On the application of information theory to the optimum state-space reconstruction of the short-term solar radio flux (10.7 cm), and its prediction via a neural network

The prediction of a time series using a neural network involves an optimum state-space reconstruction. The state space of the daily 10.7-cm solar radio flux is reconstructed using an information theory approach. A multi-layer feed-forward neural net is used for short-term prediction of the time series. The convergence of the synaptic weights is obtained partially by simulated annealing and partially by the 'quick prop' variation of back-propagation. The result gives a reasonably accurate short-term prediction.     

基于深度学习的太阳F_10.7辐射通量的短期预报研究

F_10.7太阳辐射通量作为输入参数被广泛运用于大气经验模型、电离层模型等空间环境模型,其预报精度直接影响航天器轨道预报精度.采用时间序列法统计了太阳辐射通量F10.7指数和太阳黑子数(SSN)的关系,给出了两者之间的线性关系,在此基础上提出了一种基于长短时记忆神经网络(Long and Short Term Memory,LSTM)的预报方法,方法结合了54 d太阳辐射通量指数和SSN历史数据来对F_10.7进行未来7 d短期预报,并与其他预报方法的预报结果进行了比较,结果表明:(1)所建短期预报7 d方法模型的性能优于美国空间天气预报中心(Space Weather Prediction Center, SWPC)的方法,预测值和观测值的相关系数(CC)达到0.96,同时其均方根误差约为11.62个太阳辐射通量单位(sfu),预报结果的均方根误差(RMSE)低于SWPC,下降约11%;(2)对预测的23、24周太阳活动年结果统计表明,太阳活动高年的第7 d F10.7指数预报平均绝对百分比误差(MAPE)最优可达12.9%以内,低年最优可达2...     

A Search for Periodicities in F10.7 Solar Radio Flux Data

The radio frequency emission at 10.7 cm (or 2800 MHz) wavelength (considered as solar flux density) out of different possible wavelengths is usually selected to identify periodicities because of its high correlation with solar extreme ultraviolet radiation as well as its complete and long observational record other than sunspot related indices. The solar radio flux at 10.7 cm wavelength plays a very valuable role for forecasting the space weather because it is originated from lower corona and chromospheres region of the Sun. Also, solar radio flux is a magnificent indicator of major solar activity. Here in the present work the solar radio flux data from 1965 to 2014 observed at the Domimion Radio Astrophysical Observatory in Penticton, British Columbiahas been processed using Date Compensated Discrete Fourier Transform (DCDFT) to identify predominant periods within the data along with their confidence levels. Also, the multi-taper method (MTM) for periodicity analysis is used to validate the observed periods. Present investigation exhibits multiperiodicity of the time series F10.7 solar radio flux data around 27, 57, 78, 127, 157, 4096 days etc. The observed periods are also compared with the periods of MgII Index data using same algorithm as MgII Index data has 99.9% correlation with F10.7 Solar Radio Flux data. It can be observed that the MgII index data exhibits similar periodicities with very high confidence levels.Present investigation also clearly indicates that the computed results are very much confining with the results obtained in different communication for the similar data of 10.7 cm Solar Radio Flux as well as for the other solar activities.

     

Modeling Research of the 27-day Forecast of 10.7 cm Solar Radio Flux (I)

Adopting the autoregressive method for time-series modeling, we have made a study on the medium-term forecast of solar 10.7 cm radio flux (F10.7). The result of forecast experiments and the error analysis indicate that when the solar activity is at a rather low level and the 27-day periodicity of F10.7 is apparent, the autoregressive forecast method has a high accuracy and relatively ideal effectiveness, but when a large active region appears or disappears on the solar dusk, the forecast effectiveness is not ideal. This means that the autoregressive method for the time-series modeling can reflect well the 27-day periodicity of F10.7, and that it has certain applicability for building a mediumterm forecast model of F10.7. By comparing the forecast results in the period from 21th September 2005 to 7th June 2007, it is demonstrated that the accuracy of the autoregressive forecast method is equivalent to that of the forecast made by the American Air Force.     

Historical Dataset Reconstruction and a Prediction Method of Solar 10.7 cm Radio Flux

We reconstruct the developing history of solar 10.7 cm radio flux (F10.7) since 1848, based on the yearly sunspot number and the variations. A relationship between the maximum and the linear regression slope of the first 3 years starting from minimum of the solar cycle is considered. We put forward a method of predicting the maximum of F10.7 by means of the slope-maximum relationship. Running tests for cycles 19 to 23 indicate that the method can properly predict the peak of F10.7.     

