An Estimate for the Size of Cycle 23 Using Multivariate Relationships

A new technique based on multivariate analysis is described which allows for the prediction of the size or maximum amplitude of cycle 23. The technique uses the number of geomagnetic disturbances at selected times during the decline of cycle 22 (as precursors) to predict a maximum of about 152 (in terms of smoothed monthly mean sunspot numbers) for cycle 23. On the basis of this technique, hindcasts for cycles 17–22 are shown to agree with observed values within 5%.     

An Early Prediction of Maximum Sunspot Number in Solar Cycle 24

A non-linear coupling function between sunspot maxima and aa minima modulations has been found as a result of a wavelet analysis of geomagnetic index aa and Wolf sunspot number yearly means since 1844. It has been demonstrated that the increase of these modulations for the past 158 years has not been steady, instead, it has occurred in less than 30 years starting around 1923. Otherwise sunspot maxima have oscillated about a constant level of 90 and 141, prior to 1923 and after 1949, respectively. The relevance of these findings regarding the forecasting of solar activity is analyzed here. It is found that if sunspot cycle maxima were still oscillating around the 141 constant value, then the Gnevyshev–Ohl rule would be violated for two consecutive even–odd sunspot pairs (22–23 and 24–25) for the first time in 1700 years. Instead, we present evidence that solar activity is in a declining episode that started about 1993. A value for maximum sunspot number in solar cycle 24 (87.5±23.5) is estimated from our results.     

Prediction of Solar Cycle 24 Using Sunspot Number near the Cycle Minimum

Correlations between monthly smoothed sunspot numbers at the solar-cycle maximum [R _max] and duration of the ascending phase of the cycle [T _rise], on the one hand, and sunspot-number parameters (values, differences and sums) near the cycle minimum, on the other hand, are studied. It is found that sunspot numbers two?–?three years around minimum correlate with R _max or T _rise better than those exactly at the minimum. The strongest correlation (Pearson’s r=0.93 with P<0.001 and Spearman’s rank correlation coefficient r _S=0.95 with P=9×10^?12) proved to be between R _max and the sum of the increase of activity over 30 months after the cycle minimum and the drop of activity over 30 or 36 months before the minimum. Several predictions of maximal amplitude and duration of the ascending phase for Solar Cycle 24 are given using sunspot-number parameters as precursors. All of the predictions indicate that Solar Cycle 24 is expected to reach a maximal smoothed monthly sunspot number (SSN) of 70?–?100. The prediction based on the best correlation yields the maximal amplitude of 90±12. The maximum of Solar Cycle 24 is expected to be in December 2013?–?January 2014. The rising and declining phases of Solar Cycle 24 are estimated to be about 5.0 and 6.3 years, respectively. The minimum epoch between Solar Cycles 24 and 25 is predicted to be at 2020.3 with minimal SSN of 5.1?–?5.4. We predict also that Solar Cycle 25 will be slightly stronger than Solar Cycle 24; its maximal SSN will be of 105?–?110.     

Group Sunspot Numbers: Sunspot Cycle Characteristics

We examine the `Group' sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group sunspot numbers to Zürich (International) sunspot numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zürich numbers follow the 10.7-cm radio flux and total sunspot area measurements only slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zürich numbers. We find that the `Waldmeier Effect' – the anti-correlation between cycle amplitude and the elapsed time between minimum and maximum of a cycle – is much more apparent in the Zürich numbers. The `Amplitude–Period Effect' – the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum – is also much more apparent in the Zürich numbers. The `Amplitude–Minimum Effect' – the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zürich numbers and the Group numbers. The `Even–Odd Effect' – in which odd-numbered cycles are larger than their even-numbered precursors – is somewhat stronger in the Group numbers but with a tighter relationship in the Zürich numbers. The `Secular Trend' – the increase in cycle amplitudes since the Maunder Minimum – is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80-year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zürich numbers are slightly more useful for characterizing the on-going levels of solar activity.     

A Preliminary Estimate of the Size of the Coming Solar Cycle 24, based on Ohl’s Precursor Method

For many purposes (e.g., satellite drag, operation of power grids on Earth, and satellite communication systems), predictions of the strength of a solar cycle are needed. Predictions are made by using different methods, depending upon the characteristics of sunspot cycles. However, the method most successful seems to be the precursor method by Ohl and his group, in which the geomagnetic activity in the declining phase of a sunspot cycle is found to be well correlated with the sunspot maximum of the next cycle. In the present communication, the method is illustrated by plotting the 12-month running means aa(min ) of the geomagnetic disturbance index aa near sunspot minimum versus the 12-month running means of the sunspot number Rz near sunspot maximum [aa(min ) versus Rz(max )], using data for sunspot cycles 9 – 18 to predict the Rz(max ) of cycle 19, using data for cycles 9 – 19 to predict Rz(max ) of cycle 20, and so on, and finally using data for cycles 9 – 23 to predict Rz(max ) of cycle 24, which is expected to occur in 2011 – 2012. The correlations were good (∼+0.90) and our preliminary predicted Rz(max ) for cycle 24 is 142±24, though this can be regarded as an upper limit, since there are indications that solar minimum may occur as late as March 2008. (Some workers have reported that the aa values before 1957 would have an error of 3 nT; if true, the revised estimate would be 124±26.) This result of the precursor method is compared with several other predictions of cycle 24, which are in a very wide range (50 – 200), so that whatever may be the final observed value, some method or other will be discredited, as happened in the case of cycle 23.     

