Evolution of the Level of Sunspot Activity in Solar Cycles I. Evolution in the Descending Phase

Taking the 13-point smoothed monthly sunspot number,Ri, and the deviation of the 13 associated monthly sunspot numbers from the smoothed one, Di, as a number-pair describing the global level of sunspot activity, the evolution of the level is statistically studied for the period from the month which is just 48 months before the minimum to the minimum in the descending phase, using the observed data of Solar Cycles 10 to 22. Our results show （1） for 46 months （94%） of the studied 49 months it is found that for a given month, the distribution of the 13 pairs which come from the 13 solar cycles on a log Ri - Di plane may be fitted by a straight line with a correlation coefficient larger than the critical one at confidence level a = 5%, and for 36 months （73%） the fitting is even better, for a = 1%; （2） time variations of these two parameters and their correlations in the studied period can be described respectively by functions of time, whose main trends may be expressed by a linear or simple curvilinear function; （3） the evolutionary path of the level of sunspot activity may be represented by a logarithmic function as log/~ = 0.704 lnDi - 0.291.

Low-dimensional chaos and fractal properties of long-term sunspot activity

Two primary solar-activity indicators- sunspot numbers （SNs） and sunspot areas （SAs） in the time interval from November 1874 to December 2012 - are used to determine the chaotic and fractal properties of solar activity. The results show that （1） the long-term solar activity is governed by a low-dimensional chaotic strange attractor, and its fractal motion shows a long-term persistence on large scales; （2） both the fractal dimension and maximal Lyapunov exponent of SAs are larger than those of SNs, implying that the dynamical system of SAs is more chaotic and complex than SNs; （3） the predictions of solar activity should only be done for short- to mid-term behaviors due to its intrinsic complexity; moreover, the predictability time of SAs is obviously smaller than that of SNs and previous results.

Phase asynchrony between flare index and sunspot activity

In this paper, the relative phase relationship between flare index and sunspot activity （sunspot numbers and sunspot areas） is investigated. It is found that （i） the flare index and sunspot activity are asynchronous in phase space at all period scales, and the former lags behind the latter, which implies our results are supported for the integral response model; （ii） their different definitions and physical meanings may be a major reason for their phase asynchrony between them, and the solar flare activity favor to be related to the magnetic complex rather than magnetic strength.

The relationships of solar flares with both sunspot and geomagnetic activity

The relationships between solar flare parameters （total importance, time duration, flare index, and flux） and sunspot activity （R z ） as well as those between geomagnetic activity （aa index） and the flare parameters can be well described by an integral response model with the response time scales of about 8 and 13 months, respectively. Compared with linear relationships, the correlation coefficients of the flare parameters with R z , of aa with the flare parameters, and of aa with R z based on this model have increased about 6%, 17%, and 47% on average, respectively. The time delays between the flare parameters with respect to R z , aa to the flare parameters, and aa to R z at their peaks in a solar cycle can be predicted in part by this model （82%, 47%, and 78%, respectively）. These results may be further improved when using a cosine filter with a wider window. It implies that solar flares are related to the accumulation of solar magnetic energy in the past through a time decay factor. The above results may help us to understand the mechanism of solar flares and to improve the prediction of the solar flares.

Wavelet Analysis of Several Important Periodic Properties in the Relative Sunspot Numbers

We investigate the wavelet transform of yearly mean relative sunspot number series from 1700 to 2002. The curve of the global wavelet power spectrum peaks at 11-yr, 53-yr and 101-yr periods. The evolution of the amplitudes of the three periods is studied. The results show that around 1750 and 1800, the amplitude of the 53-yr period was much higher than that of the the 11-yr period, that the ca. 53-yr period was apparent only for the interval from 1725 to 1850, and was very low after 1850, that around 1750, 1800 and 1900, the amplitude of the 101-yr period was higher than that of the 11-yr period and that, from 1940 to 2000, the 11-yr period greatly dominates over the other two periods.

