Short-Term Solar Flare Prediction Using a Sequential Supervised Learning Method

Solar flares are powered by the energy stored in magnetic fields, so evolutionary information of the magnetic field is important for short-term prediction of solar flares. However, the existing solar flare prediction models only use the current information of the active region. A sequential supervised learning method is introduced to add the evolutionary information of the active region into a prediction model. The maximum horizontal gradient, the length of the neutral line, and the number of singular points extracted from SOHO/MDI longitudinal magnetograms are used in the model to describe the nonpotentiality and complexity of the photospheric magnetic field. The evolutionary characteristics of the predictors are analyzed by using autocorrelation functions and mutual information functions. The analysis results indicate that a flare is influenced by the 3-day photospheric magnetic field information before flare eruption. A sliding-window method is used to add evolutionary information of the predictors into machine learning algorithms, then C4.5 decision tree and learning vector quantization are employed to predict the flare level within 48 hours. Experimental results indicate that the performance of the short-term solar flare prediction model within the sequential supervised learning framework is significantly improved.     

Cycle 23 Variation in Solar Flare Productivity

The NOAA listings of solar flares in cycles 21?–?24, including the GOES soft X-ray magnitudes, enable a simple determination of the number of flares each flaring active region produces over its lifetime. We have studied this measure of flare productivity over the interval 1975?–?2012. The annual averages of flare productivity remained approximately constant during cycles 21 and 22, at about two reported M- or X-flares per region, but then increased significantly in the declining phase of cycle 23 (the years 2004?–?2005). We have confirmed this by using the independent RHESSI flare catalog to check the NOAA events listings where possible. We note that this measure of solar activity does not correlate with the solar cycle. The anomalous peak in flare productivity immediately preceded the long solar minimum between cycles 23 and 24.     

Evolution of Magnetic Nonpotentiality in NOAA AR 9077

Based on photospheric vector magnetograms obtained at Huairou Solar Observing Station, we have studied the evolution of magnetic nonpotentiality in NOAA AR 9077 from 11 to 15 July 2000. We focus our analysis on the daily change of nonpotential characteristics in the photospheric magnetic field preceding the `Bastille Day' flare. We have identified the following evolving patterns: (1) The shear-angle distribution underwent dramatic change in the filament channel. At a key site of the filament environment, the magnetic shear changed sign from positive to negative. (2) The old current systems disrupted, and new but weaker systems formed before this major event. Similar changes are identified for the longitudinal current helicity. (3) The source field weakened before the flare, and the density of free magnetic energy decreased at the photospheric level. These obvious changes lasted at least nine hours before the `Bastille Day' flare, and they took place where a large amount of magnetic flux disappeared in magnetic flux cancellation. The site of dramatic changes is also found to coincide with the base of helical magnetic ropes which were seen in a 3-D force-free reconstruction. We suggest that the observed evolution of the magnetic nonpotentiality represents a continuous transportation of magnetic energy and complexity from the lower atmosphere to the corona. This transportation seems to be responsible for the energy build-up for the major flare. Moreover, the slow magnetic reconnection in the lower atmosphere, observed as magnetic flux cancellation, appears to play a key role in this energy build-up process. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014258426134     

Phase Relationship Between Sunspot Number, Flare Index and Solar Radio Flux

To understand better the variation of solar activity indicators originated at different layers of the solar atmosphere with respect to sunspot cycles, we carried out a study of phase relationship between sunspot number, flare index and solar radio flux at 2800 MHz from January 1966 to May 2008 by using cross-correlation analysis. The main results are as follows: (1) The flare index and sunspot number have synchronous phase for cycles 21 and 22 in the northern hemisphere and for cycle 20 in the southern hemisphere. (2) The flare index has a noticeable time lead with respect to sunspot number for cycles 20 and 23 in the northern hemisphere and for cycles 22 and 23 in the southern hemisphere. (3) For the entire Sun, the flare index has a noticeable time lead for cycles 20 and 23, a time lag for cycle 21, and no time lag or time lead for cycle 22 with respect to sunspot number. (4) The solar radio flux has a time lag for cycles 22 and 23 and no time lag or time lead for cycles 20 and 21 with respect to sunspot number. (5) For the four cycles, the sunspot number and flare index in the northern hemisphere are all leading to the ones in the southern hemisphere. These results may be instructive to the physical processes of flare energy storage and dissipation.     

