A Simple Model to Describe Solar Cycle Periodicities below 11 Years

Together with the main 11-year cycle, solar activity also displays intracycle periodicities. A simple nonlinear model that describes the 11-year solar cycle with subperiodicities can be derived from the usual α – ω dynamo theory in the form of a Van der Pol equation with a forcing term. In this paper the results obtained from the Van der Pol oscillator describing the amplitude modulations and periodicities observed from the data set of the global daily coronal emission of the Fe xiv line at 530.3 nm are presented.     

第22和23太阳周太阳活动预测

本文首先分析指出第22太阳周前半周的太阳活动所具有的特点:(1)有最高的起始极小值;(2)上升速度快;(3)升段时间最短;(4)峰期长,可能有双峰;(5)个别时段活动水平极高.然后对第22周后半周的活动情况做了预计:在后半周将可能观测到大约2800个活动区,28000个耀斑,210个X级X射线爆发和大约80次太阳质子事件.最后,应用本文给出的太阳周参量关系式.预报第23周太阳黑子数月均平滑值的峰值为119,位于2001.6年.     

Simple Model of a Stochastically Excited Solar Dynamo

The aim of this paper is to investigate the dynamical nature of the complexity observed in the time evolution of the sunspot number. We report a detailed analysis of the sunspot number time series, and use the daily records to build the phase space of the underlying dynamical system. The observed features of the phase space prompted us to describe the global behavior of the solar cycle in terms of a noise-driven relaxation oscillator. We find the equations whose solutions best fit the observed series, which adequately describe the shape of the peaks and the oscillations of the system. The system of equations obtained from this fitting procedure is shown to be equivalent to a truncation of the dynamo equations. A linear transformation maps the phase space of these equations into the phase space reconstructed from the observations. The irregularities of the solar cycle were modeled through the introduction of a stochastic parameter in the equations to simulate the randomness arising in the process of eruption of magnetic flow to the solar surface. The mean values and deviations obtained for the periods, rise times and peak values, are in good agreement with the values obtained from the sunspot time series.     

Prediction of Solar Cycle Maximum Using Solar Cycle Lengths

If the rise time RT, fall time FT, and total time TT (i.e., RT+FT) of a solar cycle are compared against the maximum amplitude Rz(max ) for the following cycle, then only the association between TT and Rz(max ) is inferred to be well anticorrelated, inferring that the larger (smaller) the value of Rz(max ) for the following cycle, the shorter (longer) the TT of the preceding cycle. Although the inferred correlation (−0.68) is statistically significant, the inferred standard error of estimate is quite large, so predictions using the inferred correlation are not very precise. Removal of cycle pairs 15/16, 19/20, and 20/21 (statistical outliers) yields a regression that is highly statistically significant (−0.85) and reduces the standard error of estimate by 18%. On the basis of the adjusted regression and presuming TT=140 months for cycle 23, the present ongoing cycle, cycle 24’s 90% prediction interval for Rz(max ) is estimated to be about 94±44, inferring only a 5% probability that its Rz(max ) will be larger than about 140, unless of course cycle pair 23/24 is a statistical outlier.     

A Prediction of the Peak Sunspot Number for Solar Cycle 23

We use a precursor technique based on the geomagneticaa index during the decline (last 30%) of solar cycle 22 to predict a peak sunspot number of 158 (± 18) for cycle 23, under the assumption that solar minimum occurred in May 1996. This method appears to be as reliable as those that require a year of data surrounding the geomagnetic minimum, which typically follows the smoothed sunspot minimum by about six months.     

Solar Cycle Workshop

Conclusion Clearly there is no concensus or agreement at present about the nature and mechanism of the solar cycle or, indeed, about many of its observed features. However, by highlighting these areas of agreement and disagreement through the presentations and discussions during this meeting, it is hoped that the work of the Workshop Groups will be directed to resolving at least some of these questions at or before the next meeting (planned for August, 1987). In particular, it is hoped that Group V (The Sun as a Star) will be able to contribute through studies of the sun in relation to stellar cycles and activity.     

A Transfer Function Model for the Sunspot Cycle

The mean annual sunspot record for the time interval 1700–2002 can be considered as a sequence of independent, partly overlapping events, triggered quasi-periodically at intervals of the order of 11 years. The individual cycles are approximated by the step response of a band-pass dynamical system and the resulting model consists of the superposition of the response to the independent pulses. The simulated sunspot data explain 98.4% of the cycle peak height variance and the residual standard deviation is 8.2 mean annual sunspots. An empirical linear relationship is found between the amplitude of the transfer function model for each cycle and the pulse interval of the preceding cycle that can be used as a tool of short-term forecasting of solar activity. A peak height of 112 for the solar cycle 23 occurring in 2000 is predicted, whereas the next cycle would start at about 2007 and will have a maximum around 110 in 2011. Cycle 24 is expected to have an annual mean peak value in the range 95 to 125. The model reproduces the high level of amplitude modulation in the interval 1950–2000 with a decrease afterwards, but the peak values for the cycles 18, 19, 21, and 22 are fairly underestimated. The semi-empirical model also recreates recurring sunspot minima and is linked to the phenomenon of the reversal of the solar magnetic field.     

