Sunspot Number Record Research Articles

A Geomagnetic Estimate of Heliospheric Modulation Potential over the Last 175 Years

Galactic cosmic rays (GCRs) interact with the Earth’s atmosphere to produce energetic neutrons and cosmogenic radionuclides, such as 14C. The atmosphere is partially shielded from the interstellar GCR spectrum by both the geomagnetic and solar magnetic fields. Solar shielding is often expressed as the heliospheric modulation potential ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document}, which consolidates information about the strength and structure of the solar magnetic field into a single parameter. For the period 1951 to today, ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} can be estimated from ground-based neutron monitor data. Prior to 1950, 14C in tree rings can be used to estimate ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} and hence the solar magnetic field, back centuries or millennia. Bridging the gap in the ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} record is therefore of vital importance for long-term solar reconstructions. One method is to model ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} using the sunspot number (SN) record. However, the SN record is only an indirect measure of the Sun’s magnetic field, introducing uncertainty, and the record suffers from calibration issues. Here we present a new reconstruction of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} based on geomagnetic data, which spans both the entire duration of the neutron monitor record and stretches back to 1845, providing a significant overlap with the 14C data. We first modify and test the existing model of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} based on a number of heliospheric parameters, namely the open solar flux FS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$F_{S}$\\end{document}, the heliospheric current sheet tilt angle α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha $\\end{document}, and the global heliospheric magnetic polarity p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$p$\\end{document}. This modified model is applied to recently updated geomagnetic estimates of FS\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$F_{S}$\\end{document} and cyclic variations of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\alpha $\\end{document} and p\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$p$\\end{document}. This approach is shown to produce an annual estimate of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} in excellent agreement with that obtained from neutron monitors over 1951 – 2023. It also suggests that ionisation chamber estimates of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} – which have previously been used to extend the instrumental estimate back from 1951 to 1933 – are not well calibrated. Comparison of the new geomagnetic ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} with 14C estimates of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} suggests that the long-term trend is overestimated in the most recent 14C data, possibly due to hemispheric differences in the Suess effect, related to the release of carbon by the burning of fossil fuels. We suggest that the new geomagnetic estimate of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$\\phi $\\end{document} will provide an improved basis for future calibration of long-term solar activity reconstructions.

Including Planet 9 in the Solar System Increases the Coherence between the Sunspot Number Record and Solar Inertial Motion

The Sun would be subject to a significant variation of orbital motion about the solar system barycentre if a small planet is orbiting at a very large distance. This paper assesses if the Planet 9 hypothesis, the existence of a ninth planet, is consistent with the planetary hypothesis: the synchronisation of sunspot emergence to solar inertial motion (SIM) induced by the planets. We show that SIM would be profoundly affected if Planet 9 exists and that the hypothesised effect of SIM on sunspot emergence would be radically different from the effect of SIM due to the existing eight planets. We compare the frequency and time variation of Sun to barycentre distance, RB, calculated for both the eight and nine planet systems, with the frequency and time variation of sunspot number (SSN). We show that including Planet 9 improves the coherence between RB and SSN in the decadal, centennial and millennial time range. Additionally, as the variation of RB is sensitive to the longitude and period of Planet 9, it is possible to adjust both parameters to fit the variation of RB to the SSN record and obtain new estimates of the period and present longitude of Planet 9. Finally, we develop the hypothesis that planetary induced solar acceleration reduces meridional flow and consequently sunspot emergence thereby providing an explanation for the observed coincidence of grand solar minima with intervals of extreme solar acceleration.

Hemispheric injection of magnetic helicity by surface flux transport

Aims. We estimate the injection of relative magnetic helicity into the solar atmosphere by surface flux transport over 27 solar cycles (1700–2009). Methods. We determine the radial magnetic field evolution using two separate surface flux transport models: one driven by magnetogram inputs and another by statistical active region insertion guided by the sunspot number record. The injection of relative magnetic helicity is then computed from this radial magnetic field together with the known electric field in the flux transport models. Results. Neglecting flux emergence, solar rotation is the dominant contributor to the helicity injection. At high latitudes, the injection is always negative/positive in the northern/southern hemisphere, while at low latitudes the injection tends to have the opposite sign when integrated over the full solar cycle. The overall helicity injection in a given solar cycle depends on the balance between these two contributions. This net injected helicity correlates well with the end-of-cycle axial dipole moment.

