Grand Maximum Research Articles

Evolution of the solar irradiance during the Holocene

Aims. We present a physically consistent reconstruction of the total solar irradiance for the Holocene. Methods. We extend the SATIRE models to estimate the evolution of the total (and partly spectral) solar irradiance over the Holocene. The basic assumption is that the variations of the solar irradiance are due to the evolution of the dark and bright magnetic features on the solar surface. The evolution of the decadally averaged magnetic flux is computed from decadal values of cosmogenic isotope concentrations recorded in natural archives employing a series of physics-based models connecting the processes from the modulation of the cosmic ray flux in the heliosphere to their record in natural archives. We then compute the total solar irradiance (TSI) as a linear combination of the jth and jth + 1 decadal values of the open magnetic flux. Results. Reconstructions of the TSI over the Holocene, each valid for a di_erent paleomagnetic time series, are presented. Our analysis suggests that major sources of uncertainty in the TSI in this model are the heritage of the uncertainty of the TSI since 1610 reconstructed from sunspot data and the uncertainty of the evolution of the Earth's magnetic dipole moment. The analysis of the distribution functions of the reconstructed irradiance for the last 3000 years indicates that the estimates based on the virtual axial dipole moment are significantly lower at earlier times than the reconstructions based on the virtual dipole moment. Conclusions. We present the first physics-based reconstruction of the total solar irradiance over the Holocene, which will be of interest for studies of climate change over the last 11500 years. The reconstruction indicates that the decadally averaged total solar irradiance ranges over approximately 1.5 W/m2 from grand maxima to grand minima.

THE RISE AND FALL OF OPEN SOLAR FLUX DURING THE CURRENT GRAND SOLAR MAXIMUM

We use geomagnetic activity data to study the rise and fall over the past century of the solar wind flow speed V SW, the interplanetary magnetic field strength B, and the open solar flux F S. Our estimates include allowance for the kinematic effect of longitudinal structure in the solar wind flow speed. As well as solar cycle variations, all three parameters show a long-term rise during the first half of the 20th century followed by peaks around 1955 and 1986 and then a recent decline. Cosmogenic isotope data reveal that this constitutes a grand maximum of solar activity which began in 1920, using the definition that such grand maxima are when 25-year averages of the heliospheric modulation potential exceeds 600 MV. Extrapolating the linear declines seen in all three parameters since 1985, yields predictions that the grand maximum will end in the years 2013, 2014, or 2027 using V SW, F S, or B, respectively. These estimates are consistent with predictions based on the probability distribution of the durations of past grand solar maxima seen in cosmogenic isotope data. The data contradict any suggestions of a floor to the open solar flux: we show that the solar minimum open solar flux, kinematically corrected to allow for the excess flux effect, has halved over the past two solar cycles.

Forecasting the parameters of sunspot cycle 24 and beyond

Solar variability is controlled by the internal dynamo which is a non-linear system. We develop a physical–statistical method for forecasting solar activity that takes into account the non-linear character of the solar dynamo. The method is based on the generally accepted mechanisms of the dynamo and on recently found systematic properties of the long-term solar variability. The amplitude modulation of the Schwabe cycle in dynamo's magnetic field components can be decomposed in an invariant transition level and three types of oscillations around it. The regularities that we observe in the behaviour of these oscillations during the last millennium enable us to forecast solar activity. We find that the system is presently undergoing a transition from the recent Grand Maximum to another regime. This transition started in 2000 and it is expected to end around the maximum of cycle 24, foreseen for 2014, with a maximum sunspot number R max=68±17. At that time a period of lower solar activity will start. That period will be one of regular oscillations, as occurred between 1730 and 1923. The first of these oscillations may even turn out to be as strongly negative as around 1810, in which case a short Grand Minimum similar to the Dalton one might develop. This moderate-to-low-activity episode is expected to last for at least one Gleissberg cycle (60–100 years).

A History of Solar Activity over Millennia

AbstractPresented 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 10Be 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 verification and 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 to millennia) 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.

For how long will the current grand maximum of solar activity persist?

