ENSO Index Variations and Links with Solar and Volcanic Activity

In this paper, we investigated the Oceanic Niño Index (ONI), for simplicity called in this paper an El Nino Southern Oscillation (ENSO) index in 1950-2023 by applying the wavelet spectral transform and the IBM SPSS correlations analysis. ONI follows the three months’ current measurements of the average temperature of the sea surface in the East-Central tropical part of the Pacific Ocean nearby the international line of the date change over the average sea surface temperature over the past 30 years. The ENSO index is found to have a strong (>87%) correlation with the Global Land-Ocean Temperature (GLOT). The scatter plots of the ENSO-GLOT correlation with the linear and cubic fits have shown that the ENSO index is better fit by the cubic polynomial increasing proportionally to a cubic power of the GLOT variations. The wavelet analysis allowed us to detect the two key periods in the ENSO (ONI) index: 4 - 5 years and 12 years. The smaller period of 4.5 years can be linked to the motion of tectonic plates while the larger period of 12 years is shown to have a noticeable correlation of 25% with frequencies of the underwater (submarine) volcanic eruptions in the areas with ENSO occurrences. Not withholding any local terrestrial factors considered to contribute to the ENSO occurrences, we investigated the possibility of the volcanic eruptions causing ENSO to be also induced by the tidal forces of Jupiter and Sun showing the correlation of the underwater volcanic eruption frequency with the Jupiter-Earth distances to be 12% and with the Sun-Earth distances, induced by the solar inertial motion, in January, when the Earth is turned to the Sun with the southern hemisphere where the ENSO occurs, to become 15%. Hence, the underwater volcanic eruptions induced by tidal forces of Jupiter and Sun can be the essential additional factors imposing this 12 year period of the ENSO (ONI) index variations.

The relationships of solar flares with both sunspot and geomagnetic activity

The relationships between solar flare parameters （total importance, time duration, flare index, and flux） and sunspot activity （R z ） as well as those between geomagnetic activity （aa index） and the flare parameters can be well described by an integral response model with the response time scales of about 8 and 13 months, respectively. Compared with linear relationships, the correlation coefficients of the flare parameters with R z , of aa with the flare parameters, and of aa with R z based on this model have increased about 6%, 17%, and 47% on average, respectively. The time delays between the flare parameters with respect to R z , aa to the flare parameters, and aa to R z at their peaks in a solar cycle can be predicted in part by this model （82%, 47%, and 78%, respectively）. These results may be further improved when using a cosine filter with a wider window. It implies that solar flares are related to the accumulation of solar magnetic energy in the past through a time decay factor. The above results may help us to understand the mechanism of solar flares and to improve the prediction of the solar flares.

Evolution of the Level of Sunspot Activity in Solar Cycles I. Evolution in the Descending Phase

Taking the 13-point smoothed monthly sunspot number,Ri, and the deviation of the 13 associated monthly sunspot numbers from the smoothed one, Di, as a number-pair describing the global level of sunspot activity, the evolution of the level is statistically studied for the period from the month which is just 48 months before the minimum to the minimum in the descending phase, using the observed data of Solar Cycles 10 to 22. Our results show （1） for 46 months （94%） of the studied 49 months it is found that for a given month, the distribution of the 13 pairs which come from the 13 solar cycles on a log Ri - Di plane may be fitted by a straight line with a correlation coefficient larger than the critical one at confidence level a = 5%, and for 36 months （73%） the fitting is even better, for a = 1%; （2） time variations of these two parameters and their correlations in the studied period can be described respectively by functions of time, whose main trends may be expressed by a linear or simple curvilinear function; （3） the evolutionary path of the level of sunspot activity may be represented by a logarithmic function as log/~ = 0.704 lnDi - 0.291.

Periodic variation and phase analysis of grouped solar flare with sunspot activity

Studies on the periodic variation and the phase relationship between different solar activity indicators are useful for understanding the long-term evolution of solar activity cycles.Here we report the statistical analysis of grouped solar flare(GSF) and sunspot number(SN) during the time interval from January 1965 to March 2009.We find that,(1) the significant periodicities of both GSF and SN are related to the differential rotation periodicity,the quasi-biennial oscillation(QBO),and the eleven-year Schwabe cycle(ESC),but the specific values are not absolutely identical;(2) the ESC signal of GSF lags behind that of SN with an average of 7.8 months during the considered time interval,which implies that the systematic phase delays between GSF and SN originate from the inter-solar-cycle signal.Our results may provide evidence about the storage of magnetic energy in the corona.

