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.     

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.     

太阳黑子月平均面积数活动周及其特征

我们对第12周至第22周的太阳黑子月平均面积数进行统计分析,并与相应的太阳黑子月平均数相比较,结果表明太阳黑子月平均面积数活动周与太阳黑子月平均数活动周有一定的关系。在多数情况下,太阳黑子出现最大值的时间与太阳黑子面积数出现最大值的时间上不一致;太阳黑子平滑月平均数活动周上升期与太阳黑子平滑月平均面积数上升期在大多数情况下不相同;太阳黑子平滑月平均数活动周平均效果的瓦德迈尔效应(Waldmeiereffect)一般要比太阳黑子平滑平均面积数的活动周明显;文中还对太阳黑子平滑月平均面积数活动周的特征进行了分析。     

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.     

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.     

10.7-cm Solar radio flux and the magnetic complexity of active regions

During sunspot cycles 20 and 21, the maximum in smoothed 10.7-cm solar radio flux occurred about 1.5 yr after the maximum smoothed sunspot number, whereas during cycles 18 and 19 no lag was observed. Thus, although 10.7-cm radio flux and Zürich suspot number are highly correlated, they are not interchangeable, especially near solar maximum. The 10.7-cm flux more closely follows the number of sunspots visible on the solar disk, while the Zürich sunspot number more closely follows the number of sunspot groups. The number of sunspots in an active region is one measure of the complexity of the magnetic structure of the region, and the coincidence in the maxima of radio flux and number of sunspots apparently reflects higher radio emission from active regions of greater magnetic complexity. The presence of a lag between sunspot-number maximum and radio-flux maximum in some cycles but not in others argues that some aspect of the average magnetic complexity near solar maximum must vary from cycle to cycle. A speculative possibility is that the radio-flux lag discriminates between long-period and short-period cycles, being another indicator that the solar cycle switches between long-period and short-period modes.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

Solar Cycle Prediction: Combining Precursor Methods with McNish and Lincoln Technique

Medium-term and long-term prediction of the magnitude of the maximum of smoothed sunspot numbers, and thus of the solar cycle time profile, is a basic input for many space environment predictions. The widely used statistical technique of McNish and Lincoln is systematically compared to predictions based on precursors, either related to the cycle time profile characteristics or to geomagnetic indices. It is shown that when cycles 13 – 23 are considered, all prediction methods give, at least for one of the cycles, an error much larger than 20%, an inadequate result. None of the methods is fully reliable. Thus, it is proposed to combine the predictions based on precursors and to improve McNish and Lincoln results with them in order to limit such rare but large errors and to improve significantly the reliability of the predictions performed in the course of the solar cycle ascending phase.     

23周太阳活动的现状和展望

本文给出了太阳２３ 周开始时间的确定、从开始到现在近两年间太阳活动的状况以及２３周上升期间的一些特点。分析表明,１９９６ 年１０ 月是２３ 周的第一个月,它的月平滑值是８ ．８ ;２３ 周的太阳活动虽然可能是高活动周,例如,国际推荐值为２０００ 年３ 月的１６０ ,但它可能不会超过前两周。根据上升期太阳活动的一些特征,还给出了在２３ 周峰年联测和空间灾害性扰动事件预报和预报方法研究中应注意的几个问题     

A Bayesian Analysis of the Correlations Among Sunspot Cycles

Sunspot numbers form a comprehensive, long-duration proxy of solar activity and have been used numerous times to empirically investigate the properties of the solar cycle. A number of correlations have been discovered over the 24 cycles for which observational records are available. Here we carry out a sophisticated statistical analysis of the sunspot record that reaffirms these correlations, and sets up an empirical predictive framework for future cycles. An advantage of our approach is that it allows for rigorous assessment of both the statistical significance of various cycle features and the uncertainty associated with predictions. We summarize the data into three sequential relations that estimate the amplitude, duration, and time of rise to maximum for any cycle, given the values from the previous cycle. We find that there is no indication of a persistence in predictive power beyond one cycle, and we conclude that the dynamo does not retain memory beyond one cycle. Based on sunspot records up to October 2011, we obtain, for Cycle 24, an estimated maximum smoothed monthly sunspot number of 97±15, to occur in January??C?February 2014 ± six months.     

第23太阳活动周发展趋势预测

利用压强改正莫斯科中子监测值,对第２３太阳活动周的未来发展趋势作了预测,推测第 ２３周太阳活动和第 ２２周相当,约在 ２００１年达到 １５１± １６的极大月平均黑子相对数．     

Dynamo-based scheme for forecasting the magnitude of solar activity cycles

In this paper we present a general framework for forecasting the smoothed maximum level of solar activity in a given cycle, based on a simple understanding of the solar dynamo. This type of forecasting requires knowledge of the Sun's polar magnetic field strength at the preceeding activity minimum. Because direct measurements of this quantity are difficult to obtain, we evaluate the quality of a number of proxy indicators already used by other authors which are physically related to the Sun's polar field. We subject these indicators to a rigorous statistical analysis, and specify in detail the analysis technique for each indicator in order to simplify and systematize reanalysis for future use. We find that several of these proxies are in fact poorly correlated or uncorrelated with solar activity, and thus are of little value for predicting activity maxima.We also present a scheme in which the predictions of the individual proxies are combined via an appropriately weighted mean to produce a compound prediction. We then apply the scheme to the current cycle 22, and estimate a maximum smoothed International sunspot number of 171 ± 26, which can be expressed alternatively as a smoothed 2800 MHz radio flux (F _10.7) of 211 ± 23 × (10^–22 Wm^–2Hz^–1), or as a smoothed sunspot area of 2660 ± 430 millionths of a solar disk. Once the actual maximum for cycle 22 has been established, we will have both additional statistics for all the proxy indicators, and a clearer indication of how accurately the present scheme can predict solar activity levels.     