Phase analysis of sunspot group numbers on both solar hemispheres

Cross-correlation analysis and wavelet transform methods are proposed to investigate the phase relationship between the monthly sunspot group numbers in the solar northern and southern hemispheres. It is found that （1） the monthly sunspot group numbers in the northern hemisphere begin two months earlier than those in the southern one, which should lead to phase asynchrony between them but with a slight effect; （2） the Schwabe cycle length for the monthly sunspot group numbers in the two hemispheres obviously differs from each other, and the mean Schwabe cycle length of the monthly sunspot group numbers in the northern hemisphere is slightly larger than that in the southern one; （3） the monthly sunspot group numbers in the northern hemisphere precede those in the southern hemisphere during the years of about 1874- 1927, after which, the southern hemisphere leads the northern hemisphere in the years 1928-1964, and then the northern hemisphere leads in time till the present.

Can Asymmetry of Solar Activity be Extended into Extended Cycle?

With the use of the Royal Greenwich Observatory data set of sunspot groups, an attempt is made to examine the north-south asymmetry of solar activity in the 'extended' solar cycles. It is inferred that the asymmetry established for individual solar cycles does not extend to the 'extended' cycles.

An Electron Density Model above the Sunspot from a Mapping of NOAA 7260 at 17 GHz

The brightness temperature distribution of microwave emission in a solar active region generally shows a ring structure, with a dip at the centre. However, no dip was found in the Nobeyama Radioheliograph left handed circular polarization (LCP) image on 1992 August 18; instead, there was a peak. This is a completely LCP source with zero right-handed circular polarization (RCP). We examine this structure in terms of the joint effect of gyroresonance and bremsstrahlung mechanism with a raised electron density above the central part of the sunspot, and the commonly assumed temperature and vertical dipole magnetic field models. The raised electron density is found to be 1.4 × 1011 cm-3 at the chromosphere base.

Latitudinal migration of sunspots based on the ESAI database

The latitudinal migration of sunspots toward the equator,which implies there is propagation of the toroidal magnetic flux wave at the base of the solar convection zone,is one of the crucial observational bases for the solar dynamo to generate a magnetic field by shearing of the pre-existing poloidal magnetic field through differential rotation.The Extended time series of Solar Activity Indices（ESAI）elongated the Greenwich observation record of sunspots by several decades in the past.In this study,ESAI＇s yearly mean latitude of sunspots in the northern and southern hemispheres during the years 1854 to 1985 is utilized to statistically test whether hemispherical latitudinal migration of sunspots in a solar cycle is linear or nonlinear.It is found that a quadratic function is statistically significantly better at describing hemispherical latitudinal migration of sunspots in a solar cycle than a linear function.In addition,the latitude migration velocity of sunspots in a solar cycle decreases as the cycle progresses,providing a particular constraint for solar dynamo models.Indeed,the butterfly wing pattern with a faster latitudinal migration rate should present stronger solar activity with a shorter cycle period,and it is located at higher latitudinal position,giving evidence to support the Babcock-Leighton dynamo mechanism.

Characteristics of Drought and Flood in Zhejiang Province,East China:Past and Future

On the basis of large amount of historical and measured data, this paper analyzed the regional, periodic, frequency, continuing, and response characteristics of droughts and floods in Zhejiang and proposed the conception of ratio of peak runoff. Main characteristics of droughts and floods in Zhejiang are as follows： 1） The western Zhejiang region is plum rain major control area, and the eastern coastal region of Zhejiang is typhoon major control area. 2） Within a long period in the future, Zhejiang will be in the long period that features droughts. 3） In Zhejiang the 17th century was frequent drought and flood period, the 16th, 19th, and 20th centuries were normal periods, while the 18th century was spasmodic drought and flood period. 4） The severe and medium floods in Zhejiang were all centered around the M-or m-year of the 11-year sunspot activity period. 5） There are biggish years of annual runoff occurred in E1 Nifio year （E） or the following year （E＋1） in Zhejiang. The near future evolution trend of droughts and floods in Zhejiang is as follows： 1） Within a relatively long period in the future, Zhejiang Province will be in the long period of mostly drought years. 2） Between 1999 and 2009 this area will feature drought years mainly, while the period of 2010-2020 will feature flood years mostly. 3） Zhejiang has a good response to the sunspot activities, and the years around 2009, 2015, and 2020 must be given due attention, especially around 2020 there might be an extremely severe flood year in Zhejiang. 4） Floods in Zhejiang have good response to El Nifio events, in El Nifio year or the following year much attention must be paid to. And 5） In the future, the first, second, and third severe typhoon years in Zhejiang will be 2009. 2012. and 2015. resnectivelv.

