A Neuro-Fuzzy modeling for prediction of solar cycles 24 and 25

The paper presents a Neuro-Fuzzy model to predict the features of the forthcoming sunspot cycles 24 and 25. The sunspot time series were analyzed with the proposed model. It is optimized based on Backpropagation scheme and applied to the yearly smoothed sunspot numbers. The appropriate number of network inputs for the sunspots data series is obtained based on sequential forward search for the Neuro-Fuzzy model. According to the model prediction the maximum amplitudes of the cycles 24 and 25 will occur in the year 2013 and year 2022 with peaks of 101±8 and 90.7±8, respectively. The correlation and error analysis are discussed to ensure the performance of the proposed Neuro-Fuzzy approach as a predictor for sunspot time series. The correlation coefficient between Neuro-Fuzzy model forecasted sunspot number values with the actual ones is 0.96.     

Some notes concerning the prediction of the amplitude of the solar activity cycles

The parameter G, which is determined from the general number of sunspots groups N _g according to the daily observations G=∑(1/N _g )², is offered. This parameter is calculated for the days when there is at least one sunspots group. It characterizes the minimum epoch solar activity. Parameter G mounts to the maximum during the epoch close to the minimal activity of sunspots. According to the data of the sequence of sunspots group in Greenwich–USAF/NOAA observatory format, observation data of Kislovodsk solar station and also daily Wolf number, the changes of parameter G during 100 years were reconstructed. It is demonstrated in the paper that parameter G’s amplitude in minimal solar activity n is linked with the sunspot cycle’s amplitude W _n+1 or one and half cycles. The 24th activity cycle prediction is calculated, which makes W ₂₄=135(±12).     

Regression modeling method of space weather prediction

A regression modeling method of space weather prediction is proposed. It allows forecasting Dst index up to 6 hours ahead with about 90% correlation. It can also be used for constructing phenomenological models of interaction between the solar wind and the magnetosphere. With its help two new geoeffective parameters were found: latitudinal and longitudinal flow angles of the solar wind. It was shown that Dst index remembers its previous values for 2000 hours.     

The periodicity of solar activity cycles

On the basis of published Wolf Numbers and Schove Row, solar activity cycles in the interval of 11 to hundreds of years have been investigated. In this case the method of investigation of pulsating stars showing the Blazhko effect was applied. The elements of cycles and O-C were calculated and compared with results of solar activity parameters determined by classical methods.     

Preliminary prediction of solar cycles 24 and 25 based on the correlation between cycle parameters

The correlation between various parameters of solar cycles 1–23 is investigated. The derived regressions are used to make predictions of solar cycles 24 and 25. It is expected that solar cycle 24 will reach its maximum amplitude of 110.2 ± 33.4 in April–June 2012 and the next minimum will occur in December 2018–January 2019. The duration of solar cycle 24 will be about 11.1 years. Solar cycle 25 will reach its maximum amplitude of 112.3 ± 33.4 approximately in April–June 2023.     

A method for foF2 short-term prediction

A method for foF2 short-term prediction with 1–24 hour lead times is proposed. It is based on ΔfoF2 (deviation of hourly foF2 from running median) regression with the previous ΔfoF2 observations and hourly spline-interpolated daily Ap index. An optimum training time interval of 25–30 days, which is close to one solar rotation, has been revealed. The effect of Ap index inclusion is seen only for large (more than 3 hours) lead time prediction. The prediction accuracy was shown to depend on Ap/foF2 time shift interval, the latter being dependent on local time of the storm onset and this may be taken into account in the prediction method. For quiet and moderate disturbed conditions the basic method provides foF2 forecast with relative mean deviation of 8–13% which is acceptable from practical point of view. A version of the basic method is proposed to predict foF2 during severe storm periods. This modified method in comparison with the basic one and the Wrenn's et al., (1987) approach was shown to provide the best prediction accuracy and may be recommended for practical use.     

