Group Sunspot Number Research Articles

A CRITICAL COMMENT ON THE CLAIMED RELATION BETWEEN THE SOLAR MAXIMUM AMPLITUDE AND MAX-MAX CYCLE LENGTH

In this paper, we revisit a correlation between the amplitude of a solar cycle, Rm , and the max-max solar cycle length two solar cycles before, P max – 2, which was proposed by Du to be used as a tool for solar cycle forecasting. We vary the time interval used in the statistical analysis and also use different long-term series of sunspot numbers: International sunspot number and Group sunspot number. We show that the claimed correlation appears unstable as it depends on the time interval and the selected data series. This suggests that the relationship between the two parameters is not stationary and more complex than previously thought and, therefore, this relationship should not be used to predict solar activity.

The persistence of solar activity indicators and the descent of the Sun into Maunder Minimum conditions

[1] The recent low and prolonged minimum of the solar cycle, along with the slow growth in activity of the new cycle, has led to suggestions that the Sun is entering a Grand Solar Minimum (GSMi), potentially as deep as the Maunder Minimum (MM). This raises questions about the persistence and predictability of solar activity. We study the autocorrelation functions and predictability R2L(t) of solar indices, particularly group sunspot number RG and heliospheric modulation potential Φ for which we have data during the descent into the MM. For RG and Φ, R2L(t) > 0.5 for times into the future of t ≈ 4 and ≈ 3 solar cycles, respectively: sufficient to allow prediction of a GSMi onset. The lower predictability of sunspot number RZ is discussed. The current declines in peak and mean RG are the largest since the onset of the MM and exceed those around 1800 which failed to initiate a GSMi.

How well do we know the sunspot number?

AbstractWe show that only two adjustments are necessary to harmonize the Group Sunspot Number with the Zürich Sunspot Number. The latter has been increased from the 1940s on to the present by 20% due to weighting of sunspot counts according to size of the spots and can be corrected by increasing the earlier values as well. The Group Sunspot Number before ~1885 is too low by ~50%. With these adjustments a single sunspot number series results. Of note is that there is no longer a distinct Modern Grand Maximum.

Evolution of Solar and Geomagnetic Activity Indices, and Their Relationship: 1960 – 2001

We employ annually averaged solar and geomagnetic activity indices for the period 1960 – 2001 to analyze the relationship between different measures of solar activity as well as the relationship between solar activity and various aspects of geomagnetic activity. In particular, to quantify the solar activity we use the sunspot number Rs, group sunspot number Rg, cumulative sunspot area Cum, solar radio flux F10.7, and interplanetary magnetic field strength IMF. For the geomagnetic activity we employ global indices Ap, Dst and Dcx, as well as the regional geomagnetic index RES, specifically estimated for the European region. In the paper we present the relative evolution of these indices and quantify the correlations between them. Variations have been found in: i) time lag between the solar and geomagnetic indices; ii) relative amplitude of the geomagnetic and solar activity peaks; iii) dual-peak distribution in some of solar and geomagnetic indices. The behavior of geomagnetic indices is correlated the best with IMF variations. Interestingly, among geomagnetic indices, RES shows the highest degree of correlation with solar indices.

Statistical Effects in the Solar Activity Cycles during AD 1823–1996

General statistical properties of solar activity cycles during the period AD 1823–1996—including the Gnevyshev-Ohl and Waldmeier effects as well as an amplitude-period effect—were analyzed using Wolf number, group sunspot number, and extended total sunspot area series. It was found out that the Gnevyshev-Ohl effect GO2 (the positive correlation between intensity of the even cycles 2N and intensity of the odd cycles 2N+1) and the Waldmeier effect W2 (the anticorrelation between rise times of sunspot cycles and their amplitudes) are the most universal and robust features of the solar cycle. Other statistical relations were found appreciably sensitive to the selection of solar index, the interval of analysis, and the way of the cycle feature determination.

Temporal evolution of statistical features of the sunspot cycles

Analysis of the general statistical features of the sunspot cycles in the period 1700–1996 AD, including the Gnevyshev–Ohl rule, Waldmeier rule and an amplitude–period effect, was performed for both Wolf numbers and group sunspot numbers. It was shown that for both solar indices all the statistical effects are weaker over the time interval 1700–1855 AD than over the time interval 1856–1996 AD. Possible causes of this difference are discussed.