Correlation between Solar Flare Productivity and Photospheric Magnetic Field Properties II. Magnetic Gradient and Magnetic Shear

With 1353 vector magnetograms observed at Huairou Solar Observing Station (HSOS), a statistical analysis is made on the relationship among solar flares, magnetic gradient, and magnetic shear. The results suggest that flare productivity has positive correlations with the gradient and the shear, which can be well fitted by the Boltzmann sigmoidal function. In the vicinity of neutral lines, high gradient and strong shear are roughly coincident in time but barely in position. In addition, flare productivity is more sensitive to the length of neutral lines with strong gradient and shear (L _gs) than independently with strong gradient (L _g) or strong shear (L _s), which means that L _gs can be a better parameter for solar flare forecasting models. Finally, an algorithm to evaluate projection effects on the statistical results is proposed.     

Statistical Assessment of Photospheric Magnetic Features in Imminent Solar Flare Predictions

In this study we use the ordinal logistic regression method to establish a prediction model, which estimates the probability for each solar active region to produce X-, M-, or C-class flares during the next 1-day time period. The three predictive parameters are (1) the total unsigned magnetic flux T _flux, which is a measure of an active region’s size, (2) the length of the strong-gradient neutral line L _gnl, which describes the global nonpotentiality of an active region, and (3) the total magnetic dissipation E _diss, which is another proxy of an active region’s nonpotentiality. These parameters are all derived from SOHO MDI magnetograms. The ordinal response variable is the different level of solar flare magnitude. By analyzing 174 active regions, L _gnl is proven to be the most powerful predictor, if only one predictor is chosen. Compared with the current prediction methods used by the Solar Monitor at the Solar Data Analysis Center (SDAC) and NOAA’s Space Weather Prediction Center (SWPC), the ordinal logistic model using L _gnl, T _flux, and E _diss as predictors demonstrated its automatic functionality, simplicity, and fairly high prediction accuracy. To our knowledge, this is the first time the ordinal logistic regression model has been used in solar physics to predict solar flares.     

High abnormal rotation rates of sunspots and flare productivity

Solar activity, such as flares and CMEs, affect the interplanetary medium, and Earth’s atmosphere. Therefore, to understand the Space Weather, we need to understand the mechanisms of solar activity. Towards this end, we use 1135 events of solar H_α flares and the positional data of sunspots from the archive of Solar Geophysical Data (SGD) for the period January–April, 2000 and compute the abnormal rotation rates that lead to high flare productivity. We report that the occurrence of 5 or more flares in a day in association with a given sunspot group can be defined as high flare productivity and the sunspots that have an abnormal rotation rates of ～4–10 deg day^?1 trigger high flare productivity. Further, in order to compare the flare productivity expressed as the strength of the flux emitted, especially the soft X-ray (SXR) flares in the frequency range of 1–8 Å, we compute the flare index of SXR flares and find that 8 out of 28 active regions used in this study satisfy the requirement for being flare productive. This enables us to conclude that the high rotation rates of sunspots are an important mechanism to understand the flare productivity, especially numerical flare productivity that includes flares of all class.     

Multifractality as a Measure of Complexity in Solar Flare Activity

In this paper we use the notion of multifractality to describe the complexity in Hα flare activity during the solar cycles 21, 22, and 23. Both northern and southern hemisphere flare indices are analyzed. Multifractal behavior of the flare activity is characterized by calculating the singularity spectrum of the daily flare index time series in terms of the Hölder exponent. The broadness of the singularity spectrum gives a measure of the degree of multifractality or complexity in the flare index data. The broader the spectrum, the richer and more complex is the structure with a higher degree of multifractality. Using this broadness measure, complexity in the flare index data is compared between the northern and southern hemispheres in each of the three cycles, and among the three cycles in each of the two hemispheres. Other parameters of the singularity spectrum can also provide information about the fractal properties of the flare index data. For instance, an asymmetry to the left or right in the singularity spectrum indicates a dominance of high or low fractal exponents, respectively, reflecting a relative abundance of large or small fluctuations in the total energy emitted by the flares. Our results reveal that in the even (22nd) cycle the singularity spectra are very similar for the northern and southern hemispheres, whereas in the odd cycles (21st and 23rd) they differ significantly. In particular, we find that in cycle 21, the northern hemisphere flare index data have higher complexity than its southern counterpart, with an opposite pattern prevailing in cycle 23. Furthermore, small-scale fluctuations in the flare index time series are predominant in the northern hemisphere in the 21st cycle and are predominant in the southern hemisphere in the 23rd cycle. Based on these findings one might suggest that, from cycle to cycle, there exists a smooth switching between the northern and southern hemispheres in the multifractality of the flaring process. This new observational result may bring an insight into the mechanisms of the solar dynamo operation and may also be useful for forecasting solar cycles.     

