Nonlinear mean-field dynamo and prediction of solar activity

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 α 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.