An ACE/CRIS-observation-based Galactic Cosmic Rays heavy nuclei spectra model II

An observation-based Galactic Cosmic Ray (GCR) spectral model for heavy nuclei is developed. Zhao and Qin (J. Geophys. Res. Space Phys.118, 1837(2013)) proposed an empirical elemental GCR spectra model for nuclear charge 5-28 over the energy range from 30 to 500 MeV/nuc, which is proved to be successful in predicting yearly averaged GCR heavy nuclei spectra.Based on the latest highly statistically precise measurements from ACE/CRIS,a further elemental GCR model with monthly averaged spectra is presented. The model can reproduce the past and predict the futureGCR intensity monthly by correlating model parameters with thecontinuous sunspot number (SSN) record. The effects of solar activity on GCR modulation are considered separately for odd and even solar cycles. Compared with other comprehensive GCR models, our modeling results are satisfyingly consistent with the GCR spectral measurements from ACE/SIS and IMP-8, and have comparable prediction accuracy as the Badhwar & O'Neill 2014 model.A detailed error analysis is also provided.Finally, the GCR carbon and iron nuclei fluxes for the subsequent two solar cycles (SC 25 and 26) are predicted and they show a potential trend in reduced flux amplitude, which is suspected to be relevant to possible weak solar cycles.

Visualization of the challenges and limitations of the long-term sunspot number record

The solar cycle periodically reshapes the magnetic structure and radiative output of the Sun and determines its impact on the heliosphere roughly every 11 years. Besides this main periodicity, it shows century-long variations (including periods of abnormally low solar activity called grand minima). The Maunder Minimum (1645-1715) has generated significant interest as the archetype of a grand minimum in magnetic activity for the Sun and other stars, suggesting a potential link between the Sun and changes in terrestrial climate. Recent reanalyses of sunspot observations have yielded a conflicted view on the evolution of solar activity during the past 400 years (a steady increase versus a constant level). This has ignited a concerted community-wide effort to understand the depth of the Maunder Minimum and the subsequent secular evolution of solar activity. The goal of this Perspective is to review recent work that uses historical data to estimate long-term solar variability, and to provide context to users of these estimates that may not be aware of their limitations. We propose a clear visual guide than can be used to easily assess observational coverage for different periods, as well as the level of disagreement between currently proposed sunspot group number series.

An econometric investigation of the sunspot number record since the year 1700 and its prediction into the 22nd century

Solar activity, as measured by the yearly revisited time series of sunspot numbers (SSN) for the period 1700–2014 (Clette et al., 2014), undergoes in this paper a triple statistical and econometric checkup. The conclusions are that the SSN sequence: (1) is best modeled as a signal that features nonlinearity in mean and variance, long memory, mean reversion, ‘threshold’ symmetry, and stationarity; (2) is best described as a discrete damped harmonic oscillator which linearly approximates the flux-transport dynamo model; (3) its prediction well into the 22nd century testifies of a substantial fall of the SSN centered around the year 2030. In addition, the first and last Gleissberg cycles show almost the same peak number and height during the period considered, yet the former slightly prevails when measured by means of the estimated smoother. All of these conclusions are achieved by making use of modern tools developed in the field of Financial Econometrics and of two new proposed procedures for signal smoothing and prediction.

The heliospheric Hale cycle over the last 300 years and its implications for a “lost” late 18th century solar cycle

