A review of solar cycle prediction methods and their performance is given, including forecasts for cycle 24 and focusing on aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle. Prediction methods form three main groups. Precursor methods rely on the value of some measure of solar activity or magnetism at a specified time to predict the amplitude of the following solar maximum. Their implicit assumption is that each numbered solar cycle is a consistent unit in itself, while solar activity seems to consist of a series of much less tightly intercorrelated individual cycles. Extrapolation methods, in contrast, are based on the premise that the physical process giving rise to the sunspot number record is statistically homogeneous, i.e., the mathematical regularities underlying its variations are the same at any point of time, and therefore it lends itself to analysis and forecasting by time series methods. Finally, instead of an analysis of observational data alone, model based predictions use physically (more or less) consistent dynamo models in their attempts to predict solar activity. In their overall performance precursor methods have clearly been superior to extrapolation methods. Nevertheless, some extrapolation methods may still be worth further study. Model based forecasts have not yet have had a chance to prove their skills. One method that has yielded predictions consistently in the right range during the past few solar cycles is that of K. Schatten et al., whose approach is mainly based on the polar field precursor. The incipient cycle 24 will probably mark the end of the Modern Maximum, with the Sun switching to a state of less strong activity.
We use helioseismic data from ground and space-based instruments to analyze how solar rotation has changed since the beginning of solar Cycle 23 with emphasis on studying the differences between Cycles 23 and 24. We find that the nature of solar rotation is indeed different for the two cycles. While the changes in the latitudinally independent component follows solar-cycle indices, some of the other components have a more complicated behavior. There is a substantial change in the behavior of the solar zonal flows and their spatial gradients too. While the zonal flows are in general weaker in C…
It is very important to forecast the future solar activity due to its effect on our planet and near space. Here, we employ the new version of the sunspot number index (version 2) to analyse the relationship between the solar maximum amplitude and max-max cycle length proposed by Du (2006). We show that the correlation between the parameters used by Du (2006) for the prediction of the sunspot number (amplitude of the cycle, Rm, and max-max cycle length for two solar cycles before, Pmax-2) disappears when we use solar cycles prior to solar cycle 9. We conclude that the correlation between these …
Solar activity cycle varies in amplitude. The last Cycle 24 is the weakest in the past century. Sun's activity dominates Earth's space environment. The frequency and intensity of the Sun's activity are accordant with the solar cycle. Hence there are practical needs to know the amplitude of the upcoming Cycle 25. The dynamo-based solar cycle predictions not only provide predictions, but also offer an effective way to evaluate our understanding of the solar cycle. In this article we apply the method of the first successful dynamo-based prediction developed for Cycle 24 to the prediction of Cycle…
We analyzed the daily sunspot-group data reported by the Greenwich Photoheliographic Results (GPR) during the period 1874-1976 and Debrecen Photoheligraphic Data (DPD) during the period 1977-2017, and the revised Version-2 of ISSN during the period 1874-2017. We determined the amplitude of the Solar Cycles 12-24 and the 13-month smoothed monthly mean corrected areas of the sunspot groups in the Sun's whole-sphere (WSGA), northern hemisphere (NSGA), and southern hemisphere (SSGA) at the epochs of the maxima of the Solar Cycles 12-24. Using all these we obtained the relations similar to that fou…
The maximum of a solar cycle contain two or more peaks, known as Gnevyshev peaks. Studies of this property of solar cycles may help for better understanding the solar dynamo mechanism. We analysed the 13-month smoothed monthly mean Version-2 international sunspot number (SN) during the period 1874-2017 and found that there exists a good correlation between the amplitude (value of the main and highest peak) and the value of the second maximum (value of the second highest peak) during the maximum of a solar cycle.Using this relationship and the earlier predicted value 86 (~92) of the amplitude o…
There are many proposed prediction methods for solar cycles behavior. In a previous paper we updated the full-shape curve prediction of the current solar cycle 24 using a non-linear dynamics method and we compared the results with the predictions collected by the NOAA/SEC prediction panel, using observed data up to October 2010. The aim of the present paper is to give a quantitative evaluation, a posteriori, of the performances of these prediction methods using a specific global error, updated on a monthly basis, which is a measure of the global performance on the predicted shape (both amplitu…
