Prediction verification of solar cycles 18–24 and a preliminary prediction of the maximum amplitude of solar cycle 25 based on the Precursor Method

Predictions of the strength of solar cycles are important and are necessary for planning long-term missions.A new solar cycle 25 is coming soon,and the amplitude is needed for space weather operators.Some predictions have been made using different methods and the values are drastically different.However,since 2015 July 1,the original sunspot number data have been entirely replaced by the Version 2.0 data series,and the sunspot number values have changed greatly.In this paper,using Version 2 smoothed sunspot numbers and aa indices,we verify the predictions for cycles 18–24 based on Ohl’s Precursor Method.Then a similar-cycles method is used to evaluate the aa minimum of 9.7(±1.1)near the start of cycle 25 and based on the linear regression relationship between sunspot maxima and aa minima,our predicted Version 2maximum sunspot number for cycle 25 is 121.5(±32.9).     

Chinese sunspot drawings and their digitization –(Ⅱ) accuracy analysis for digitized sunspot hand-drawing records of Yunnan Observatories

Sunspots are the most striking and easily observed magnetic structures of the Sun, and statistical analysis of solar historical data could reveal a wealth of information on the long-term variation of solar activity cycle. The hand-drawn sunspot records of Yunnan Observatories, Chinese Academy of Sciences have been accumulating for more than 60 years, and nearly 16 000 images have been preserved. In the future, the observation mode of recording sunspots by hand-drawing will be replaced inevitably by digital images observed either at ground or in space. To connect the hand-drawn sunspot data and the purely digital sunspot data in future, it is necessary to analyze the systematic errors of the data which are observed by the two observation modes in the period of transition. In this paper, we choose 268 round sunspots(Htype in modified Zurich sunspot classification) from the drawing of Yunnan Observatories to compare their positions and areas with the CCD observations made by Helioseismic and Magnetic Imager(HMI) on board Solar Dynamic Observatory(SDO) and Global Oscillation Network Group(GONG). We find that the latitude and longitude accuracy of hand-drawn sunspot are within-0.127 and 2.29 degree respectively,and the area accuracy is about 16.36 sunspot unit(μHem). Systematic errors apparently decrease with large sunspot.     

Verification of a Similar Cycle Prediction for the Ascending and Peak Phases of Solar Cycle 23

Reviews of long-term predictions of solar cycles have shown that a precise prediction with a lead time of 2 years or more of a solar cycle remains an unsolved problem. We used a simple method, the method of similar cycles, to make long-term predictions of not only the maximum amplitude but also the smoothed monthly mean sunspot number for every month of Solar Cycle 23. We verify and compare our prediction with the latest available observational results.     

Spotless days and geomagnetic index as the predictors of solar cycle 25

We study the sunspot activity in relation to spotless days(SLDs) during the descending phase of solar cycles 11-24 to predict the amplitude of sunspot cycle 25.For this purpose,in addition to SLD,we also consider the geomagnetic activity(aa index) during the descending phase of a given cycle.A very strong correlation of the SLD(0.68) and aa index(0.86) during the descending phase of a given cycle with the maximum amplitude of next solar cycle has been estimated.The empirical relationship led us to deduce the amplitude of cycle 25 to be 99.13± 14.97 and 104.23± 17.35 using SLD and aa index,respectively as predictors.Both the predictors provide comparable amplitude for solar cycle 25 and reveal that solar cycle 25 will be weaker than cycle 24.Further,we predict that the maximum of cycle 25 is likely to occur between February and March 2024.While the aa index has been utilized extensively in the past,this work establishes SLDs as another potential candidate for predicting the characteristics of the next cycle.     

The prediction method of similar cycles

The concept of degree of similarity(η),is proposed to quantitatively describe the similarity of a parameter(e.g.the maximum amplitude Rmax)of a solar cycle relative to a referenced one,and the prediction method of similar cycles is further developed.For two parameters,the solar minimum(Rmin)and rising rate(βa),which can be directly measured a few months after the minimum,a synthesis degree of similarity(ηs)is defined as the weighted-average of theηvalues around Rmin and βa,with the weights given by the coef...     

Magnetic flux participation in solar surface magnetism during solar cycle 24

This study aims at investigating surface magnetic flux participation among different types of magnetic features during solar cycle 24. State-of-the-art observations from SDO/HMI and Hinode/SOT are combined to form a unique database in the interval from April 2010 to October 2015. Unlike previous studies, the statistics presented in this paper are feature-detection-based. More than 20 million magnetic features with relatively large scale, such as sunspot/pore, enhanced and quiet networks, are automatically detected and categorized from HMI observations, and the internetwork features are identified from SOT/SP observations. The total flux from these magnetic features reaches 5.9×10~(22) Mx during solar minimum and2.4 × 10~(23) Mx in solar maximum. Flux occupation from the sunspot/pore region is 29% in solar maximum.Enhanced and quiet networks contribute 18% and 21% flux during the solar minimum, and 50% and 9% flux in the solar maximum respectively. The internetwork field contributes over 55% of flux in the solar minimum, and its flux contribution exceeds that of sunspot/pore features in the solar maximum. During the solar active condition, the sunspot field increases its area but keeps constant flux density of about 150 G,while the enhanced network follows the sunspot number variation showing increasing flux density and area,but the quiet network displays decreasing area and somewhat increasing flux density of about 6%. The origin of the quiet network is not known exactly, but is suggestive of representing the interplay between mean-field and local dynamos. The source, magnitude and possible importance of ‘hidden flux' are discussed in some detail.     

