Prediction for the amplitude of solar cycle 24 from the pattern of activity near the cycle minimum

Correlations are investigated between the pattern of solar activity described by the smoothed monthly relative sunspot numbers (Wolf numbers) near the minimum of a solar cycle and the cycle amplitude. The closest correlation is found between the amplitude of a solar cycle and the sum of the decrease in activity over two years prior to the cycle minimum and the increase in activity over two years after the minimum; the correlation coefficient between these parameters is 0.92. This parameter is used as a precursor to predict the amplitude of solar cycle 24, which is expected to reach its maximum amplitude (85 ± 12) in February 2014. Based on the correlations between the mean parameters of solar cycles, cycle 24 is expected to last for approximately 11.3 years and the minimum of the next cycle 25 is predicted for May 2020.     

Predicting maximum sunspot number in solar cycle 24

A few prediction methods have been developed based on the precursor technique which is found to be successful for forecasting the solar activity. Considering the geomagnetic activity aa indices during the descending phase of the preceding solar cycle as the precursor, we predict the maximum amplitude of annual mean sunspot number in cycle 24 to be 111 ± 21. This suggests that the maximum amplitude of the upcoming cycle 24 will be less than cycles 21–22. Further, we have estimated the annual mean geomagnetic activity aa index for the solar maximum year in cycle 24 to be 20.6 ± 4.7 and the average of the annual mean sunspot number during the descending phase of cycle 24 is estimated to be 48 ± 16.8.     

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.     

Optimal prediction of the peak of the next 11-year activity cycle and of the peaks of several succeeding cycles on the basis of long-term variations in the solar radius or solar constant

We propose a new technique for the optimal prediction of the peak of the next 11-year activity cycle prior to the cycle beginning and of the peaks of several succeeding cycles on the basis of long-term variations in the solar radius or solar constant. The method is based on the already established fact that the long-term cyclic variations of the activity, radius, and solar constant are correlated in both phase and amplitude, since they are caused by some common processes in the Sun. The peak of the succeeding cycle 24 is expected to have the height W _max = 70 ± 10 (in units of relative sunspot number). The subsequent cycles 25 and 26, which will be formed during the descent of the current secular cycle, will have still lower peaks with the heights W _max = 50 ± 15 and W _max = 35 ± 20.     

Solar cycle 24 from the standpoint of solar paleoastrophysics

The predictions of the maximum yearly mean sunspot number in the current cycle 24 made by means of the astrophysical approach (by analyzing the instrumental data on solar activity and using various dynamo models) and the paleoastrophysical approach (by analyzing the paleoreconstructions of solar activity spanning the interval from 8555 BC to 1605 AD) are compared. The paleoastrophysical predictions are shown to be considerably more accurate. The amplitude of the next cycle 25 is predicted. It is shown that from the standpoint of solar paleoastrophysics, cycle 25 will most likely be of medium power, R ^max(25) = 85.0 ± 30.5.     

Forecasting the Peak Amplitude of the 24th and 25th Sunspot Cycles and Accompanying Geomagnetic Activity

Forecasting solar and geomagnetic levels of activity is essential to help plan missions and to design satellites that will survive for their useful lifetimes. Therefore, amplitudes of the upcoming solar cycles and the geomagnetic activity were forecasted using the neuro-fuzzy approach. Results of this work allow us to draw the following conclusions: Two moderate cycles are estimated to approach their maximum sunspot numbers, 110 and 116 in 2011 and 2021, respectively. However, the predicted geomagnetic activity shown to be in phase with the peak of the 24th sunspot cycle will reach its minimum three years earlier, then it will rise sharply to reach the 25th maximum a year earlier (i.e., 2020). Our analysis of the three-century long sunspot number data-set suggests that the quasi-periodic variation of the long-term evolution of solar activity could explain the irregularity of the short-term cycles seen during the past decades.     

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.     