The prediction of solar activity is important for advanced technologies and space activities. The peak sunspot number (SSN), which can represent the solar activity, has declined continuously in the past four solar cycles (21$-$24), and the Sun would experience a Dalton-like minimum, or even the Maunder-like minimum, if the declining trend continues in the following several cycles, so that the predictions of solar activity for cycles 25 and 26 are crucial. In Qin & Wu, 2018, ApJ, we established an SSN prediction model denoted as two-parameter modified logistic prediction (TMLP) model, which can…
Through meticulous daily observation of the Sun's large-scale magnetic field the Wilcox Solar Observatory (WSO) has catalogued two magnetic (Hale) cycles of solar activity. Those two (~22-year long) Hale cycles have yielded four ($\sim$11-year long) sunspot cycles (numbers 21 through 24). Recent research has highlighted the persistence of the "Extended Solar Cycle" (ESC) and its connection to the fundamental Hale Cycle - albeit through a host of proxies resulting from image analysis of the solar photosphere, chromosphere and corona. This short manuscript presents the correspondence of the ESC,…
Solar variability occurs over a broad range of spatial and temporal scales, from the Sun's brightening over its lifetime to the fluctuations commonly associated with magnetic activity over minutes to years. The latter activity includes most prominently the 11-year sunspot solar cycle and its modulations. Space weather events, in the form of solar flares, solar energetic particles, coronal mass ejections, and geomagnetic storms, have long been known to approximately follow the solar cycle occurring more frequently at solar maximum than solar minimum. These events can significantly impact our ad…
We study the differences in the heavy ion composition of solar energetic particle (SEP) events between solar cycles 23 and 24. We have surveyed the SOHO/ERNE heavy ion data from the beginning of solar cycle 23 until the end of June 2015, that is, well into the declining phase of cycle 24. We used this long observation period to study the properties of heavy ions (from C to Fe) and to compare the two solar cycles in this respect. We surveyed the data for SEP events with enhancements in the Fe/C and Fe/O intensity ratios in the energy range 5-15 MeV per nucleon, and associated the events with so…
The evolution of the solar activity comprises, apart from the well-known 11-year cycle, various temporal scales ranging from months up to the secondary cycles known as mid-term oscillations. Its nature deserves a physical explanation. In this work, we consider the 5-to-6 year oscillations as derived both from sunspot and from solar magnetic dipole time series. Using the solar dynamo model, we deduced that these variations may be a manifestation of the dynamo nonlinearities and non-harmonic shape of the solar activity cycles. We conclude that the observed mid-term oscillations are related to th…
Solar activity forecasting is an important topic for numerous scientific and technological areas, such as space mission operations, electric power transmission lines, power transformation stations and earth geophysical and climatic impact. Nevertheless, the well-known difficulty is how to accurately predict, on the basis of various recorded solar activity indices, the complete evolution of future solar cycles, due to highly complex dynamical and stochastic processes involved, mainly related to interaction of different components of internal magnetic fields. There are two main distinct classes …
The solar cycle onset at mid-latitudes, the slow down of the sunspot drift toward the equator, the tail-like attachment and the overlap of successive cycles at the time of activity minimum are delicate issues in $αΩ$ dynamo wave and flux transport dynamo models. Very different parameter values produce similar results, making it difficult to understand the origin of these solar cycle properties. We use GONG helioseismic data to investigate the progression of the solar cycle as observed in intermediate-degree global $p$-mode frequency shifts at different latitudes and subsurface layers, from the…
A new formula for predicting solar cycles based on the current theoretical understanding of the solar cycle from flux transport dynamo is presented. Two important processes---fluctuations in the Babcock-Leighton mechanism and variations in the meridional circulation, which are believed to be responsible for irregularities of the solar cycle---are constrained by using observational data. We take the polar field near minima of the cycle as a measure of the randomness in the Babcock-Leighton process, and the decay rate near the minima as a consequence of the change in meridional circulation. We c…