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.     

Prediction of the Amplitude of Sunspot Cycle 23

A few prediction methods have been developed using the precursor techniques and are found to be successful. On the basis of geomagnetic activity aa indices during the descending phase of the preceding cycle, we have established an expression which predicts the maximum annual mean sunspot number in cycle 23 to be 166.2. This indicates that cycle 23 would be a highly active and historic cycle. The average geomagnetic activity aa index during the ascending phase of cycle 23 would be about 24.9, comparable to 22.2 and 24.8 in cycles 21 and 22, respectively. This further indicates that during the ascending phase of cycle 23 energetic two-ribbon flares will be produced so as to give rise to strong proton events.     

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.     

Estimating the Size and Timing of the Maximum Amplitude of Solar Cycle 24

A simple statistical method is used to estimate the size and timing of maximum amplitude of the next solar cycle (cycle 24). Presuming cycle 23 to be a short cycle (as is more likely), the minimum of cycle 24 should occur about December 2006 (±2 months) and the maximum, around March 2011 (±9 months), and the amplitude is 189.9 ±15.5, if it is a fast riser, or about 136, if it is a slow riser. If we presume cycle 23 to be a long cycle (as is less likely), the minimum of cycle 24 should occur about June 2008 (±2 months) and the maximum, about February 2013 (±8 months) and the maximum will be about 137 or 80, according as the cycle is a fast riser or a slow riser.     

Evolution of Sunspot Characteristics in Cycle 23

The aim of this work is to present a statistical study of several parameters (variables) that define sunspot groups. These variables include maximum area, growth and decay times, as well as the evolution families, and solar-cycle phase the groups belong to. We classified group types based on the Zurich classification, which allows us to define a set of families based on their evolution patterns. The time variation of the area of a group was also studied, and a relationship between the maximum area and the growth and decay times was sought. Another study was carried out to find the correlation among different characteristics of the groups, as well as how the probability of a certain value of decay time can vary depending on morphological characteristics defined by these variables. Thus, a program based on a weight matrix combining the variables necessary to classify a group, together with the calculation of the probability for a specific event, has been produced. This approach allows us to predict the future behavior of a group from its historical evolution.     

太阳黑子的世纪周期及对24、25活动周的预报

太阳活动除了具有公认的11 a周期以外,还存在着一个80～120 a变化的世纪周期,也称为Gleissberg周期.使用傅里叶变换和小波分析的方法,分析了1700～2008年的年均黑子数世纪周期的变化规律.得到结果:在太阳活动世纪周期的低谷期,所对应11 a太阳周的极大年和极小年的黑子数目都比其他太阳周的低.在这300多年里,世纪周期的周期长度也有变化.由世纪周期的变化趋势,预测第24、25太阳活动周将处于世纪周期的低谷期.通过对以前3个世纪周期的谷期黑子数求平均的方法,得到第24,25太阳周极大年年均黑子数为63.6±21.1,极小年的为2.2±2.1.这些结果有助于理解当前太阳活动反常宁静这一现象.     

The Behavior of Sunspot Contrast during Cycle 23

Results are presented from a study of various sunspot contrast parameters in broadband red (672.3 nm) Cartesian full-disk digital images taken at the San Fernando Observatory (SFO) over eight years, 1997 – 2004, of the twenty-third sunspot cycle. A subset of over 2700 red sunspots was analyzed and values of average and maximum sunspot contrast as well as maximum umbral contrast were compared to various sunspot parameters. Average and maximum sunspot contrasts were found to be significantly correlated with sunspot area (r _s=− 0.623 and r _s=− 0.714, respectively). Maximum umbral contrast was found to be significantly correlated with umbral area (r _s=− 0.535). These results are in agreement with the works of numerous other authors. No significant dependence was detected between average contrast, maximum contrast, or maximum umbral contrast during the rising phase of the solar cycle (r _s=0.024, r _s=0.033, and r _s=0.064, respectively). During the decay phase, no significant correlation was found between average contrast or maximum contrast and time (r _s=− 0.057 and r _s=0.009, respectively), with a weak dependence seen between maximum umbral contrast and cycle (r _s=0.102).     

Extrema in Sunspot Cycle Linked to Sun's Motion

Partitions of 178.8-year intervals between instances of retrograde motion in the Sun's oscillation about the center of mass of the solar system seem to provide synchronization points for the timing of minima and maxima in the 11-year sunspot cycle. In the investigated period 1632–1990, the statistical significance of the relationship goes beyond the level P=0.001. The extrapolation of the observed pattern points to sunspot maxima around 2000.6 and 2011.8. If a further connection with long-range variations in sunspot intensity proves reliable, four to five weak sunspot cycles (R0) are to be expected after cycle 23 with medium strength (R100).     

