Sunspot Number Research Articles

Predicting the 25th and 26th solar cycles using the long short-term memory method

Abstract Solar activities directly or indirectly affect space missions, geophysical environment, space climate, and human activities. We used the long short-term memory (LSTM) deep learning method to predict the amplitude and peak time of solar cycles (SCs) 25 and 26 by using the monthly relative sunspot number data taken from the National Astronomical Observatory of Japan (NAOJ). The dataset is divided into eight schemes of two to nine slices for training, showing that the five-slice LSTM model with root mean square error of 11.38 is the optimal model. According to the prediction, SC 25 will be about 21$\%$ stronger than SC 24, with a peak of 135.2 occurring in 2024 April. SC 26 will be similar to SC 25 and reach its peak of 135.0 in 2035 January. Our analysis results indicate that the sunspot data from NAOJ is highly credible and comparable.

Comparing the impact of solar activities on rainfall under varying climates during the solar cycle 24

A ten-year (2009 – 2018) data sets of rainfall and sunspot numbers obtained from the Nigerian Meteorological (NIMET) agency and Sunspot Index and Long term Solar Observations (SILSO) respectively were studied using correlation and trend analysis and their results were compared. Variations in annual and monthly rainfall in Port Harcourt and Sokoto stations during solar cycle 24 were observed. The results of the correlation between rainfall (RF) and sunspot numbers (SSN) showed that all the months in Sokoto correlated negatively as expected while half of the months in Port Harcourt were negatively correlated. Again, monthly RF/SSN correlation results in Sokoto were high except in March, August, and December with -0.1827, -0.1338, and -0.0.1653 respectively, whereas only January, March, April, and May in Port Harcourt had high correlations with -0.5309, 0.5773, -0.5499, and -0.6710. While trend analysis of SSN and RF in Sokoto showed a coincidence in the peaks of Sunspot numbers and rainfall in 2014, that between SSN and RF in Port Harcourt showed that RF peaked 3 years after SSN peak. The results suggest a possible effect of solar activity on climate change and also the impact of aerosols and atmospheric air contaminations in the solar activity – rainfall relationship.

On the Strength and Duration of Solar Cycle 25: A Novel Quantile-Based Superposed-Epoch Analysis

The sunspot number (SSN) is an important – albeit nuanced – parameter that can be used as an indirect measure of solar activity. Predictions of upcoming active intervals, including the peak and timing of solar maximum, can have important implications for space weather planning. Forecasts for the strength of Solar Cycle 25 have varied considerably, from being very weak to one of the strongest cycles in recorded history. In this study, we develop a novel quantile-based superposed-epoch analysis that currently predicts that Solar Cycle 25 will be very modest (within the lowest 25th percentile of all numbered cycles), with a monthly-averaged (13-month average) peak of ≈ 130 (110) likely occurring in December 2024. We validate the model by performing retrospective forecasts (hindcasts) for the previous 24 cycles, finding that it outperforms the baseline (reference) model (the “average cycle”) 75% of the time.

Understanding the Relationship between Solar Coronal Abundances and F10.7 cm Radio Emission

Sun-as-a-star coronal plasma composition, derived from full-Sun spectra, and the F10.7 radio flux (2.8 GHz) have been shown to be highly correlated (r = 0.88) during solar cycle 24. However, this correlation becomes nonlinear during increased solar magnetic activity. Here we use cotemporal, high spatial resolution, multiwavelength images of the Sun to investigate the underlying causes of the nonlinearity between coronal composition (FIP bias) and F10.7 solar index correlation. Using the Karl G. Jansky Very Large Array, Hinode/EIS (EUV Imaging Spectrometer), and the Solar Dynamics Observatory, we observed a small active region, AR 12759, throughout the solar atmosphere from the photosphere to the corona. The results of this study show that the magnetic field strength (flux density) in active regions plays an important role in the variability of coronal abundances, and it is likely the main contributing factor to this nonlinearity during increased solar activity. Coronal abundances above cool sunspots are lower than in dispersed magnetic plage regions. Strong magnetic concentrations are associated with stronger F10.7 cm gyroresonance emission. Considering that as the solar cycle moves from minimum to maximum, the sizes of sunspots and their field strength increase with the gyroresonance component, the distinctly different tendencies of radio emission and coronal abundances in the vicinity of sunspots is the likely cause of saturation of Sun-as-a-star coronal abundances during solar maximum, while the F10.7 index remains well correlated with the sunspot number and other magnetic field proxies.