We analyzed the daily sunspot-group data reported by the Greenwich Photoheliographic Results (GPR) during the period 1874-1976 and Debrecen Photoheliographic Data (DPD) during the period 1977-2017 and studied North-South asymmetry in the maxima and minima of the Solar Cycles 12-24. We derived the time series of the 13-month smoothed monthly mean corrected whole-spot areas of the sunspot groups in the Sun's whole sphere (WSGA), northern hemisphere (NSGA), and southern hemisphere (SSGA). From these smoothed time series we obtained the values of the maxima and minima, and the corresponding epochs…
The study of variations in solar activity is important for understanding the underlying mechanism of solar activity and for predicting the level of activity in view of the activity impact on space weather and global climate. Here we have used the amplitudes (the peak values of the 13-month smoothed international sunspot number) of Solar Cycles 1-24 to predict the relative amplitudes of the solar cycles during the rising phase of the upcoming Gleissberg cycle. We fitted a cosine function to the amplitudes and times of the solar cycles after subtracting a linear fit of the amplitudes. The best c…
Prediction of solar cycle is an important goal of Solar Physics both because it serves as a touchstone for our understanding of the sun and also because of its societal value for a space faring civilization. The task is difficult and progress is slow. Schatten et al. (1978) suggested that the magnitude of the magnetic field in the polar regions of the sun near solar minimum could serve as a precursor for the evolution and amplitude of the following solar cycle. Since then, this idea has been the foundation of somewhat successful predictions of the size of the last four cycles, especially of th…
The prediction of the evolution of individual solar cycles is a developing field, faced with divergence of forecasts even for a few years in the future. Specifically for solar flares, long-term modeling is practically absent even in rough terms. In this article a forecast for the evolution of solar cycle 25 in terms of solar flares activity is presented. It is derived from an existing phenomenological model based on the coupling of an internal solar component and a planetary component. In addition to competent temporal resolution, the predictions are characterized by features which both differ…
Is Solar Cycle 24 anomalous? How do we predict the main features of a forthcoming cycle? In order to reply such questions, this work partitions quantitatively each cycle into valley, ascend, peak, and descend phases, statistically investigate the correlations between valley phase and the forthcoming cycle. We find that the preceding valley phase may dominate and can be predictor of the forthcoming cycle: (1) The growth rate in ascend phase strongly negatively correlates to valley length and strongly positively correlates to cycle maximum. (2) The cycle maximum strongly negatively correlates to…
We present observational signatures of solar cycle 25 onset. Those signatures are visibly following a migratory path from high to low latitudes. They had starting points that are asymmetrically offset in each hemisphere at times that are 21-22 years after the corresponding, same polarity, activity bands of solar cycle 23 started their migration. Those bands define the so-called "extended solar cycle." The four magnetic bands currently present in the system are approaching a mutually cancelling configuration, and solar minimum conditions are imminent. Further, using a tuned analysis of the dail…
Helioseismic data for solar cycles 23 and 24 have shown unequivocally that solar dynamics changes with solar activity. Changes in solar structure have been more difficult to detect. Basu & Mandel (2004) had claimed that the then available data revealed changes in the HeII ionization zone of the Sun. The amount of change, however, indicated the need for larger than expected changes in the magnetic fields. Now that helioseismic data spanning two solar cycles are available, we have redone the analysis using improved fitting techniques. We find that there is indeed a change in the region around th…
The prediction of the strength of future solar cycles is of interest because of its practical significance for space weather and as a test of our theoretical understanding of the solar cycle. The Babcock-Leighton mechanism allows predictions by assimilating the observed magnetic field on the surface. But the emergence of sunspot groups has the random properties, which make it impossible to accurately predict the solar cycle and also strongly limit the scope of cycle predictions. Hence we develop the scheme to investigate the predictability of the solar cycle over one cycle. When a cycle has be…
We study the complexity of the supergranular network through fractal dimension by using Ca II K digitized data archive obtained from Kodaikanal solar observatory. The data consists of 326 visually selected supergranular cells spread across the 23rd solar cycle. Only cells that were well-defined were chosen for the analysis and we discuss the potential selection effect thereof, mainly that it favors cells of a smaller size (< 20 Mm). Within this sample, we analyzed the fractal dimension of supergranules across the Solar cycle and find that it is anticorrelated with the activity level.
