Prediction of the Beginning of Solar Activity Cycle 24 by the Similar Cycle Method

In this paper, the method of similar cycles is applied to predict the start time of the 24th cycle of solar activity and the sunspot numbers in the later part of the descending phase of cycle 23. According to the characteristic parameters and the morphological characters of the descending phase of cycle 23 and of cycles 9, 10, 11, 15, 17 and 20 (cycles selected as the similar cycles for the descending phase of cycle 23), the start time of cycle 24 is predicted to be in 2007 yr 5 ± 1m, the smoothed monthly mean spot number, 7.1 ± 2.6 and the length of the 23rd cycle, 11.1 yr. These results agree rather well with those stated in Refs.[11] & [12] as well as those of MSFC. Our work shows that the method of similar cycles can well be applied to the long-term prediction of solar activity.     

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.     

Longterm Prediction of Solar Activity Using the Combined Method

The Combined Method is a non-parametric regression technique for long-term prediction of smoothed monthly sunspot numbers. Starting from a solar minimum, a prediction of the succeeding maximum is obtained by using a dynamo-based relation between the geomagnetic aa index and succeeding solar maxima. Then a series of predictions is calculated by computing the weighted average of past cycles of similar level. This technique leads to a good prediction performance, particularly in the ascending phase of the solar cycle where purely statistical methods tend to be inaccurate. For cycle 23 the combined method predicts a maximum of 160 (in terms of smoothed sunspot number) early in the year 2000.     

预报第23周平滑月平均太阳黑子数的一种方法

利用已知的22个完整太阳活动周平滑月平均黑子数的记录，对正在进行的太阳周发展趋势给出了预测方法，并应用于第23周，同时与其他预报方法的结果进行了比较。     

Sunspot groups at high latitude

Data of sunspot groups at high latitude (35°), from the year 1874 to the present (2000 January), are collected to show their evolutional behaviour and to investigate features of the yearly number of sunspot groups at high latitude. Subsequently, an evolutional pattern of sunspot group number at high latitude is given in this paper. Results obtained show that the number of sunspot groups of a solar cycle at high latitude rises to a maximum value about 1 yr earlier than the time of the maximum of sunspot relative numbers of the solar cycle, and then falls to zero more rapidly. The results also show that, at the moment, solar activity described by the sunspot relative numbers has not yet reached its minimum. In general, sunspot groups at high latitude have not appeared on the solar disc during the last 3 yr of a Wolf solar cycle. The asymmetry of the high latitude sunspot group number of a Wolf solar cycle can reflect the asymmetry of solar activity in the Wolf solar cycle, and it is suggested that one could further use the high latitude sunspot group number during the rising time of a Wolf solar cycle, maximum year included, to judge the asymmetry of solar activity over the whole solar cycle.     

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...     

PREDICTIONS OF THE FEATURES FOR SUNSPOT CYCLE 23

Smoothed monthly mean Ap indices are decomposed into two components (Ap) _c and (Ap) _n. The former is directly correlated with the current sunspot numbers, while the latter is shown to achieve its maximum correlation with the sunspot numbers after some time lag. This latter property is used to develop a method for predicting the sunspot maximum based on the observed value of (Ap) _n maximum which occurs during the preceding cycle. The value of R _M for cycle 23 predicted by this method is 149.3 ± 19.9. A method to estimate the rise time (from solar minimum to maximum) has been developed (based on analyses of Hathaway, Wilson, and Reichmann, 1994) and yields a value of 4.2 years. Using an estimate that the minimum between cycles 22 and 23 occurred in May 1996, it is predicted that the sunspot maximum for cycle 23 will occur in July 2000.     

A Stochastic Prediction Model for the Sunspot Cycles

A stochastic prediction model for the sunspot cycle is proposed. The prediction model is based on a modified binary mixture of Laplace distribution functions and a moving-average model over the estimated model parameters. A six-parameter modified binary mixture of Laplace distribution functions is used for the modeling of the shape of a generic sunspot cycle. The model parameters are estimated for 23 sunspot cycles independently, and the primary prediction-model parameters are derived from these estimated model parameters using a moving-average stochastic model. A correction factor (hump factor) is introduced to make an initial prediction. The hump factor is computed for a given sunspot cycle as the ratio of the model estimated after the completion of a sunspot cycle (post-facto model) and the prediction of the moving-average model. The hump factors can be applied one at a time over the moving-average prediction model to get a final prediction of a sunspot cycle. The present model is used to predict the characteristics of Sunspot Cycle 24. The methodology is validated using the previous Sunspot Cycles 21, 22, and 23, which shows the adequacy and the applicability of the prediction model. The statistics of the variations of sunspot numbers at high solar activity are used to provide the lower and upper bound for the predictions using the present model.     

