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.     

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.     

The 27-Day and 22-Year Cycles in Solar and Geomagnetic Activity

We study the evolution of the longitudinal asymmetry in solar activity through the wave packet technique applied to the period domain of 25 – 31 days (centered at the 27-day solar rotation period) for the sunspot number and geomagnetic aa index. We observe the occurrence of alternating smaller and larger amplitudes of the 11-year cycle, resulting in a 22-year periodicity in the 27-day signal. The evolution of the 22-year cycle shows a change of regime around the year 1912 when the 22-year period disappears from the sunspot number series and appears in the aa index. Other changes, such as a change in the correlation between solar and geomagnetic activity, took place at the same time. Splitting the 27-day frequency domain of aa index shows an 11-year cycle for higher frequencies and a pure22-year cycle for lower frequencies, which we attribute to higher latitude coronal holes. This evidence is particularly clear after 1940, which is another benchmark in the evolution of the aa index. We discuss briefly the mechanisms that could account for the observed features of the 22-year cycle evolution.     

The green corona,the solar wind and geoactivity

The long-term distribution of the Green Corona Low Brightness Regions (GCLBR) on the solar surface is investigated. The frequency curves of the GCLBR follow the solar cycle, but are displaced considerably relative to the curve of the sunspot number cycle. The observed displacement increases with the size of the GCLBR and reaches up to 4–5 years for the largest regions. It is, however, interesting that the displacement in the equatorial zone is opposite to that in the higher-latitude zones.An older idea on the physical affinity between GCLBR and coronal holes led us to study the frequency of GCLBR and the properties of High-Speed Plasma Streams (HSPS) in the solar wind. Maximum velocity and duration of the coronal-hole-related HSPS seem to be well correlated with the number and size of GCLBR located in the N 60-N 20 and S 20-S 60 latitudinal zones. This is particularly evident at the end of the solar cycle.Geophysical Kp and aa indices are used to demonstrate a possible genetic dependence of geoactivity on the size, position on the Sun's surface and frequency of the GCLBR. In this sense, the most pronounced period is 1973–1976.

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Prediction of the sunspot maximum of solar cycle 23 by extrapolation of spectral components

A simple method MEM-MRA, where spectral peaks are located by MEM (Maximum Entropy Method) and about a dozen most prominent ones are used in MRA (Multiple Regression Analysis) to estimate their amplitudes and phases, was applied to the sunspot number (Rz) series of 1748–1996. Spectral characteristics were different in the successive 3 intervals of 83 years each. Hence, for predictions, only data for the recent 83 years were considered relevant. From the spectra for 1914–1996, the most significant peaks at 5.3, 8.3, 10.5, 12.2, 47 years were used for reconstruction. The match between observed and reconstructed values was good (correlation +0.90). When extrapolated, the reconstructed values indicate a sunspot number maximum for the present solar cycle 23 as 140±9, to occur in year 2000 and for the next solar cycle 24 as 105±9, to occur in year 2010–2011.     

Differential rotation of the sun determined tracing sunspots and oscillations of sunspot tilt angle

The time and spatial characteristics of 324 large sunspots (S50 millionths of the solar hemisphere) selected from the Abastumani Astrophysical Observatory photoheliogram collection (1950–1990) have been studied. The variations of sunspot angular rotation velocity residuals and oscillations of sunspot tilt angle were analyzed. It has been shown that the differential rotation rate of selected sunspots correlates on average with the solar cycle. The deceleration of differential rotation of large sunspots begins on the ascending arm of the activity curve and ends on the descending arm reaching minimum near the epochs of solar activity maxima. This behavior disappears during the 21st cycle. The amplitudes and periods of sunspot tilt-angle oscillations correlate well with the solar activity cycle. Near the epochs of activity maximum there appear sunspots with large amplitudes and periods showing a significant scatter while the scatter near the minimum is rather low. We also found evidence of phase difference between the sunspot angular rotation velocity and the amplitudes and periods of tilt-angle oscillations.     

The eight-schwabe-cycle pulsation

The shape of the Sun’s secular activity cycle is found to be a saw-tooth curve. The additional Schwabe cycle 4′ (1793–1799) suggested by Usoskin, Mursula, and Kovaltsov (2001a) is taken into account in the telescopic sunspot record (1610–2001). Instead of a symmetrical Gleissberg cycle, a saw-tooth of exactly eight Schwabe sunspot maxima (‘Pulsation’) is found. On average, the last sunspot maximum of an eight-Schwabe-cycle saw-tooth pulsation has been about three times as high as its first maximum. The Maunder Minimum remains an exception to this pattern. The Pulsation is defined as a secular-scale envelope of Schwabe-cycle maxima, whereas the Gleissberg cycle is a result of long-term smoothing of the sunspot series.     