Solar Cycle Workshop

The presentations and discussions which took place during the second meeting of the Solar Cycle Workshop are summarized under the headings: sunspot minimum, the extended cycle, the large-scale photospheric motions, the large-scale magnetic fields and the polar reversal, the small-scale fields, global cyclic phenomena and the fundamental processes. The progress achieved so far is assessed and the directions for future observational and theoretical work are suggested.     

A Note on Solar Cycle Length Estimates

Recently, new estimates of the solar cycle length (SCL) have been calculated using the Zurich Sunspot Number (R_Z) and the Regression-Fourier-Calculus (RFC)-method, a mathematically rigorous method involving multiple regression, Fourier approximation, and analytical expressions for the first derivative. In this short contribution, we show estimates of the solar cycle length using the RFC-method and the Group Sunspot Number (R_G) instead the R_Z. Several authors have showed the advantages of R_G for the analysis of sunspot activity before 1850. The use of R_G solves some doubtful solar cycle length estimates obtained around 1800 using R_Z.     

Flattening Index of the Solar Corona and the Solar Cycle

The photometrical flattening index of the solar corona a+b is defined according to Ludendorff. In this paper we have investigated how the flattening index varies with respect to the phase of solar activity and the sunspot number. We have compiled 170 values of the flattening index using the data on 60 total solar eclipses from 1851 to 2010. We have found that the flattening index takes values from 0 to 0.4, and is anticorrelated with solar activity. The value of the flattening index at the beginning of solar cycle 24 was used as a precursor to forecast the amplitude of the cycle. It was found that the amplitude of solar cycle 24 will be about 95 in terms of the smoothed monthly sunspot numbers.     

The Solar Cycle Workshop

The contributions to the third meeting of the Solar Cycle Workshop are briefly summarized. The topics discussed at the meeting included (i) predictions and precursors, (ii) large and small-scale magnetic fields, (iii) photospheric velocity fields, (iv) coronal phenomena, (v) the Sun as a star, (vi) limb temperature measurements and helioseismic data, (vii) theoretical modelling of the cycle, (viii) cyclic activity in stars, and (ix) the interpretation of the Elatina Sandstone Layers.This paper was presented at the third meeting of the Solar Cycle Workshop, held in Sydney, Australia, January 9–13, 1989.     

A Complete Catalogue of High-Speed Solar Wind Streams during Solar Cycle 23

High-speed solar wind streams (HSSWSs) are ejected from the Sun and travel into the interplanetary space. Because of their high speed, they carry out energetic particles such as protons and heavy ions, which leads to an increase in the mean interplanetary magnetic field (IMF). Since the Earth is in the path of those streams, Earth’s magnetosphere interacts with the disturbed magnetic field, leading to a significant radiation-induced degradation of technological systems. These interactions provide an enhanced energy transfer from the solar wind/IMF system into the Earth’s magnetosphere and initiate geomagnetic disturbances that may have a possible impact on human health. Solar cycle 23 was a particularly unusual cycle with many energetic phenomena during its descending phase and also had an extended minimum. We have identified and catalogued the HSSWSs of this cycle and determined their characteristics, such as their maximum velocity, beginning and ending time, duration, and possible sources. We identified 710 HSSWSs and compared them with the corresponding characteristics of the streams of previous solar cycles. For first time, we used the CME data to study the stream sources, which led to useful results for the monitoring and forecasting of space weather effects.     

Modulation of the Solar Magnetic Cycle

The modulation model of the solar magnetic cycle for the time interval from 1650 to 1996 A.D. describes an harmonic oscillator with a basic (22.13 ± 0.05)-yr period, which is subjected to amplitude and phase variations that can be represented by a sum of trigonometric series. The simulated sunspot data explain 97.9% of cycle peak height variance and the residual standard deviation is 8.6 mean annual sunspots. A peak height of 139 for cycle 23 occurring in 2001 is predicted, whereas cycle 24 would have a maximum around 132 in 2014. Simulation of the sunspot numbers from 1000 until 2400 A.D. shows that the model recreates recurring minima (Maunder and Spörer Minimum). The prediction also expects a high level of amplitude modulation in the interval 1950–2010 with a rapid decrease afterwards. A greatly reduced cycle activity is reproduced by the simulation from about 2065 to 2100 A.D. No direct explanation of the long-term periodicities of the model can be advanced. The high-frequency contribution of the phase modulation, which accounts for the skewness of the solar cycle, shows coincidences with the orbital periods of Jupiter and Saturn, but no physical basis for the matching periodicities can be conceived.     