Understanding the Sun's magnetic activity is important because of its impact on the Earth's environment. The sunspot record since 1610 shows irregular 11‐year cycles of activity; they are modulated on longer timescales and were interrupted by the Maunder minimum in the 17th century. Future behavior cannot easily be predicted – even in the short‐term. Recent activity has been abnormally high for at least 8 cycles: is this grand maximum likely to terminate soon or even to be followed by another (Maunder‐like) grand minimum? To answer these questions we use, as a measure of the Sun's open magnetic field, a composite record of the solar modulation function Φ, reconstructed principally from the proxy record of cosmogenic 10Be abundances in the GRIP icecore from Greenland. This Φ record extends back for almost 10,000 years, showing many grand maxima and grand minima (defined as intervals when Φ is within the top or bottom 20% of a Gaussian distribution). We carry out a statistical analysis of this record and calculate the life expectancy of the current grand maximum. We find that it is only expected to last for a further 15–36 years, with the more reliable methods yielding shorter expectancies, and we therefore predict a decline in solar activity within the next two or three cycles. We are not able, however, to predict the level of the ensuing minimum.

Solar activity and its influence on climate

AbstractSolar activity, as manifested by its many equatorial as well as high-latitude components of short-term variability is regulated by the Sun’s dynamo. This constitutes an intricate interplay between the solar toroidal and poloidal magnetic field components. The dynamo originates in the tachocline, which is a thin layer situated about 200,000 km beneath the solar surface. The dynamo is a non-linear system with deterministic chaotic elements, hence in principle unpredictable. Yet there are regularities in the past behaviour, such as the Grand Maxima (example: the recent high maximum of the 2nd half of the 20th century) the Grand Minima (e.g. the Maunder Minimum between 1650 and 1710) and the Regular Oscillations such as those between 1730 and 1923. Their occurrences are described by a phase diagram in which a specific point can be identified: the Transition Point. This diagram plays an essential role in determining the future solar activity. Guided by its quasi-regularities and by recent measurements of the solar magnetic fields we find that the Sun is presently undergoing a transition between the past Grand Maximum and a forthcoming period of Regular Oscillations. We forecast that this latter period will start in a few years and will continue for at least one Gleissberg cycle and that the next solar maximum (expected for 2014) will be low (Rmax ~ 68).We discuss the heliospheric drivers of Sun-climate interaction and find that the low-latitude magnetic regions contribute most to tropospheric temperatures but that also the influence of the - so far always neglected - polar activity is significant. Subtraction of these components from the observed temperatures of the past 400 years shows a residual series of relative peaks and dips in the temperature. These tops and lows last for periods of the order of the Gleissberg cycle. One of these is the recent period of global warming, which, from this point of view, is not an exceptional period.

Grand minima and maxima of solar activity: new observational constraints

Using a reconstruction of sunspot numbers stretching over multiple millennia, we analyze the statistics of the occurrence of grand minima and maxima and set new observational constraints on long-term solar and stellar dynamo models. We present an updated reconstruction of sunspot number over multiple millennia, from $^{14}$C data by means of a physics-based model, using an updated model of the evolution of the solar open magnetic flux. A list of grand minima and maxima of solar activity is presented for the Holocene (since 9500 BC) and the statistics of both the length of individual events as well as the waiting time between them are analyzed. The occurrence of grand minima/maxima is driven not by long-term cyclic variability, but by a stochastic/chaotic process. The waiting time distribution of the occurrence of grand minima/maxima deviates from an exponential distribution, implying that these events tend to cluster together with long event-free periods between the clusters. Two different types of grand minima are observed: short (30--90 years) minima of Maunder type and long ($>$110 years) minima of Sp\"orer type, implying that a deterministic behaviour of the dynamo during a grand minimum defines its length. The duration of grand maxima follows an exponential distribution, suggesting that the duration of a grand maximum is determined by a random process. These results set new observational constraints upon the long-term behaviour of the solar dynamo.