Low-dimensional chaos and fractal properties of long-term sunspot activity

Two primary solar-activity indicators- sunspot numbers （SNs） and sunspot areas （SAs） in the time interval from November 1874 to December 2012 - are used to determine the chaotic and fractal properties of solar activity. The results show that （1） the long-term solar activity is governed by a low-dimensional chaotic strange attractor, and its fractal motion shows a long-term persistence on large scales; （2） both the fractal dimension and maximal Lyapunov exponent of SAs are larger than those of SNs, implying that the dynamical system of SAs is more chaotic and complex than SNs; （3） the predictions of solar activity should only be done for short- to mid-term behaviors due to its intrinsic complexity; moreover, the predictability time of SAs is obviously smaller than that of SNs and previous results.

Periodicities in Solar Activity, Solar Radiation and Their Links with Terrestrial Environment

Solar magnetic activity is expressed via variations of sunspots and active regions varying on different timescales. The most accepted is an 11-year period supposedly induced by the electromagnetic solar dynamo mechanism. There are also some shorter or longer timescales detected: the biennial cycle (2 - 2.7 years), Gleisberg cycle (80 - 100 years), and Hallstatt’s cycle (2100 - 2300 years). Recently, using Principal Component Analysis (PCA) of the observed solar background magnetic field (SBMF), another period of 330 - 380 years, or Grand Solar Cycle (GSC), was derived from the summary curve of two eigenvectors of SBMF. In this paper, a spectral analysis of the averaged sunspot numbers, solar irradiance, and the summary curve of eigenvectors of SBMF was carried out using Morlet wavelet and Fourier transforms. We detect a 10.7-year cycle from the sunspots and modulus summary curve of eigenvectors as well a 22-year-cycle and the grand solar cycle of 342 - 350-years from the summary curve of eigenvectors. The Gleissberg centennial cycle is only detected on the full set of averaged sunspot numbers for 400 years or by adding a quadruple component to the summary curve of eigenvectors. Another period of 2200 - 2300 years is detected in the Holocene data of solar irradiance measured from the abundance of 14C isotope. This period was also confirmed with the period of about 2000 - 2100 years derived from a baseline of the solar background magnetic field, supposedly, caused by the solar inertial motion (SIM) induced by the gravitation of large planets. The implication of these findings for different deposition of solar radiation into the northern and southern hemispheres of the Earth caused by the combined effects of the solar activity and solar inertial motion on the terrestrial atmosphere is also discussed.

Terrestrial Temperature, Sea Levels and Ice Area Links with Solar Activity and Solar Orbital Motion

This paper explores the links between terrestrial temperature, sea levels and ice areas in both hemispheres with solar activity indices expressed through averaged sunspot numbers together with the summary curve of eigenvectors of the solar background magnetic field (SBMF) and with changes of Sun-Earth distances caused by solar inertial motion resulting from the gravitation of large planets in the solar system. Using the wavelet analysis of the GLB and HadCRUTS datasets two periods: 21.4 and 36 years in GLB, set and the period of about 19.6 years in the HadCRUTS are discovered. The 21.4-year period is associated with variations in solar activity defined by the summary curve of the largest eigenvectors of the SBMF. A dominant 21.4-year period is also reported in the variations of the sea level, which is linked with the period of 21.4 years detected in the GLB temperature and the summary curve of the SBMF variations. The wavelet analysis of ice and snow areas shows that in the Southern hemisphere, it does not show any links to solar activity periods while in the Northern hemisphere, the ice area reveals a period of 10.7 years equal to a usual solar activity cycle. The TSI in March-August of every year is found to grow with every year following closely the temperature curve, because the Sun moves closer to the Earth orbit owing to gravitation of large planets (solar inertial motion, SIM), while the variations of solar radiation during a whole year have more steady distribution without a sharp TSI increase during the last two centuries. The additional TSI contribution caused by SIM is likely to secure the additional energy input and exchange between the ocean and atmosphere.