Estimating the Size and Timing of the Maximum Amplitude of Solar Cycle 24

A simple statistical method is used to estimate the size and timing of maximum amplitude of the next solar cycle (cycle 24). Presuming cycle 23 to be a short cycle (as is more likely), the minimum of cycle 24 should occur about December 2006 (±2 months) and the maximum, around March 2011 (±9 months), and the amplitude is 189.9 ±15.5, if it is a fast riser, or about 136, if it is a slow riser. If we presume cycle 23 to be a long cycle (as is less likely), the minimum of cycle 24 should occur about June 2008 (±2 months) and the maximum, about February 2013 (±8 months) and the maximum will be about 137 or 80, according as the cycle is a fast riser or a slow riser.     

The north-south asymmetry of solar filaments separately at low and high latitudes in solar cycle 23

We present the results of a study on the north-south asymmetry of solar filaments at low(50°) and high(60°) latitudes using daily filament numbers from January 1998 to November 2008(solar cycle 23). It is found that the northern hemisphere is dominant at low latitudes for cycle 23. However, a similar asymmetry does not occur for solar filaments at high latitudes. The present study indicates that the hemispheric asymmetry of solar filaments at high latitudes in a cycle appears to have little connection with that at low latitudes. Our results support that the observed magnetic fields at high latitudes include two components: one comes from the emergence of the magnetic fields from the solar interior and the other comes from the drift of the magnetic activity at low latitudes.     

Long-term Evolution of Solar Activity and Prediction of the Following Solar Cycles

Solar activities have a great impact on modern high-tech systems, such as human aerospace activities, satellite communication and navigation, deep space exploration, and related scientific research. Therefore, studying the long-term evolution trend of solar activity and accurately predicting the future solar cycles are highly anticipated.Based on the wavelet transform and empirical function fitting of the longest recorded data of the annual average relative sunspot number(ASN) series of 323 yr t...     

Solar cycle prediction using a long short-term memory deep learning model

In this paper,we propose a long short-term memory(LSTM)deep learning model to deal with the smoothed monthly sunspot number(SSN),aiming to address the problem whereby the prediction results of the existing sunspot prediction methods are not uniform and have large deviations.Our method optimizes the number of hidden nodes and batch sizes of the LSTM network structures to 19 and 20,respectively.The best length of time series and the value of the timesteps were then determined for the network training,and one-step and multi-step predictions for Cycle 22 to Cycle 24 were made using the well-established network.The results showed that the maximum root-mean-square error(RMSE)of the one-step prediction model was6.12 and the minimum was only 2.45.The maximum amplitude prediction error of the multi-step prediction was 17.2%and the minimum was only 3.0%.Finally,the next solar cycles(Cycle 25)peak amplitude was predicted to occur around 2023,with a peak value of about 114.3.The accuracy of this prediction method is better than that of the other commonly used methods,and the method has high applicability.     

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, D_i, 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-D_i plane may be fitted by a straight line with a correlation coefficient larger than the critical one at confidence level α= 5%, and for 36 months (73%) the fitting is even better, for α= 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 R_i=0.704 In D_i-0.291.     

Wavelet Analysis of the Schwabe Cycle Properties in Solar Activity

Properties of the Schwabe cycles in solar activity are investigated by using wavelet transform. We study the main range of the Schwabe cycles of the solar activity recorded by relative sunspot numbers, and find that the main range of the Schwabe cycles is the periodic span from 8-year to 14-year. We make the comparison of 11-year‘s phase between relative sunspot numbers and sunspot group numbers. The results show that there is some difference between two phases for the interval from 1710 to 1810, while the two phases are almost the same for the interval from 1810 to 1990.     

Short-Term Period Variation of Relative Sunspot Numbers

We use wavelet transform to analyze the daily relative sunspot number series over solar cycles 10-23. The characteristics of some of the periods shorter than - 600-day are discussed. The results exhibit not only the variation of some short periods in the 14 solar cycles but also the characteristics and differences around solar peaks and valley years. The short periodic components with larger amplitude such as ～27, ～ 150 and ～360-day are obvious in some solar cycles, all of them are time-variable, also their lengths and amplitudes are variable and intermittent in time. The variable characteristics of the periods are rather different in different solar cycles.     

The Prediction of Maximum Amplitudes of Solar Cycles and the Maximum Amplitude of Solar Cycle 24

We present a brief review of predictions of solar cycle maximum amplitude with a lead time of 2 years or more. It is pointed out that a precise prediction of the maximum amplitude with such a lead-time is still an open question despite progress made since the 1960s. A method of prediction using statistical characteristics of solar cycles is developed: the solar cycles are divided into two groups, a high rising velocity (HRV) group and a low rising velocity (LRV) group, depending on the rising velocity in the ascending phase for a given duration of the ascending phase. The amplitude of Solar Cycle 24 can be predicted after the start of the cycle using the formula derived in this paper. Now, about 5 years before the start of the cycle, we can make a preliminary prediction of 83.2-119.4 for its maximum amplitude.     