A Hale cycle, one complete magnetic cycle of the Sun, spans two complete Schwabe cycles (also referred to as sunspot and, more generally, solar cycles). The approximately 22-year Hale cycle is seen in magnetic polarities of both sunspots and polar fields, as well as in the intensity of galactic cosmic rays reaching Earth, with odd- and even-numbered solar cycles displaying qualitatively different waveforms. Correct numbering of solar cycles also underpins empirical cycle-to-cycle relations which are used as first-order tests of stellar dynamo models. There has been much debate about whether the unusually long solar cycle 4 (SC4), spanning 1784–1799, was actually two shorter solar cycles combined as a result of poor data coverage in the original Wolf sunspot number record. Indeed, the group sunspot number does show a small increase around 1794–1799 and there is evidence of an increase in the mean latitude of sunspots at this time, suggesting the existence of a cycle “4b”. In this study, we use cosmogenic radionuclide data and associated reconstructions of the heliospheric magnetic field (HMF) to show that the Hale cycle has persisted over the last 300 years and that data prior to 1800 are more consistent with cycle 4 being a single long cycle (the “no SC4b” scenario). We also investigate the effect of cycle 4b on the HMF using an open solar flux (OSF) continuity model, in which the OSF source term is related to sunspot number and the OSF loss term is determined by the heliospheric current sheet tilt, assumed to be a simple function of solar cycle phase. The results are surprising; Without SC4b, the HMF shows two distinct peaks in the 1784–1799 interval, while the addition of SC4b removes the secondary peak, as the OSF loss term acts in opposition to the later rise in sunspot number. The timing and magnitude of the main SC4 HMF peak is also significantly changed by the addition of SC4b. These results are compared with the cosmogenic isotope reconstructions of HMF and historical aurora records. These data marginally favour the existence of SC4b (the “SC4b” scenario), though the result is less certain than that based on the persistence of the Hale cycle. Thus while the current uncertainties in the observations preclude any definitive conclusions, the data favour the “no SC4b” scenario. Future improvements to cosmogenic isotope reconstructions of the HMF, through either improved modelling or additional ice cores from well-separated geographic locations, may enable questions of the existence of SC4b and the phase of Hale cycle prior to the Maunder minimum to be settled conclusively.

Global temperatures and sunspot numbers. Are they related? Yes, but non linearly. A reply to Gil-Alana et al. (2014)

Recently Gil-Alana et al. (2014) compared the sunspot number record and the temperature record and found that they differ: the sunspot number record is characterized by a dominant 11-year cycle while the temperature record appears to be characterized by a “singularity” or “pole” in the spectral density function at the “zero” frequency. Consequently, they claimed that the two records are characterized by substantially different statistical fractional models and rejected the hypothesis that the Sun influences significantly global temperatures. I will show that: (1) the “singularity” or “pole” in the spectral density function of the global surface temperature at the “zero” frequency does not exist—the observed pattern derives from the post 1880 warming trend of the temperature signal and is a typical misinterpretation that discrete power spectra of non-stationary signals can suggest; (2) appropriate continuous periodograms clarify the issue and also show a signature of the 11-year solar cycle (amplitude ≤0.1°C), which since 1850 has an average period of about 10.4 year, and of many other natural oscillations; (3) the solar signature in the surface temperature record can be recognized only using specific techniques of analysis that take into account non-linearity and filtering of the multiple climate change contributions; (4) the post 1880-year temperature warming trend cannot be compared or studied against the sunspot record and its 11-year cycle, but requires solar proxy models showing short and long scale oscillations plus the contribution of anthropogenic forcings, as done in the literature. Multiple evidences suggest that global temperatures and sunspot numbers are quite related to each other at multiple time scales. Thus, they are characterized by cyclical fractional models. However, solar and climatic indexes are related to each other through complex and non-linear processes. Finally, I show that the prediction of a semi-empirical model for the global surface temperature based on astronomical oscillations and anthropogenic forcing proposed by Scafetta since 2009 has, up to date, been successful.

Centennial variations in sunspot number, open solar flux, and streamer belt width: 1. Correction of the sunspot number record since 1874

AbstractWe analyze the widely used international/Zürich sunspot number record, R, with a view to quantifying a suspected calibration discontinuity around 1945 (which has been termed the “Waldmeier discontinuity”). We compare R against the composite sunspot group data from the Royal Greenwich Observatory network and the Solar Optical Observing Network, using both the number of sunspot groups, NG, and the total area of the sunspots, AG. In addition, we compare R with the recently developed interdiurnal variability geomagnetic indices IDV and IDV(1d). In all four cases, linearity of the relationship with R is not assumed and care is taken to ensure that the relationship of each with R is the same before and after the putative calibration change. It is shown the probability that a correction is not needed is of order 10−8 and that R is indeed too low before 1945. The optimum correction to R for values before 1945 is found to be 11.6%, 11.7%, 10.3%, and 7.9% using AG, NG, IDV, and IDV(1d), respectively. The optimum value obtained by combining the sunspot group data is 11.6% with an uncertainty range 8.1–14.8% at the 2σ level. The geomagnetic indices provide an independent yet less stringent test but do give values that fall within the 2σ uncertainty band with optimum values are slightly lower than from the sunspot group data. The probability of the correction needed being as large as 20%, as advocated by Svalgaard (2011), is shown to be 1.6 × 10−5.