TIME DISTRIBUTIONS OF LARGE AND SMALL SUNSPOT GROUPS OVER FOUR SOLAR CYCLES

Here we analyze solar activity by focusing on time variations of the number of sunspot groups (SGs) as a function of their modified Zurich class. We analyzed data for solar cycles 2023 by using Rome (cycles 2021) and Learmonth Solar Observatory (cycles 2223) SG numbers. All SGs recorded during these time intervals were separated into two groups. The first group includes small SGs (A, B, C, H, and J classes by Zurich classification) and the second group consists of large SGs (D, E, F, and G classes). We then calculated small and large SG numbers from their daily mean numbers as observed on the solar disk during a given month. We report that the time variations of small and large SG numbers are asymmetric except for the solar cycle 22. In general large SG numbers appear to reach their maximum in the middle of the solar cycle (phase 0.450.5), while the international sunspot numbers and the small SG numbers generally peak much earlier (solar cycle phase 0.290.35). Moreover, the 10.7 cm solar radio flux, the facular area, and the maximum CME speed show better agreement with the large SG numbers than they do with the small SG numbers. Our results suggest that the large SG numbers are more likely to shed light on solar activity and its geophysical implications. Our findings may also influence our understanding of long term variations of the total solar irradiance, which is thought to be an important factor in the Sun - Earth climate relationship.

North–South asymmetry of the sunspot indices and its quasi-biennial oscillations

The space–time distribution of asymmetry in the area and total number of sunspot groups was considered over the time interval 1874–2009. The time behavior of the asymmetry in these indices of sunspot activity was shown to be similar on both small and large time scales. Spectral variation analysis (SVAN) was applied to study the spectral characteristics. Quasi–biennial oscillations (QBO) were revealed in the asymmetry of both indices under discussion. The SVAN diagrams for the asymmetry of the areas and numbers of sunspots in the range of QBO periods display pronounced similarity. In the activity indices per se, these effects are much weaker: the mutual correlation of the indices is lower, the QBO are less pronounced, and the similarity of the SVAN diagrams in the QBO range is absent. The effect of negative correlation between the QBO power and absolute value of the asymmetry over a long time interval was revealed: the increase in asymmetry is accompanied by a decrease in QBO amplitude regardless of which hemisphere is more active at the moment. This underlines the global nature of QBO and the relation of asymmetry to the quadrupole component of the solar large-scale magnetic field. The asymmetry is an independent fundamental characteristic of solar activity, which does not reduce to the classical characteristics of the 11-year cycle.

Width of Sunspot Generating Zone and Reconstruction of Butterfly

Based on the extended Greenwich-NOAA/USAF catalogue of sunspot groups it is demonstrated that the parameters describing the latitudinal width of the sunspot generating zone (SGZ) are closely related to the current level of solar activity, and the growth of the activity leads to the expansion of SGZ. The ratio of the sunspot number to the width of SGZ shows saturation at a certain level of the sunspot number, and above this level the increase of the activity takes place mostly due to the expansion of SGZ. It is shown that the mean latitudes of sunspots can be reconstructed from the amplitudes of solar activity. Using the obtained relations and the group sunspot numbers by Hoyt and Schatten (1998), the latitude distribution of sunspot groups ("the Maunder butterfly diagram") for the 18th and the first half of the 19th centuries is reconstructed and compared with historical sunspot observations.

Explosive volcanic eruptions triggered by cosmic rays: Volcano as a bubble chamber

Volcanoes with silica-rich and highly viscous magma tend to produce violent explosive eruptions that result in disasters in local communities and that strongly affect the global environment. We examined the timing of 11 eruptive events that produced silica-rich magma from four volcanoes in Japan (Mt. Fuji, Mt. Usu, Myojin-sho, and Satsuma-Iwo-jima) over the past 306 years (from AD 1700 to AD 2005). Nine of the 11 events occurred during inactive phases of solar magnetic activity (solar minimum), which is well indexed by the group sunspot number. This strong association between eruption timing and the solar minimum is statistically significant to a confidence level of 96.7%. This relationship is not observed for eruptions from volcanoes with relatively silica-poor magma, such as Izu-Ohshima. It is well known that the cosmic-ray flux is negatively correlated with solar magnetic activity, as the strong magnetic field in the solar wind repels charged particles such as galactic cosmic rays that originate from outside of the solar system. The strong negative correlation observed between the timing of silica-rich eruptions and solar activity can be explained by variations in cosmic-ray flux arising from solar modulation. Because silica-rich magma has relatively high surface tension (~ 0.1 Nm −1), the homogeneous nucleation rate is so low that such magma exists in a highly supersaturated state without considerable exsolution, even when located relatively close to the surface, within the penetration range of cosmic-ray muons (1–10 GeV). These muons can contribute to nucleation in supersaturated magma, as documented by many authors studying a bubble chamber, via ionization loss. This radiation-induced nucleation can lead to the pre-eruptive exsolution of H 2O in the silica-rich magma. We note the possibility that the 1991 Mt. Pinatubo eruption was triggered by the same mechanism: an increase in cosmic-ray flux triggered by Typhoon Yunya, as a decrease in atmospheric pressure results in an increase in cosmic-ray flux. We also speculate that the snowball Earth event was triggered by successive large-scale volcanic eruptions triggered by increased cosmic-ray flux due to nearby supernova explosions.