BoxCox multi-output linear regression for 10.7 cm solar radio flux prediction

We consider the problem of predicting the mid-term daily 10.7 cm solar radio flux(F10.7),a widely-used solar activity index.A novel approach is proposed for this task,in which BoxCox transformation with a proper parameter is first applied to make the data satisfy the property of homoscedasticity that is a basic assumption of regression models,and then a multi-output linear regression model is used to predict future F10.7 values.The experiment shows that the BoxCox transformation significantly improves the predictive performance and our new approach works substantially better than the prediction from the US Airforce and other alternative methods like Auto-regressive Model,Multi-layer Perceptron,and Support Vector Regression.     

What do the solar activity indices represent?

Sunspot number, sunspot area, and radio flux at 10.7 cm are the indices which are most frequently used to describe the long‐term solar activity. The data of the daily solar full‐disk magnetograms measured at Mount Wilson Observatory from 19 January 1970 to 31 December 2012 are utilized together with the daily observations of the three indices to probe the relationship of the full‐disk magnetic activity respectively with the indices. Cross correlation analyses of the daily magnetic field measurements at Mount Wilson observatory are taken with the daily observations of the three indices, and the statistical significance of the difference of the obtained correlation coefficients is investigated. The following results are obtained: (1) The sunspot number should be preferred to represent/reflect the full‐disk magnetic activity of the Sun to which the weak magnetic fields (outside of sunspots) mainly contribute, the sunspot area should be recommended to represent the strong magnetic activity of the Sun (in sunspots), and the 10.7 cm radio flux should be preferred to represent the full‐disk magnetic activity of the Sun (both the weak and strong magnetic fields) to which the weak magnetic fields mainly contribute. (2) On the other hand, the most recommendable index that could be used to represent/reflect the weak magnetic activity is the 10.7 cm radio flux, the most recommendable index that could be used to represent the strong magnetic activity is the sunspot area, and the most recommendable index that could be used to represent the full‐disk magnetic activity of the Sun is the 10.7cm radio flux. Additionally, the cycle characteristics of the magnetic field strengths on the solar disk are given. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Changing Relationships Between Sunspot Number,Total Sunspot Area and $F_{10.7}$ in Cycles 23 and 24

This article is an update of a study (Tapping and Valdès in Solar Phys. 272, 337, 2011) made in the early part of Cycle 24 using an intercomparison of various solar activity indices (including sunspot number and the 10.7 cm solar radio flux), in which it was concluded that a change in the relationship between photospheric and chromospheric/coronal activity took place just after the maximum of Cycle 23 and continued into Cycle 24. Precursors (short-term variations) were detected in Cycles 21 and 22. Since then the sunspot number index data have been substantially revised. This study is intended to be an update of the earlier study and to assess the impact of the revision of the sunspot number data upon those conclusions. This study compares original and revised sunspot number, total sunspot area, and 10.7 cm solar radio flux. The conclusion is that the transient changes in Cycles 21 and 22, and the more substantial change in Cycle 23, remain evident. Cycle 24 shows indications that the deviation was probably another short-term one.     

A Comparison of the 10.7-cm Radio Flux Values and the International Sunspot Numbers for Solar Activity Cycles 19, 20, and 21

A nonlinear analysis of the daily 10.7-cm radio flux values for each of Solar Cycles 19, 20, and 21 is used to determine if the results match those of the International Sunspot Numbers for each of these cycles. Fractals and chaos are described and a brief review of utilizing fractals and chaos is given. The origin of the 10.7-cm radio flux is discussed and a short review of recent work discussing its measurement and its relation to the international sunspot number and other proxies for solar activity cycles given. The parameters used to describe chaos for the 10.7-cm radio flux are discussed. The length of the data sets for either statistical analysis or nonlinear analysis of the 10.7-cm radio flux values is considered. These results indicate that the 10.7-cm radio flux values appear to be stochastic for Cycle 19 and chaotic for Cycles 20 and 21. The International Sunspot Numbers show similar behavior for these three cycles. A day-by-day comparison of the dimensionless 10.7-cm radio flux values and the dimensionless International Sunspot Numbers differences shows a linear trend. The results remain consistent in that the 10.7-cm radio flux values indicate, as did the International Sunspot Numbers, that there is a transition from stochastic behavior for Cycle 19 to chaotic behavior in Cycles 20 and 21. The day-by-day comparison of the 10.7-cm radio flux values and the International Sunspot Numbers emphasizes that the 10.7?cm radio flux values are responding to the magnetic field associated with the sunspots.     