Solar activity imprints in tree ring width from Chile (1610–1991)

We have investigated the solar activity signal in tree ring data from two locations in Chile. The tree ring time series extended over a period of ∼400 yr. Spectral and wavelet analysis techniques were employed. We have found evidence for the presence of the solar activity Schwabe (∼11 yr), Hale (∼22 yr), fourth-harmonic of the 208-yr Suess cycle (∼52 yr) and Gleissberg (∼80 yr) cycles. The Gleissberg cycle of tree ring data is in anti-phase with solar activity. Wavelet and cross-wavelet techniques revealed that the periods found are intermittent, possibly because solar activity signals observed in tree rings are mostly due to solar influence on local climate (rainfall, temperature, and cloud cover) where trees grow up. Further, cross-wavelet analysis between sunspot and tree ring time series showed that the cross power around the 11 yr solar cycle is more significant during periods of high solar activity (grand maximum) than during periods of low solar activity (grand minimum). As Glaciar Pio XI is practically at the Pacific Ocean level, the tree-ring response may be stronger due to the heating of the Pacific Ocean water following an increase of the solar radiation incidence rather than at the higher altitudes of Osorno region.

Understanding the origin of the solar cyclic activity for an improved earth climate prediction

This review is dedicated to the processes which could explain the origin of the great extrema of the solar activity. We would like to reach a more suitable estimate and prediction of the temporal solar variability and its real impact on the Earth climatic models. The development of this new field is stimulated by the SoHO helioseismic measurements and by some recent solar modelling improvement which aims to describe the dynamical processes from the core to the surface. We first recall assumptions on the potential different solar variabilities. Then, we introduce stellar seismology and summarize the main SOHO results which are relevant for this field. Finally we mention the dynamical processes which are presently introduced in new solar models. We believe that the knowledge of two important elements: (1) the magnetic field interplay between the radiative zone and the convective zone and (2) the role of the gravity waves, would allow to understand the origin of the grand minima and maxima observed during the last millennium. Complementary observables like acoustic and gravity modes, radius and spectral irradiance from far UV to visible in parallel to the development of 1D–2D–3D simulations will improve this field. PICARD, SDO, DynaMICCS are key projects for a prediction of the next century variability. Some helioseismic indicators constitute the first necessary information to properly describe the Sun–Earth climatic connection.

Behavior of the ionosphere and thermosphere subject to extreme solar cycle conditions

A 1‐D global average ionosphere and thermosphere (GAIT) model is used to examine the climatological behavior of the upper atmosphere, subject to both extremely low and high solar flux. These extremes are justified, in part, by the Maunder Minimum and Grand Maximum epochs described by J. A. Eddy, as well as other studies involving cosmogenic isotopes and Sun‐like stars. As the irradiance falls below normal solar minimum levels, the concentration of O+ decreases rapidly relative to the molecular ions, such that the ratio foF2/foF1 approaches unity. When subject to exceptionally high solar fluxes, the ionospheric peak electron density (NmF2) unexpectedly plateaus, remaining relatively constant even as the photon flux continues to increase. In both cases, the state of the underlying thermosphere, particularly the neutral gas temperature, is found to be largely responsible. Model trends are discussed in relation to ionospheric observations, specifically the preponderance of so‐called ionospheric G conditions at solar minimum and foF2 saturation at solar maximum, as well as the problem of Earth's global helium budget.

Deep minima in stellar dynamos

We study a Cartesian analogy for a solar dynamo model to investigate systematically a dynamo model limited by the back reaction of the Lorentz force on the dierential rotation. In particular, we investigate intermittent behaviour found at low turbulent magnetic Prandtl numbers, and determine empirical scaling laws with. We find this class of models to be incapable of producing extended periods of normal behaviour separated by occasional grand minima - rather the behaviour is a mirror image, with occasional grand maxima. Further we find the existence of solar-like torsional oscillations to be incompatible with low magnetic Prandtl number intermittent regimes.

