List of Figures

View Image 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.
View Image Figure 2:
Maunder butterfly diagram of sunspot occurrence reconstructed by Arlt (2013) for 1825 – 1867 using recovered drawing of S.H. Schwabe.
View Image Figure 3:
Cyclic variations since 1951. Panel a: Time profiles of sunspot numbers (External Link; Panel b: Cosmic-ray flux as the count rate of a polar neutron monitor (Oulu NM External Link, Climax NM data used before 1964), 100% NM count rate corresponds to May 1965.
View Image Figure 4:
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).
View Image Figure 5:
Schematic view of an atmospheric cascade caused by energetic cosmic rays in the atmosphere. Left-to-right are denoted, respectively, the soft, muon and hadronic components of the cascade. Symbols “N, p, n, μ, π, e, e+, and γ” denote nuclei, protons, neutrons, muons, pions, electrons, positrons, and photons, respectively. Stars denote nuclear collisions, ovals – decay processes. This sketch does not represent the full development of the cascade and serves solely as an illustration for the processes discussed in the text. Image reproduced by permission from Usoskin (2011), copyright by SAIt.
View Image Figure 6:
Schematic representation of 14C (left) and 10Be (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.
View Image Figure 7:
Radiocarbon series for the Holocene. Upper panel: Measured content of Δ14C 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 14C in the atmosphere, reconstructed from the measured Δ14C (Usoskin and Kromer, 2005).
View Image Figure 8:
Differential production rate for cosmogenic isotopes and ground-based neutron monitors as a function of cosmic-ray energy. Panel A: Yield functions of the globally averaged and polar 10Be production (Webber and Higbie, 2003), global 14C production (Kovaltsov et al., 2012), polar neutron monitor (Clem and 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 10Be production, global 14C production, and polar neutron monitor.
View Image Figure 9:
Globally-averaged production rate of 14C as a function of the modulation potential ϕ and geomagnetic dipole moment M, computed using the yield function by Kovaltsov et al. (2012), LIS by Burger et al. (2000) and cosmic-ray–modulation model by Usoskin et al. (2005). Another often used model (Masarik and Beer, 2009) yields a similar result.
View Image Figure 10:
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 Δ14C of this particular reservoir expressed in per mil. Image reproduced by permission from Bard et al. (1997), copyright by Elsevier.
View Image Figure 11:
The frequency characteristics of the carbon cycle: attenuation (left-hand panel) and phase shift (right-hand panel) as a function of the frequency of the 14C production signal. Lines stand for a classical Oeschger–Siegenthaler box model (Siegenthaler et al., 1980), and open circles for a sophisticated PANDORA model (Bard et al., 1997).
View Image Figure 12:
Wet (panel a) and dry (panel b) deposition of 10Be, computed using the NASA GISS model (Field et al., 2006) for a fixed sea-surface temperature.
View Image Figure 13:
Scatter plot of smoothed group sunspot numbers vs. (2-year delayed) 10Be 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 in panel (a). (After Usoskin and Kovaltsov, 2004).
View Image Figure 14:
An unsuccessful attempt of the reconstruction of cosmic-ray intensity in the past using a regression with sunspot numbers. Dots represent the observed cosmic-ray intensity since 1951. Note the absence of a long-term trend. Image reproduced by permission from Belov et al. (2006), copyright by Elsevier.
View Image Figure 15:
Several reconstructions of the decade-averaged modulation potential ϕ for the last few centuries: from sunspot numbers (SN(U02) – Usoskin et al., 2002b), from 14C data (14C(S04), 14C(M05), 14C(M07) – Solanki et al., 2004; Muscheler et al., 2005, 2007, respectively), from Antarctic 10Be 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., 2011) and ionization chambers since 1936 (McCracken and Beer, 2007).
View Image Figure 16:
An example of reconstruction of the heliospheric magnetic field at Earth orbit for the last 600 years from 10Be data. Image reproduced by permission from McCracken (2007), copyright by AGU.
View Image Figure 17:
Long-term sunspot-number reconstruction from 14C 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.
View Image Figure 18:
10-year averaged sunspot numbers: Actual group sunspot numbers (thick grey line) and the reconstructions based on 10Be (thin curve, Usoskin et al., 2003c) and on 14C (thick curve with error bars, Solanki et al., 2004). The horizontal dotted line depicts the high activity threshold.
View Image Figure 19:
Immediate 44Ti 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 44Ti activity, computed using the method of Usoskin et al. (2006c) and different reconstructions of ϕ shown in Figure 15.
View Image Figure 20:
Reconstruction of the solar modulation potential over the Holocene based on a composite record (Section 3.8), along with 1σ uncertainties. Time is given in year BP. Image reproduced by permission from Steinhilber et al. (2012).
View Image Figure 21:
Sunspot activity (over decades, smoothed with a 12221 filter) throughout the Holocene, reconstructed from 14C by Usoskin et al. (2007) using geomagnetic data by Yang et al. (2000). Blue and red areas denote grand minima and maxima, respectively.
View Image Figure 22:
Wavelet (Morlet basis) spectrum of the sunspot-number reconstruction shown in Figure 21. 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. Hatched areas depict the cone of influence where the result is not fully reliable because of the proximity of the edges of the time series.
View Image Figure 23:
Histogram of the duration of grand minima from Table 1.
View Image Figure 24:
Daily fluence of solar energetic particles (dashed curve – Tylka and Dietrich, 2009) and galactic cosmic rays (solid curve) for the day of January 20, 2005. Open circles represent space-borne measurements (Mewaldt, 2006; Mewaldt et al., 2012).
View Image Figure 25:
Time profiles of the measured Δ14C content in Japanese cedar (M12 – Miyake et al., 2012) and German oak (ETH Zürich & Mannheim AMS – Usoskin et al., 2013) trees for the period around 775 AD. Smooth black and grey lines depict a family of best fit Δ14C profiles, calculated using a family of realistic carbon cycle models for an instantaneous injection of 14C into the stratosphere (Usoskin and Kovaltsov, 2012). Image after Usoskin et al. (2013).
View Image Figure 26:
Cumulative probability (with the 90% confidence interval) of occurrence of a SEP event with fluence (> 30 MeV) exceeding the given value F30, as assessed from the data for the space era 1956 – 2008 (triangles), cosmogenic isotope annual data (stars), and cosmogenic isotope decadal data (circles). Gray dotted curve depicts the best-fit exponent. Image reproduced by permission from Usoskin and Kovaltsov (2012), copyright by AAS.
View Image Figure 27:
Measured (dots) and calculated (curves) 14C activity in a lunar sample 68815 (Jull et al., 1998). The big diamond implies contamination of a thin surface layer by 14C 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.
View Image Figure 28:
Cumulative frequency distribution of SEP events with fluences greater than F10 (for particles with energies above 10 MeV). Red histogram: satellite-based direct observations; Blue diamonds: conservative upper limits derived from lunar isotopes (see Section 5.2); Blue dashed line: upper limit based on 14C record (Hudson, 2010); Image reproduced by permission from Schrijver et al. (2012), copyright by AGU.