Study of the Relationship Between Sunspot Number and the Duration of the ≈ 1.6 – 2.2 Year Period in Neutron Monitor Counting Rates

Neutron monitor counting rates show periodicities in the ≈ 1.6 – 2.2-year range. These periodicities have been associated with a solar origin affecting the cosmic ray propagation conditions through the heliosphere. Our hypothesis is that the periodicities in the ≈ 1.6 – 2.2-years range correspond to a single periodicity that changes its duration over time.López-Comazzi and Blanco (Astrophys. J.927(2), 155, 2022) found that the duration of the ≈ 1.6 – 2.2-year period (tau ) is linearly related to the average sunspot number (SSN_{a}) in each solar cycle. The relationship shows that shorter ≈ 1.6 – 2.2-year periods occur during stronger cycles when SSN_{a} is higher. Therefore, the duration of this period varies from one solar cycle to another. This study focuses on this relation. For obtaining this relation, the values of the duration of the ≈ 1.6 – 2.2-year period in global neutron monitor counting rates (a virtual station determined by averaging of the different neutron monitor counting rates along the world) along the Solar Cycles 20 – 24 have been used. We extend the sample by adding the duration of the ≈ 1.6 – 2.2-year period in Huancayo neutron monitor counting rates along Solar Cycle 19 to this linear relationship. Once the linear relationship is extended, tau for the current Solar Cycle 25 is computed giving ≈ 2.24 years. Drawing on this more accurate relationship given by SSN_{a} = (-120 pm 10) : tau + (320 pm 20), we computed tau for the cycles previous to the existence of neutron monitors (Solar Cycles 7 – 18).These ≈ 1.6 – 2.2-year periodicities in neutron monitor counting rates could be produce by variations in the solar magnetic field due to an internal mechanism of the solar dynamo called Rossby waves. Concretely, the harmonic of fast Rossby waves with m=1 and n=8 fit with the detected ≈ 1.6 – 2.2-year periodicity. In addition, the variation of the solar magnetic-field strength from weaker to stronger solar cycles could explain the different periods detected in each cycle. Based on the detected periodicities using the dispersion relation for fast Rossby waves, a solar tachocline magnetic-field strength of ≈ 7 – 25 kG has been estimated.

Influence of the Gleissberg Cycle on Variations of the 11-Year Cycle of Solar Activity in 1700–2021

The wavelet analysis was used to study the spectral composition of the sunspot numbers SN during1700–2021. In addition to the dominant 11-year component, two powerful components of the Gleissbergcycle can be traced in the spectrum: before 1880, a branch with a period of ~60 years; from 1850 a branch of~115 years is found. It is found that the series of lengths and amplitudes of the solar cycle as a whole areinversely related (correlation coefficient k = –0.5–0.63). The interval between the series at which the maximumanticorrelation is reached depends on time. In the 18th and early 19th centuries, the lag was equal toone cycle, in the 19th century it was two cycles, and from 1950 to our time the lag decreased to 2 years. Quasiperiodicstructures, which are typical for long periods of low solar activity, have been identified. Such a spectralfeature in ~1800 (Dalton minimum) was caused by the influence of the 60-year branch, while the onethat has been forming since the beginning of the 21st century is due to the weaker influence of the circa-centenarybranch. Therefore, it should be expected that the next solar cycles will be higher and shorter thanduring the period of the Dalton minimum. It has been shown that solar cycle length variations for the last321 years can be described within the framework of the model, which is an 11-year oscillation that is subjectto frequency modulation by the branches of the Gleisberg cycle (60 and 115 years) with time-varying influencesof the modulator

Estimation of the Average Values of the Wolf Numbers of Cycles of the Dalton Minimum Based on the Characteristics of Reliable Cycles of a Series

The source material for the number of Wolf numbers is both archival records of disparate observationsand regular observatory observations. Many researchers rely on a series of Wolf numbers, includingrestored data of archival records, although the properties and characteristics of the restored and reliable partsof the series differ significantly. The parameters of the restored part itself are also contradictory. Naturally,matching the properties of the reconstructed and reliable series will smooth the contradictions and expandthe array of more reliable data. Taking the relationship between the characteristics of significant cycles intoaccount, options for group correction of the average values of cycles I–IX are presented. Since local dataresiduals play a lesser role when comparing extended fragments, by relying on the integral estimates of thesefragments (without detailing the conditions for their formation) we obtained more weighted interval estimates.The parameters of intervals (groups of cycles) of a reliable series serve as the basis for correction.