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.     

Evolution of polar coronal holes and sunspots during cycles 21 and 22

A very good correlation between the evolution of polar coronal hole size and sunspot number half a solar cycle later was found by Bravo and Otaola for solar cycle 21. In this paper we use a more complete set of data to reanalyse the relationship for solar cycle 21 and investigate the same relationship for solar cycle 22. We find that the complete set of data for cycle 21 yields a slightly different time shift for the best correlation between sunspots and holes and that the time shift for cycle 22 is different from that of cycle 21. However, because of limited availability of data of cycle 22, we consider it necessary to wait until the end of this cycle in order to decide if the difference is statistically significant or not. We also found that the time between successive peaks of smoothed polar hole area and smoothed sunspot number is the same in both cycles. This may provide a useful tool for the forecasting of future sunspot maxima. The constant of proportionality between polar coronal hole area and sunspot number can be seen to be different in both cycles. We discuss this difference and interpret it in terms of a different magnitude of the polar field strength in the two cycles.     

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。     

What the Sunspot Record Tells Us About Space Climate

The records concerning the number, sizes, and positions of sunspots provide a direct means of characterizing solar activity over nearly 400 years. Sunspot numbers are strongly correlated with modern measures of solar activity including: 10.7-cm radio flux, total irradiance, X-ray flares, sunspot area, the baseline level of geomagnetic activity, and the flux of galactic cosmic rays. The Group Sunspot Number provides information on 27 sunspot cycles, far more than any of the modern measures of solar activity, and enough to provide important details about long-term variations in solar activity or “Space Climate.” The sunspot record shows: 1) sunspot cycles have periods of 131± 14 months with a normal distribution; 2) sunspot cycles are asymmetric with a fast rise and slow decline; 3) the rise time from minimum to maximum decreases with cycle amplitude; 4) large amplitude cycles are preceded by short period cycles; 5) large amplitude cycles are preceded by high minima; 6) although the two hemispheres remain linked in phase, there are significant asymmetries in the activity in each hemisphere; 7) the rate at which the active latitudes drift toward the equator is anti-correlated with the cycle period; 8) the rate at which the active latitudes drift toward the equator is positively correlated with the amplitude of the cycle after the next; 9) there has been a significant secular increase in the amplitudes of the sunspot cycles since the end of the Maunder Minimum (1715); and 10) there is weak evidence for a quasi-periodic variation in the sunspot cycle amplitudes with a period of about 90 years. These characteristics indicate that the next solar cycle should have a maximum smoothed sunspot number of about 145 ± 30 in 2010 while the following cycle should have a maximum of about 70 ± 30 in 2023.     

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.     

Effects of Hysteresis Between Maximum CME Speed Index and Typical Solar Activity Indicators During Cycle 23

Using the smoothed time series of maximum CME speed index for solar cycle 23, it is found that this index, analyzed jointly with six other solar activity indicators, shows a hysteresis phenomenon. The total solar irradiance, coronal index, solar radio flux (10.7?cm), Mg?ii core-to-wing ratio, sunspot area, and H?? flare index follow different paths for the ascending and the descending phases of solar cycle?23, while a saturation effect exists at the maximum phase of the cycle. However, the separations between the paths are not the same for the different solar activity indicators used: the H?? flare index and total solar irradiance depict broad loops, while the Mg?ii core-to-wing ratio and sunspot area depict narrow hysteresis loops. The lag times of these indices with respect to the maximum CME speed index are discussed, confirming that the hysteresis represents a clue in the search for physical processes responsible for changing solar emission.     

Using geomagnetic indices to forecast the next sunspot maximum

The Babcock solar dynamo model and known interactions of the interplanetary magnetic field with the earth's magnetosphere are used to explain the relations found between geomagnetic indices at solar minimum and the sunspot number at the following solar maximum. We augment the work of Kane (1987) by updating his method of analysis, including recent smoothed aa and A_P indices. We predict a smoothed maximum sunspot number of 163±40 to peak in October 1990±9 months for solar cycle 22. This value is close to the Schatten and Sofia (1987) predicted value of 170±25, using more direct solar indicators.Now at Dept. of Astronomy, Univ. of Washington     

Did Predictions of the Maximum Sunspot Number for Solar Cycle 23 Come True?

For solar cycle 23, the maximum sunspot number was predicted by several workers, and the range was very wide, 80–210. Cycle 23 started in 1996 and seems to have peaked in 2000, with a smoothed sunspot number maximum of 122. From about 20 predictions, 8 were within 122±20. There is an indication that a long-term oscillation of 80–100 years may be operative and might have peaked near cycle 20 (1970), and sunspot maxima in cycles in the near future may be smaller and smaller for the next 50 years or so and rebound thereafter in the next 50 years or so.     

Long-Term Sunspot Number Prediction based on EMD Analysis and AR Model

The Empirical Mode Decomposition (EMD) and Auto-Regressive model (AR) are applied to a long-term prediction of sunspot numbers. With the sample data of sunspot numbers from 1848 to 1992, the method is evaluated by examining the measured data of the solar cycle 23 with the prediction: different time scale components are obtained by the EMD method and multi-step predicted values are combined to reconstruct the sunspot number time series. The result is remarkably good in comparison to the predictions made by the solar dynamo and precursor approaches for cycle 23. Sunspot numbers of the coming solar cycle 24 are obtained with the data from 1848 to 2007, the maximum amplitude of the next solar cycle is predicted to be about 112 in 2011-2012.