A Study of the Earth-Affecting CMEs of Solar Cycle 24

Using in situ observations from the Advanced Composition Explorer (ACE), we have identified 70 Earth-affecting interplanetary coronal mass ejections (ICMEs) in Solar Cycle 24. Because of the unprecedented extent of heliospheric observations in Cycle 24 that has been achieved thanks to the Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI) instruments onboard the Solar Terrestrial Relations Observatory (STEREO), we observe these events throughout the heliosphere from the Sun to the Earth, and we can relate these in situ signatures to remote sensing data. This allows us to completely track the event back to the source of the eruption in the low corona. We present a summary of the Earth-affecting CMEs in Solar Cycle 24 and a statistical study of the properties of these events including the source region. We examine the characteristics of CMEs that are more likely to be strongly geoeffective and examine the effect of the flare strength on in situ properties. We find that Earth-affecting CMEs in the first half of Cycle 24 are more likely to come from the northern hemisphere, but after April 2012, this reverses, and these events are more likely to originate in the southern hemisphere, following the observed magnetic asymmetry in the two hemispheres. We also find that as in past solar cycles, CMEs from the western hemisphere are more likely to reach Earth. We find that Cycle 24 lacks in events driving extreme geomagnetic storms compared to past solar cycles.     

On the Possibility for Action Conservation in the Solar Cycle

The sunspot series are investigated in detail by use of a wavelet transform. By simple arguments, we present a reduced sunspot time-series, which can be argued to be approximately proportional to the magnetic flux density at the coronal surface. This reduced sunspot index correctly reproduces the (average) 22 year solar cycle. Closer scrutiny of the sunspot variation shows that the frequency of the solar cycle and the energy in the magnetic field vary consistently with conservation of action, i.e., energy divided by frequency. The analysis is based on the available data beginning with the year 1700, and analyzed by a wavelet transform. The present results relate to observations reported previously in the literature.     

Solar Rotation Rate during Solar Activity Cycle 23

We studied the solar rotation rate and its temporal change, using the sunspot data obtained during activity cycle 23 (1996 – 2006). The equatorial rotation rate is nearly the same as in the former cycle 22, while the latitudinal gradient of differential rotation considerably increased. Comparison of our results with others indicates the existence of a long-term periodicity of about eight cycles in differential rotation. In addition, no significant asymmetry in differential rotation between the northern and southern hemispheres during cycle 23 was found. The equatorial rotation rate and the latitudinal gradient of the differential rotation in the period of cycle 23 are approximately constant, except for the initial and final phases in the cycle.     

Multiperiodicity, Chaos, and Intermittency in a Reduced Model of the Solar Cycle

In a recent paper, Durney (2000) has discussed a physically plausible procedure whereby the dynamo equations describing magnetic field regeneration in Babcock–Leighton models of the solar cycle can be reduced to a one-dimensional iterative map. This procedure is used here to investigate the behavior of various dynamo-inspired maps. Durney's explanation of the so-called odd–even effect in sunspot cycle peak amplitudes, which he ascribed to a period-2 limit cycle, is found to be robust with respect the choice of nonlinearity defining the map, and to the action of strong stochastic forcing. In fact, even maps without limit cycles are found to show a strong odd–even signal in the presence of forcing. Some of the stochastically forced maps are found to exhibit a form of on-off intermittency, with periods of activity separated by quiescent phases of low cycle amplitudes. In one such map, a strong odd–even signal is found to be a good precursor to the transition from bursting to quiescent behavior.     

A Running Average Method for Predicting the Size and Length of a Solar Cycle

The running correlation coefficient between the solar cycle amplitudes and the max-max cycle lengths at a given cycle lag is found to vary roughly in a cyclical wave with the cycle number, based on the smoothed monthly mean Group sunspot numbers available since 1610. A running average method is proposed to predict the size and length of a solar cycle by the use of the varying trend of the coefficients. It is found that, when a condition (that the correlation becomes stronger) is satisfied, the mean prediction error (16.1) is much smaller than when the condition is not satisfied (38.7). This result can be explained by the fact that the prediction must fall on the regression line and increase the strength of the correlation. The method itself can also indicate whether the prediction is reasonable or not. To obtain a reasonable prediction, it is more important to search.for a running correlation coefficient whose varying trend satisfies the proposed condition, and the result does not depend so much on the size of the correlation coefficient. As an application, the peak sunspot number of cycle 24 is estimated as 140.4±15.7, and the peak as May 2012± 11 months.     

A Note on Solar Cycle Length During the Medieval Climate Anomaly

The growing interest in the Medieval Climate Anomaly (MCA) and its possible link to anomalous solar activity has prompted new reconstructions of solar activity based on cosmogenic radionuclides. However, these proxies do not sufficiently constrain the total solar irradiance (TSI) range and are often defined at low temporal resolution, inadequate to infer the solar-cycle length (SCL). We have reconstructed the SCL (average duration of 10.72±0.20 years) during the MCA using observations of naked-eye sunspot and aurora sightings. The solar activity was probably not exceptionally intense, supporting the view that internal variability of the coupled ocean–atmosphere system was the main driver of the MCA.