Support Vector Machine combined with K-Nearest Neighbors for Solar Flare Forecasting

A method combining the support vector machine (SVM) the K-Nearest Neighbors (KNN), labelled the SVM-KNN method, is used to construct a solar flare forecasting model. Based on a proven relationship between SVM and KNN, the SVM-KNN method improves the SVM algorithm of classification by taking advantage of the KNN algorithm according to the distribution of test samples in a feature space. In our flare forecast study, sunspots and 10cm radio flux data observed during Solar Cycle 23 are taken as predictors, and whether an M class flare will occur for each active region within two days will be predicted. The SVM- KNN method is compared with the SVM and Neural networks-based method. The test results indicate that the rate of correct predictions from the SVM-KNN method is higher than that from the other two methods. This method shows promise as a practicable future forecasting model.     

Solar indices and solar u.v.-irradiances

Solar radio fluxes, Zurich relative sunspot number R_z, and Solar Call plage indexes daily values for the period 1957–1980 are analyzed in order to test the stability of the series with respect to time and solar activity. It is found that between the series of the 3,8 and 10 cm radio fluxes and the series of R_z no significant trend with time, solar activity or solar cycle exists when mean values for periods of the order of one year are considered.Then, the daily solar u.v.-irradiances measured since 1969 for H-Lyman-alpha and-beta, the Hel-resonance line and HeII-Lyman-alpha are compared with the 10.7 cm radio fluxes and adjusted. After adjustment, the behaviour of the four series of irradiances with respect to the 10.7 cm flux shows a similar structure as the behaviour typical for the series of the 3 cm or the 8 cm fluxes.This adjustment allows the determination of the slope of the mean variation of the u.v.-irradiances with solar activity. The increases from solar minimum to solar maximum related to the minimum values are respectively : 60% for H-Lyman-alpha, 80% for H-Lyman-beta and 90% for Hel and Hell.     

An Early Prediction of the Amplitude of Solar Cycle 25

A “Solar Dynamo” (SODA) Index prediction of the amplitude of Solar Cycle 25 is described. The SODA Index combines values of the solar polar magnetic field and the solar spectral irradiance at 10.7 cm to create a precursor of future solar activity. The result is an envelope of solar activity that minimizes the 11-year period of the sunspot cycle. We show that the variation in time of the SODA Index is similar to several wavelet transforms of the solar spectral irradiance at 10.7 cm. Polar field predictions for Solar Cycles 21?–?24 are used to show the success of the polar field precursor in previous sunspot cycles. Using the present value of the SODA index, we estimate that the next cycle’s smoothed peak activity will be about \(140 \pm30\) solar flux units for the 10.7 cm radio flux and a Version 2 sunspot number of \(135 \pm25\). This suggests that Solar Cycle 25 will be comparable to Solar Cycle 24. The estimated peak is expected to occur near \(2025.2 \pm1.5\) year. Because the current approach uses data prior to solar minimum, these estimates may improve as the upcoming solar minimum draws closer.     

22周上升段太阳射电缓变成分的一些统计特性

本文根据1987年1月—1989年11月期间,2cm、3.4cm、6cm、10.7cm和21.2cm五个波段每日总辐射流量与日面上占主导地位的活动区黑子视面积之间的关系,对第22周上升段若干大活动区的射电缓变成分的统计特性进行了分析研究,发现有几个大活动区在日面时S-Ay图上处在平均曲线之下,当黑子面积增加时,射电流量的增加并不明显。     

Variation of solar irradiance and mode frequencies during Maunder minimum

Using the sunspot numbers reported during the Maunder minimum and the empirical relations between the mode frequencies and solar activity indices, the variations in the total solar irradiance and 10.7 cm radio flux for the period 1645 to 1715 is estimated. We find that the total solar irradiance and radio flux during the Maunder minimum decreased by 0.19% and 52% respectively, as compared to the values for solar cycle 22. This revised version was published online in July 2006 with corrections to the Cover Date.     

Hysteresis,time lag,and relation between solar activity and cosmic rays during solar cycle 24

We study galactic cosmic ray (GCR) modulation during solar cycle 24. For this study we utilize neutron monitor data together with sunspot number (SSN) and 10.7 cm solar radio flux (SRF) data. We plot hysteresis curve between the GCR intensity and SSN, and GCR intensity and SRF. We performed time-lag correlation analysis to determine the time lag between GCR intensity and solar activity parameters. The time lag is determined not only for the whole solar cycle, but also during the two polarity states of the heliosphere (A<0 and A>0) in solar cycle 24. We notice differences in time lags during two polarity epochs of the solar cycle. We discuss these differences in the light of existing modulation models. We compare the results of this very weak solar activity cycle with the corresponding results reported for the previous comparatively more active solar cycles.     