Solar Trans-equatorial Activity

We have found that solar flares in NOAA active region (AR) 10696 were often associated with large-scale trans-equatorial activities. These trans-equatorial activities appeared to be very common and manifest themselves through i) the formation and eruption of trans-equatorial loops (TELs), ii) the formation and eruption of trans-equatorial filaments (TEFs), and iii) the trans-equatorial brightening (TEB) in the chromosphere. It is determined that the TEF was formed following episodic plasma ejecta from flares occurring in the AR. The TEF eruption was associated with a trans-equatorial flare. All flares in the AR that were accompanied by trans-equatorial activities were associated with halo coronal mass ejections (CMEs). It was noticed that one or several major flares in the AR were followed by an increase of brightness and nonpotentiality of a TEL. These coupled events had a lifetime of more than 12 hours. In addition their associated halo CMEs always had a positive acceleration, indicating prolonged magnetic reconnections in the outer corona at high altitudes.     

Variations of magnetic fields and electric currents associated with a solar flare

The high-resolution vector magnetograms obtained with the solar telescope magnetograph of the Beijing Astronomical Observatory of the active region AR 4862 on 7 October, 1987, close before and after a solar flare, were used to calculate the electric current densities in the region. Then the relations between the flare and the magnetic fields as well as the electric currents were studied. The results are: (i) the transverse magnetic fields, and hence the longitudinal electric currents in the region before and after the flare, are evidently different, while the longitudinal magnetic fields remain unchanged; (ii) this confirms the result obtained previously that the flare kernels coincide with the peaks of longitudinal electric density in active regions; (iii) the close relation between the flare kernels and the electric currents indicates that the variations of the transverse magnetic fields and the longitudinal electric currents arise not from the general global evolution of the active region, but from the flare. These results tend to the conclusion that the triggering of a solar flare might be related with the plasma instability caused by the surplus longitudinal electric currents at some local regions in the solar atmosphere.     

A Statistical Study on Photospheric Magnetic Nonpotentiality of Active Regions and Its Relationship with Flares During Solar Cycles 22?–?23

A statistical study is carried out on the photospheric magnetic nonpotentiality in solar active regions and its relationship with associated flares. We select 2173 photospheric vector magnetograms from 1106 active regions observed by the Solar Magnetic Field Telescope at Huairou Solar Observing Station, National Astronomical Observatories of China, in the period of 1988??C?2008, which covers most of the 22nd and 23rd solar cycles. We have computed the mean planar magnetic shear angle ( $\overline{\Delta\phi}$ ), mean shear angle of the vector magnetic field ( $\overline{\Delta\psi}$ ), mean absolute vertical current density ( $\overline{|J_{z}|}$ ), mean absolute current helicity density ( $\overline{|h_{\mathrm{c}}|}$ ), absolute twist parameter (|?? _av|), mean free magnetic energy density ( $\overline{\rho_{\mathrm{free}}}$ ), effective distance of the longitudinal magnetic field (d _E), and modified effective distance (d _Em) of each photospheric vector magnetogram. Parameters $\overline{|h_{\mathrm{c}}|}$ , $\overline{\rho_{\mathrm{free}}}$ , and d _Em show higher correlations with the evolution of the solar cycle. The Pearson linear correlation coefficients between these three parameters and the yearly mean sunspot number are all larger than 0.59. Parameters $\overline {\Delta\phi}$ , $\overline{\Delta\psi}$ , $\overline{|J_{z}|}$ , |?? _av|, and d _E show only weak correlations with the solar cycle, though the nonpotentiality and the complexity of active regions are greater in the activity maximum periods than in the minimum periods. All of the eight parameters show positive correlations with the flare productivity of active regions, and the combination of different nonpotentiality parameters may be effective in predicting the flaring probability of active regions.     