Estimating the Size and Timing of the Maximum Amplitude of Solar Cycle 24

A simple statistical method is used to estimate the size and timing of maximum amplitude of the next solar cycle （cycle 24）. Presuming cycle 23 to be a short cycle （as is more likely）, the minimum of cycle 24 should occur about December 2006 （±2 months） and the maximum, around March 2011 （±9 months）, and the amplitude is 189.9 ± 15.5, if it is a fast riser, or about 136, if it is a slow riser. If we presume cycle 23 to be a long cycle （as is less likely）, the minimum of cycle 24 should occur about June 2008 （±2 months） and the maximum, about February 2013 （±8 months） and the maximum will be about 137 or 80, according as the cycle is a fast riser or a slow riser.

Neural network prediction of solar cycle 24

The ability to predict the future behavior of solar activity has become extremely import due to its effect on the environment near the Earth. Predictions of both the amplitude and timing of the next solar cycle will assist in estimating the various consequences of space weather. The level of solar activity is usually expressed by in- ternational sunspot number （Rz）. Several prediction techniques have been applied and have achieved varying degrees of success in the domain of solar activity prediction. We predict a solar index （Rz） in solar cycle 24 by using a neural network method. The neural network technique is used to analyze the time series of solar activity. According to our predictions of yearly sunspot number, the maximum of cycle 24 will occur in the year 2013 and will have an annual mean sunspot number of 65. Finally, we discuss our results in order to compare them with other suggested predictions.

The Relation between the Amplitude and the Period of Solar Cycles

The maximum amplitudes of solar activity cycles are found to be well anticorrelated （r = -0.72） with the newly defined solar cycle lengths three cycles before （at lag -3） in 13-month running mean sunspot numbers during the past 190 years. This result could be used for predicting the maximum sunspot numbers. The amplitudes of Cycles 24 and 25 are estimated to be 149.5±27.6 and 144.3±27.6, respectively.

The prediction method of similar cycles

The concept of degree of similarity （η）, is proposed to quantitatively describe the similarity of a parameter （e.g. the maximum amplitude Rmax） of a solar cycle relative to a referenced one, and the prediction method of similar cycles is further developed. For two parameters, the solar minimum （Rmin） and rising rate （βa）, which can be directly measured a few months after the minimum, a synthesis degree of similarity （ηs） is defined as the weighted-average of the η values around Rmin and βa, with the weights given by the coefficients of determination of Rmax with Rmin and βa, respectively. The monthly values of the whole referenced cycle can be predicted by averaging the corresponding values in the most similar cycles with the weights given by the ηs values. As an application, Cycle 24 is predicted to peak around January 2013 i8 （month） with a size of about Rmax = 84 ± 17 and to end around September 2019.

What does the Sun tell and hint now?

Some historical records, which have held since the beginning of modern solar activity cycles, are being broken by the present Sun： cycle 23 records the longest cycle length and fall time; latitudes of high-latitude sunspots belonging to a new cycle around the minimum time of the cycle are statistically the lowest at present, compared with those of other cycles; there are only one or no sunspots in a month appearing at high latitudes for 58 months, which is the first time that such a long duration has been observed. The solar dynamo is believed to be slowing down due to： （1） the minimum smoothed monthly mean sunspot number is the smallest since cycle 16 onwards, and even probably among all modern solar cycles; and （2） once the time interval between the first observations of two neighboring sunspot groups is larger than 14 d, it should be approximately regarded as an observation of no sunspots on the visible solar disk, called a spotless event. Spotless events occur with the highest frequency around the minimum time of cycle 24, and the longest spotless event also appears around the minimum time for observations of the Sun since cycle 16. Cycle 24 is expected to have the lowest level of sunspot activity from cycle 16 onwards and even probably for all of the modern solar cycles.

