Preliminary prediction of solar cycles 24 and 25 based on the correlation between cycle parameters

The correlation between various parameters of solar cycles 1–23 is investigated. The derived regressions are used to make predictions of solar cycles 24 and 25. It is expected that solar cycle 24 will reach its maximum amplitude of 110.2 ± 33.4 in April–June 2012 and the next minimum will occur in December 2018–January 2019. The duration of solar cycle 24 will be about 11.1 years. Solar cycle 25 will reach its maximum amplitude of 112.3 ± 33.4 approximately in April–June 2023.     

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.     

Prediction of solar cycle 24 and beyond

In the previous study (Hiremath, Astron. Astrophys. 452:591, 2006a), the solar cycle is modeled as a forced and damped harmonic oscillator and from all the 22 cycles (1755–1996), long-term amplitudes, frequencies, phases and decay factor are obtained. Using these physical parameters of the previous 22 solar cycles and by an autoregressive model, we predict the amplitude and period of the present cycle 23 and future fifteen solar cycles. The period of present solar cycle 23 is estimated to be 11.73 years and it is expected that onset of next sunspot activity cycle 24 might starts during the period 2008.57±0.17 (i.e., around May–September 2008). The predicted period and amplitude of the present cycle 23 are almost similar to the period and amplitude of the observed cycle. With these encouraging results, we also predict the profiles of future 15 solar cycles. Important predictions are: (i) the period and amplitude of the cycle 24 are 9.34 years and 110 (±11), (ii) the period and amplitude of the cycle 25 are 12.49 years and 110 (±11), (iii) during the cycles 26 (2030–2042 AD), 27 (2042–2054 AD), 34 (2118–2127 AD), 37 (2152–2163 AD) and 38 (2163–2176 AD), the sun might experience a very high sunspot activity, (iv) the sun might also experience a very low (around 60) sunspot activity during cycle 31 (2089–2100 AD) and, (v) length of the solar cycles vary from 8.65 years for the cycle 33 to maximum of 13.07 years for the cycle 35.     

Amplitude and period of the dynamo wave and prediction of the solar cycle

The relation of the solar cycle period and its amplitude is a complex problem as there is no direct correlation between these two quantities. Nevertheless, the period of the cycle is of important influence to the Earth's climate, which has been noted by many authors. The present authors make an attempt to analyse the solar indices data taking into account recent developments of the asymptotic theory of the solar dynamo. The use of the WKB method enables us to estimate the amplitude and the period of the cycle versus dynamo wave parameters in the framework of the nonlinear development of the one-dimensional Parker migratory dynamo. These estimates link the period T and the amplitude a with dynamo number D and thickness of the generation layer of the solar convective zone h. As previous authors, we have not revealed any considerable correlation between the above quantities calculated in the usual way. However, we have found some similar dependences with good confidence using running cycle periods. We have noticed statistically significant dependences between the Wolf numbers and the running period of the magnetic cycle, as well as between maximum sunspot number and duration of the phase of growth of each sunspot cycle. The latter one supports asymptotic estimates of the nonlinear dynamo wave suggested earlier. These dependences may be useful for understanding the mechanism of the solar dynamo wave and prediction of the average maximum amplitude of solar cycles. Besides that, we have noted that the maximum amplitude of the cycle and the temporal derivative of the monthly Wolf numbers at the very beginning of the phase of growth of the cycle have high correlation coefficient of order 0.95. The link between Wolf number data and their derivative taken with a time shift enabled us to predict the dynamics of the sunspot activity. For the current cycle 23 this yields Wolf numbers of order 107±7.     

Some features of Pc5 pulsations during a solar cycle

The morphological features of Pc5 pulsations during a solar cycle are studied using Fort Churchill data for the years 1962–1972. Some of the characteristics noted are as follows: (1) Increasing sunspot numbers show little influence on the diurnal variation of the occurrence, amplitude and the period except perhaps some noticeable change in the absolute magnitude of these parameters during different hours of the day. (2) The morning occurrence peak dominates during all phases of the solar cycle. (3) As noted earlier (Gupta 1973a), with increasing magnetic activity the day side region(s) of generation of Pc5 is found to shift closer to the subsolar point and in the midnight sector, the occurrence region (presumably the region of open and closed field lines) seemed to shift towards earlier hours with increasing magnetic activity and towards later hours with increasing sunspot numbers. (4) Despite the smaller number of data points for high magnetic activity levels the analysis indicates that the amplitude of Pc5 pulsations is directly related to all the levels of magnetic activity. (5) The periods of Pc5 pulsations show strong correlation with increasing sunspot numbers and the amplitude and occurrences are found to vary in accordance with the magnetic activity all through the cycle. (6) The annual and semi-annual variations of Pc5 parameters have been demonstrated especially for the pulsations occurring in the morning close to 8 ± 1 h LT and for those occurring near the midnight hours. (7) A suspected 27-day recurrence tendency has been clearly noticed for the occurrence, amplitude and period of Pc5 pulsations.     