The assessment of the semi-analytical method in the long-term orbit prediction of Earth satellites

To understand the long-term evolution and distribution of the space objects, it is necessary to predict their orbits. Compared with the short-term prediction of a few days, the priority concerns of the long-term orbit prediction are the calculation speed, and the accuracies of major orbital elements, including the semi-major axis and eccentricity which define the shape of the orbit, as well as the orbital inclination and the right ascension of ascending node which define the orientation of the orbit. Given these requirements, it is preferable to adopt the semi-analytical method, which averages the system over the orbital period, and integrates the averaged system using the numerical method. It is not new, however, in the available literature, we can hardly find a quantitative assessment regarding its accuracy and speed when it is applied to various types of orbits. In this paper, we would like to report our implementation and assessment of the semi-analytical method, expecting that it would help to estimate its feasibility in the long-term orbit prediction. The quantitative assessment covers the commonly used orbits for the Earth satellites. In some rare and special cases where the performance of our method appears abnormal, we discuss the reasons and possible solutions. We hope our results can provide some useful reference for the similar applications of the semi-analytical method since our method is a relatively common approach in terms of both accuracy and implementation.     

The large-scale build-up of solar magnetic cycles

The purpose of the present article is to analyze the solar cycles from the point of view of the large-scale surface magnetic field (LSMF) polarity distributions. Using synoptic charts of the LSMF for the 1870–1991 time interval at maxima and minima and the spherical harmonic analysis of the polarity distributions, a connection between magnetic cycles has been found. The weight of the large-scale sectoral mode (m = 1) in the common LSMF polarity distribution at minima of the sunspot cycle is the source of sunspot activity at maxima after 16–18 years. The connections found suggest that surface LSMFs have a dual nature - the main source below the convective zone and a secondary source (sunspot production). The sunspot production has no visible influence on the LSMF cycles.     

Short-term solar flare prediction using multi-model integration method

A multi-model integration method is proposed to develop a multi-source and heterogeneous model for short-term solar flare prediction.Different prediction models are constructed on the basis of extracted predictors from a pool of observation databases.The outputs of the base models are normalized first because these established models extract predictors from many data resources using different prediction methods.Then weighted integration of the base models is used to develop a multi-model integrated model(MIM).The weight set that single models assign is optimized by a genetic algorithm.Seven base models and data from Solar and Heliospheric Observatory/Michelson Doppler Imager longitudinal magnetograms are used to construct the MIM,and then its performance is evaluated by cross validation.Experimental results showed that the MIM outperforms any individual model in nearly every data group,and the richer the diversity of the base models,the better the performance of the MIM.Thus,integrating more diversified models,such as an expert system,a statistical model and a physical model,will greatly improve the performance of the MIM.     

Application of the integral variation method to satellite orbit prediction

The Integral Variation (IV) method is a technique to generate an approximate solution to initial value problems involving systems of first-order ordinary differential equations. The technique makes use of generalized Fourier expansions in terms of shifted orthogonal polynomials. The IV method is briefly described and then applied to the problem of near Earth satellite orbit prediction. In particular, we will solve the Lagrange planetary equations including the first three zonal harmonics and drag. This is a highly nonlinear system of six coupled first-order differential equations. Comparison with direct numerical integration shows that the IV method indeed provides accurate analytical approximations to the orbit prediction problem.Advanced Systems Studies; Bldg. 254EElectro-Optical Systems Laboratory; Bldg. 201.     

The sector structure of the active longitudes in solar cycles

The longitudinal distributions of the polar faculae, bright K Ca⁺ points, and sunspot areas have been investigated in three-year intervals at the minima and maxima of the last five solar cycles in the rotation system which corresponds to the background magnetic field:T = 27.23 days (Mikhailutsa, 1994b). It has been shown that there were three specific features of the polar faculae and bright K Ca⁺ point longitudinal distributions: (1) The longitudes of maxima and minima of the distributions were approximately the same in the last five solar cycles. (2) There were predominantly two opposite longitudinal maxima and two opposite longitudinal minima in the distributions of each hemisphere. (3) The distributions of the northern and southern hemispheres were in opposite phase. The extremes of the sunspot area longitudinal distributions were preferentially between the longitudes of the polar facular extremes. The period of the sector structure rotation was defined more precisely:T = 27.227 ± 0.003 days. The results found can serve as an indication that there is a global foursector structure seated in the solar interior which plays a visible role in the polar facular and sunspot distributions.     