Solar Magnetism and the Activity Telescope at HSOS

A new solar telescope system is described, which has been operating at Huairou Solar Observing Station （HSOS）, National Astronomical Observatories, Chinese Academy of Sciences （CAS）, since the end of 2005. This instrument, the Solar Magnetism and Activity Telescope （SMAT）, comprises two telescopes which respectively make measurements of full solar disk vector magnetic field and Ha observation. The core of the full solar disk video vector magnetograph is a birefringent filter with 0.1A bandpass, installed in the tele-centric optical system of the telescope. We present some preliminary observational results of the full solar disk vector magnetograms and Ha filtergrams obtained with this telescope system.

Phase analysis of sunspot group numbers on both solar hemispheres

Cross-correlation analysis and wavelet transform methods are proposed to investigate the phase relationship between the monthly sunspot group numbers in the solar northern and southern hemispheres. It is found that （1） the monthly sunspot group numbers in the northern hemisphere begin two months earlier than those in the southern one, which should lead to phase asynchrony between them but with a slight effect; （2） the Schwabe cycle length for the monthly sunspot group numbers in the two hemispheres obviously differs from each other, and the mean Schwabe cycle length of the monthly sunspot group numbers in the northern hemisphere is slightly larger than that in the southern one; （3） the monthly sunspot group numbers in the northern hemisphere precede those in the southern hemisphere during the years of about 1874- 1927, after which, the southern hemisphere leads the northern hemisphere in the years 1928-1964, and then the northern hemisphere leads in time till the present.

The Evolution of Photospheric Current Density During an X9.3-Class Solar Flare

This paper deduced the temporal evolution of the magnetic field through a series of high-resolution vector magnetograms and calculated the fine distribution map of current density during an X9.3-class flare eruptions using Ampère's law.The results show that a pair of conjugate current ribbons exist on both sides of the magnetic neutral line in this active region,and these conjugate current ribbons persist before,during,and after the flare.It was observed that the X9.3-class flare brightened in the form of a bright core and evolved into a double-ribbon flare over time.Importantly,the position of the double-ribbon flare matches the position of the current ribbons with high accuracy,and their morphologies are very similar.By investigating the complexity of current density and flare morphology,we discovered a potential connection between the eruption of major flares and the characteristics of current density.

A Statistical Study of Magnetic Flux Emergence in Solar Active Regions Prior to Strongest Flares

Using the data on magnetic field maps and continuum intensity for Solar Cycles 23 and 24,we explored 100 active regions(ARs)that produced M5.0 or stronger flares.We focus on the presence/absence of the emergence of magnetic flux in these ARs 2-3 days before the strong flare onset.We found that 29 ARs in the sample emerged monotonically amidst quiet-Sun.A major emergence of a new magnetic flux within a pre-existing AR yielding the formation of a complex flare-productive configuration was observed in another 24 cases.For 30 ARs,an insignificant(in terms of the total magnetic flux of pre-existing AR)emergence of a new magnetic flux within the pre-existing magnetic configuration was observed;for some of them the emergence resulted in a formation of a configuration with a small δ-sunspot;11 out of 100 ARs exhibited no signatures of magnetic flux emergence during the entire interval of observation.In six cases the emergence was in progress when the AR appeared on the Eastern limb,so that the classification and timing of emergence were not possible.We conclude that the recent flux emergence is not a necessary and/or sufficient condition for strong flaring of an AR.The flux emergence rate of flare-productive ARs analyzed here was compared with that of flare-quiet ARs analyzed in our previous studies.We revealed that the flare-productive ARs tend to display faster emergence than the flare-quiet ones do.