The shape of the sunspot cycle

The temporal behavior of a sunspot cycle, as described by the International sunspot numbers, can be represented by a simple function with four parameters: starting time, amplitude, rise time, and asymmetry. Of these, the parameter that governs the asymmetry between the rise to maximum and the fall to minimum is found to vary little from cycle to cycle and can be fixed at a single value for all cycles. A close relationship is found between rise time and amplitude which allows for a representation of each cycle by a function containing only two parameters: the starting time and the amplitude. These parameters are determined for the previous 22 sunspot cycles and examined for any predictable behavior. A weak correlation is found between the amplitude of a cycle and the length of the previous cycle. This allows for an estimate of the amplitude accurate to within about 30% right at the start of the cycle. As the cycle progresses, the amplitude can be better determined to within 20% at 30 months and to within 10% at 42 months into the cycle, thereby providing a good prediction both for the timing and size of sunspot maximum and for the behavior of the remaining 7–12 years of the cycle. The U.S. Government right to retain a non-exclusive, royalty free licence in and to any copyright is acknowledged.     

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.     

Search for relationship between duration of the extended solar cycles and amplitude of sunspot cycle

Duration of the extended solar cycles is taken into the consideration. The beginning of cycles is counted from the moment of polarity reversal of large-scale magnetic field in high latitudes, occurring in the sunspot cycle n till the minimum of the cycle n + 2. The connection between cycle duration and its amplitude is established. Duration of the “latent” period of evolution of extended cycle between reversals and a minimum of the current sunspot cycle is entered. It is shown, that the latent period of cycles evolution is connected with the next sunspot cycle amplitude and can be used for the prognosis of a level and time of a sunspot maximum. The 24th activity cycle prognosis is made. The found dependences correspond to transport dynamo model of generation of solar cyclicity, it is possible with various speed of meridional circulation. Long-term behavior of extended cycle's lengths and connection with change of a climate of the Earth is considered. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Predicting the start and maximum amplitude of solar cycle 24 using similar phases and a cycle grouping

We find that the solar cycles 9, 11, and 20 are similar to cycle 23 in their respective descending phases. Using this similarity and the observed data of smoothed monthly mean sunspot numbers (SMSNs) available for the descending phase of cycle 23, we make a date calibration for the average time sequence made of the three descending phases of the three cycles, and predict the start of March or April 2008 for cycle 24. For the three cycles, we also find a linear correlation of the length of the descending phase of a cycle with the difference between the maximum epoch of this cycle and that of its next cycle.Using this relationship along with the known relationship between the rise-time and the maximum amplitude of a slowly rising solar cycle, we predict the maximum SMSN of cycle 24 of 100.2±7.5 to appear during the period from May to October 2012.     

Polar coronal holes and the sunspot cycle. A new method to predict sunspot numbers

Twenty years ago, Ohl (1966, 1968) found a correlation between geomagnetic activity around the minimum of the solar cycle and the Wolf sunspot number in the maximum of the following solar cycle. In this paper we shall show that such a relation means indeed a relation between the polar coronal holes area around the minimum of the solar cycle and the sunspot number in the maximum of the next. In fact, a very high positive correlation exists between the temporal evolution of the size of polar coronal holes and the Wolf sunspot number 6.3. years later.     

Hysteresis,time lag,and relation between solar activity and cosmic rays during solar cycle 24

We study galactic cosmic ray (GCR) modulation during solar cycle 24. For this study we utilize neutron monitor data together with sunspot number (SSN) and 10.7 cm solar radio flux (SRF) data. We plot hysteresis curve between the GCR intensity and SSN, and GCR intensity and SRF. We performed time-lag correlation analysis to determine the time lag between GCR intensity and solar activity parameters. The time lag is determined not only for the whole solar cycle, but also during the two polarity states of the heliosphere (A<0 and A>0) in solar cycle 24. We notice differences in time lags during two polarity epochs of the solar cycle. We discuss these differences in the light of existing modulation models. We compare the results of this very weak solar activity cycle with the corresponding results reported for the previous comparatively more active solar cycles.     

Do polar faculae on the sun predict a sunspot cycle?