Use of ground-based coronal data to predict the date of solar-cycle maximum

Prediction of the exact date of the maximum of the 11-year solar activity cycle is a matter of disagreement among solar scientists and of some importance to satellite operators, space-system designers, etc. Most predictions are based on physical conditions occurring at or before the solar-cycle minimum preceding the maximum in question. However, another indicator of the timing of the maximum occurs early in the rise phase of the solar cycle. A study of the variation over two previous solar cycles of coronal emission features in Fe xiv from the National Solar Observatory at Sacramento Peak has shown that, prior to solar maximum, emission features appear above 50° latitude in both hemispheres and begin to move towards the poles at a rate of 8° to 11° of latitude per year. This motion is maintained for a period of 3 or 4 years, at which time the emission features disappear near the poles. This phenomenon has been referred to as the `Rush to the Poles'. These observations show that the maximum of solar activity, as seen in the sunspot number, occurs approximately 19 ± 2 months before the features reach the poles. In 1997, Fe xiv emission features appeared near 55° latitude, and began to move towards the poles. Using the above historical data from cycles 21 and 22, we will see how the use of progressively more data from cycle 23 affects the prediction of the date of solar maximum. The principal conclusion is that the date of solar maximum for cycle 23 could be predicted to within 6 months as early as 1997. For solar cycle 24, when this phenomenon first becomes apparent later this decade, the average parameters for cycles 21–23 can be used to predict the date of solar maximum.     

Evolution of the Green Corona in 1996–2002

We analysed the green-line coronal intensities (530.3 nm, Fexiv), both their time- latitudinal distribution as well as the coronal index of solar activity (CI) over the period 1996–2002. Maximum values of the CI (smoothed) were observed in mid-August 2001, even though the `first' peak was observed in the period January–April 2000. The maximum of the Wolf number occurred in 2000, April – July, and the `second peak' occurred in December 2001–March 2002. Both indices have a similar course in the cycle, but their maxima are shifted by 1.5 year. There was high correlation between CI and Wolf number, the 2800 MHz radio flux, the X-ray 0.1–0.8 nm flux and cosmic-ray flux. The CI values in present cycle 23 are lower than those of the two former solar cycles 21 and 22 by about 1/3. Polar branches, which separated from the principal equatorward branch at mid-latitudes in the cycle minimum, 1996, reached the poles around 2000. The new principal branch for cycle 24 split in 2001, turned over around ±60° in 2002.5 and moves to the equator, where it will end in 2019. Minimum between cycles 23 and 24 will occur around 2007.5, cycle maximum 24 around 2012.5. Poleward branches in cycle 24 will reach the solar poles in 2011.     

A Prediction of Solar Cycle 24 Using a Modified Precursor Method

Based on cycles 17 – 23, linear correlations are obtained between 12-month moving averages of the number of disturbed days when Ap is greater than or equal to 25, called the Disturbance Index (DI), at thirteen selected times (called variate blocks 1, 2,… , each of six-month duration) during the declining portion of the ongoing sunspot cycle and the maximum amplitude of the following sunspot cycle. In particular, variate block 9, which occurs just prior to subsequent cycle minimum, gives the best correlation (0.94) with a minimum standard error of estimation of ± 13, and hindcasting shows agreement between predicted and observed maximum amplitudes to about 10%. As applied to cycle 24, the modified precursor technique yields maximum amplitude of about 124±23 occurring about 45±4 months after its minimum amplitude occurrence, probably in mid to late 2011.     

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.     

A Bayesian Analysis of the Correlations Among Sunspot Cycles

Sunspot numbers form a comprehensive, long-duration proxy of solar activity and have been used numerous times to empirically investigate the properties of the solar cycle. A number of correlations have been discovered over the 24 cycles for which observational records are available. Here we carry out a sophisticated statistical analysis of the sunspot record that reaffirms these correlations, and sets up an empirical predictive framework for future cycles. An advantage of our approach is that it allows for rigorous assessment of both the statistical significance of various cycle features and the uncertainty associated with predictions. We summarize the data into three sequential relations that estimate the amplitude, duration, and time of rise to maximum for any cycle, given the values from the previous cycle. We find that there is no indication of a persistence in predictive power beyond one cycle, and we conclude that the dynamo does not retain memory beyond one cycle. Based on sunspot records up to October 2011, we obtain, for Cycle 24, an estimated maximum smoothed monthly sunspot number of 97±15, to occur in January??C?February 2014 ± six months.     