Grand minima of solar activity during the last millennia

AbstractIn this review we discuss the occurrence and statistical properties of Grand minima based on the available data covering the last millennia. In particular, we consider the historical record of sunspot numbers covering the last 400 years as well as records of cosmogenic isotopes in natural terrestrial archives, used to reconstruct solar activity for up to the last 11.5 millennia, i.e. throughout the Holocene. Using a reconstruction of solar activity from cosmogenic isotope data, we analyze statistics of the occurrence of Grand minima. We find that: the Sun spends about most of the time at moderate activity, 1/6 in a Grand minimum and some time also in a Grand maximum state; Occurrence of Grand minima is not a result of long-term cyclic variations but is defined by stochastic/chaotic processes; There is a tendency for Grand minima to cluster with the recurrence rate of roughly 2000-3000 years, with a weak ≈210-yr periodicity existing within the clusters. Grand minima occur of two different types: shorter than 100 years (Maunder-type) and long ≈150 years (Spörer-type). It is also discussed that solar cycles (most possibly not sunspots cycle) could exist during the Grand minima, perhaps with stretched length and asymmetric sunspot latitudinal distribution.These results set new observational constraints on long-term solar and stellar dynamo models.

Long-term behavior of the concentration of the minor constituents in the mesosphere – a model study

Abstract. We investigate the influence the rising concentrations of methane, nitrous oxide and carbon dioxide which have occurred since the pre-industrial era, have had on the chemistry of the mesosphere. For this investigation we use our global 3-D-model COMMA-IAP which was designed for the exploration of the MLT-region and in particular the extended mesopause region. Assumptions and approximations for the trends in the Lyman-α flux (needed for the water vapor dissociation rate), methane and the water vapor mixing ratio at the hygropause are necessary to accomplish this study. To approximate the solar Lyman-α flux back to the pre-industrial time, we derived a quadratic fit using the sunspot number record which extends back to 1749 and is the only solar proxy available for the Lyman-α flux prior to 1947. We assume that methane increases with a constant growth rate from the pre-industrial era to the present. An unsolved problem for the model calculations consists of how the water vapor mixing ratio at the hygropause should be specified during this period. We assume that the hygropause was dryer during pre-industrial times than the present. As a consequence of methane oxidation, the model simulation indicates that the middle atmosphere has become more humid as a result of the rising methane concentration, but with some dependence on height and with a small time delay of few years. The solar influence on the water vapor mixing ratio is insignificant below about 80 km in summer high latitudes, but becomes increasingly more important above this altitude. The enhanced water vapor concentration increases the hydrogen radical concentration and reduces the mesospheric ozone. A second region of stronger ozone decrease is located in the vicinity of the stratopause. Increases in CO2 concentration enhance slightly the concentration of CO in the mesosphere. However, its influence upon the chemistry is small and its main effect is connected with a cooling of the upper atmosphere. The long-term behavior of water vapor is discussed in particular with respect to its impact on the NLC region.

Pre-`Little Ice Age' glacier fluctuations in Garibaldi Provincial Park, Coast Mountains, British Columbia, Canada

Holocene glacier fluctuations prior to the `Little Ice Age' in Garibaldi Provincial Park in the British Columbia Coast Mountains were reconstructed from geomorphic mapping and radiocarbon ages on 37 samples of growth-position and detrital wood from glacier forefields. Glaciers in Garibaldi Park were smaller than at present in the early Holocene, although some evidence exists for minor, short-lived advances at this time. The first well-documented advance dates to 7700—7300 14C yr BP. Subsequent advances date to 6400—5100, 4300, 4100—2900 and 1600—1100 14C yr BP. Some glaciers approached their maximum Holocene limits several times during the past 10 000 years. Periods of advance in Garibaldi Park are broadly synchronous with advances elsewhere in the Canadian Cordillera, suggesting a common climatic cause. The Garibaldi Park glacier record is also broadly synchronous with the record of Holocene sunspot numbers, supporting previous research that suggests solar activity may be an important climate forcing mechanism.

Are solar cycles predictable?

