Sunspot and Auroral Activity During Maunder Minimum

The extremely low sunspot activity during the period of the Maunder minimum 1645–1715 was confirmed by group sunspot numbers, a new sunspot index constructed by Hoyt and Schatten (1998a,b). Neither sunspots nor auroral data time behavior indicate the presence of 11-year solar cycles as stated by Eddy (1976). The evidence for solar cycles was found in the butterfly diagram, constructed from observations made at Observatoire de Paris. After Clivier, Boriakoff, and Bounar (1998) the solar cycles were reflected also in geomagnetic activity. Results are supported by the variation of cosmogenic isotopes ¹⁰Be and ¹⁴C. The majority of the observed 14 naked-eye sunspots occurred on days when telescopic observations were not available. A part of them appeared in the years when no spot was allegedly observed. Two-ribbon flares appear in plages with only very small or no sunspots. Some of these flares are geoactive. Most aurorae (90%), which were observed during the Maunder minimum, appeared in years when no spot was observed. Auroral events as a consequence of proton flares indicate that regions with enhanced magnetic field can occur on the Sun when these regions do not produce any sunspots.     

Prediction of Solar Cycle 24 Using Sunspot Number near the Cycle Minimum

Correlations between monthly smoothed sunspot numbers at the solar-cycle maximum [R _max] and duration of the ascending phase of the cycle [T _rise], on the one hand, and sunspot-number parameters (values, differences and sums) near the cycle minimum, on the other hand, are studied. It is found that sunspot numbers two?–?three years around minimum correlate with R _max or T _rise better than those exactly at the minimum. The strongest correlation (Pearson’s r=0.93 with P<0.001 and Spearman’s rank correlation coefficient r _S=0.95 with P=9×10^?12) proved to be between R _max and the sum of the increase of activity over 30 months after the cycle minimum and the drop of activity over 30 or 36 months before the minimum. Several predictions of maximal amplitude and duration of the ascending phase for Solar Cycle 24 are given using sunspot-number parameters as precursors. All of the predictions indicate that Solar Cycle 24 is expected to reach a maximal smoothed monthly sunspot number (SSN) of 70?–?100. The prediction based on the best correlation yields the maximal amplitude of 90±12. The maximum of Solar Cycle 24 is expected to be in December 2013?–?January 2014. The rising and declining phases of Solar Cycle 24 are estimated to be about 5.0 and 6.3 years, respectively. The minimum epoch between Solar Cycles 24 and 25 is predicted to be at 2020.3 with minimal SSN of 5.1?–?5.4. We predict also that Solar Cycle 25 will be slightly stronger than Solar Cycle 24; its maximal SSN will be of 105?–?110.     

太阳黑子面积数与黑子数指标在大气预报中的应用对比分析

分别应用太阳黑子视面积数和太阳黑子相对数代表太阳活动水平与天津夏季降水总量进行相关分析,结果表明黑子面积指标明显优于黑子数.     

The Intermediate-Term Quasi-Cycles of Wolf Number and Group Sunspot Number Fluctuations

I apply spectral and auto-correlation analyses to the monthly Wolf number fluctuations for 22 solar cycles and to the group sunspot number fluctuations for 18 solar cycles and find the existence of an 11-month quasi-periodicity in these data. Its strength correlates very well (ρ ⑈ 0.8) with the variance of fluctuations. Moreover, for both Wolf and group sunspot indexes I divide a stationary version of fluctuation time series into two parts: those from periods of low and high solar activity. I find statistically significant quasi-periodicity (9 months) in both high- and low-activity data sets. I also find the quasi-period of about 15 months in the time series of high-activity periods.     

Forecast of the Decadal Average Sunspot Number

The forecast of the decadal average sunspot number (SN) becomes possible with an extension of telescopic observations based on proxy reconstructions using the tree ring radiocarbon data during the Holocene. These decadal numbers (SN_RC) provide a powerful statistic to verify the forecasting methods. Complicated dynamics of long-term solar activity and noise of proxy-based reconstruction make the one-step-ahead forecast challenging for any forecasting method. Here we construct a continuous data set of SN_RC which extends the group sunspot number and the international sunspot number. The known technique of nonlinear forecast, the local linear approximation, is adapted to estimate the coming SN. Both the method and the continuous data set were tested and tuned to obtain the minimum of a normalized average prediction error (E) during the last millennium using several past millennia as a training data set. E=0.58σ _D is achieved to forecast the SN successive differences whose standard deviation is σ _D=7.39 for the period of training. This corresponds to the correlation (r=0.97) between true and forecasted SN. This error is significantly smaller than the prediction error when the surrogate data were used for the training data set, and proves the nonlinearity in the decadal SN. The estimated coming SN is smaller than the previous one.     

A comparison of the spectral characteristics of the Wolf Sunspot Number (R Z) and Group Sunspot Number (R G)

The objective of this paper is to compare the spectral features of the recently derived Group Sunspot Numbers (R _G) and the traditional Wolf Sunspot Numbers (R _Z) for the 1700–1995 period. In order to study the spectral features of both time series, two methods were used, including: (a) the multitaper analysis and (b) the wavelet analysis. Well-known features of the solar variability, such as the 98.6-yr (Gleissberg cycle), 10–11-yr (Schwabe cycle) and 5-yr (second solar harmonic) periodicities were identified with high confidence using the multitaper analysis. Also observed was a larger amount of power spread in high frequencies for R _Z than for R _G spectra. Furthermore, a multitaper analysis of two subsets, A (1700–1850) and B (1851–1995), has indicated that the main differences occurred in the first subset and seem to be due to uncertainties in the early observations. The wavelet transform, which allows observing the spectra evolution of both series, showed a strong and persistent 10–11-yr signal that remained during the whole period. The Meyer Wavelet Transform was applied to both R _Z and R _G. This study indicates that the main spectral characteristics of both series are similar and that their long-term variability has the same behavior.     

Nonlinear Time Series Analysis of Sunspot Data

This article deals with the analysis of sunspot number time series using the Hurst exponent. We use the rescaled range (R/S) analysis to estimate the Hurst exponent for 259-year and 11 360-year sunspot data. The results show a varying degree of persistence over shorter and longer time scales corresponding to distinct values of the Hurst exponent. We explain the presence of these multiple Hurst exponents by their resemblance to the deterministic chaotic attractors having multiple centers of rotation.     

The Sunspot and Auroral Activity Cycle Derived from Korean Historical Records of the 11th–18th Century

Historical records of sunspots and aurorae are valuable information to examine variations of solar activity and the terrestrial climate on a long-term scale. We have collected the historical records of Korea during the 11th–18th century. Through a power-spectrum analysis of these data, we have found solar activity cycles, which coincide with the Schwabe cycle and the Gleissberg cycle on short and long-term periods, respectively.