Relationship between group sunspot numbers and Wolf sunspot numbers

AbstractContinuous wavelet transform and cross‐wavelet transform have been used to investigate the phase periodicity and synchrony of the monthly mean Wolf (Rz) and group (Rg) sunspot numbers during the period of June 1795 to December 1995. The Schwabe cycle is the only one common period in Rg and Rz, but it is not well‐defined in case of cycles 5–7 of Rg and in case of cycles 5 and 6 of Rz. In fact, the Schwabe period is slightly different in Rg and Rz before cycle 12, but from cycle 12 onwards it is almost the same for the two time series. Asynchrony of the two time series is more obviously seen in cycles 5 and 6 than in the following cycles, and usually more obviously seen around the maximum time of a cycle than during the rest of the cycle. Rg is found to fit Rz better in both amplitudes and peak epoch during the minimum time time of a solar cycle than during the maximum time of the cycle, which should be caused by their different definition, and around the maximum time of a cycle, Rg is usually less than Rz. Asynchrony of Rg and Rz should somewhat agree with different sunspot cycle characteristics exhibited by themselves (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Hemispheric variation of coronal mass ejections in cycle 23

In this paper, we analyse the behaviour of the activity of coronal mass ejection (CME) observed by the Large Angle and Spectrometric Coronagraph Experiment on board the Solar and Heliospheric Observatory (SOHO/LASCO) in cycle 23 from 1997 to 2007 separately for the Northern and Southern hemispheres. The results show the following. (1) At all and low latitudes, the dominant hemisphere of the activity of CME changes from the Northern hemisphere before cycle maxima to the Southern hemisphere after cycle maxima; a southern dominance of the activity of CME is shown to occur in cycle 23. This is consistent with sunspot studies. The relationship between the two lines of the cumulative counts of monthly CME numbers for the Northern and Southern hemispheres is similar to those of monthly sunspot group numbers and sunspot areas. (2) At high latitudes, prior to 2002, the trend of the monthly values of the north-south asymmetry of numbers of CMEs is similar to those of sunspot group numbers and sunspot areas; the relationship between the two lines of the cumulative counts of monthly CME numbers for the Northern and Southern hemispheres is similar to those of sunspot group numbers and sunspot areas. However, after 2001, the trend of dominant hemisphere of the activity of CME at high latitudes is different from those of sunspot group numbers and sunspot areas; the relationship between the two lines of the cumulative counts of monthly CME numbers for the Northern and Southern hemispheres at high latitudes is different from those sunspot group numbers and sunspot areas. Our results seem to suggest that the activity of CME at high latitudes should have close connection with 'rush to the poles'.

Prediction of cycle 24 based on information about solar activity during the last 10 000 years

The average and maximal numbers of sunspot groups in the approaching solar cycle (cycle 24) have been predicted using paleoastrophysical information about solar activity during the last more than 10000 years. The linear and nonlinear prediction methods have been applied. It has been indicated that, from the standpoint of solar paleoastrophysics, the next cycle will most probably be average: the number of sunspot groups at a maximum will reach 68-101. The probability that cycle 24 will be powerful (more than 160 sun� spot groups), which was predicted by some researchers, is low (not higher than 2%).

Comparison of three solar activity indices based on sunspot observations

The following sunspot formation indices are analyzed: the relative sunspot number R z , the normal- ized sunspot group number R g , and the total sunspot area A. Six empirical formulas are derived to describe the relations among these indices after 1908. The earlier data exhibit systematic deviations from these formulas, which can be attributed to systematic errors of the indices. The Greenwich data on the sunspot total area A and the sunspot group number in 1874-1880 are found to be doubtful. Erroneous data at the beginning of the Green- wich series must spoil the values of the index R g in the XVII-XIX centuries. The Hoyt-Schatten series of R g may be less reliable than the well-known Wolf number series R z .