预报第23周平滑月平均太阳黑子数的一种方法

利用已知的22个完整太阳活动周平滑月平均黑子数的记录，对正在进行的太阳周发展趋势给出了预测方法，并应用于第23周，同时与其他预报方法的结果进行了比较。     

Tilt of Sunspot Bipoles in Solar Cycles 15 to 24

We use recently digitized sunspot drawings from Mount Wilson Observatory to investigate the latitudinal dependence of tilt angles of active regions and its change with solar cycle. The drawings cover the period from 1917 to present and contain information as regards polarity and strength of magnetic field in sunspots. We identified clusters of sunspots of same polarity, and used these clusters to form “bipole pairs”. The orientation of these bipole pairs was used to measure their tilts. We find that the latitudinal profile of tilts does not monotonically increase with latitude as most previous studies assumed, but instead, it shows a clear maximum at about 25?–?30 degree latitudes. Functional dependence of tilt (\(\gamma\)) on latitude (\(\varphi\)) was found to be \(\gamma= (0.20\pm0.08) \sin(2.80 \varphi) + (-0.00\pm0.06)\). We also find that latitudinal dependence of tilts varies from one solar cycle to another, but larger tilts do not seem to result in stronger solar cycles. Finally, we find the presence of a systematic offset in tilt of active regions (non-zero tilts at the equator), with odd cycles exhibiting negative offset and even cycles showing the positive offset.     

Correlation Function Analysis between Sunspot Cycle Amplitudes and Rise Times

The running cross-correlation coefficient between solar-cycle amplitudes and rise times at a certain cycle lag is found to vary in time, when using the smoothed monthly-mean sunspot group numbers available for 1610 – 1995. It may be negative or positive for different periods of time. The Waldmeier effect (in which the rise times decrease with amplitude) is also found to be very weak for some cycles. This result represents an observational constraint on solar-dynamo models and can help us better understand the long-term evolution of solar activity.     

A New Method for Prediction of Peak Sunspot Number and Ascent Time of the Solar Cycle

The purpose of the present study is to develop an empirical model based on precursors in the preceding solar cycle that can be used to forecast the peak sunspot number and ascent time of the next solar cycle. Statistical parameters are derived for each solar cycle using “Monthly” and “Monthly smoothed” (SSN) data of international sunspot number (R _i). Primarily the variability in monthly sunspot number during different phases of the solar cycle is considered along with other statistical parameters that are computed using solar cycle characteristics, like ascent time, peak sunspot number and the length of the solar cycle. Using these statistical parameters, two mathematical formulae are developed to compute the quantities [Q _C] _n and [L] _n for each nth solar cycle. It is found that the peak sunspot number and ascent time of the n+1th solar cycle correlates well with the parameters [Q _C] _n and [L] _n /[S _Max] _n+1 and gives a correlation coefficient of 0.97 and 0.92, respectively. Empirical relations are obtained using least square fitting, which relates [S _Max] _n+1 with [Q _C] _n and [T _a] _n+1 with [L] _n /[S _Max] _n+1. These relations predict a peak of 74±10 in monthly smoothed sunspot number and an ascent time of 4.9±0.4 years for Solar Cycle 24, when November 2008 is considered as the start time for this cycle. Three different methods, which are commonly used to define solar cycle characteristics are used and mathematical relations developed for forecasting peak sunspot number and ascent time of the upcoming solar cycle, are examined separately.     

Nature of Tilt Angles of Sunspot Groups During the 22nd Solar Cycle

Daily white-light images from Kodaikanal Observatory have been utilized to study the nature of tilt angles of sunspot groups during the 22nd solar cycle. 2416 spot groups have been measured to find the tilt angle. An average tilt angle of +4.6 ± 0.4 deg has been obtained for all these spot groups, where the positive sign indicates that the leading part of the group is closer to the equator. It is found that the number of poleward and equatorward spot groups showed an opposite trend as the cycle advanced. The spot groups with positive (equatorward) tilt angles declined in number whereas the spot groups with negative (poleward) tilt angles increased towards the end of the cycle. It is also noticed that the number of spot groups, which changed the sign of tilt angle during their lifetime or passage across the disc, increased during the maximum activity period of the cycle. These findings were confirmed from the analysis of data from the 21st cycle. These results are discussed in this paper along with the daily variation of tilt angles of some of the spot groups from the selected data.     

Fluctuations of Solar Activity during the Declining Phase of the 11-Year Sunspot Cycle

The number of coronal mass ejections (CMEs) erupting from the Sun follows a trend similar to that of sunspot numbers during the rising and maximum phase of the solar cycle. In the declining phase, the CME number has large fluctuations, dissimilar to those of sunspot numbers. In several studies of solar – interplanetary and solar – terrestrial relationships, the sunspot numbers and the 2800-MHz flux (F10) are used as representative of solar activity. In the rising phase, this may be adequate, but in the declining phase, solar parameters such as CMEs may have a different behaviour. Cosmic-ray Forbush decreases may occur even when sunspot activity is low. Therefore, when studying the solar influence on the Earth, one has to consider that although geomagnetic conditions at solar maximum will be disturbed, conditions at solar minimum may not be necessarily quiet.