ВЛИЯНИЕ ЦИКЛИЧЕСКОЙ СОЛНЕЧНОЙ АКТИВНОСТИ НА ПОКАЗАТЕЛИ НАСИЛЬСТВЕННОЙ СМЕРТИ

The article is devoted to the study of the influence of solar activity on mortality from violent causes (by the example of various kinds of violent death). Research material: astronomical observations of solar activity; demographic indicators of Russia; statistical indicators of the activities of the Bureau of Forensic Medical examination of the country and St. Petersburg over the past 25 years; database of murderers. Methods: isolation and fixation of information, grouping of data, frequency analysis, correlation analysis, comparison, analysis and generalization of the revealed patterns. It was found that the number of sudden deaths suspected of violent death (as a result of diseases of the cardiovascular or nervous system, oncological or infectious diseases) directly correlates with the Wolf–Schwabe number (correlation coefficient from 0.21 to 0.40, p<0.05). For the specific number of suicides, the correlation coefficient is 0.24 (p<0.01), for the specific number of murders – 0.46 (p<0.05), for the specific number of accidents (for example, fatal cold injury) – 0.50 (p<0.01). The coefficient of linear correlation between the number of future murderers born during the year and the number of sunspots in the previous year (year of conception) is 0.36 (p<0.05). In the control group (men with no criminal history), the correlation coefficient of the number of births and the Wolf-Schwabe number is 0.12 (p<0.05). The data obtained indicate a significant influence of solar activity on the processes taking place in society, affecting various elements – from the economy and public health to public safety. Currently, there is an increase in solar activity, the peak of which is projected to reach in 2025, which requires adequate consideration when planning health resources.

Behavior of the solar coronal holes around the maximum activity of the cycle 24

The behavior of coronal holes (CHs) as open magnetic field lines and a substrate for the high-speed exit of solar winds is an essential aspect of solar activity. This paper studies the statistical properties of CHs around the maximum activity of cycle 24 (13 May 2010 to 31 October 2017) observed by the Atmospheric Imaging Assembly at 193 Å images. We showed that the size of CHs follows the power-law distributions indicating the scale-free behavior of CHs. The butterfly diagram of CHs demonstrates that the overall number of CHs shows a similar distribution in the two hemispheres. Large CHs with sizes ⩾2.57×105 arcsec2 (top 3% of observed CHs) more commonly appear at latitudes above 30∘ closer to the poles. We found that the largest CHs with sizes ⩾7.71×105 arcsec2 (top 0.03% of observed CHs) occur in the northern hemisphere. The appearance and disappearance of large CHs exhibit the asymmetrical behavior between the two hemispheres. Also, it is observed that CHs tend to have a latitudinal drift towards the poles in each hemisphere. A significant correlation between the number of sunspots and the eccentricity of equatorial CHs appeared near the solar disk center revealed that most of the CHs have elongated shapes at the maximum solar activity. In contrast, they have less abnormality during solar minimum. Applying detrended fluctuation and rescaled range analyses to the time series of CHs, we realized that the CHs have a long-term correlation and form a self-organized system.

Late-Holocene paleoceanographic and climatic changes and their impact on Indian socio-economic conditions: Benthic foraminiferal evidence from the Bay of Bengal

The present work is pursued on the benthic foraminiferal groups obtained from NGHP core samples of the western Bay of Bengal to understand the variations of paleoceanography and Indian Summer Monsoon (ISM), as well as socio-economic changes in ancient India. Benthic foraminiferal AMS 14C dating reveals that the studied interval spans between 335 BC and 1355 AD, covering the history of the last 1690 years. We compared foraminifera group counts with published isotopes, sunspot number, summer monsoon index, hematite-stained grain, Al/Ca, 14C data sets. Angular Asymmetrical Benthic Foraminifera, infaunal, and dysoxic groups exhibit declining trends with warm, humid intervals with intensified ISM signature from 335 BC to 406 AD (Roman Warm Period) and from 787 to 1202 AD (Medieval Warm Period). The Increasing trend of the above foraminiferal groups captures the signature of weak ISM from 406 to 787 AD (Dark Age Cold Period) and from 1202 to 1355 AD (Medieval Warm Period and Little Ice Age Transition). Whereas rounded symmetrical benthic foraminifera, epifaunal, and oxic groups show a reverse relation with the abovementioned groups. Spectral analysis of foraminiferal groups shows significant periodicities of 563/561, 450, 321, 281/250, 22/27, and 17/16/15 years, corresponding to various solar cycles. This research uncovers the relationship between solar activity and monsoonal changes, which influenced India’s economic growth and played a crucial role in the establishment and demise of successive dynasties throughout the Indian subcontinent during the late-Holocene.

