The Sidc: World Data Center for the Sunspot Index

Since January 1981, the Royal Observatory of Belgium (ROB) has operated the Sunspot Index Data Center (SIDC), the World Data Center for the Sunspot Index. From 2000, the SIDC obtained the status of Regional Warning Center (RWC) of the International Space Environment Service (ISES) and became the “Solar Influences Data analysis Center”. As a data analysis service of the Federation of Astronomical and Geophysical data analysis Services (FAGS), the SIDC collects monthly observations from worldwide stations in order to calculate the International Sunspot Number, R _i . The center broadcasts the daily, monthly, yearly sunspot numbers, with middle-range predictions (up to 12 months). Since August 1992, hemispheric sunspot numbers are also provided. Deceased.     

Dependence of SSNM on SSNm – a Reconsideration for Predicting the Amplitude of a Sunspot Cycle

An improved correlation between maximum sunspot number (SSN_M) and the preceding minimum (SSN_m) is reported when the monthly mean sunspot numbers are smoothed with a 13-month running window. This relation allows prediction of the amplitude of a sunspot cycle by making use of the sunspot data alone. The estimated smoothed maximum sunspot number (126±26) and time of maximum epoch (second half of 2000) of cycle 23 are in good agreement with the predictions made by some of the precursor methods.     

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.     

Solar Cycle Predictions based on Solar Activity at Different Solar Latitudes

Many methods of predictions of sunspot maximum number use data before or at the preceding sunspot minimum to correlate with the following sunspot maximum of the same cycle, which occurs a few years later. Kane and Trivedi (Solar Phys. 68, 135, 1980) found that correlations of R _z(max) (the maximum in the 12-month running means of sunspot number R _z) with R _z(min) (the minimum in the 12-month running means of sunspot number R _z) in the solar latitude belt 20° – 40°, particularly in the southern hemisphere, exceeded 0.6 and was still higher (0.86) for the narrower belt > 30° S. Recently, Javaraiah (Mon. Not. Roy. Astron. Soc. 377, L34, 2007) studied the relationship of sunspot areas at different solar latitudes and reported correlations 0.95 – 0.97 between minima and maxima of sunspot areas at low latitudes and sunspot maxima of the next cycle, and predictions could be made with an antecedence of more than 11 years. For the present study, we selected another parameter, namely, SGN, the sunspot group number (irrespective of their areas) and found that SGN(min) during a sunspot minimum year at latitudes > 30° S had a correlation +0.78±0.11 with the sunspot number R _z(max) of the same cycle. Also, the SGN during a sunspot minimum year in the latitude belt (10° – 30° N) had a correlation +0.87±0.07 with the sunspot number R _z(max) of the next cycle. We obtain an appropriate regression equation, from which our prediction for the coming cycle 24 is R _z(max )=129.7±16.3.     

Prediction of the Maximum Amplitude and Timing of Sunspot Cycle 24

Precursor techniques, in particular those using geomagnetic indices, often are used in the prediction of the maximum amplitude for a sunspot cycle. Here, the year 2008 is taken as being the sunspot minimum year for cycle 24. Based on the average aa index value for the year of the sunspot minimum and the preceding four years, we estimate the expected annual maximum amplitude for cycle 24 to be about 92.8±19.6 (1-sigma accuracy), indicating a somewhat weaker cycle 24 as compared to cycles 21 – 23. Presuming a smoothed monthly mean sunspot number minimum in August 2008, a smoothed monthly mean sunspot number maximum is expected about October 2012±4 months (1-sigma accuracy).     

Solar Cycle Prediction: Combining Precursor Methods with McNish and Lincoln Technique

Medium-term and long-term prediction of the magnitude of the maximum of smoothed sunspot numbers, and thus of the solar cycle time profile, is a basic input for many space environment predictions. The widely used statistical technique of McNish and Lincoln is systematically compared to predictions based on precursors, either related to the cycle time profile characteristics or to geomagnetic indices. It is shown that when cycles 13 – 23 are considered, all prediction methods give, at least for one of the cycles, an error much larger than 20%, an inadequate result. None of the methods is fully reliable. Thus, it is proposed to combine the predictions based on precursors and to improve McNish and Lincoln results with them in order to limit such rare but large errors and to improve significantly the reliability of the predictions performed in the course of the solar cycle ascending phase.     

Modeling of Sunspot Numbers by a Modified Binary Mixture of Laplace Distribution Functions

This paper presents a new approach for describing the shape of 11-year sunspot cycles by considering the monthly averaged values. This paper also brings out a prediction model based on the analysis of 22 sunspot cycles from the year 1749 onward. It is found that the shape of the sunspot cycles with monthly averaged values can be described by a functional form of modified binary mixture of Laplace density functions, modified suitably by introducing two additional parameters in the standard functional form. The six parameters, namely two locations, two scales, and two area parameters, characterize this model. The nature of the estimated parameters for the sunspot cycles from 1749 onward has been analyzed and finally we arrived at a sufficient set of the parameters for the proposed model. It is seen that this model picks up the sunspot peaks more closely than any other model without losing the match at other places at the same time. The goodness of fit for the proposed model is also computed with the Hathaway – Wilson – Reichmann measure, which shows, on average, that the fitted model passes within 0.47 standard deviations of the actual averaged monthly sunspot numbers.     