Calibration of Vector Magnetogram with the Nonlinear Least-squares Fitting Technique

To acquire Stokes profiles from observations of a simple sunspot with the Video Vector Magnetograph at Huairou Solar Observing Station (HSOS), we scanned the FeI λ5324.19 A line over the wavelength interval from 150mA redward of the line center to 150mA blueward, in steps of 10mA. With the technique of analytic inversion of Stokes profiles via nonlinear least-squares, we present the calibration coefficients for the HSOS vector magnetic magnetogram. We obtained the theoretical calibration error with linear expressions derived from the Unno-Becker equation under weak-field approximation.

A possible explanation of the Maunder minimum from a flux transport dynamo model

We propose that the poloidal field at the end of the last sunspot cycle before the Maunder minimum fell to a very low value due to fluctuations in the Babcock-Leighton process. With this assumption, a flux transport dynamo model is able to explain various aspects of the historical records of the Maunder minimum remarkably well by suitably choosing the parameters of the model to give the correct growth time.

A New Method to Determine Epochs of Solar Cycle Extrema

A weighted average method is proposed to determine the epochs of solar cycle extrema and hence the solar cycle lengths. Comparing to the previous methods, this method has the advantage that the extremum epochs are easily and uniquely determined.

Temporal variation of hemispheric solar rotation

The daily sunspot numbers of the whole disk as well as the northern and southern hemispheres from 1945 January 1 to 2010 December 31 are used to investi- gate the temporal variation of rotational cycle length through the continuous wavelet transformation analysis method. Auto-correlation function analysis of daily hemi- spheric sunspot numbers shows that the southern hemisphere rotates faster than the northern hemisphere. The results obtained from the wavelet transformation analysis are that no direct relationship exists between the variation trend of the rotational cy- cle length and the solar activity in the two hemispheres and that the rotational cycle length of both hemispheres has no significant period appearing at 11 yr, but has a sig- nificant period of about 7.6 yr. Analysis concerning the solar cycle dependence of the rotational cycle length shows that acceleration seems to appear before the minimum time of solar activity in the whole disk and the northern hemisphere, respectively. Furthermore, the cross-correlation study indicates that the rotational cycle length of the two hemispheres has different phases, and that the rotational cycle length of the whole disk as well as the northern and southern hemispheres, also has phase shifts with corresponding solar activity. In addition, the temporal variation of the north-south （N- S） asymmetry of the rotational cycle length is also studied. This displays the same variation trend as the N-S asymmetry of solar activity in a solar cycle, as well as in the considered time interval, and has two significant periods of 7.7 and 17.5 yr. Moreover, the rotational cycle length and the N-S asymmetry of solar activity are highly corre- lated. It is inferred that the northern hemisphere should rotate faster at the beginning of solar cycle 24.

On the line profile changes observed during the X2.2 class flare in the active region NOAA 11158

The solar active region NOAA 11158 produced a series of flares during its passage through the solar disk. The first major flare （of class X2.2） of the current solar cycle occurred in this active region on 2011 February 15 around 01：50 UT. We have analyzed the Dopplergrams and magnetograms obtained by the Helioseismic and Magnetic Imager （HMI） instrument onboard Solar Dynamics Observatory to examine the photospheric velocity and magnetic field changes associated with this flare. The HMI instrument provides high-quality Doppler and magnetic maps of the solar disk with 0.5＂ spatial scale at a cadence of 45 s along with imaging spectroscopy. We have identified five locations of velocity transients in the active region during the flare. These transient velocity signals are located in and around the flare ribbons as observed by Hinode in the Ca II H wavelength and the footpoints of hard X-ray enhancement are in the energy range 12-25 keV from RHESSI. The changes in shape and width of two circular polarization states have been observed at the time of transients in three out of five locations. Forward modeling of the line profiles shows that the change in atmospheric parameters such as magnetic field strength, Doppler velocity and source function could explain the observed changes in the line profiles with respect to the pre-flare condition.