Study on the Hemispheric Asymmetry of Thermospheric Density Based on In-Situ Measurements from APOD Satellite

In this article, high spatiotemporal resolution data obtained by the atmospheric density detector carried by China’s APOD satellite are used to study the hemispheric asymmetry of thermospheric density. A detailed analysis is first performed on the dual magnetic storm event that occurred near the autumnal equinox on 8 September 2017. The results show that the enhancement ratio of atmospheric density in the southern polar region (SPR) on the duskside was approximately 1.33–1.65 times that of the northern polar region (NPR), demonstrating a strong hemispheric asymmetry of thermospheric atmospheric density response during the magnetic storm. However, the asymmetry response was smaller on the dawnside, suggesting that the hemispheric density response asymmetry is related to local time (LT). The energy injection in high-latitude regions increases local atmospheric density and forms traveling atmospheric disturbances (TADs). TADs can propagate to low-latitude regions over several hours and affect the global distribution of thermospheric atmospheric density. Similarly, the geomagnetic index fitting slope of SPR relative density difference is greater than that of NPR. The SuperDARN convection pattern indicates that the plasma convection velocity of SPR is significantly greater than that of NPR, indicating that joule heating caused by neutral friction of ions in the Southern Hemisphere may be stronger. Subsequently, an analysis of annual solar activity and seasons was carried out on the thermospheric NPR, SPR atmospheric density, and their differences from December 2015 to December 2020. The results show that thermospheric atmospheric density decreases overall as the number of sunspots decreases. The differences between the NPR and SPR atmospheric densities in the thermosphere exhibits a noticeable annual periodicity. The NPR and SPR atmospheric densities appear to have different distribution characteristics in different seasons. The NPR density peak is mainly in March or April. In particular, the “double-peak” phenomenon occurred in 2017, with peaks in March and September, while the most obvious feature of SPR atmospheric density is that its minimum value occurs in the summer months of June and July. This paper reveals the annual, seasonal, and magnetic storm response characteristics of the hemispheric asymmetry of thermospheric atmospheric density, which has significant implications for the study of multilayer energy coupling of the magnetosphere–ionosphere–thermosphere.

Solar cycle 25 amplitude prediction based on sunspot number increase rate

We propose a prediction of the amplitude of the 25th cycle of solar activity based on the analysis of data on 24 previous solar cycles, which relate to the statistical relationship between the rate of increase in the number of sunspots in the phase of the growth curve and the amplitude of the cycle. It turned out that the forecasting result depends on several initial assumptions, in particular, which section of the growth curve is taken into account for forecasting, as well as whether all 24 cycles are considered, or only the odd ones. The assumption of a monotonic or non-monotonic growth curve also plays an important role. Regarding the latter, the cluster analysis showed that until the 35th month of the cycle, there are no visible signs of non-monotonicity of the growth curve, similar to the one that was in the 24th cycle. We conclude that the maximum smoothed number of sunspots in the 25th cycle Wmax (25), most likely, should be equal to 185 ± 18 units in the new system, which corresponds to the average power of the solar cycle, with the implementation of the Hnievyshev-Ohl rule. With such parameters of this cycle, there are no signs of approaching the deep minimum of the age cycle in the middle 21st century. This does not exclude the fact that this deep age minimum can occur suddenly and sharply immediately after the 25th cycle, as was the case, for example, in the Dalton minimum. A possible sign of the upcoming age cycle may be the abnormally long decline phase of the current 25th cycle, about 10 years, as it was in the 4th cycle.

