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تسجيل مستخدم جديدTowards an algebraic method of solar cycle prediction II. Reducing the need for detailed input data with ARDoR
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An algebraic method for the reconstruction and potentially prediction of the solar dipole moment value at sunspot minimum (known to be a good predictor of the amplitude of the next solar cycle) was suggested in the first paper in this series. The method sums up the ultimate dipole moment contributions of individual active regions in a solar cycle: for this, detailed and reliable input data would in principle be needed for thousands of active regions in a solar cycle. To reduce the need for detailed input data, here we propose a new active region descriptor called ARDoR (Active Region Degree of Rogueness). In a detailed statistical analysis of a large number of activity cycles simulated with the 2$times$2D dynamo model we demonstrate that ranking active regions by decreasing ARDoR, for a good reproduction of the solar dipole moment at the end of the cycle it is sufficient to consider the top $N$ regions on this list explicitly, where $N$ is a relatively low number, while for the other regions the ARDoR value may be set to zero. E.g., with $N=5$ the fraction of cycles where the dipole moment is reproduced with an error exceeding $pm$30% is only 12%, significantly reduced with respect to the case $N=0$, i.e. ARDoR set to zero for all active regions, where this fraction is 26%. This indicates that stochastic effects on the intercycle variations of solar activity are dominated by the effect of a low number of large ``rogue active regions, rather than the combined effect of numerous small ARs. The method has a potential for future use in solar cycle prediction.
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We discuss the potential use of an algebraic method to compute the value of the solar axial dipole moment at solar minimum, widely considered to be the most reliable precursor of the activity level in the next solar cycle. The method consists of summ
ing up the ultimate contributions of individual active regions to the solar axial dipole moment revtwo{at the end of the cycle}. A potential limitation of the approach is its dependence on the underlying surface flux transport (SFT) model details. We demonstrate by both analytical and numerical methods that the factor relating the initial and ultimate dipole moment contributions of an active region displays a Gaussian dependence on latitude with parameters that only depend on details of the SFT model through the parameter $eta/Delta_u$ where $eta$ is supergranular diffusivity and $Delta_u$ is the divergence of the meridional flow on the equator. In a comparison with cycles simulated in the 2$times$2D dynamo model we further demonstrate that the inaccuracies associated with the algebraic method are minor and the method may be able to reproduce the dipole moment values in a large majority of cycles.
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. Neverthele
ss, 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 of solar cycle prediction methods: the precursor-like ones and the mathematical-numerical ones. The main characteristic of precursor techniques, both purely solar and geomagnetic, is their physical basis. Conversely, the non-precursor methods use different mathematical and/or numerical properties of the known temporal evolution of solar activity indices to extract useful information for predicting future activity. For current solar cycle #24 we obtained fairly good statistical performances from both precursor and purely numerical methods, such as the so-called solar precursor and nonlinear ones. To further check the performances of these prediction techniques, we compared the early predictions for the next solar cycle #25. Preliminary results support some coherence of the prediction methods considered and confirm the current trend of a relatively low solar activity.
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 restric
ted 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.
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 yielded predictions consistently in the right range during the past few solar cycles is the polar field precursor. Nevertheless, some extrapolation methods may still be worth further study. Model based forecasts are quickly coming into their own, and, despite not having a long proven record, their predictions are received with increasing confidence by the community.
Context. The variations of solar activity over long time intervals using a solar activity reconstruction based on the cosmogenic radionuclide 10Be measured in polar ice cores are studied. Methods. By applying methods of nonlinear dynamics, the solar
activity cycle is studied using solar activity proxies that have been reaching into the past for over 9300 years. The complexity of the system is expressed by several parameters of nonlinear dynamics, such as embedding dimension or false nearest neighbors, and the method of delay coordinates is applied to the time series. We also fit a damped random walk model, which accurately describes the variability of quasars, to the solar 10Be data and investigate the corresponding power spectral distribution. The periods in the data series were searched by the Fourier and wavelet analyses. The solar activity on the long-term scale is found to be on the edge of chaotic behavior. This can explain the observed intermittent period of longer lasting solar activity minima. Filtering the data by eliminating variations below a certain period (the periods of 380 yr and 57 yr were used) yields a far more regular behavior of solar activity. A comparison between the results for the 10Be data with the 14C data shows many similarities. Both cosmogenic isotopes are strongly correlated mutually and with solar activity. Finally, we find that a series of damped random walk models provides a good fit to the 10Be data with a fixed characteristic time scale of 1000 years, which is roughly consistent with the quasi-periods found by the Fourier and wavelet analyses.
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