Solar activity during first six years of solar cycle 24 and 23: a comparative study

Attempt to look into the nature of solar activity and variability have increased importance in recent days because of their terrestrial relationships. In the present work we have attempted to compare the solar activity events during first six years (2008–2013) of the ongoing solar cycle 24 with first six years (1996–2001) of solar cycle 23. To that end, we have considered sunspot numbers, F10.7 cm solar flux, halo CMEs and geomagnetic storms as comparison parameters. Sunspot number during the year 2008–2013 varied from 0 to 96.7 while during the year 1996 to 2001 it was observed from 0.9 to 170.1. Solar radio flux (F10.7 cm index) varied from 65 to 190 during the years 2008–2013 while it was observed from 65 to 283 during the years 1996–2001. 197 cases of halo CMEs (width=360^°) in solar cycle 23 (1996–2001) and 177 cases of halo CMEs (width=360^°) in solar cycle 24 (2008–2013) are investigated. 287 and 104 geomagnetic storm cases (Dst varies between ?50 and ?350 nT) are analysed during the half period of solar cycle 23 and 24 respectively. Comparative results indicate that solar cycle 23 was more pronounced in comparison of solar cycle 24.     

The Ratio of the radio and optical diameters of the sun at centimeter wavelengths

The ratios of radio to optical diameter of the solar disc at 10.7 and 3 cm wavelengths are examined. The radio observations are daily east–west scans of the solar disc, made over the period 1975–1992, which includes almost two complete solar cycles. We find that the apparent disc diameter is slightly greater at solar minimum than it is at solar maximum, suggesting that the radio diameter varies over the cycle. Moreover, the ratio is smaller at 3 cm wavelength than it is at 10.7 cm, at both solar maximum and minimum.     

Monitoring the Dynamics of the Ionosphere–Plasmasphere System by Ground-Based ULF Wave Observations

Cross-spectral analysis of ULF wave measurements recorded at ground magnetometer stations closely spaced in latitude allows accurate determinations of magnetospheric field line resonance (FLR) frequencies. This is a useful tool for remote sensing temporal and spatial variations of the magnetospheric plasma mass density. The spatial configuration of the South European GeoMagnetic Array (SEGMA, 1.56 <  L <  1.89) offers the possibility to perform such studies at low latitudes allowing to monitor the dynamical coupling between the ionosphere and the inner plasmasphere. As an example of this capability we present the results of a cross-correlation analysis between FLR frequencies and solar EUV irradiance (as monitored by the 10.7-cm solar radio flux F10.7) suggesting that changes in the inner plasmasphere density follow the short-term (27-day) variations of the solar irradiance with a time delay of 1–2 days. As an additional example we present the results of a comparative analysis of FLR measurements, ionospheric vertical soundings and vertical TEC measurements during the development of a geomagnetic storm.     

明安图射电频谱日像仪图像的强度定标方法

明安图射电频谱日像仪(Mingantu Spectral Radioheliograph, MUSER)能够在0.4--15GHz超宽频带内实现高时间、高空间、高频率分辨率的太阳射电成像. 而射电亮温度是描述太阳物理过程的一个重要的参数, 在研究不同射电辐射机制、太阳磁场以及太阳爆发过程中非热粒子加速等问题上有着非常重要的作用, 因此必须对MUSER观测的图像进行亮温度定标. 将介绍一种适用于射电日像仪图像强度定标的方法. 太阳射电图像中包含着太阳圆盘的结构信息, 利用射电日像仪短基线的可视度函数拟合第一类贝塞尔函数, 可以得到图像中宁静太阳圆盘的射电半径和强度, 再利用瑞利-金斯定律和每天的太阳射电流量可以计算得到每天图像的定标因子$G_c$, 从而实现对MUSER图像强度的定标. 将该方法应用到MUSER的实际观测数据中, 包括宁静太阳和有太阳射电爆发等不同的情况, $G_c$的误差基本不超过10%, 得到的宁静太阳亮温度与其他宁静太阳的结果具有较高的相关性, 表明了此方法的可行性和有效性.     

5303 Å Coronal Irradiance and Its Relation to the Photospheric Magnetic Activity

The association of Lomnický tít data of coronal green line irradiance (CI) to photospheric magnetic activity is studied for the years 1975–1994 using the Carrington rotation averaged photospheric magnetic flux data. It is found that the CI correlates well with photospheric magnetic flux of active regions and the total disk-integrated magnetic flux on longer time scales (11-year solar cycle) and fails (about 50% of the time) to show a strong dependence on shorter time scales. A comparison of the association of CI and of the 10.7 cm radio flux with the photospheric magnetic flux data indicated that the CI might basically represent the background coronal irradiance.