Short-Term Period Variation of Relative Sunspot Numbers

We use wavelet transform to analyze the daily relative sunspot number series over solar cycles 10-23. The characteristics of some of the periods shorter than ～ 600-day are discussed. The results exhibit not only the variation of some short periods in the 14 solar cy-cles but also the characteristics and differences around solar peaks and valley years. The short periodic components with larger amplitude such as ～27,～150 and ～360-day are obvious in some solar cycles,all of them are time-variable,also their lengths and amplitudes are vari-able and intermittent in time. The variable characteristics of the periods are rather different in different solar cycles.     

The Relation between the Amplitude and the Period of Solar Cycles

The maximum amplitudes of solar activity cycles are found to be well anti-correlated (r = -0.72) with the newly defined solar cycle lengths three cycles before (at lag -3) in 13-month running mean sunspot numbers during the past 190 years. This result could be used for predicting the maximum sunspot numbers. The amplitudes of Cycles 24 and 25 are estimated to be 149.5±27.6 and 144.3±27.6, respectively.     

Temporal variation of solar flare index during solar cycles 21–24

The present investigation attempts to quantify the temporal variation of Solar Flare Index(SFI)with other activity indices during solar cycles 21-24 by using different techniques such as linear regression,correlation,cross-correlation with phase lag-lead,etc.Different Solar Activity Indices(SAI)considered in this present study are Sunspot Number(SSN),10.7 cm Solar Radio Flux(F10.7),Coronal Index(CI)and MgⅡCore-to-Wing Ratio(MgⅡ).The maximum cycle amplitude of SFI and considered SAI has a decreasing trend from solar cycle 22,and cycle 24 is the weakest solar cycle among all other cycles.The SFI with SSN,F10.7,CI and MgⅡshows hysteresis during all cycles except for solar cycle 22 where both paths for ascending and descending phases are intercepting each other,thereby representing a phase reversal.A positive hysteresis circulation exists between SFI and considered SAI during solar cycles 22 and 23,whereas a negative circulation exists in cycles 21 and 24.SFI has a high positive correlation with coefficient values of 0.92,0.94,0.84 and 0.81 for SSN,F10.7,CI and MgⅡrespectively.According to crosscorrelation analysis,SFI has a phase lag with considered SAI during an odd-number solar cycle(solar cycles21 and 23)but no phase lag/lead during an even-numbered solar cycle(solar cycles 22 and 24).However,the entire smoothed monthly average SFI data indicate an in-phase relationship with SSN,F10.7 and MgⅡ,and a one-month phase lag with CI.The presence of those above characteristics strongly confirms the outcomes of different research work with various solar indices and the highest correlation exists between SFI and SSN as well as F10.7 which establishes that SFI may be considered as one of the prime activity indices to interpret the characteristics of the Sun’s active region as well as for more accurate short-range or long-range forecasting of solar events.     

A brief report on the statistical study of net electric current in solar active regions with longitudinal fields of opposite polarity

Dynamic processes occurring in solar active regions are dominated by the solar magnetic field. As of now, observations using a solar magnetograph have supplied us with the vector components of a solar photospheric magnetic field. The two transverse components of a photospheric magnetic field allow us to compute the amount of electric current. We found that the electric current in areas with positive (negative) polarity due to the longitudinal magnetic field have both positive and negative signs in an active region, however, the net current is found to be an order-of-magnitude less than the mean absolute magnitude and has a preferred sign. In particular, we have statistically found that there is a systematic net electric current from areas with negative (positive) polarity to areas with positive (negative) polarity in solar active regions in the northern (southern) hemisphere, but during the solar minimum this tendency is reversed over time at some latitudes. The result indicates that there is weak net electric current in areas of solar active regions with opposite polarity, thus providing further details about the hemispheric helicity rule found in a series of previous studies.     

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.     

THE 152-DAY PERIODICITY OF THE OCCURRENCE RATE OF SOLAR MICROWAVE BURSTS

It has been found for a long time, with analysing the variation of the relative number of sunspot, that there exist the periodicity of 11 years in solar activity. With the deepening research of the varied solar active phenomena, a series of periodicities with different periods have been also found in solar activity. For example, there is the periodicity of about 80 days for the occurrence, rate of proton flares for solar activity cycles 19 and 20 found by Ai and Fan ci:i at 1974. Recently a periodicity of about 152 days of the occurrence rate of solar flares has been proposed by some authors. a3'5>7:i The existence of this periodicity hsa been proved in the various solar flares. In this paper using the data of solar microwave bursts from January 1986 to December 1988, a Fourier analysis of the occurrence rate of solar microwave bursts has been made. There was no periodicity for the occurrence rate of solar microwave bursts of about 152 days found. This is a new result for solar cycle 22 in the first thr