Predictions of the maximum amplitude for solar cycle 23 and its subsequent behavior using nonlinear methods

Two nonlinear methods are employed for the prediction of the maximum amplitude for solar cycle 23 and its declining behavior. First, a new heuristic method based on the second derivative of the (conveniently smoothed) sunspot data is proposed. The curvature of the smoothed sunspot data at cycle minimum appears to correlate (R 0.92) with the cycle's later-occurring maximum amplitude. Secondly, in order to predict the near-maximum and declining activity of solar cycle 23, a neural network analysis of the annual mean sunspot time series is also performed. The results of the present study are then compared with some other recent predictions.     

Prediction of the Maximum Amplitude of Solar Cycles Using the Ascending Inflexion Point

To predict solar cycle maximum in terms of smooth sunspot numbers, a method based on the slope at the inflexion point observed during the ascending phase of the cycle is proposed. Application to cycle 23 (beginning in May 1996) gives a predicted value of 103±20 (r.m.s.) for the sunspot number maximum. A comparison with predictions using other methods is given.     

A Running Average Method for Predicting the Size and Length of a Solar Cycle

The running correlation coefficient between the solar cycle amplitudes and the max-max cycle lengths at a given cycle lag is found to vary roughly in a cyclical wave with the cycle number, based on the smoothed monthly mean Group sunspot numbers available since 1610. A running average method is proposed to predict the size and length of a solar cycle by the use of the varying trend of the coefficients. It is found that, when a condition (that the correlation becomes stronger) is satisfied, the mean prediction error (16.1) is much smaller than when the condition is not satisfied (38.7). This result can be explained by the fact that the prediction must fall on the regression line and increase the strength of the correlation. The method itself can also indicate whether the prediction is reasonable or not. To obtain a reasonable prediction, it is more important to search.for a running correlation coefficient whose varying trend satisfies the proposed condition, and the result does not depend so much on the size of the correlation coefficient. As an application, the peak sunspot number of cycle 24 is estimated as 140.4±15.7, and the peak as May 2012± 11 months.     

Modulation of the Solar Magnetic Cycle

The modulation model of the solar magnetic cycle for the time interval from 1650 to 1996 A.D. describes an harmonic oscillator with a basic (22.13 ± 0.05)-yr period, which is subjected to amplitude and phase variations that can be represented by a sum of trigonometric series. The simulated sunspot data explain 97.9% of cycle peak height variance and the residual standard deviation is 8.6 mean annual sunspots. A peak height of 139 for cycle 23 occurring in 2001 is predicted, whereas cycle 24 would have a maximum around 132 in 2014. Simulation of the sunspot numbers from 1000 until 2400 A.D. shows that the model recreates recurring minima (Maunder and Spörer Minimum). The prediction also expects a high level of amplitude modulation in the interval 1950–2010 with a rapid decrease afterwards. A greatly reduced cycle activity is reproduced by the simulation from about 2065 to 2100 A.D. No direct explanation of the long-term periodicities of the model can be advanced. The high-frequency contribution of the phase modulation, which accounts for the skewness of the solar cycle, shows coincidences with the orbital periods of Jupiter and Saturn, but no physical basis for the matching periodicities can be conceived.     

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.     

Features of the Solar Active Cycles

1　ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｏｌａｒａｃｔｉｖｅｃｙｃｌｅｉｓｕｓｕａｌｌｙｄｅｓｃｒｉｂｅｄｗｉｔｈｔｈｅｒｅｌａｔｉｖｅｓｕｎｓｐｏｔｎｕｍｂｅｒｓ.Ａｎａｌｙｓｅｓｏｆｈｉｓ ｔｏｒｉｃａｌｄａｔａｏｎｔｈｅｒｅｌａｔｉｖｅｓｕｎｓｐｏｔｎｕｍｂｅｒｓｈａｖｅｒｅｖｅａｌｅｄａｗｅａｌｔｈｏｆｉｎｆｏｒｍａｔｉｏｎａｂｏｕｔｔｈｅｓｏｌａｒａｃｔｉｖｅｃｙｃｌｅ (ＨｏｎｇＱｉｎｆａｎｇ 1 990 ,1 994;ＺｈｏｎｇＳｈｕｈｕａ 1 991 ,1 995 ) .Ｔｈｅｓｏ ｃａｌｌｅｄ 1 1 ｙｅａｒｐｅ ｒｉｏ…     

Dependence of SSNM on SSNm – a Reconsideration for Predicting the Amplitude of a Sunspot Cycle

An improved correlation between maximum sunspot number (SSN_M) and the preceding minimum (SSN_m) is reported when the monthly mean sunspot numbers are smoothed with a 13-month running window. This relation allows prediction of the amplitude of a sunspot cycle by making use of the sunspot data alone. The estimated smoothed maximum sunspot number (126±26) and time of maximum epoch (second half of 2000) of cycle 23 are in good agreement with the predictions made by some of the precursor methods.     