无黑子耀斑的研究进展

太阳无黑子耀斑是太阳耀斑的特殊表现，无黑子耀斑的研究是太阳耀斑研究的重要组成部分。在本文中总结了太阳无黑子耀斑观测研究的以下几个方面的进展概况：自然产率，位置分布特征，观测与形态特征，触发机制能量来源，可能的解释模型。     

Flare rates and the McIntosh active-region classifications

Multiple linear regression analysis was used to derive the effective solar flare contributions of each of the McIntosh classification parameters. The best fits to the combined average number of M- and X-class X-ray flares per day were found when the flare contributions were assumed to be multiplicative rather than additive. This suggests that nonlinear processes may amplify the effects of the following different active-region properties encoded in the McIntosh classifications: the length of the sunspot group, the size and shape of the largest spot, and the distribution of spots within the group. Since many of these active-region properties are correlated with magnetic field strengths and fluxes, we suggest that the derived correlations reflect a more fundamental relationship between flare production and the magnetic properties of the region. The derived flare contributions for the individual McIntosh parameters can be used to derive a flare rate for each of the three-parameter McIntosh classes. These derived flare rates can be interpreted as smoothed values that may provide better estimates of an active region's expected flare rate when rare classes are reported or when the multiple observing sites report slightly different classifications. Guest Worker at NOAA/Space Environment Laboratory     

Heavy solar cosmic rays in the January 25, 1971 solar flare

A detailed study of the charge composition of heavy solar cosmic rays measured in the January 25, 1971 solar flare including differential fluxes for the even charged nuclei from carbon through argon is presented. The measurements are obtained for varying energy intervals for each nuclear species in the energy range from 10 to 35 MeV nucleon^?1. In addition, abundances relative to oxygen are computed for all the above nuclei in the single energy interval from 15 to 25 MeV nucleon^?1. This interval contains measurements for all of the species and as a result requires no spectral extrapolations. An upper limit for the abundance of calcium nuclei is also presented. These measurements, when combined with other experimental results, enable the energy dependence of abundance measurements as a function of nuclear charge to be discussed. It is seen that at energies above about 10 MeV nucleon^?1, the variations of abundance ratios are limited to about a factor of 3 from flare to flare, in spite of large variations in other characteristics of these solar events.     

Statistical Models for the Solar Flare Interval Distribution in Individual Active Regions

This article discusses statistical models for the solar flare interval distribution in individual active regions. We analyzed solar flare data in 55 active regions that are listed in the Geosynchronous Operational Environmental Satellite (GOES) soft X-ray flare catalog for the years from 1981 to 2005. We discuss some problems with a conventional procedure to derive probability density functions from any data set and propose a new procedure, which uses the maximum likelihood method and Akaike Information Criterion (AIC) to objectively compare some competing probability density functions. Previous studies of the solar flare interval distribution in individual active regions only dealt with constant or time-dependent Poisson process models, and no other models were discussed. We examine three models – exponential, lognormal, and inverse Gaussian – as competing models for probability density functions in this study. We found that lognormal and inverse Gaussian models are more likely models than the exponential model for the solar flare interval distribution in individual active regions. The possible solar flare mechanisms for the distribution models are briefly mentioned. We also briefly investigated the time dependence of probability density functions of the solar flare interval distribution and found that some active regions show time dependence for lognormal and inverse Gaussian distribution functions. The results suggest that solar flares do not occur randomly in time; rather, solar flare intervals appear to be regulated by solar flare mechanisms. Determining a solar flare interval distribution is an essential step in probabilistic solar flare forecasting methods in space weather research. We briefly mention a probabilistic solar flare forecasting method as an application of a solar flare interval distribution analysis. The application of our distribution analysis to a probabilistic solar flare forecasting method is one of the main objectives of this study.     

The Effect of Relative Sunspot Numbers,Solar Flare Numbers and Variable Component of 10.7 cm Solar Flux on The Seasonal Variation of 6300 Å Line Intensity at Calcutta

The paper presents the seasonal variation of 6300 Å line intensity at Calcutta with relative sunspot number, solar flare number and variable component of 10.7 cm solar flux. A study has been made and important results have been obtained which are as follows. (i) Intensity of 6300 Å line shows periodic variation with relative sunspot number, solar flare number and variable component of 10.7 cm solar flux during the period 1984–1986 which is the secondary peak of the descending phase of 21st solar cycle. (ii) 6300 Å line intensity at Cachoeira Paulista station, taken by Sahai et al. (1988), also shows periodic variation with solar parameters during the period 1978–1980 which is the peak phase of the solar cycle. (iii) A possible explanation of such a type of variation is also presented.     