AbstractVarious methods (or recipes) have been proposed to predict future solar activity levels – with mixed success. Among these, some precursor methods based upon quantities determined around or a few years before solar minimum have provided rather high correlations with the strength of the following cycles. Recently, data assimilation with an advection‐dominated (flux‐transport) dynamo model has been proposed as a predictive tool, yielding remarkably high correlation coefficients. After discussing the potential implications of these results and the criticism that has been raised, we study the possible physical origin(s) of the predictive skill provided by precursor and other methods. It is found that the combination of the overlap of solar cycles and their amplitude‐dependent rise time (Waldmeier's rule) introduces correlations in the sunspot number (or area) record, which account for the predictive skill of many precursor methods. This explanation requires no direct physical relation between the precursor quantity and the dynamo mechanism (in the sense of the Babcock‐Leighton scheme or otherwise). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Solar Magnetic Activity and Total Irradiance Since the Maunder Minimum

We develop a model for estimating solar total irradiance since 1600 AD using the sunspot number record as input, since this is the only intrinsic record of solar activity extending back far enough in time. Sunspot number is strongly correlated, albeit nonlinearly with the 10.7-cm radio flux (F10.7), which forms a continuous record back to 1947. This enables the nonlinear relationship to be estimated with usable accuracy and shows that relationship to be consistent over multiple solar activity cycles. From the sunspot number record we estimate F10.7 values back to 1600 AD. F10.7 is linearly correlated with the total amount of magnetic flux in active regions, and we use it as input to a simple cascade model for the other magnetic flux components. The irradiance record is estimated by using these magnetic flux components plus a very rudimentary model for the modulation of energy flow to the photosphere by the subphotospheric magnetic flux reservoir feeding the photospheric magnetic structures. Including a Monte Carlo analysis of the consequences of measurement and fitting errors, the model indicates the mean irradiance during the Maunder Minimum was about 1 ± 0.4 W m−2 lower than the mean irradiance over the last solar activity cycle.

Fluctuations in Babcock‐Leighton Dynamos. II. Revisiting the Gnevyshev‐Ohl Rule

The Gnevyshev-Ohl rule refers to apattern of alternating higher and lower than average solar cycle amplitudes observed in the sunspot number record. In this paper, we show that such a pattern arises naturally in Babcock-Leighton models of the solar cycle as a consequence of the long time delay built into the dynamo regenerative loop. This is investigated using a simple but well-validated iterative map formulation, as well as a seasoned two-dimensional axisymmetric kinematic dynamo model. The good agreement between the results obtained via these two very different modeling approaches offers confidence that Gnevyshev-Ohl–like patterns of cycle amplitude fluctuations are a robust feature of this class of solar cycle models. Subject headingg Sun: activity — Sun: magnetic fields 1. THE GNEVYSHEV-OHL RULE The recent international efforts in space weather forecasting have renewed interest in the origin of the fluctuations observed in the Sun’s magnetic activity cycle, including the prominent variations in the amplitude of the sunspot cycle observed in the past four centuries. The good correlation of the sunspot number time series with other long records of solar activity, such as the 10.7 cm solar radio flux and polar facular counts, leaves no doubt that these fluctuations are not restricted to sunspots, but also characterize the broader manifestations of solar activity.

Long-term solar activity reconstructions: direct test by cosmogenic $^{\mathsf{4}\mathsf{4}}$Ti in meteorites

Aims. Long-term solar activity in the past is usually estimated from cosmogenic isotopes, 10 Be or 14 C, deposited in terrestrial archives such as ice cores and tree rings. A number of such reconstruction models have been proposed which differ from each other significantly. This approach suffers, however, from uncertainties due to the sensitivity of the data to several terrestrial processes. Here we propose a method to constrain these solar activity reconstructions using cosmogenic 44 Ti activity in meteorites which is not affected by terrestrial processes. Methods. We test the veracity of recent solar activity reconstructions using the data on the activity of cosmogenic isotope 44 Ti in meteorites which fell during the past 235 years, and provide an independent and direct measure of the cosmic ray flux near the Earth and allow decoupling of solar activity variations from terrestrial influences. Results. We demonstrate that the 44 Ti data can distinguish between various reconstructions of past solar activity based on cosmogenic isotope data in terrestrial archives, allowing unrealistic models to be ruled out. We also show that a model based on the sunspot number record is consistent with the data on 44 Ti activity in meteorites, thus confirming the validity of the method. In particular the 44 Ti data confirm significant secular variations of the solar magnetic flux during the last century.

Was one sunspot cycle in the 18th century really lost?