A review of solar cycle prediction methods and their performance is given, including early forecasts for cycle 25. The review focuses on those aspects of the solar cycle prediction problem that have a bearing on dynamo theory. The scope of the review is further restricted to the issue of predicting the amplitude (and optionally the epoch) of an upcoming solar maximum no later than right after the start of the given cycle. In their overall performance during the course of the last few solar cycles, precursor methods have clearly been superior to extrapolation methods. One method that has yielde…
Homogeneous coronal data set (HCDS) of the green corona (Fe XIV) and coronal index of the solar activity (CI) have been used to study time-latitudinal distribution in solar cycles 18-24 and compared with similar distribution of sunspots, the magnetic fields and the solar radio flux 10.7 cm. The most important results are: (a) distribution of coronal intensities related to the cycle maximum are different for individual cycles, (b) the poleward migration of the HCDS from mid latitudes in each cycle exists, even in extremely weak Cycle 24, and the same is valid for the equatorward migration (c) t…
According to the scheme of action of the solar dynamo, the poloidal magnetic field can be considered a source of production of the toroidal magnetic field by the solar differential rotation. From the polar magnetic field proxies, it is natural to expect that solar Cycle 25 will be weak as recorded in sunspot data. We suggest that there are parameters of the zonal harmonics of the solar surface magnetic field, such as the magnitude of the $\ell$=3 harmonic or the effective multipole index, that can be used as a reasonable addition to the polar magnetic field proxies. We discuss also some specif…
Coronal Mass Ejections (CMEs) contributes to the perturbation of solar wind in the heliosphere. Thus, depending on the different phases of the solar cycle and the rate of CME occurrence, contribution of CMEs to solar wind parameters near the Earth changes. In the present study, we examine the long term occurrence rate of CMEs, their speeds, angular widths and masses. We attempt to find correlation between near sun parameters, determined using white light images from coronagraphs, with solar wind measurements near the Earth from in-situ instruments. Importantly, we attempt to find what fraction…
The relative abundance of alpha particles with respect to proton, usually expressed as $A_{He}$ = ($n_α/n_p$)*100, is known to respond to solar activity although changes in its behaviour in the last four solar cycles are not known. In this letter, by systematically analysing inter-calibrated $A_{He}$ data obtained from the first Lagrangian point of the Sun-Earth system, we show that $A_{He}$ variations are distinctively different in solar cycle 24 as compared to the last three cycles. The frequency of $A_{He}$ = 2-3% events is significantly higher in slow/intermediate solar winds in cycle 24 a…
We examine the solar-cycle variation of the power in the low-degree helioseismic modes by looking at binned power spectra from 45 years of observations with the Birmingham Solar Oscillations Network, which provides a more robust estimate of the mode power than that obtained by peak fitting. The solar-cycle variation of acoustic mode power in the five-minute band is clearly seen. Unusually, even though Cycle 24 was substantially weaker in terms of surface magnetic activity than Cycle 23, the reduction in mode power at solar maximum is very similar for the two cycles, suggesting that the relatio…
We compare spectra of the zonal harmonics of the large-scale magnetic field of the Sun using observation results and solar dynamo models. The main solar activity cycle as recorded in these tracers is a much more complicated phenomenon than the eigen solution of solar dynamo equations with the growth saturated by a back reaction of the dynamo-driven magnetic field on solar hydrodynamics. The nominal 11(22)-year cycle as recorded in each mode has a specific phase shift varying from cycle to cycle; the actual length of the cycle varies from one cycle to another and from tracer to tracer. Both the…
The level of solar magnetic activity, as exemplified by the number of sunspots and by energetic events in the corona, varies on a wide range of time scales. Most prominent is the 11-year solar cycle, which is significantly modulated on longer time scales. Drawing from dynamo theory together with empirical results of past solar activity and of similar phenomena on solar-like stars, we show that the variability of the solar cycle can be essentially understood in terms of a weakly nonlinear limit cycle affected by random noise. In contrast to ad-hoc `toy models' for the solar cycle, this leads to…
Predictions of solar cycle 24 obtained from advection-dominated and diffusion-dominated kinematic dynamo models are different if the Babcock-Leighton mechanism is the only source of the poloidal field. Yeates et al. (2008) argue that the discrepancy arises due to different memories of the solar dynamo for advection- and diffusion-dominated solar convection zones. We aim to investigate the differences in solar cycle memory obtained from advection-dominated and diffusion-dominated kinematic solar dynamo models. Specifically, we explore whether the inclusion of Parker's mean-field $α$ effect, in …
While it has been relatively easy to determine solar-cycle related changes in solar dynamics, determining changes in structure in the deeper layers of the Sun has proved to be difficult. By using helioseismic data obtained over two solar cycles, and sacrificing resolution in favour of lower uncertainties, we show that there are significant changes in the solar convection zone, and perhaps even below it. Using MDI data, we find a relative squared sound-speed difference of $(2.56\pm 0.71)\times 10^{-5}$ at the convection-zone base between the maximum of solar Cycle~23 and the minimum between Cyc…
