with the fluence above 1010 protons/cm2 .
Note that estimates based on lunar-rock samples (arrows in Figure 24) provide only an upperbound for SEP fluence, since they are based on an extreme assumption that the net fluence wasproduced in a few extreme events. Therefore, extra-strong SEP events with the fluence exceeding
1012 cm–2 are very improbable.
However, the method has a drawback as noted by McCracken et al. (2001b). The measured
nitrate effect depends not only on the total fluence F 30 but also on the energy spectrum of SEP,
namely, high energy particles produce more ionization and thus lead to more nitrate effect thanlower-energy particles. Accordingly, the measured nitrate signal can be converted into the SEP
fluence only by assuming a fixed energy spectrum of SEP by normalizing all data to, e.g., the eventof August 1972 (McCracken et al., 2001b; Shea et al., 2006). However, the actual energy spectrumof SEP remains a free parameter in such a reconstruction (Usoskin et al., 2006b). Moreover, thenitrate record is only an indirect proxy of strong SEP events whose efficiency is not 100% (Palmer
et al., 2001).

5.3

Summary

In this section, estimates of the averaged long-term flux of solar energetic particles (SEPs) are
discussed.
Measurements of cosmogenic isotopes with different life times in lunar and meteoritic rocks
allow one to make rough estimates of the SEP flux over different timescales. The directly spaceborne-measured SEP flux for past decades is broadly consistent with estimates on longer timescales– up to millions of years.
Measurements of nitrates in polar ice make it possible to reconstruct strong SEP events fornearly the past five centuries.
An analysis of various kinds of data suggests that the distribution of the intensity of SEP events
has taken a break, and the occurrence of extra-strong events (with the F 30 fluence exceeding 1012 )is unlikely.

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Conclusions

In this review the present knowledge of long-term solar activity on a multi-millennial timescale, as
reconstructed using the indirect proxy method, is discussed.
Although the concept of solar activity is intuitively understandable as a deviation from the“quiet” sun concept, there is no clear definition for it, and different indices have been proposed toquantify different aspects of variable solar activity. One of the most common and practical indicesis sunspot number, which forms the longest available series of direct scientific observations. While
all other indices have a high correlation with sunspot numbers, dominated by the 11-year cycle, therelationship between them at other timescales (short and long-term trends) may vary to a great
extent.
On longer timescales, quantitative information of past solar activity can only be obtainedusing the method based upon indirect proxy, i.e., quantitative parameters, which can be measured
nowadays but represent the signatures, stored in natural archives, of the different effects of solar
magnetic activity in the past. Such traceable signatures can be related to nuclear or chemical
effects caused by cosmic rays in the Earth’s atmosphere, lunar rocks or meteorites. The mostcommon proxy of solar activity is formed by data from the cosmogenic radionuclides, 10 Be and 14 C,
produced by cosmic rays in the Earth’s atmosphere and stored in independently-dated stratified
natural archives, such as tree rings or ice cores. Using a recently-developed physics-based model
it is now possible to reconstruct the temporal behavior of solar activity in the past, over many
millennia. The most robust results can be obtained for the Holocene epoch, which started morethan 11,000 years ago, whose stable climate minimizes possible uncertainties in the reconstruction.
An indirect verification of long-term solar-activity reconstructions supports their veracity andconfirms that variations of cosmogenic nuclides on the long-term scale (centuries to millennia)
during the Holocene make a solid basis for studies of solar variability in the past. However,such reconstructions may still contain systematic uncertainties related to unknown changes in thegeomagnetic field or climate of the past, especially in the early part of the Holocene.
Measurements of nitrates in polar ice allow the reconstruction of strong solar energetic particle(SEP) events in the past, over the five past centuries. Together with independent measurementsof the concentration of different cosmogenic isotopes in lunar and meteoritic rocks, it leads toestimates of the SEP flux on different timescales. Directly space-borne-measured SEP flux forrecent decades is broadly consistent with estimates on longer timescales – up to millions of years,
and the occurrence of extra-strong events is unlikely.
In general, the following main features are observed in the long-term evolution of solar magnetic
activity.
• Solar activity is dominated by the 11-year Schwabe cycle on an interannual timescale. Some
additional longer characteristic times can be found, including the Gleissberg secular cycle,de Vries/Suess cycle, and a quasi-cycle of 2000 – 2400 years. However, all these longer cycles
are intermittent and cannot be regarded as strict phase-locked periodicities.
• One of the main features of long-term solar activity is that it contains an essential chaotic/
stochastic component, which leads to irregular variations and makes solar-activity predictions
impossible for a scale exceeding one solar cycle.
• The sun spends about 70% of its time at moderate magnetic activity levels, about 15 – 20%of its time in a grand minimum and about 10 – 15% in a grand maximum. Modern solar
activity corresponds to a grand maximum.
• Grand minima are a typical but rare phenomena in solar behavior. Their occurrence appears
not periodically, but rather as the result of a chaotic process within clusters separated by

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2000 – 2500 years. Grand minima tend to be of two distinct types: short (Maunder-like) andlonger (Spörer-like).
• The modern level of solar activity (after the 1940s) is very high, corresponding to a grandmaximum. Grand maxima are also rare and irregularly occurring events, though the exact
rate of their occurrence is still a subject of debates.
These observational features of the long-term behavior of solar activity have important implications, especially for the development of theoretical solar-dynamo models and for solar-terrestrial
studies.

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7

Ilya G. Usoskin

Acknowledgements

I thank the editorial board of the Living Reviews in Solar Physics for the invitation to prepare thisreview and organizational aid. This work would be impossible without encouraging discussions, aswell as direct and indirect help, from my colleagues Gennady Kovaltsov and Sami Solanki, whose
invaluable support is acknowledged with my greatest gratitude. I have also greatly benefited
from lively and open discussions and debates with Edouard Bard, Jürg Beer, Narendra Bhandari, late Giuliana Cini Castagnoli, Paul Charbonneau, Vincent Courtillot, Cornelis de Jager,
Gisella Dreschhoff, Erwin Flückiger, Peter Foukal, Yves Gallet, Agnés Genevey, David Hathaway,
Monika Korte, Natalia Krivova, Bernd Kromer, Devendra Lal, Michael Lockwood, Ken McCracken,
David Moss, Kalevi Mursula, Raimund Muscheler, Hiroko Miyahara, Heikki Nevanlinna, Valery
Ostryakov, Alexander Ruzmaikin, Dieter Schmitt, Manfred Schüssler, Margaret Shea, Don Smart,
Ian Snowball, Dmitry Sokoloff, Willie Soon, Carla Taricco, Jóse Vaquero, and many others. I thankEvguenia Usoskina for help with editing this text. I am happy to acknowledge those colleagues
who work in this field and make it living and vibrant.

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