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.     

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.     

Study of the Diurnal Variation of Cosmic Rays during Different Phases of Solar Activity

The pressure-corrected hourly counting rate data of ground-based super neutron monitor stations, situated in different latitudes, have been employed to study the characteristics of the long-term variation of cosmic-ray diurnal anisotropy for a long (44-year) period (1965?–?2008). Some of these super neutron monitors are situated in low latitudes with high cutoff rigidity. Annual averages of the diurnal amplitudes and phases have been obtained for each station. It is found that the amplitude of the diurnal anisotropy varies with a period of one solar activity cycle (11 years), whereas the diurnal phase varies with a period of 22 years (one solar magnetic cycle). The average diurnal amplitudes and phases have also been calculated by grouping the days on the basis of ascending and descending periods of each solar cycle (Cycles 20, 21, 22, and 23). Systematic and significant differences are observed in the characteristics of the diurnal variation between the descending periods of the odd and even solar cycles. The overall vector averages of the descending periods of the even solar cycles (20 and 22) show significantly smaller diurnal amplitudes compared to the vector averages of the descending periods of the odd solar cycles (21 and 23). In contrast, we find a large diurnal phase shift to earlier hours only during the descending periods of even solar cycles (20 and 22), as compared to almost no shift in the diurnal phase during the descending periods of odd solar cycles. Further, the overall vector average diurnal amplitudes of the ascending period of odd and even solar cycles remain invariant from one ascending period to the other, or even between the even and odd solar cycles. However, we do find a significant diurnal phase shift to earlier hours during the ascending periods of odd solar cycles (21 and 23) in comparison to the diurnal phase in the ascending periods of even solar cycles (20 and 22).     

Solar cycle distribution of great geomagnetic storms

The distribution properties of great geomagnetic storms (Dst≤−200 nT) and super geomagnetic storms (Dst≤−300 nT) across the solar cycles (19–23) are investigated. The results show that 73.2% of the great geomagnetic storms took place in the descending phase of the solar cycles. 72.7% of super geomagnetic storms occurred in the descending phase of the solar cycles. About 83% of the great geomagnetic storms appeared during the period from the two years before solar cycle peak and the three years after solar cycle peak time. 90.9% of the super geomagnetic storms appeared between the two years before solar cycle peak and the three years after solar cycle peak. When a solar cycle is very strong, the phenomenon that great geomagnetic storms concentrated during the period from the two years before the solar cycle peak time to the three years after the solar cycle peak time is very prominent. The launch time of space science satellite is suggested according to the distribution properties of great geomagnetic storms and super geomagnetic storms in solar cycles.     

Prediction of the Beginning of Solar Activity Cycle 24 by the Similar Cycle Method

In this paper, the method of similar cycles is applied to predict the start time of the 24th cycle of solar activity and the sunspot numbers in the later part of the descending phase of cycle 23. According to the characteristic parameters and the morphological characters of the descending phase of cycle 23 and of cycles 9, 10, 11, 15, 17 and 20 (cycles selected as the similar cycles for the descending phase of cycle 23), the start time of cycle 24 is predicted to be in 2007 yr 5 ± 1m, the smoothed monthly mean spot number, 7.1 ± 2.6 and the length of the 23rd cycle, 11.1 yr. These results agree rather well with those stated in Refs.[11] & [12] as well as those of MSFC. Our work shows that the method of similar cycles can well be applied to the long-term prediction of solar activity.     

THE CORRELATION BETWEEN SUNSPOT AND CORONAL HOLE CYCLES AND A FORECAST OF THE MAXIMUM OF SUNSPOT CYCLE 23

We have shown in previous papers that a close relationship exists between the evolution of polar coronal hole area, estimated from K-coronameter observations, and the Wolf sunspot number, with a time lag of about half a solar cycle. In this paper we study the same relationship, but with the total coronal hole area at the base of the corona as obtained from a potential field model of the coronal magnetic field, which provides a more complete series of about three solar cycles. We confirm the relationship for the two last cycles and find that the forward time shift in the coronal hole area for the best correlation with sunspot number is almost the same for cycles 21 and 22, and this shift is also the time between peaks in both series. We use this result to make an early prediction of the time and size of the sunspot maximum for solar cycle 23, and find that this should occur early in 2001 and have a magnitude of about 190, similar to that of the two previous sunspot cycles.     

Observation of hysteresis between solar activity indicators andp-mode frequency shifts for solar cycle 22

Using intermediate degreep-mode frequency data sets for solar cycle 22, we find that the frequency shifts and magnetic activity indicators show a “hysteresis” phenomenon. It is observed that the magnetic indices follow different paths for the ascending and descending phases of the solar cycle while for radiative indices, the separation between the paths are well within the error limits.     

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.     

