Nonlinear mean-field dynamo and prediction of solar activity

Abstract

We apply a nonlinear mean-field dynamo model which includes a budget equation for the dynamics of Wolf numbers to predict solar activity. This dynamo model takes into account the algebraic and dynamic nonlinearities of the $\unicode[STIX]{x1D6FC}$ effect, where the equation for the dynamic nonlinearity is derived from the conservation law for the magnetic helicity. The budget equation for the evolution of the Wolf number is based on a formation mechanism of sunspots related to the negative effective magnetic pressure instability. This instability redistributes the magnetic flux produced by the mean-field dynamo. To predict solar activity on the time scale of one month we use a method based on a combination of the numerical solution of the nonlinear mean-field dynamo equations and the artificial neural network. A comparison of the results of the prediction of the solar activity with the observed Wolf numbers demonstrates a good agreement between the forecast and observations.

Large-Scale Properties of the Tilt of Sunspot Groups and Joy’s Law Near the Solar Equator

“…В данном разделе мы проведем оценки величины тильта в солнечном цикле для реалистичного магнитного поля, полученного в ранее разработанной модели нелинейного самосогласованного динамо, основанной на балансе спиральностей, которая особенно удачно описывает в деталях процесс образования солнечных пятен за последние пять циклов активности, начиная с 20-го солнечного цикла (Safiullin et al, 2018).…”

“…Kleeorin et al (2003);Zhang et al (2006);Zhang et al (2012);Kleeorin et al 2016), которая принимает во внимание алгебраическую и динамическую части нелинейности альфа-эффекта, опирающаяся на наблюдаемую магнитную спиральность. Эта динамо-модель была откалибрована по длительным рядам наблюдений солнечных пятен, и она позволила рассчитать помесячный прогноз солнечной активности(Safiullin et al 2018). …”

Optimal neural network feature selection for spatial-temporal forecasting

“…There is only one example [24], as far as we are aware, of actual spatial-temporal forecasts using neural networks (see also [144], [145] where a neural network forecast of the magnetic flux, which is related to sunspots, is forecast for latitude/longitude datasets). There are also a few examples of forecasting the butterfly diagram sunspot data in both space and time (latitude/time) [22], [161]- [165] but none of these used neural networks, rather all of those used other statistical methods or numerical physical modelling.…”

Zonal harmonics of solar magnetic field for solar cycle forecast

“…Thus, prediction of the height of the following cycle is reduced to calculating or directly measuring the polar field during the minimum of the SSN cycle. Unfortunately, the existing studies in this field are very contradictory (e.g., Dikpati and Gilman (2006); Choudhuri et al (2007); Jiang et al (2007); Dikpati et al (2008); Safiullin et al (2018)). The problem is associated with the need to take into account the stochastic component, which drives the dynamo out of the deterministic regime, and with uncertainties in the input parameters (Bushby and Tobias, 2007;Karak and Nandy, 2012;Pipin et al, 2012), while the direct measurements of the polar magnetic field are not accurate enough for prediction (see, e.g., Pevtsov et al, 2021).…”