Data driven pathway analysis and forecast of global warming and sea level rise

Climate change is a critical issue of our time, and its causes, pathways, and forecasts remain a topic of broader discussion. In this paper, we present a novel data driven pathway analysis framework to identify the key processes behind mean global temperature and sea level rise, and to forecast the magnitude of their increase from the present to 2100. Based on historical data and dynamic statistical modeling alone, we have established the causal pathways that connect increasing greenhouse gas emissions to increasing global mean temperature and sea level, with its intermediate links encompassing humidity, sea ice coverage, and glacier mass, but not for sunspot numbers. Our results indicate that if no action is taken to curb anthropogenic greenhouse gas emissions, the global average temperature would rise to an estimated 3.28 °C (2.46–4.10 °C) above its pre-industrial level while the global sea level would be an estimated 573 mm (474–671 mm) above its 2021 mean by 2100. However, if countries adhere to the greenhouse gas emission regulations outlined in the 2021 United Nations Conference on Climate Change (COP26), the rise in global temperature would lessen to an average increase of 1.88 °C (1.43–2.33 °C) above its pre-industrial level, albeit still higher than the targeted 1.5 °C, while the sea level increase would reduce to 449 mm (389–509 mm) above its 2021 mean by 2100.

Relationships Between foF2 and Various Solar Activity Proxies

AbstractTo study ionospheric climate, to model the ionosphere (e.g., the International Reference Ionosphere—IRI) and to investigate its long‐term changes and trends, solar activity proxies/indices have been used, because long and homogeneous data series of solar ionizing flux are not available. To identify the optimum solar activity proxies, we use yearly average foF2 data of 11 ionospheric stations from middle and low/equatorial latitudes of four continents over 1976–2014 and six solar activity proxies, F10.7, sunspot numbers, F30, Mg II, He II, and solar H Lyman‐α flux. Mg II and F30 are found to be the best solar proxies for variability of foF2 at middle latitudes, not the usually used F10.7 or sunspot numbers. At equatorial latitudes the situation seems to be different with likely He II as the optimum solar proxy but all low/equatorial results are very preliminary. Solar activity describes 99% of the total variance of yearly foF2 and the foF2 dependence on solar proxies is highly linear at middle latitudes. The dependence of foF2 on F10.7 and sunspot numbers is significantly steeper in 1996–2014 than in 1976–1995, whereas for F30 both intervals provide the same dependence. We recommend for investigating the midlatitude yearly values of foF2 the solar proxy F30 followed by Mg II as the second one, not traditional F10.7 or sunspot numbers.

Solar Cycle 25 Prediction Using N-BEATS

Solar activities lead to Sun variation with an 11 yr periodicity. The periodic variation affects space weather and heliophysics research. So it is important to accurately predict solar cycle variations. In this paper, we predicted the ongoing Solar Cycle 25 using neural basis expansion analysis for the interpretable time series deep learning method. 13 months of smoothed monthly total sunspot numbers taken by sunspot Index and Long-term Solar Observations are selected to train and evaluate our model. We used root mean square error (RMSE) and mean absolute time lag (MATL) to evaluate our model performance. RMSE and MATL measure the difference between our predicted values and the actual values along the Y- and X-axis, respectively. The RMSE value is 26.62 ± 1.56 and the MATL value is 1.34 ± 0.35, demonstrating that our model is able to better predict sunspot number variation. Finally, we predicted the variation of the sunspot numbers for Solar Cycle 25 using the model. The sunspot number of Solar Cycle 25 will peak around 2024 February with an amplitude of 133.9 ± 7.2. This means that Solar Cycle 25 will be slightly more intense than Solar Cycle 24.

What to Do When the F10.7 Goes Out?

AbstractThe solar radio flux at 10.7 cm, known as F10.7, is a critical operational space weather index. However, without a clear backup, any interruption to the service can result in substantial errors in model outputs. In this paper we show the impact of one such outage in March 2022 on the models TIE‐GCM and NeQuick, and present a number of alternative solutions that could be used for future outages. The analysis is extended to the F10.7 time series since 1951 and the approach resulting in the smallest reconstruction error of F10.7 uses the solar radio flux observations at alternative wavelengths (the best giving a percentage error of 3.1%). Alternatively, use of Sunspot Number, a regular, robust alternative observation, results in a mean percentage error of 8.2% and is also a reliable fallback solution. Additionally, analysis of the error on the use of the conversion between the 12‐month rolling sunspot number (R12) and its conversion to F10.7 is included.