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.     

An Estimate for the Size of Sunspot Cycle 24

For the sunspot cycles in the modern era (cycle?10 to the present), the ratio of R _Z(max)/R _Z(36th month) equals 1.26±0.22, where R _Z(max) is the maximum amplitude of the sunspot cycle?using smoothed monthly mean sunspot number and R _Z(36th month) is the smoothed monthly mean sunspot number 36 months after cycle?minimum. For the current sunspot cycle?24, the 36th month following the cycle?minimum occurred in November 2011, measuring?61.1. Hence, cycle?24 likely will have a maximum amplitude of about 77.0±13.4 (the one-sigma prediction interval), a value well below the average R _Z(max) for the modern era sunspot cycles (about 119.7±39.5).     

Prediction of Solar Cycle 24 Using Geomagnetic Precursors: Validation and Update

In the previous study (Dabas et al. in Solar Phys. 250, 171, 2008), to predict the maximum sunspot number of the current solar cycle 24 based on the geomagnetic activity of the preceding sunspot minimum, the Ap index was used which is available from the last six to seven solar cycles. Since a longer series of the aa index is available for more than the last 10 – 12 cycles, the present study utilizes aa to validate the earlier prediction. Based on the same methodology, the disturbance index (DI), which is the 12-month moving average of the number of disturbed days (aa≥50), is computed at thirteen selected times (called variate blocks 1,2,…,13; each of them in six-month duration) during the declining portion of the ongoing sunspot cycle. Then its correlation with the maximum sunspot number of the following cycle is evaluated. As in the case of Ap, variate block 9, which occurs exactly 48 months after the current cycle maximum, gives the best correlation (R=0.96) with a minimum standard error of estimation (SEE) of ± 9. As applied to cycle 24, the aa index as precursor yields the maximum sunspot number of about 120±16 (the 90% prediction interval), which is within the 90% prediction interval of the earlier prediction (124±23 using Ap). Furthermore, the same method is applied to an expanded range of cycles 11 – 23, and once again variate block 9 gives the best correlation (R=0.95) with a minimum SEE of ± 13. The relation yields the modified maximum amplitude for cycle 24 of about 131±20, which is also close to our earlier prediction and is likely to occur at about 43±4 months after its minimum (December 2008), probably in July 2012 (± 4 months).     

Predicting Solar Cycle 24 Using a Geomagnetic Precursor Pair

We describe using Ap and F_10.7 as a geomagnetic-precursor pair to predict the amplitude of Solar Cycle 24. The precursor is created by using F_10.7 to remove the direct solar-activity component of Ap. Four peaks are seen in the precursor function during the decline of Solar Cycle 23. A recurrence index that is generated by a local correlation of Ap is then used to determine which peak is the correct precursor. The earliest peak is the most prominent but coincides with high levels of non-recurrent solar activity associated with the intense solar activity of October and November 2003. The second and third peaks coincide with some recurrent activity on the Sun and show that a weak cycle precursor closely following a period of strong solar activity may be difficult to resolve. A fourth peak, which appears in early 2008 and has recurrent activity similar to precursors of earlier solar cycles, appears to be the “true” precursor peak for Solar Cycle 24 and predicts the smallest amplitude for Solar Cycle 24. To determine the timing of peak activity it is noted that the average time between the precursor peak and the following maximum is ≈?6.4 years. Hence, Solar Cycle 24 would peak during 2014. Several effects contribute to the smaller prediction when compared with other geomagnetic-precursor predictions. During Solar Cycle 23 the correlation between sunspot number and F_10.7 shows that F_10.7 is higher than the equivalent sunspot number over most of the cycle, implying that the sunspot number underestimates the solar-activity component described by F_10.7. During 2003 the correlation between aa and Ap shows that aa is 10 % higher than the value predicted from Ap, leading to an overestimate of the aa precursor for that year. However, the most important difference is the lack of recurrent activity in the first three peaks and the presence of significant recurrent activity in the fourth. While the prediction is for an amplitude of Solar Cycle 24 of 65±20 in smoothed sunspot number, a below-average amplitude for Solar Cycle 24, with maximum at 2014.5±0.5, we conclude that Solar Cycle 24 will be no stronger than average and could be much weaker than average.     