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).     

Similarities and Dissimilarities between the Variations of CME and Other Solar Parameters at Different Heliographic Latitudes and Time Scales

From the LASCO CME (Coronal Mass Ejection) catalog, the occurrence frequencies of all CMEs (all strong and weak CMEs, irrespective of their widths) were calculated for 3-month intervals and their 12-month running means determined for cycle 23 (1996 – 2007) and were compared with those of other solar parameters. The annual values of all-CME frequency were very well correlated (+ 0.97) with sunspot numbers, but several other parameters also had similarly high correlations. Comparisons of 12-month running means indicated that the sunspot numbers were very well correlated with solar electromagnetic radiations (Lyman-α, 2800-MHz flux, coronal green line index, solar flare indices, and X-ray background); but for corpuscular radiations [proton fluxes, solar energetic particles (SEP), CMEs, interplanetary CMEs (ICMEs), and stream interaction regions (SIR)] and solar open magnetic fields, the correlations were lower. A notable feature was the appearance of two peaks during 2000 – 2002, and those double peaks in different parameters matched approximately except for proton fluxes and SEP and SIR frequencies. When hemispheric intensities were considered, north – south asymmetries appeared, more in some parameters than in others. When intensities in smaller latitude belts (10°) were compared, sunspot group numbers (SGN) were found to be confined mostly to latitudes within ± 30° of the solar equator, showing two peaks in all latitude belts, and during the course of the 11-year cycle, the double peaks shifted from middle to equatorial solar latitudes, just as seen in the Maunder butterfly diagrams. In contrast, CME frequency was comparable at all latitude belts (including high, near-polar latitudes), having more than two peaks in almost all latitude belts, and the peaks were almost simultaneous in all latitude belts. Thus, the matching of SGN peaks with those of CME peaks was poor. Incidentally, the CME frequency data for all events (all widths) after 2003 are not comparable to earlier data, owing to inclusion of very weak (narrow) CMEs in later years. The frequencies are comparable with earlier data only for widths exceeding about 70°.     

Correlation Function Analysis between Sunspot Cycle Amplitudes and Rise Times

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

Latitude Dependence of the Variations of Sunspot Group Numbers (SGN) and Coronal Mass Ejections (CMEs) in Cycle 23

The 12-month running means of the conventional sunspot number Rz, the sunspot group numbers (SGN) and the frequency of occurrence of Coronal Mass Ejections (CMEs) were examined for cycle 23 (1996 – 2006). For the whole disc, the SGN and Rz plots were almost identical. Hence, SGN could be used as a proxy for Rz, for which latitude data are not available. SGN values were used for 5° latitude belts 0° – 5°, 5° – 10°, 10° – 15°, 15° – 20°, 20° – 25°, 25° – 30° and > 30°, separately in each hemisphere north and south. Roughly, from latitudes 25° – 30° N to 20° – 25° N, the peaks seem to have occurred later for lower latitudes, from latitudes 20° – 25° N to 15° – 20° N, the peaks are stagnant or occur slightly earlier, and then from latitudes 15° – 20° N to 0° – 5° N, the peaks seem to have occurred again later for lower latitudes. Thus, some latitudinal migration is suggested, clearly in the northern hemisphere, not very clearly in the southern hemisphere, first to the equator in 1998, stagnant or slightly poleward in 1999, and then to the equator again from 2000 onwards, the latter reminiscent of the Maunder butterfly diagrams. Similar plots for CME occurrence frequency also showed multiple peaks (two or three) in almost all latitude belts, but the peaks were almost simultaneous at all latitudes, indicating no latitudinal migration. For similar latitude belts, SGN and CME plots were dissimilar in almost all latitude belts except 10° – 20° S. The CME plots had in general more peaks than the SGN plots, and the peaks of SGN often did not match with those of CME. In the CME data, it was noticed that whereas the values declined from 2002 to 2003, there was no further decline during 2003 – 2006 as one would have expected to occur during the declining phase of sunspots, where 2007 is almost a year of sunspot minimum. An inquiry at GSFC-NASA revealed that the person who creates the preliminary list was changed in 2004 and the new person picks out more weak CMEs. Thus a subjectivity (overestimates after 2002) seems to be involved and hence, values obtained before and during 2002 are not directly comparable to values recorded after 2002, except for CMEs with widths exceeding 60°.     