Analysis of Ionosphere Day to Day Variability using Parametric Methods on GPS TEC

The development of global positioning systems (GPS) has cleared the way for a better understanding of the globe and the systems surrounding the earth. The GPS signals that are sent out and received by GPS receivers are affected by severe space weather (in the ionosphere) as well as atmospheric weather and lithospheric disturbances. These disturbances not only result in inaccuracies in GPS location but also make it difficult to make the necessary corrections to those faults. The study of these perturbations is helpful in gaining an understanding of the phenomenal changes that occur in the ionosphere as a result of the Sun and its solar effects, which include solar flares, sunspot numbers, solar winds, geomagnetic fields, and natural disasters such as earthquakes and thunderstorms, among other things. In this study, an effort is made to highlight the distinctions between geomagnetic calm days and disturbed days that occurred in January 2022. The research is carried out by using parametric approaches to the GPS vertical total electron content (VTEC) at Hyderabad (17.4°N, 78.5°E), which is a station with a low height. An examination of the power spectral densities (PSDs) of both the tranquil and the disturbed conditions is carried out. The improvement in VTEC data was noted on two days in January 2022 that had low geomagnetic activity; these days were the 6th and 13th. On the sixth of January 2022, enhancements can be seen at the normalised frequencies of 0.4966 and 0.7683, with a power spectral density (PSD) of -10.14dB and -12.94dB, respectively. On the thirteenth of January 2022, enhancements can be seen at the normalised frequencies of 0.5005 and 0.956, with PSDs of -9.264dB and -8.392dB. When compared to the preceding records, it can be seen very clearly that the PSDs of both geomagnetically tranquil and disturbed days are rather comparable to one another.

Predicting the Functional Dependence of the Sunspot Number in the Solar Activity Cycle Based on Elman Artificial Neural Network

Predicting the Functional Dependence of the Sunspot Number in the Solar Activity Cycle Based on Elman Artificial Neural Network

Hemispheric Sunspot Numbers from the Astronomical Observatory of the University of Valencia (1940 – 1956)

In this work, we present hemispheric sunspot number counts made in the Astronomical Observatory of the University of Valencia for the period 1940 – 1956. We found these data in a secondary source (the bulletins of the Madrid Astronomical Observatory). We digitized the hemispheric sunspot number and group number recorded by the observers. Unfortunately, the sunspot positions or areas were not published in this secondary source. A machine-readable version of the dataset is available as supplementary material. We compare the Valencia hemispheric series with others from other observatories, such as the Madrid Astronomical Observatory, finding similar hemispheric behaviors. We also computed the asymmetry index from the hemispheric data. We found that the northern hemisphere was predominant in our study period (declining phase of Solar Cycle 17, Solar Cycle 18, and rising phase of Solar Cycle 19), and the southern hemisphere was leading. These results agree with those obtained in previous studies. Therefore, the Valencia hemispheric records are one more piece of information to know the behavior of the northern and southern hemispheres during the 20th century.

Comparison of solar activity proxies: eigenvectors versus averaged sunspot numbers

ABSTRACTWe explore the links between the averaged sunspot numbers (SSN) and a modulus summary curve (MSC) of two largest eigenvectors of the solar background magnetic field (SBMF) derived from principal component analysis. MSC has rather close correspondence with the whole set of SSN revealing close cycle timings, duration, and maxima times for the cycles 12–24, 6, 7, and −4, −3, while for a few cycles in the mid-18th and mid-19th centuries there are discrepancies in the maximum amplitudes, durations, and times of the maxima. Possible reasons of these discrepancies related to uncertainties in the SSN observations in the 18th–19th centuries, in MSC definition and the different solar activity entities they represent: toroidal (SSN) and poloidal (MSC) magnetic fields, are discussed. Wavelet and Fourier spectral analysis of SSN and MSC series reveal within 95 per cent confidence levels the same prominent period of 10.7 yr, whereas SSN series show a period of 101 yr and MSC of 342 yr close to or above 95 per cent red-noise level. The correlation coefficients between SSN and MSC series vary from 0.25 for the whole SSN data set (from 1700), to 0.56 for the data sets from 1860, to 0.67 for the data sets from 1900 when all SSN restorations agree. These SSN and MSC data sets are confirmed to be closely but not identically related representing the solar activity in different entities of solar dynamo. Use of the summary curve and MSC of eigenvectors of SBMF can provide additional information to SSN for better understanding of solar activity.