Short-term prediction and a new method of classification of Pc 1 pulsation occurrences

Because of their known tendency to occur in the interval 2–7 days after the start of a geomagnetic storm, Pc 1 pulsations (0.2–5 Hz) are particularly well suited for a method of occurrence prediction based on the comparison of running means of a geomagnetic activity index. By comparing the running mean of a short interval (～ 2 days) of activity data with the mean of a longer interval (～ 5 days), it is possible to isolate the intervals of declining activity that contain a large proportion (if 66%) of Pc 1 pulsation occurrences. Assuming the real time availability of a daily activity index, predictions can be made for 3–10 days ahead of the probability of Pc 1 occurrences. The method of prediction generalizes the previous observations on the relation between Pc 1 pulsations and geomagnetic storms, and one of its important features is its ability to divide Pc 1 pulsation occurrences into a unified system of categories. It is probable that this system can be exploited to provide new information about the pulsations.     

Rhythm of physical sunspot cycles

The time series of the relative sunspot number is interpreted as a sequence of physical cycles of sunspot activity overlapping in the minimum. The cycle periodicity, i.e., the time interval between neighboring cycles, can be considered as a quantitative characteristic of the sequence. Estimates of this interval have been obtained for 11 and 22-year cycles. In the growth phase and in the century cycle maximum, the 22-year cycles follow one another with an interval of 21 ± 0.4 years, and in the decline phase, 23 ± 0.3 years. This division of intervals into two groups depending on the century cycle phase should be taken into consideration when developing a theory of solar activity cycles.     

On stellar activity cycles

The relation between the average magnetic fieldB, the angular velocity , and the periodP of stellar activity cycles is studied. For the calculations we have used Leighton's (1969) model for the solar cycle with the additional assumption that the differential rotation and the cyclonic turbulence (Parker, 1955) (that is the sunspot tilt or the -effect) are both proportional to . We then find thatB is roughly proportional to and thatP decreases with increasing . The period of the solar cycle increases therefore with the age of the Sun.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Changing stellar activity cycles

We investigated continuous long-term photometric datasets of thirteen active stars, Ca II variability of one single mainsequence star, and 10.7 cm radio data of the Sun, with simple Fourier- and time-frequency analysis. The data reflect the strength of the activity manifested in magnetic spots. All studied stars show multiple (2 to 4) cycles of different lengths. The time-frequency analysis reveals, that in several cases of the sample one or two of the cycles exhibit continuous changes (increase or decrease). For four stars (V711 Tau, IL Hya, HK Lac, HD 100180) and for the Sun we find that the cycle length changes are strong, amounting to 10–50% during the observed time intervals. The cycle lengths are generally longer for stars with longer rotational periods. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The analysis of the characteristics of variation and change patterns of sunspot cycles

The paper focus on the variation character of sunspot number and solar cycles based on the new version sunspot number (SSN) data. According to seven main variables describing solar cycles, including peak value, the length of cycle, the length of ascending phase, the ratio of the ascending time to the descending time, slope, half width, and area under the curve of solar cycle, clustering, principal component and factor analysis, are applied to analyze variation characteristic and patterns of the 24 solar cycles. We cluster these 24 cycles to find groups in these solar cycles, and search for the main factor determining strength, length and occurrence time of the peak, and the furthest cycle from the average. The cycles within a cluster will be similar or related to one another and different from or unrelated to the cycles in other clusters. These results could help us search for similar cycles conveniently, obtain the understanding of the characteristics of solar cycle variation and analysis of sunspot number change and evolution characteristics, and analyze the origin and the variation mechanism of solar cycle.     

Peak years of various solar cycles

Using more extensive data than before, we have verified the 11-year, 60-year and ~250-year periods in solar activity and identified the peak years of these cycles.     

Approximation of 11-year solar cycles

We propose to approximate every 11-year cycle of solar activity by a function with three parameters. The first parameter determines the cycle position on the time axis, the second one shows the length of the growth phase of the activity index, and the third one is the maximum of smoothed index value. Values of these parameters for cycles 8–23 do not contradict in general the cycle parameters similar in sense and obtained from observations by the conventional method.     

Planetary tides and sunspot cycles

There is an empirical function of the heights of tides on the Sun produced by Venus, Earth, and Jupiter whose period is nearly equal to that of the 11-yr sunspot cycle (Wood, 1972). This period match has been used in suggestions that planetary tides cause sunspots and, indirectly, terrestrial climate changes and earthquakes. We derive the period of the tidal function in terms of the planetary orbital periods and show that it is artificially lengthened by aliasing. Furthermore, there exists a class of functions whose measure in frequency space is so great that, in the absence of a physical justification for preferring one member, no statistically significant period match can possibly be made with current sunspot data.