Turbulence In The Solar Atmosphere: Manifestations And Diagnostics Via Solar Image Processing

Intermittent magnetohydrodynamical turbulence is most likely at work in the magnetized solar atmosphere. As a result, an array of scaling and multi-scaling image-processing techniques can be used to measure the expected self-organization of solar magnetic fields. While these techniques advance our understanding of the physical system at work, it is unclear whether they can be used to predict solar eruptions, thus obtaining a practical significance for space weather. We address part of this problem by focusing on solar active regions and by investigating the usefulness of scaling and multi-scaling image-processing techniques in solar flare prediction. Since solar flares exhibit spatial and temporal intermittency, we suggest that they are the products of instabilities subject to a critical threshold in a turbulent magnetic configuration. The identification of this threshold in scaling and multi-scaling spectra would then contribute meaningfully to the prediction of solar flares. We find that the fractal dimension of solar magnetic fields and their multi-fractal spectrum of generalized correlation dimensions do not have significant predictive ability. The respective multi-fractal structure functions and their inertial-range scaling exponents, however, probably provide some statistical distinguishing features between flaring and non-flaring active regions. More importantly, the temporal evolution of the above scaling exponents in flaring active regions probably shows a distinct behavior starting a few hours prior to a flare and therefore this temporal behavior may be practically useful in flare prediction. The results of this study need to be validated by more comprehensive works over a large number of solar active regions. Sufficient statistics may also establish critical thresholds in the values of the multi-fractal structure functions and/or their scaling exponents above which a flare may be predicted with a high level of confidence. Based on the author's contributed talk “Manifestations and Diagnostics of Turbulence in the Solar Atmosphere”, presented at the Solar Image Processing Workshop II, Annapolis, Maryland, USA, 3–5 November 2004.     

利用GPS探测电离层异常中的高斯过程处理方法

平静状态下电离层总电子含量（TEC）随时间的变化通常可以视为平稳随机过程。然而，太阳或地球的突发事件（如太阳耀斑、地磁场的扰动）会引起电离层的扰动，破坏该平稳过程，从而引起其统计参数的变化。依据平稳随机过程——高斯过程的相关性质，利用其自协方差函数和TEC时间系列，构建了独立同标准正态分布的观测样本，并利用X^2假设检验的方法来探测电离层异常现象。此外，还利用了2000年7月14日太阳耀斑期间我国国际IGS跟踪站武汉GPS跟踪站的数据，进行了实例分析。结果表明，该方法可以有效地探测电离层异常现象。     

Frequency distributions and correlations of solar X-ray flare parameters

We have determined frequency distributions of flare parameters from over 12000 solar flares recorded with the Hard X-Ray Burst Spectrometer (HXRBS) on the Solar Maximum Mission (SMM) satellite. These parameters include the flare duration, the peak counting rate, the peak hard X-ray flux, the total energy in electrons, and the peak energy flux in electrons (the latter two computed assuming a thick-target flare model). The energies were computed above a threshold energy between 25 and 50 keV. All of the distributions can be represented by power laws above the HXRBS sensitivity threshold. Correlations among these parameters are determined from linear regression fits as well as from the slopes of the frequency distributions. Variations of the frequency distributions were investigated with respect to the solar activity cycle.Theoretical models for the frequency distribution of flare parameters depend on the probability of flaring and the temporal evolution of the flare energy build-up. Our results are consistent with stochastic flaring and exponential energy build-up, with an average build-up time constant that is 0.5 times the mean time between flares. The measured distributions of flares are also consistent with predicted distributions of flares from computer simulations of avalanche models that are governed by the principle of self-organized criticality.     

A statistical study on property of spatial magnetic field for solar active region

Magnetic fields dominate most solar activities, there exist direct relations between solar flare and the distributions of magnetic field, and also its corresponding magnetic energy. In this paper, the statistical results about the relationships between the spatial magnetic field and solar flare are given basing on vector magnetic field observed by the Solar Magnetic Field Telescope (SMFT) at Huairou Solar Observing Station (HSOS). The spatial magnetic fields are obtained by extrapolated photosphere vector magnetic field observed by SMFT. There are 23 active regions with flare eruption are chosen as data samples, which were observed from 1997 to 2007. The results are as follows: 1. Magnetic field lines become lower after flare for 16 (69 %) active regions; 2. The free energy are decreased after flare for 17 (74 %) active regions. It can conclude that for most active regions the changes of magnetic field after solar flare re coincident with the previous observations and studies.