A Confined Two-peaked Solar Flare Observed by EAST and SDO

The solar flare is one of the most violent explosions,and can disturb the near-Earth space weather.Except for commonly single-peaked solar flares in soft X-ray,some special flares show intriguing a two-peak feature that is deserved much more attentions.Here,we reported a confined two-peaked solar flare and analyzed the associated eruptions using high-quality observations from Educational Adaptive-optics Solar Telescope and Solar Dynamics Observatory.Before the flare,a magnetic flux rope(MFR)formed through partially tether-cutting reconnection between two sheared arches.The flare occurred after the MFR eruption that was confined by the overlying strong field.Interestingly,a small underlying filament immediately erupted,which was possibly destabilized by the flare ribbon.The successive eruptions were confirmed by the analysis of the emission measure and the reconnection fluxes.Therefore,we suggest that the two peaks of the confined solar flare are corresponding to two episodes of magnetic reconnection during the successive eruptions of the MFR and the underlying filament.

The Effect of Solar Activity on the Annual Precipitation in the Beijing Area

Using continuous wavelet transform, we examine the relationship between solar activity and the annual precipitation in the Beijing area. The results indicate that the annual precipitation is closely related to the variation of sunspot numbers, and that solar activity probably plays an important role in influencing the precipitation on land.

Forecast daily indices of solar activity, F10.7, using support vector regression method

The 10.7 cm solar radio flux （F10.7）, the value of the solar radio emission flux density at a wavelength of 10.7 cm, is a useful index of solar activity as a proxy for solar extreme ultraviolet radiation. It is meaningful and important to predict F10.7 values accurately for both long-term （months-years） and short-term （days） forecasting, which are often used as inputs in space weather models. This study applies a novel neural network technique, support vector regression （SVR）, to forecasting daily values of F10.7. The aim of this study is to examine the feasibility of SVR in short-term F10.7 forecasting. The approach, based on SVR, reduces the dimension of feature space in the training process by using a kernel-based learning algorithm. Thus, the complexity of the calculation becomes lower and a small amount of training data will be sufficient. The time series of F10.7 from 2002 to 2006 are employed as the data sets. The performance of the approach is estimated by calculating the norm mean square error and mean absolute percentage error. It is shown that our approach can perform well by using fewer training data points than the traditional neural network.

Wavelet Analysis of Several Important Periodic Properties in the Relative Sunspot Numbers

We investigate the wavelet transform of yearly mean relative sunspot number series from 1700 to 2002. The curve of the global wavelet power spectrum peaks at 11-yr, 53-yr and 101-yr periods. The evolution of the amplitudes of the three periods is studied. The results show that around 1750 and 1800, the amplitude of the 53-yr period was much higher than that of the the 11-yr period, that the ca. 53-yr period was apparent only for the interval from 1725 to 1850, and was very low after 1850, that around 1750, 1800 and 1900, the amplitude of the 101-yr period was higher than that of the 11-yr period and that, from 1940 to 2000, the 11-yr period greatly dominates over the other two periods.

Predicting the 25th solar cycle using deep learning methods based on sunspot area data

It is a significant task to predict the solar activity for space weather and solar physics. All kinds of approaches have been used to forecast solar activities, and they have been applied to many areas such as the solar dynamo of simulation and space mission planning. In this paper, we employ the long-shortterm memory(LSTM) and neural network autoregression(NNAR) deep learning methods to predict the upcoming 25 th solar cycle using the sunspot area(SSA) data during the period of May 1874 to December2020. Our results show that the 25 th solar cycle will be 55% stronger than Solar Cycle 24 with a maximum sunspot area of 3115±401 and the cycle reaching its peak in October 2022 by using the LSTM method. It also shows that deep learning algorithms perform better than the other commonly used methods and have high application value.

How much has the Sun influenced Northern Hemisphere temperature trends?An ongoing debate