Systematic Time Delay of Hemispheric Solar Activity

Five solar-activity indices - the monthly-mean sunspot numbers from January 1945 to March 2008, the monthly-mean sunspot areas during the period of May 1874 to March 2008, the monthly numbers of sunspot groups from May 1874 to May 2008, the monthly-mean flare indices from January 1966 to December 2006, and the numbers of solar filaments per Carrington rotation in the time interval of solar rotations 876 to 1823 - have been used to show a systematic time delay between northern and southern hemispheric solar activities in a cycle. It is found that solar activity does not occur synchronously in the northern and southern hemispheres, and there is a systematic time lag or lead (phase shift) between northern and southern hemispheric solar activity in a cycle. About an eight-cycle period is inferred to exist in such phase shifts. The activity on the Sun may be governed by two different and coupled processes, not by a single process.

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.

A Robust Correlation between Growth Rate and Amplitude of Solar Cycles: Consequences for Prediction Methods

We consider the statistical relationship between the growth rate of activity in the early phase of a solar cycle with its subsequent amplitude on the basis of four data sets of global activity indices (Wolf sunspot number, group sunspot number, sunspot area, and 10.7 cm radio flux). In all cases, a significant correlation is found: stronger cycles tend to rise faster. Owing to the overlapping of sunspot cycles, this correlation leads to an amplitude-dependent shift of the solar minimum epoch. We show that this effect explains the correlations underlying various so-called precursor methods for the prediction of solar cycle amplitudes and also affects the prediction tool of Dikpati et al. based on a dynamo model. Inferences as to the nature of the solar dynamo mechanism resulting from predictive schemes which (directly or indirectly) use the timing of solar minima should therefore be treated with caution.

A Running Average Method for Predicting the Size and Length of a Solar Cycle

The running correlation coefficient between the solar cycle amplitudes and the max-max cycle lengths at a given cycle lag is found to vary roughly in a cyclical wave with the cycle number, based on the smoothed monthly mean Group sunspot numbers available since 1610. A running average method is proposed to predict the size and length of a solar cycle by the use of the varying trend of the coefficients. It is found that, when a condition (that the correlation becomes stronger) is satisfied, the mean prediction error (16.1) is much smaller than when the condition is not satisfied (38.7). This result can be explained by the fact that the prediction must fall on the regression line and increase the strength of the correlation. The method itself can also indicate whether the prediction is reasonable or not. To obtain a reasonable prediction, it is more important to search for a running correlation coefficient whose varying trend satisfies the proposed condition, and the result does not depend so much on the size of the correlation coefficient. As an application, the peak sunspot number of cycle 24 is estimated as 140.4±15.7, and the peak as May 2012±11 months.

Gnevyshev Peaks and Gaps for Coronal Mass Ejections of Different Widths Originating in Different Solar Position Angles

The sunspot number series at the peak of sunspot activity often has two or three peaks (Gnevyshev peaks; Gnevyshev, Solar Phys.1, 107, 1967; Solar Phys.51, 175, 1977). The sunspot group number (SGN) data were examined for 1997 – 2003 (part of cycle 23) and compared with data for coronal mass ejection (CME) events. It was noticed that they exhibited mostly two Gnevyshev peaks in each of the four latitude belts 0° – 10°, 10° – 20°, 20 ° – 30°, and > 30°, in both N (northern) and S (southern) solar hemispheres. The SGN were confined to within latitudes ± 50° around the Equator, mostly around ± 35°, and seemed to occur later in lower latitudes, indicating possible latitudinal migration as in the Maunder butterfly diagrams. In CMEs, less energetic CMEs (of widths < 71°) showed prominent Gnevyshev peaks during sunspot maximum years in almost all latitude belts, including near the poles. The CME activity lasted longer than the SGN activity. However, the CME peaks did not match the SGN peaks and were almost simultaneous at different latitudes, indicating no latitudinal migration. In energetic CMEs including halo CMEs, the Gnevyshev peaks were obscure and ill-defined. The solar polar magnetic fields show polarity reversal during sunspot maximum years, first at the North Pole and, a few months later, at the South Pole. However, the CME peaks and gaps did not match with the magnetic field reversal times, preceding them by several months, rendering any cause – effect relationship doubtful.

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°.