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

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

Short-Term Periodicities in Sunspot Activities During the Descending Phase of Solar Cycle 23

In the present study, the short-term periodicities in the daily data of the sunspot numbers and areas are investigated separately for the full disk, northern, and southern hemispheres during Solar Cycle 23 for a time interval from 1 January 2003 to 30 November 2007 corresponding to the descending and minimum phase of the cycle. The wavelet power spectrum technique exhibited a number of quasi-periodic oscillations in all the datasets. In the high frequency range, we find a prominent period of 22 – 35 days in both sunspot indicators. Other quasi-periods in the range of 40 – 60, 70 – 90, 110 – 130, 140 – 160, and 220 – 240 days are detected in the sunspot number time series in different hemispheres at different time intervals. In the sunspot area data, quasi-periods in the range of 50 – 80, 90 – 110, 115 – 130, 140 – 155, 160 – 190, and about 230 days were noted in different hemispheres within the time period of analysis. The present investigation shows that the well-known “Rieger periodicity” of 150 – 160 days reappears during the descending phase of Solar Cycle 23, but this is prominent mainly in the southern part of the Sun. Possible explanations of these observed periodicities are delivered on the basis of earlier results detected in photospheric magnetic field time series (Knaack, Stenflo, and Berdyugina in Astron. Astrophys. 438, 1067, 2005) and solar r-mode oscillations.     

Synchronization in Sunspot Indices in the Two Hemispheres

Historical sunspot records were analyzed by means of nonlinear tools to find synchronization phenomena at different time scales on the Sun. Using cross-recurrence plots it is shown that the north – south sunspot synchronization demonstrates a set of distinct periodic oscillations – 43.29, 18.52, and 7.63 years. Also we have traced the sunspot synchronization on shorter time scales. Very rare and episodic synchronization within half of the Carrington rotation rate was detected. By using the empirical mode decomposition technique the north – south sunspot time series were decomposed into intrinsic oscillatory modes. To determine which modes of the signal are responsible for synchronization we separated them into high- and low-frequency parts. It is shown that phase synchronization is detected only in the low-frequency modes. The high-frequency component demonstrates noisy behavior with amplitude synchronization and strong phase mixing.     

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.     

Analysis of Sunspot Activity Cycles

A nonlinear analysis of the daily sunspot number for each of cycles 10 to 23 is used to indicate whether the convective turbulence is stochastic or chaotic. There is a short review of recent papers considering sunspot statistics and solar activity cycles. The differences in the three possible regimes – deterministic laminar flow, chaotic flow, and stochastic flow – are discussed. The length of data sets necessary to analyze the regimes is investigated. Chaos is described and a chronology of recent results that utilize chaos and fractals to analyze sunspot numbers follows. The parameters necessary to describe chaos – time lag, phase space, embedding dimension, local dimension, correlation dimension, and the Lyapunov exponents – are determined for the attractor for each cycle. Assuming the laminar regime is unlikely if chaos is not indicated in a cycle by the calculations, the regime must be stochastic. The sunspot numbers in each of cycles 10 to 19 indicate stochastic behavior. There is a transition from stochastic to chaotic behavior of the sunspot numbers in cycles 20, 21, 22, and 23. These changes in cycles 20 – 23 may indicate a change in the scale of turbulence in the convection zone that could result in a change in the convective heat transfer and a change in the size of the convection region for these four cycles.     

Digitization of Sunspot Drawings by Staudacher in 1749 – 1796

Original drawings by J.C. Staudacher made in the period of 1749 – 1796 were digitized. The drawings provide information about the size of the sunspots and are therefore useful for analyses sensitive to sunspot area rather than Wolf numbers. The total sunspot area as a function of time is shown for the observing period. The sunspot areas measured do not support the proposition of a weak, “lost” cycle between cycles 4 and 5. We also evaluate the usefulness of the drawings for the determination of sunspot positions for future studies.     

The Shape of Sunspot Cycles Described by Monthly Sunspot Areas

In this paper, we used the same four-parameter function as Hathaway, Wilson, and Reichmann (1994) proposed and studied the temporal behavior of sunspot cycles 12–22. We used the monthly averages of sunspot areas and their 13-point smoothed data. Our results show the following. (1) The four-parameter function may reduce to a function of only two parameters. (2) As a cycle progresses, the two-parameter function can be accurately determined after 4–4.5 years from the start of the cycle. A good prediction can be made for the timing and size of the sunspot maximum and for the behavior of the remaining 5–10 years of the cycle. (3) The solar activity in the remaining and forthcoming years of cycle 23 is predicted. (4) The smoothed monthly sunspot areas are more suitable to be employed for prediction at the maximum and the descending period of a cycle, whereas at the early period of a cycle the (un-smoothed) monthly data are more suitable.     

Longterm Prediction of Solar Activity Using the Combined Method

The Combined Method is a non-parametric regression technique for long-term prediction of smoothed monthly sunspot numbers. Starting from a solar minimum, a prediction of the succeeding maximum is obtained by using a dynamo-based relation between the geomagnetic aa index and succeeding solar maxima. Then a series of predictions is calculated by computing the weighted average of past cycles of similar level. This technique leads to a good prediction performance, particularly in the ascending phase of the solar cycle where purely statistical methods tend to be inaccurate. For cycle 23 the combined method predicts a maximum of 160 (in terms of smoothed sunspot number) early in the year 2000.