In order to evaluate how much Total Solar Irradiance(TSI)has influenced Northern Hemisphere surface air temperature trends,it is important to have reliable estimates of both quantities.Sixteen different estimates of the changes in TSI since at least the 19th century were compiled from the literature.Half of these estimates are"low variability"and half are"high variability".Meanwhile,five largely-independent methods for estimating Northern Hemisphere temperature trends were evaluated using:1)only rural weather stations;2)all available stations whether urban or rural(the standard approach);3)only sea surface temperatures;4)tree-ring widths as temperature proxies;5)glacier length records as temperature proxies.The standard estimates which use urban as well as rural stations were somewhat anomalous as they implied a much greater warming in recent decades than the other estimates,suggesting that urbanization bias might still be a problem in current global temperature datasets-despite the conclusions of some earlier studies.Nonetheless,all five estimates confirm that it is currently warmer than the late 19th century,i.e.,there has been some"global warming"since the 19th century.For each of the five estimates of Northern Hemisphere temperatures,the contribution from direct solar forcing for all sixteen estimates of TSI was evaluated using simple linear least-squares fitting.The role of human activity on recent warming was then calculated by fitting the residuals to the UN IPCC’s recommended"anthropogenic forcings"time series.For all five Northern Hemisphere temperature series,different TSI estimates suggest everything from no role for the Sun in recent decades(implying that recent global warming is mostly human-caused)to most of the recent global warming being due to changes in solar activity(that is,that recent global warming is mostly natural).It appears that previous studies(including the most recent IPCC reports)which had prematurely concluded the former,had done so because they failed to adequately consider all the relevant estimates of TSI and/or to satisfactorily address the uncertainties still associated with Northern Hemisphere temperature trend estimates.Therefore,several recommendations on how the scientific community can more satisfactorily resolve these issues are provided.

What does the Sun tell and hint now?

Some historical records, which have held since the beginning of modern solar activity cycles, are being broken by the present Sun： cycle 23 records the longest cycle length and fall time; latitudes of high-latitude sunspots belonging to a new cycle around the minimum time of the cycle are statistically the lowest at present, compared with those of other cycles; there are only one or no sunspots in a month appearing at high latitudes for 58 months, which is the first time that such a long duration has been observed. The solar dynamo is believed to be slowing down due to： （1） the minimum smoothed monthly mean sunspot number is the smallest since cycle 16 onwards, and even probably among all modern solar cycles; and （2） once the time interval between the first observations of two neighboring sunspot groups is larger than 14 d, it should be approximately regarded as an observation of no sunspots on the visible solar disk, called a spotless event. Spotless events occur with the highest frequency around the minimum time of cycle 24, and the longest spotless event also appears around the minimum time for observations of the Sun since cycle 16. Cycle 24 is expected to have the lowest level of sunspot activity from cycle 16 onwards and even probably for all of the modern solar cycles.

The hemispheric asymmetry of solar activity during the last century and the solar dynamo

We believe the Babcock-Leighton process of poloidal field generation to be the main source of irregularity in the solar cycle. The random nature of this process may make the poloidal field in one hemisphere stronger than that in the other hemisphere at the end of a cycle. We expect this to induce an asymmetry in the next sunspot cycle. We look for evidence of this in the observational data and then model it theoretically with our dynamo code. Since actual polar field measurements exist only from the 1970s, we use the polar faculae number data recorded by Sheeley （1991, 2008） as a proxy of the polar field and estimate the hemispheric asymmetry of the polar field in different solar minima during the major part of the twentieth century. This asymmetry is found to have a reasonable correlation with the asymmetry of the next cycle. We then run our dynamo code by feeding information about this asymmetry at the successive minima and compare the results with observational data. We find that the theoretically computed asymmetries of different cycles compare favorably with the observational data, with the correlation coefficient being 0.73. Due to the coupling between the two hemispheres, any hemispheric asymmetry tends to get attenuated with time. The hemispheric asymmetry of a cycle either from observational data or from theoretical calculations statistically tends to be less than the asymmetry in the polar field （as inferred from the faculae data） in the preceding minimum. This reduction factor turns out to be 0.43 and 0.51 respectively in observational data and theoretical simulations.

Low Dimensional Chaos from the Group Sunspot Numbers

We examine the nonlinear dynamical properties of the monthly smoothed group sunspot number Rg and find that the solar activity underlying the time series of Rg is globally governed by a low-dimensional chaotic attractor. This finding is consistent with the nonlinear study results of the monthly Wolf sunspot numbers. We estimate the maximal Lyaponuv exponent （MLE） for the Rg series to be positive and to equal approximately 0.0187 ± 0.0023 （month^- 1）. Thus, the Lyaponuv time or predictability time of the chaotic motion is obtained to be about 4.46 ± 0.5 years, which is slightly different with the predictability time obtained from Rz. However, they both indicate that solar activity forecast should be done only for a short to medium term due to the intrinsic complexity of the time behavior concerned.