Abstract
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 summing up the ultimate contributions of individual active regions to the solar axial dipole moment 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 η/Δu where η is supergranular diffusivity and Δu is the divergence of the meridional flow on the equator. In a comparison with cycles simulated in the 2 × 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.
Highlights
Predicting the amplitude of an upcoming solar cycle is the central issue of space climate forecasting
It is widely accepted that the best performing, physically well motivated prediction method is based on the good linear correlation between the solar axial dipole moment in solar activity minimum and the amplitude of the cycle (Schatten et al, 1978; Wang & Sheeley, 2009; Muñoz-Jaramillo et al, 2013; Hathaway & Upton, 2016; Petrovay, 2020)
Our suggested algebraic approach to solar cycle prediction consists in using equation (4) to calculate the net dipole moment at the end of a solar cycle, where the dynamo effectivity f1 is given by equation (25), with kR and a taken from either a direct interpolation of the numerical results plotted in Figure 4, from their analytical approximation or even from the low-latitude limit (22)
Summary
Abstract – 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 solar cycle. The method consists of summing up the ultimate contributions of individual active regions to the solar axial dipole moment 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 g/Du where g is supergranular diffusivity and Du is the divergence of the meridional flow on the equator. In a comparison with cycles simulated in the 2 Â 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
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