The unusually long 4th solar cycle has recently been proposed by Usoskin et al. (2001) to be composed of two cycles. They argue that a weak and short cycle might have been lost in sparse sunspot data at the end of the 18th century. Here we check this hypothesis in different ways. First, we consider the sunspot number record in greater detail and compare in a statistical sense the sunspot observations of the period in question with those at other times. In a statistical sense the sunspot numbers recorded at the time of the proposed new cycle minimum are extremely untypical for other minima in the solar cycle record, but quite usual for the declining phase of the solar cycle. We also analyse other available proxies of solar activity, such as variations of the cosmogenic nuclides 10 Be and 14 C as well as auroral activity. These historical records are sufficiently long and provide an independent testimony of the cyclic behaviour of solar activity at the end of the 18th century. We found no evidence for a lost cycle in any of these data sets. Finally, we compare the proposed new cycle with the other cycles in the sunspot record. This reveals that the proposed missing cycle has very unusual properties, much more so than the original, standard cycle 4. Taken together, the evidence from these various tests strongly suggests that no cycle was missed and that the official sunspot cycle numbering and parameters are correct.

On the stability of the 11-year solar cycle period (and a few others)

The existence of an 11.1-yr periodic variation in the sunspot number record has been recognized for many years; however, periodicities other than this remain questionable. Power spectral analysis of the International sunspot number is performed and the results are compared with those for the same period using values that were taken randomly inside the error bars. The findings are that only a few periodicities show noticeable peaks. These include periodicities of 8.49, 10.01, 10.58, 11.10, 12.50, 58.50, and 97.20 yr. On the basis of these seven periodicities, one can loosely simulate the observable sunspot record (r = 0.75). We find that discrepancies in number and value of periodicities with other authors appear to be related to the length of the sunspot record used in the analysis and to the occurrence of 0.3-yr windows around the inferred periodicities.

Changes in Atmospheric Carbon-14 Attributed to a Variable Sun

The (14)C production rate in the upper atmosphere changes with time because the galactic cosmic-ray flux responsible for (14)C production is modulated by the changes in solar wind magnetic properties. The resulting changes in the atmospheric (14)C level are recorded in tree rings and are used to calculate past (14)C production rates from a carbon reservoir model that describes terrestrial carbon exchange between the atmosphere, ocean, and biosphere. These past (14)C production rate changes are compared with (14)C production rates determined from 20th-century neutron flux measurements, and a theory relating (14)C production and solar variability, as given by geomagnetic Aa indices and sunspot numbers, is developed. This theory takes into account long-term solar changes that were previously neglected. The 860-year (14)C record indicates three episodes when sunspots apparently were absent: A.D. 1654 to 1714 (Maunder minimum), 1416 to 1534 (Spörer minimum), and 1282 to 1342 (Wolf minimum). A less precisely defined minimum occurred near A.D. 1040. The part of this record after A.D. 1645 correlates well with the basic features of the historical record of sunspot numbers. The magnitude of the calculated (14)C production rates points to a further increase in cosmic-ray flux when sunspots are absent. This flux was greatest during the Spörer minimum. A record of approximate sunspot numbers and Aa indices for the current millennium is also presented.

The solar wind at the turn of the century

GEOMAGNETIC ACTIVITY is driven by the solar wind, so information on the past history of the wind can be derived from studies of geomagnetic indices1–3. Comparison of geomagnetic activity and sunspot number over the past hundred years shows that although both vary with the 11-yr solar cycle, they do so with characteristically different patterns. Geomagnetic activity rises and falls with about the same amplitude over each 11-yr solar cycle, but these variations seem to be superposed on a longer-term cycle of similar amplitude. Consequently there is a long-term variation in the 11-yr cycle minima as well as maxima. In contrast, in the sunspot number record the long cycle appears as changing amplitudes of the 11-yr cycles, with sunspot number returning to near zero at each 11-yr minimum. As geomagnetic activity reflects solar wind conditions, it is possible to extrapolate backwards in time the present-day solar wind measurements taken near the long-cycle maximum and we estimate here that around 1900, near the long-cycle minimum, either the average solar wind speed was as much as a factor of two lower, or the average southward component of the solar wind field was as much as a factor of three smaller, or both parameters were significantly less than at present. Thus, in the not too distant past the solar energy output by means of the solar wind was different from what it is now.