Towards an algebraic method of solar cycle prediction I. Calculating the ultimate dipole contributions of individual active regions

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 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.