The Shape of Sunspot Cycles Described by Monthly Sunspot Areas

In this paper, we used the same four-parameter function as Hathaway, Wilson, and Reichmann (1994) proposed and studied the temporal behavior of sunspot cycles 12–22. We used the monthly averages of sunspot areas and their 13-point smoothed data. Our results show the following. (1) The four-parameter function may reduce to a function of only two parameters. (2) As a cycle progresses, the two-parameter function can be accurately determined after 4–4.5 years from the start of the cycle. A good prediction can be made for the timing and size of the sunspot maximum and for the behavior of the remaining 5–10 years of the cycle. (3) The solar activity in the remaining and forthcoming years of cycle 23 is predicted. (4) The smoothed monthly sunspot areas are more suitable to be employed for prediction at the maximum and the descending period of a cycle, whereas at the early period of a cycle the (un-smoothed) monthly data are more suitable.     

Prediction of maximum sunspot number in solar cycle 23

Instantaneous predictions of the maximum monthly smoothed sunspot number in solar cycle 23 have been made with a linear regressive model, which gives the predicted maximum value as a function of the smoothed sunspot numbers corresponding to a given month from the minimum in all preceding cycles. These predictions indicate that the intensity of solar activity in the current cycle will be at an average level.     

Short-Term Periodicities in Sunspot Activity and Flare Index Data during Solar Cycle 23

The short-term periodicities in sunspot numbers, sunspot areas, and flare index data are investigated in detail using the Date Compensated Discrete Fourier Transform (DCDFT) for the full disk of the Sun separately over the rising, the maximum, and the declining portions of solar cycle 23 (1996 – 2006). While sunspot numbers and areas show several significant periodicities in a wide range between 23.1 and 36.4 days, the flare index data do not exhibit any significant periodicity. The earlier conclusion of Pap, Tobiska, and Bouwer (1990, Solar Phys. 129, 165) and Kane (2003, J. Atmos. Solar-Terr. Phys. 65, 1169), that the 27-day periodicity is more pronounced in the declining portion of a solar cycle than in the rising and maximum ones, seems to be true for sunspot numbers and sunspot area data analyzed here during solar cycle 23.     

太阳活动区活动性的模糊预测

运用模糊数学的理论和方法对太阳活动区的活动性进行了预测。为了综合评估和预测活动区的活动性，根据耀斑与黑子群特征因子间的关系，构造了隶属函数。通过数据处理与分析，得到了对活动区活动性较好的预测结果，预测的准确性＞95%。已成功编制了太阳活动预报的数据处理实用软件，根据黑子群的特征因子值，即刻就能得到活动区活动性的预报结果，预测结果表明模糊综合评估方法能很好地预报太阳活动。     

Automatic Short-Term Solar Flare Prediction Using Machine Learning and Sunspot Associations

In this paper, a machine-learning-based system that could provide automated short-term solar flare prediction is presented. This system accepts two sets of inputs: McIntosh classification of sunspot groups and solar cycle data. In order to establish a correlation between solar flares and sunspot groups, the system explores the publicly available solar catalogues from the National Geophysical Data Center to associate sunspots with their corresponding flares based on their timing and NOAA numbers. The McIntosh classification for every relevant sunspot is extracted and converted to a numerical format that is suitable for machine learning algorithms. Using this system we aim to predict whether a certain sunspot class at a certain time is likely to produce a significant flare within six hours time and if so whether this flare is going to be an X or M flare. Machine learning algorithms such as Cascade-Correlation Neural Networks (CCNNs), Support Vector Machines (SVMs) and Radial Basis Function Networks (RBFN) are optimised and then compared to determine the learning algorithm that would provide the best prediction performance. It is concluded that SVMs provide the best performance for predicting whether a McIntosh classified sunspot group is going to flare or not but CCNNs are more capable of predicting the class of the flare to erupt. A hybrid system that combines a SVM and a CCNN is suggested for future use.