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 Amplitude of a Solar Cycle Using the North – South Asymmetry in the Previous Cycle: II. An Improved Prediction for Solar Cycle 24

Recently, using Greenwich and Solar Optical Observing Network sunspot group data during the period 1874 – 2006, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007: Paper I), has found that: (1) the sum of the areas of the sunspot groups in 0° – 10° latitude interval of the Sun’s northern hemisphere and in the time-interval of −1.35 year to +2.15 year from the time of the preceding minimum of a solar cycle n correlates well (corr. coeff. r=0.947) with the amplitude (maximum of the smoothed monthly sunspot number) of the next cycle n+1. (2) The sum of the areas of the spot groups in 0° – 10° latitude interval of the southern hemisphere and in the time-interval of 1.0 year to 1.75 year just after the time of the maximum of the cycle n correlates very well (r=0.966) with the amplitude of cycle n+1. Using these relations, (1) and (2), the values 112±13 and 74±10, respectively, were predicted in Paper I for the amplitude of the upcoming cycle 24. Here we found that the north – south asymmetries in the aforementioned area sums have a strong ≈44-year periodicity and from this we can infer that the upcoming cycle 24 will be weaker than cycle 23. In case of (1), the north – south asymmetry in the area sum of a cycle n also has a relationship, say (3), with the amplitude of cycle n+1, which is similar to (1) but more statistically significant (r=0.968) like (2). By using (3) it is possible to predict the amplitude of a cycle with a better accuracy by about 13 years in advance, and we get 103±10 for the amplitude of the upcoming cycle 24. However, we found a similar but a more statistically significant (r=0.983) relationship, say (4), by using the sum of the area sum used in (2) and the north – south difference used in (3). By using (4) it is possible to predict the amplitude of a cycle by about 9 years in advance with a high accuracy and we get 87±7 for the amplitude of cycle 24, which is about 28% less than the amplitude of cycle 23. Our results also indicate that cycle 25 will be stronger than cycle 24. The variations in the mean meridional motions of the spot groups during odd and even numbered cycles suggest that the solar meridional flows may transport magnetic flux across the solar equator and potentially responsible for all the above relationships. The author did a major part of this work at the Department of Physics and Astronomy, UCLA, 430 Portola Plaza, Los Angeles, CA 90095-1547, USA.     

An Early Prediction of the Amplitude of Solar Cycle 25

A “Solar Dynamo” (SODA) Index prediction of the amplitude of Solar Cycle 25 is described. The SODA Index combines values of the solar polar magnetic field and the solar spectral irradiance at 10.7 cm to create a precursor of future solar activity. The result is an envelope of solar activity that minimizes the 11-year period of the sunspot cycle. We show that the variation in time of the SODA Index is similar to several wavelet transforms of the solar spectral irradiance at 10.7 cm. Polar field predictions for Solar Cycles 21?–?24 are used to show the success of the polar field precursor in previous sunspot cycles. Using the present value of the SODA index, we estimate that the next cycle’s smoothed peak activity will be about \(140 \pm30\) solar flux units for the 10.7 cm radio flux and a Version 2 sunspot number of \(135 \pm25\). This suggests that Solar Cycle 25 will be comparable to Solar Cycle 24. The estimated peak is expected to occur near \(2025.2 \pm1.5\) year. Because the current approach uses data prior to solar minimum, these estimates may improve as the upcoming solar minimum draws closer.     

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.