Measuring the Existence Value of Wildlife: Reply

We know little about the motives underlying individual responses to contingent valuation (CV) questions concerning the existence of wildlife. Yet, motives are important because they determine how the resulting value estimates should be interpreted and used in making management decisions. For example, zero bids are very common in CV, but these are often protests that do not represent zero valuation for the resource itself. Protest zero bids may be particularly prevalent in wildlife existence value studies because some people may view trade-offs between money and wildlife as unethical or immoral. If protest zero bids are not interpreted correctly, existence value estimates obviously will be biased. The motives underlying positive CV bids also matter. Unfortunately, these motives have received much less research attention and so may be more controversial. Our study of wildlife values in New England suggests that many respondents who gave positive bids were motivated by ethical concerns, altruism, or the desire to do their fair share-concerns that indicate they used decision-making processes inconsistent with the neoclassical paradigm (Stevens et al. 1991). CV results may therefore fail to measure the economic value of existence in traditional terms. The Bergson-Tintner-Samuelson formulation presented by Kohn (1993) is useful in this context because it attempts to disentangle behavior motivated by ethical concerns about existence from preferences about wildlife use. Each individual is assumed to wear two hats: one as citizen, the other as consumer. From this perspective citizens express social values, which may be ethically driven, while economic values are expressed by consumers. Kohn suggests that we make use of this distinction by first asking respondents, as citizens, to make implicit trade-offs between income and the preservation of wildlife. Respondents are then asked about their willingness to pay for the option of consuming wildlife. While this is an interesting proposal, the Bergson-Tintner-Samuelson framework is only one of several alternative theories about behavior involving ethical considerations. For discussion, these theories can be classified into three groups: (a) theories of social or group interest, (b) natural rights, and (c) theories based upon the neoclassical model of self interest. Social interest theories include the Bergson-Tintner-Samuelson formulation outlined by Kohn and the dual utilities model proposed by Margolis (1982). Margolis suggests that people are motivated by two basic concerns; (a) self-interest and (b) social or group interest. Social interest, which pertains to the welfare of society as a whole, is assumed to be governed in part by ethics, moral duty, and commitment. Expressions of social interest include charity, participation in the political process (voting), and contributions for the provision of public goods. Margolis maintains that the neoclassical theory of self-interest generally fails to adequately explain individual behavior about social interests, and he proposes a dual utilities model of individual preferences in which people have irreducibly distinct social and private preferences. Unlike the framework proposed by Kohn, there is no grand maximum where social value is traded off against private value. Rather individuals are assumed to allocate income between social and private preferences so as to do their fair share for the welfare of society as a whole. Con-

Bimodality of the solar cycle

For sunspot cycles 1‐20 (1755‐1976), all cycles occurred in strings (two to six cycles in length) during which the period remained longer or shorter than the sample mean period. These strings have coincided with long‐term trends of growth or decay in the amplitude of the cycle. In six out of six cases, the period of the cycle has switched from long to short (or the reverse) in coincidence with turning points in the long‐term trend. This suggests that the solar dynamo has two modes with different mean periods. In the short‐period mode, the amplitude of the cycle grows; in the long‐period mode, the amplitude decays. The transition between modes has occurred at irregular intervals. A persistence of the long‐period mode would eventually produce a grand minimum such as the Maunder minimum; a persistence of the short‐period mode would produce a grand maximum. Unless the present interval between transitions turns out to be shorter than any previously observed interval, the present cycle (cycle 21) is part of a long‐period, decaying trend and will be of longer‐than‐average duration (>133 months).

The solar-cycle period-amplitude relation as evidence of hysteresis of the solar-cycle nonlinear magnetic oscillation and the long-term /55 year/ cyclic modulation

A new dynamical model of the solar cycle has predicted that the cycle should have a hysteretic nature: the behavior of each 11 year cycle should depend on previous cycles. In the light of this new understanding of the dynamical mechanism of the solar cycle, Waldmeier's (hypothetical) law was examined as a yet unexplained characteristic of the cycle by studying the observed sunspot frequency curve. Contrary to this hypothetical law, however, it was found that sunspot cycle curves did not form a single-parameter family characterized by the maximum amplitude of the cycle. The evolutionary trajectories in period-amplitude phase space verified the hysteretic nature of the observed cycle and revealed long-term (55 year instead of the previously claimed 80 year) periodic modulations, called here 55 year grand cycles. Each 55 year grand cycle forms a loop in the phase space, and the characteristics of each 11 year cycle depend on its position in the ascending or descending phase of the grand cycle. This new law was analyzed by the nonlinear multiple-period dynamo oscillation model which has predicted the hysteretic nature. The era from cycle 11 to cycle 15 turned out to be an anomalous one characterized by alternating amplitudes for oddmore » and even cycles. Cycles 16--20 seem to constitute one grand cycle. If this is true, cycle 21 would be the beginning of another grand maximum and the model predicts that its duration would be short.« less