The eight-schwabe-cycle pulsation

The shape of the Sun’s secular activity cycle is found to be a saw-tooth curve. The additional Schwabe cycle 4′ (1793–1799) suggested by Usoskin, Mursula, and Kovaltsov (2001a) is taken into account in the telescopic sunspot record (1610–2001). Instead of a symmetrical Gleissberg cycle, a saw-tooth of exactly eight Schwabe sunspot maxima (‘Pulsation’) is found. On average, the last sunspot maximum of an eight-Schwabe-cycle saw-tooth pulsation has been about three times as high as its first maximum. The Maunder Minimum remains an exception to this pattern. The Pulsation is defined as a secular-scale envelope of Schwabe-cycle maxima, whereas the Gleissberg cycle is a result of long-term smoothing of the sunspot series.     

Intermediate-term periodicities in solar activity

The presence of intermediate-term periodicities in solar activity, at approximately 323 and 540 days, has been claimed by different authors. In this paper, we have performed a search for them in the historical records of two main indices of solar activity, namely, the daily sunspot areas (cycles 12–21) and the daily Zürich sunspot number (cycles 6–21). Two different methods to compute power spectra have been used, one of them being especially appropriate to deal with gapped time series. The results obtained for the periodicity near 323 days indicate that it has only been present in cycle 21, while in previous cycles no significant evidence for it has been found. On the other hand, a significant periodicity at 350 days is found in sunspot areas and Zürich sunspot number during cycles 12–21 considered all together, also having been detected in some individual cycles. However, this last periodicity must be looked into with care due to the lack of confirmation for it coming from other features of solar activity. The periodicity around 540 days is found in cycles 12, 14, and 17 in sunspot areas, while during cycles 18 and 19 it is present, with a very high significance, in sunspot areas and Zürich sunspot number. It also appears at 528 days in sunspot areas during cycles 12–21. On the other hand, it is important to note the coincidence between the asymmetry, favouring the northern hemisphere, of sunspot areas and solar flares during cycle 19, and the fact that the periodicity at 540 days was only present, with high significance, in that hemisphere during that solar cycle.     

Modeling and distance determination of planetary nebulae

The monthly probability of occurrence of southward (B _z ^– ) component of IMF estimated independent of the sector polarity observed near earth is found to change with the magnitude of solar wind velocity. The above analysis is done for each month during two years around sunspot minima and maxima in cycle 21. The results will be interpreted in terms of association of southwardB _z events with solar wind flows of distinct solar origin such as low and high speed solar wind.     

The large-scale build-up of solar magnetic cycles

The purpose of the present article is to analyze the solar cycles from the point of view of the large-scale surface magnetic field (LSMF) polarity distributions. Using synoptic charts of the LSMF for the 1870–1991 time interval at maxima and minima and the spherical harmonic analysis of the polarity distributions, a connection between magnetic cycles has been found. The weight of the large-scale sectoral mode (m = 1) in the common LSMF polarity distribution at minima of the sunspot cycle is the source of sunspot activity at maxima after 16–18 years. The connections found suggest that surface LSMFs have a dual nature - the main source below the convective zone and a secondary source (sunspot production). The sunspot production has no visible influence on the LSMF cycles.     

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.     

Short-Term Periodicities in Solar Indices

The purpose of the present communication is to identify the short-term (few tens of months) periodicities of several solar indices (sunspot number, Caii area and K index, Lyman , 2800 MHz radio emission, coronal green-line index, solar magnetic field). The procedure used was: from the 3-month running means (3m) the 37-month running means (37m) were subtracted, and the factor (3m – 37m) was examined for several parameters. For solar indices, considerable fluctuations were seen during the ± 4 years around sunspot maxima of cycles 18–23, and virtually no fluctuations were seen in the ± 2 years around sunspot minima. The spacings between successive peaks were irregular but common for various solar indices. Assuming that there are stationary periodicities, a spectral analysis was carried out which indicated periodicities of months: 5.1–5.7, 6.2–7.0, 7.6–7.9, 8.9–9.6, 10.4–12.0, 12.8–13.4, 14.5–17.5, 22–25, 28 (QBO), 31–36 (QBO), 41–47 (QTO). The periodicities of 1.3 year (15.6 months) and 1.7 years (20.4 months) often mentioned in the literature were seen neither often nor prominently. Other periodicities occurred more often and more prominently. For the open magnetic flux estimated by Wang, Lean, and Sheeley (2000) and Wang and Sheeley (2002), it was noticed that the variations were radically different at different solar latitudes. The open flux for < 45 solar latitudes had variations very similar (parallel) to the sunspot cycle, while open flux for > 45 solar latitudes had variations anti-parallel to the sunspot cycle. The open fluxes, interplanetary magnetic field and cosmic rays, all showed periodicities similar to those of solar indices. Many peaks (but not all) matched, indicating that the open flux for < 45 solar latitudes was at least partially an adequate carrier of the solar characteristics to the interplanetary space and thence for galactic cosmic ray modulation.     

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).     