Sunspot Time Series: Passive and Active Intervals

Solar activity slowly and irregularly decreases from the first spotless day (FSD) in the declining phase of the old sunspot cycle and systematically, but also in an irregular way, increases to the new cycle maximum after the last spotless day (LSD). The time interval between the first and the last spotless day can be called the passive interval (PI), while the time interval from the last spotless day to the first one after the new cycle maximum is the related active interval (AI). Minima of solar cycles are inside PIs, while maxima are inside AIs. In this article, we study the properties of passive and active intervals to determine the relation between them. We have found that some properties of PIs, and related AIs, differ significantly between two group of solar cycles; this has allowed us to classify Cycles 8?–?15 as passive cycles, and Cycles 17?–?23 as active ones. We conclude that the solar activity in the PI declining phase (a descending phase of the previous cycle) determines the strength of the approaching maximum in the case of active cycles, while the activity of the PI rising phase (a phase of the ongoing cycle early growth) determines the strength of passive cycles. This can have implications for solar dynamo models. Our approach indicates the important role of solar activity during the declining and the rising phases of the solar-cycle minimum.     

A Statistical Analysis of X1- and X2- or Higher-Class Flares during Solar Cycles 21∼23

The X1- and X2- or higher class ?ares in solar cycles 21, 22, and 23 from 1986 to 2008 have been analyzed statistically in this paper. It is found in the statistical study that the number of the X1-class ?ares accounted for 52.71% of total X- and higher class ?ares, while, the number of the X2- and higher class ?ares accounted for 47.29% of total X- and higher class ?ares. No matter whether the X1- and X2- or higher class ?ares, most of them occured in the descending phases of the solar cycles. Moreover, the weaker the intensity of the solar cycle, the higher the ratio of the ?ares occurred in the descending phase of the solar cycle, and the stronger the intensity of solar ?ares, the higher the ratio of the ?ares occurred in the descending phases of the solar cycles. In addition, the phase difference between the peak of the smoothed monthly mean number of sunspots and that of the X-class ?ares has been calculated, which shows that the smoothed monthly mean number of the X1-class ?ares had a very noticeable time advance of 1 month with respect to that of sunspots in the cycles 21 and 22, but there was a time lag of 13 months in the cycle 23, while, for the X2- and higher class ?ares, there was a time lag of 9 months in the cycle 21, but a one-month time advance existed in the cycle 22, and again a time lag of 32 months appeared in the cycle 23.     

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.     

Diurnal anisotropy of cosmic rays during intensive solar activity for the period 2001–2014

The diurnal variation of cosmic ray intensity, based on the records of two neutron monitor stations at Athens (Greece) and Oulu (Finland) for the time period 2001 to 2014, is studied. This period covers the maximum and the descending phase of the solar cycle 23, the minimum of the solar cycles 23/24 and the ascending phase of the solar cycle 24.These two stations differ in their geographic latitude and magnetic threshold rigidity. The amplitude and phase of the diurnal anisotropy vectors have been calculated on annual and monthly basis.From our analysis it is resulted that there is a different behaviour in the characteristics of the diurnal anisotropy during the different phases of the solar cycle, depended on the solar magnetic field polarity, but also during extreme events of solar activity, such as Ground Level Enhancements and cosmic ray events, such as Forbush decreases and magnetospheric events. These results may be useful to Space Weather forecasting and especially to Biomagnetic studies.     

Prediction of the height of solar cycle 23

Presuming a bimodal behaviour of even-odd solar cycle pairs (i.e., four modes designated asA, B, C, andD), we predict the amplitude of solar cycle 23. The bimodal properties include the dependence of maximum relative sunspot number (RM) on cycle rise time (TR) separately for odd-following and even cycles (both in two split modes), and the dependencies of odd-following on even cycles separately for cycle rise times and maximum relative sunspot numbers (each also split into two mode pairs). The procedure was first to identify the proper mode for cycle 22 (modeA), which then explicitly defines the mode for cycle 23 (modeC). The presumed mode-inherent relations were then used to estimate the rise time for cycle 23 (3.7 0.5 yr) and its maximum amplitude (195.1 17.1). A second estimate of maximum amplitude, based directly on a presumed mode-inherent relation between maximum amplitudes for even and odd cycle pairs, yields a somewhat lower value (181.3 44.3). Thus, the results of this analysis supports previous findings that cycle 23 may be one of the largest amplitude cycles ever observed.     