The paper reports the results of the analysis of the data on polar faculae for three solar cycles (1960–1986) at the Kislovodsk Station of the Pulkovo Observatory and on polar bright points in Ca ii K line for two solar cycles (1940–1957) at the Kodaikanal Station of the Indian Institute of Astrophysics. We have noticed that the monthly numbers of polar faculae and polar bright points in Ca ii K line and monthly sunspot areas in each hemisphere of the following solar cycle have a correlation with each other. A new cycle of polar faculae and polar bright points in the Ca ii K line begins after the polar magnetic field reversal. We find that the smaller the period between the ending of the polar field reversal and the beginning of a new sunspot cycle is, the more intense is the cycle itself. The intensity of the forthcoming solar cycle (cycle 22) and the periods of strong fluctuations in activity expected in this cycle are also discussed.     

Multi-parametric effect of solar activity on cosmic rays

The long-term modulation of cosmic ray intensity (CRI) by different solar activity (SA) parameters and an inverse correlation between individual SA parameter and CRI is well known. Earlier, it has been suggested that the concept of multi-parametric modulation of CRI may play an important role in the study of long-term modulation of CRI. In the present study, we have tried to investigate the combined effect of a set of two SA parameters in the long-term modulation of CRI. For this purpose, we have used a new statistical technique called “Running multiple correlation method”, based on the “Running cross correlation method”. The running multiple correlation functions among different sets of two SA parameters (e.g., sunspot numbers and solar flux, sunspot numbers and coronal index, sunspot numbers and grouped solar flares, etc.) and CRI have been correlated separately. It is found that the strength of multiple correlation (among two SA parameters and CRI) and cross correlation (between individual SA parameter and CRI) is almost similar throughout the period of investigation (1955–2005). It is also found that the multiple correlations among various SA parameters and CRI is stronger during ascending and descending phases of the solar cycles and it becomes weaker during maxima and minima of the solar cycles, which is in accordance with the linear relationship between SA parameters and CRI. The values of multiple correlation functions among different sets of SA parameters and CRI fall well within the 95% confidence interval. In the view of odd-even hypothesis of solar cycles, the strange behaviour of present cycle 23 (odd cycle), as this is characterized by many peculiarities with double peaks and many quiet periods (Gnevyshev gaps) interrupted the solar activity (for example April 2001, October–November 2003 and January 2005), leads us to speculate that the solar cycle 24 (even cycle) might be of exceptional nature.     

What the Sunspot Record Tells Us About Space Climate

The records concerning the number, sizes, and positions of sunspots provide a direct means of characterizing solar activity over nearly 400 years. Sunspot numbers are strongly correlated with modern measures of solar activity including: 10.7-cm radio flux, total irradiance, X-ray flares, sunspot area, the baseline level of geomagnetic activity, and the flux of galactic cosmic rays. The Group Sunspot Number provides information on 27 sunspot cycles, far more than any of the modern measures of solar activity, and enough to provide important details about long-term variations in solar activity or “Space Climate.” The sunspot record shows: 1) sunspot cycles have periods of 131± 14 months with a normal distribution; 2) sunspot cycles are asymmetric with a fast rise and slow decline; 3) the rise time from minimum to maximum decreases with cycle amplitude; 4) large amplitude cycles are preceded by short period cycles; 5) large amplitude cycles are preceded by high minima; 6) although the two hemispheres remain linked in phase, there are significant asymmetries in the activity in each hemisphere; 7) the rate at which the active latitudes drift toward the equator is anti-correlated with the cycle period; 8) the rate at which the active latitudes drift toward the equator is positively correlated with the amplitude of the cycle after the next; 9) there has been a significant secular increase in the amplitudes of the sunspot cycles since the end of the Maunder Minimum (1715); and 10) there is weak evidence for a quasi-periodic variation in the sunspot cycle amplitudes with a period of about 90 years. These characteristics indicate that the next solar cycle should have a maximum smoothed sunspot number of about 145 ± 30 in 2010 while the following cycle should have a maximum of about 70 ± 30 in 2023.     

The 10-year time delay of the solar cycle luminosity modulation of the Sun behind the solar cycle magnetic oscillation

We found an evidence that the solar cycle luminosity modulation of the Sun deduced from the total irradiance modulation which was measured by the Earth Radiation Budget (ERB) experiment on board of Nimbus 7 from November 16, 1978 to December 13, 1993 was not in phase with the solar cycle magnetic oscillation when we used the sunspot relative number as its index. The modulation was delayed in time behind the solar cycle magnetic oscillation by an amount of about 10.3 years on the order of length of one solar cycle. In order to quantitatively evaluate the correlation between the two quantities, we devised a method to extract characteristics which were proper to a particular solar cycle by defining a new index of the correlation called multiplied correlation index (MCI). We found that the characteristics of the ERB data time profile between solar cycles 21 and 22 were more similar to those of the solar cycle magnetic oscillation between solar cycles 20 and 21 than those between solar cycles 21 and 22 and thus the time profile of the luminosity modulation from the maximum phase of solar cycle 21 to the declining phase of the solar cycle 22 corresponded to the solar cycle magnetic oscillation from the maximum phase of solar cycle 20 to the declining phase of solar cycle 21. We interpret this phenomenon as an evidence that main features of the modulation is not caused by dark sunspots and bright faculae and plages on the surface of the Sun that should instantaneously affect the luminosity modulation but is caused by time-delayed modulation of global convection by the Lorentz force of the magnetic field of the solar cycle. The delay time of about 10.3 years is the time needed for the force to modify the flows of the convection and to modulate heat flow. Thus the delay time is a function of the strength of the magnetic field oscillation of the solar cycle which is represented by amplitude of the solar cycle. Accordingly, the delay time for other time intervals of the solar cycle magnetic oscillation with different amplitudes can be different from 10.3 years for the interval of the present analysis.     