A pictorial comparison of interplanetary magnetic field polarity,solar wind speed,and geomagnetic disturbance index during the sunspot cycle

Observations of interplanetary magnetic field polarity, solar wind speed, and geomagnetic disturbance index (C9) during the years 1962–1975 are compared in a 27-day pictorial format that emphasizes their associated variations during the sunspot cycle. This display accentuates graphically several recently reported features of solar wind streams including the fact that the streams were faster, wider, and longer-lived during 1962–1964 and 1973–1975 in the declining phase of the sunspot cycle than during intervening years (Bame et al., 1976; Gosling et al., 1976). The display reveals strikingly that these high-speed streams were associated with the major, recurrent patterns of geomagnetic activity that are characteristic of the declining phase of the sunspot cycle. Finally, the display shows that during 1962–1975 the association between long-lived solar wind streams and recurrent geomagnetic disturbances was modulated by the annual variation (Burch, 1973) of the response of the geomagnetic field to solar wind conditions. The phase of this annual variation depends on the polarity of the interplanetary magnetic field in the sense that negative sectors of the interplanetary field have their greatest geomagnetic effect in northern hemisphere spring, and positive sectors have their greatest effect in the fall. During 1965–1972 when the solar wind streams were relatively slow (500 km s^-1), the annual variation strongly influenced the visibility of the corresponding geomagnetic disturbance patterns.Visiting Scientist, Kitt Peak National Observatory, Tucson, Arizona.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Maximum and minimum temperatures at armagh observatory, 1844–1992, and the length of the sunspot cycle

The question of whether or not the Earth's climate is influenced by solar activity has received considerable attention since the mid-nineteenth century. Most investigations have adopted the sunspot number as the parameter of solar activity. Recently, however, it has been shown by Friis-Christensen and Lassen (1991) that the mean northern hemisphere temperature, from 1861–1990, follows a strikingly similar trend to thelength of the sunspot cycle, suggesting that the recent global warming could, at least in part, arise from changes in solar activity. In view of the importance of this result, we have examined a set of continuous meteorological records, maintained at Armagh Observatory since 1844, to assess, first, whether data from a single site can give meaningful information on global trends, and second, whether the data from this particular site for the period 1844–1866 can be used to extend the baseline of the comparison with solar activity. We find that both are indeed the case and that there is a strong correlation between the solar cycle length and the mean temperature at Armagh over the past 149 years.     

Dynamo-based scheme for forecasting the magnitude of solar activity cycles

In this paper we present a general framework for forecasting the smoothed maximum level of solar activity in a given cycle, based on a simple understanding of the solar dynamo. This type of forecasting requires knowledge of the Sun's polar magnetic field strength at the preceeding activity minimum. Because direct measurements of this quantity are difficult to obtain, we evaluate the quality of a number of proxy indicators already used by other authors which are physically related to the Sun's polar field. We subject these indicators to a rigorous statistical analysis, and specify in detail the analysis technique for each indicator in order to simplify and systematize reanalysis for future use. We find that several of these proxies are in fact poorly correlated or uncorrelated with solar activity, and thus are of little value for predicting activity maxima.We also present a scheme in which the predictions of the individual proxies are combined via an appropriately weighted mean to produce a compound prediction. We then apply the scheme to the current cycle 22, and estimate a maximum smoothed International sunspot number of 171 ± 26, which can be expressed alternatively as a smoothed 2800 MHz radio flux (F _10.7) of 211 ± 23 × (10^–22 Wm^–2Hz^–1), or as a smoothed sunspot area of 2660 ± 430 millionths of a solar disk. Once the actual maximum for cycle 22 has been established, we will have both additional statistics for all the proxy indicators, and a clearer indication of how accurately the present scheme can predict solar activity levels.     

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).     

Phase Relation Between Activities of Solar Active Prominences Separately at low and High Latitudes

In the present work, the phase relation between activities of solar active prominences respectively at low and high latitudes in the period 1957–1998 has been studied. We found that from the solar equator to the solar poles, the activity of the solar active prominences occurs earlier at higher latitudes, and that the cycle of the solar active prominences at high latitudes (larger than 50°) leads by 4 years both the sunspot cycle and the corresponding cycle of the solar active prominences at low latitudes (less than 40°).     

Variations in the solar rotation rate derived from Ca+ K plage areas

Daily calcium plage areas for the period 1951–1981 (which include the solar cycle 19 and 20) have been used to derive the rotation period of the Sun at latitude belts 10–15 ° N, 15–20 ° N, 10–15 ° S, and 15–20 ° S and also for the entire visible solar disk. The mean rotation periods derived from 10–20 ° S and N, total active area and sunspot numbers were 27.5, 27.9, and 27.8 days (synodic), respectively. A power spectral analysis of the derived rotation rate as a function of time indicates that the rotation rate in each latitude belt varies over time scales ranging from the solar activity cycle, down to about 2 years. Variations in adjacent latitude belts are in phase, whereas those in different hemispheres are not correlated. The rotation rates derived from sunspot numbers also behave similarly though the dependence over the solar cycle are not very apparent. The total plage areas, integrated over the entire visible hemisphere of the Sun shows a dominant periodicity of 7 years in rotation rate, while the other time scales are also discernible.