Different Periodicities in the Sunspot Area and the Occurrence of Solar Flares and Coronal Mass Ejections in Solar Cycle 23 – 24

In order to investigate the relationship between magnetic-flux emergence, solar flares, and coronal mass ejections (CMEs), we study the periodicity in the time series of these quantities. It has been known that solar flares, sunspot area, and photospheric magnetic flux have a dominant periodicity of about 155 days, which is confined to a part of the phase of the solar cycle. These periodicities occur at different phases of the solar cycle during successive phases. We present a time-series analysis of sunspot area, flare and CME occurrence during Cycle 23 and the rising phase of Cycle 24 from 1996 to 2011. We find that the flux emergence, represented by sunspot area, has multiple periodicities. Flares and CMEs, however, do not occur with the same period as the flux emergence. Using the results of this study, we discuss the possible activity sources producing emerging flux.     

North-south distribution of solar flares during cycle 23

In this paper, we investigate the spatial distribution of solar flares in the northern and southern hemispheres of the Sun that occurred during the period 1996 to 2003. This period of investigation includes the ascending phase, the maximum and part of the descending phase of solar cycle 23. It is revealed that the flare activity during this cycle is low compared to the previous solar cycle, indicating the violation of Gnevyshev-Ohl rule. The distribution of flares with respect to heliographic latitudes shows a significant asymmetry between northern and southern hemisphere which is maximum during the minimum phase of the solar cycle. The present study indicates that the activity dominates the northern hemisphere in general during the rising phase of the cycle (1997–2000). The dominance of northern hemisphere shifted towards the southern hemisphere after the solar maximum in 2000 and remained there in the successive years. Although the annual variations in the asymmetry time series during cycle 23 are quite different from cycle 22, they are comparable to cycle 21.     

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.     

High-Speed Solar Wind Streams and Geomagnetic Storms During Solar Cycle 24

An updated catalog is created of 303 well-defined high-speed solar wind streams that occurred in the time period 2009?–?2016. These streams are identified from solar and interplanetary measurements obtained from the OMNIWeb database as well as from the Solar and Heliospheric Observatory (SOHO) database. This time interval covers the deep minimum observed between the last two Solar Cycles 23 and 24, as well as the ascending, the maximum, and part of the descending phases of the current Solar Cycle 24. The main properties of solar-wind high-speed streams, such as their maximum velocity, their duration, and their possible sources are analyzed in detail. We discuss the relative importance of all those parameters of high-speed solar wind streams and especially of their sources in terms of the different phases of the current cycle. We carry out a comparison between the characteristic parameters of high-speed solar wind streams in the present solar cycle with those of previous solar cycles to understand the dependence of their long-term variation on the cycle phase. Moreover, the present study investigates the varied phenomenology related to the magnetic interactions between these streams and the Earth’s magnetosphere. These interactions can initiate geomagnetic disturbances resulting in geomagnetic storms at Earth that may have impact on technology and endanger human activity and health.     

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.     

Solar cycle distribution of strong solar proton events and the related solar-terrestrial phenomena

We investigated the solar cycle distribution of strong solar proton events (SPEs, peak flux ≥1000 pfu) and the solar-terrestrial phenomena associated with the strong SPEs during solar cycles 21–23. The results show that 37 strong SPEs were registered over this period of time, where 20 strong SPEs were originated from the super active regions (SARs) and 28 strong SPEs were accompanied by the X-class flares. Most strong SPEs were not associated with the ground level enhancement (GLE) event. Most strong SPEs occurred in the descending phases of the solar cycles. The weaker the solar cycle, the higher the proportion of strong SPES occurred in the descending phase of the cycle. The number of the strong SPEs that occurred within a solar cycle is poorly associated with the solar cycle size. The intensity of the SPEs is highly dependent of the location of their source regions, with the super SPEs (≥20000 pfu) distributed around solar disk center. A super SPE was always accompanied by a fast shock driven by the associated coronal mass ejection and a great geomagnetic storm. The source location of strongest GLE event is distributed in the well-connected region. The SPEs associated with super GLE events (peak increase rate ≥100%) which have their peak flux much lower than 10000 pfu were not accompanied by an intense geomagnetic storm.     

Effects of Hysteresis Between Maximum CME Speed Index and Typical Solar Activity Indicators During Cycle 23

Using the smoothed time series of maximum CME speed index for solar cycle 23, it is found that this index, analyzed jointly with six other solar activity indicators, shows a hysteresis phenomenon. The total solar irradiance, coronal index, solar radio flux (10.7?cm), Mg?ii core-to-wing ratio, sunspot area, and H?? flare index follow different paths for the ascending and the descending phases of solar cycle?23, while a saturation effect exists at the maximum phase of the cycle. However, the separations between the paths are not the same for the different solar activity indicators used: the H?? flare index and total solar irradiance depict broad loops, while the Mg?ii core-to-wing ratio and sunspot area depict narrow hysteresis loops. The lag times of these indices with respect to the maximum CME speed index are discussed, confirming that the hysteresis represents a clue in the search for physical processes responsible for changing solar emission.