Acoustic Mode Frequencies of the Sun During the Minimum Phase Between Solar Cycles 23 and 24

We investigate the spatial and temporal variations of the high-degree mode frequencies calculated over localized regions of the Sun during the extended minimum phase between solar cycles 23 and 24. The frequency shifts measured relative to the spatial average over the solar disk indicate that the correlation between the frequency shift and magnetic field strength during the low-activity phase is weak. The disk-averaged frequency shifts computed relative to a minimal activity period also reveal a moderate correlation with different activity indices, with a maximum linear correlation of about 72?%. From the investigation of the frequency shifts at different latitudinal bands, we do not find a consensus period for the onset of solar cycle 24. The frequency shifts corresponding to most of the latitudes in the northern hemisphere and 30° south of the equator indicate the minimum epoch to be February 2008, which is earlier than inferred from solar activity indices.     

Activity cycle of solar filaments

Long-term variation in the distribution of the solar filaments observed at the Observatorie de Paris, Section de Meudon from March 1919 to December 1989 is presented to compare with sunspot cycle and to study the periodicity in the filament activity, namely the periods of the coronal activity with the Morlet wavelet used. It is inferred that the activity cycle of solar filaments should have the same cycle length as sunspot cycle, but the cycle behavior of solar filaments is globally similar in profile with, but different in detail from, that of sunspot cycles. The amplitude of solar magnetic activity should not keep in phase with the complexity of solar magnetic activity. The possible periods in the filament activity are about 10.44 and 19.20 years. The wavelet local power spectrum of the period 10.44 years is statistically significant during the whole consideration time. The wavelet local power spectrum of the period 19.20 years is under the 95% confidence spectrum during the whole consideration time, but over the mean red-noise spectrum of α = 0.72 before approximate Carrington rotation number 1500, and after that the filament activity does not statistically show the period. Wavelet reconstruction indicates that the early data of the filament archive (in and before cycle 16) are more noiseful than the later (in and after cycle 17).     

Forecast of the key parameters of the 24-th solar cycle

To predict the key parameters of the solar cycle,a new method is proposed based on the empirical law describing the correlation between the maximum height of the preceding solar cycle and the entropy of the forthcoming one.The entropy of the forthcoming cycle may be estimated using this empirical law,if the maximum height of the current cycle is known.The cycle entropy is shown to correlate well with the cycle's maximum height and,as a consequence,the height of the forthcoming maximum can be estimated.In turn,the correlation found between the height of the maximum and the duration of the ascending branch(the Waldmeier rule)allows the epoch of the maximum,Tmax,to be estimated,if the date of the minimum is known.Moreover,using the law discovered,one can find out the analogous cycles which are similar to the cycle being forecasted,and hence,obtain the synoptic forecast of all main features of the forthcoming cycle.The estimates have shown the accuracy level of this technique to be 86%.The new regularities discovered are also interesting because they are fundamental in the theory of solar cycles and may provide new empirical data.The main parameters of the future solar cycle 24 are as follows: the height of the maximum is Wmax = 95±20,the duration of the ascending branch is Ta = 4.5±0.5 yr,the total cycle duration according to the synoptic forecast is 11.3 yr.     

A new solar activity parameter and the strength of 5-cycle periodicity

A weak 5-cycle periodicity (r = −0.64) is found in the maximum amplitudes of the modern era sunspot cycles (11–23), slightly stronger than the 8-cycle (Gleissberg) periodicity (r = 0.60).We propose a new parameter called ‘effective duration’, defined as the total sunspot numbers in a cycle divided by the maximum amplitude. This parameter has two advantages: one is that it is almost independent of the exact definition of minimum timing; another is that the maximum amplitude is found to be highly correlated (r = 0.86) with this parameter five cycles before, when applied to the smoothed monthly mean sunspot numbers in modern era.Implied is that this parameter carries some information of the amplitude five cycles later, and may become one of the parameters to study solar activity and the theory of solar dynamo. With the relationship above, the amplitude of cycle 24 is estimated to be 115.7 ± 19.7, where the error is the standard error.