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

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 \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.

15 pages, 5 figs. Accepted for publication in the Journal of Space Weather and Space Climate

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• Models for the long-term variations of solar activity
• Evolution of solar and stellar dynamo theory
• Physical Models for Solar Cycle Predictions
• How good is the bipolar approximation of active regions for surface flux transport?
• Comparison of physics-based prediction models of solar cycle 25
• Role of observable nonlinearities in solar cycle modulation
• Activity Complexes and A Prominent Poleward Surge During Solar Cycle 24
• Towards a live homogeneous database of solar active regions based on SOHO/MDI and SDO/HMI synoptic magnetograms. I. Automatic detection and calibration
• Impact of Anomalous Active Regions on the Large-scale Magnetic Field of the Sun
• Toroidal flux loss due to flux emergence explains why solar cycles rise differently but decay in a similar way
• Algebraic quantification of an active region's contribution to the solar cycle
• Towards an algebraic method of solar cycle prediction II. Reducing the need for detailed input data with ARDoR
• Toward a live homogeneous database of solar active regions based on SOHO/MDI and SDO/HMI synoptic magnetograms.II.parameters for solar cycle variability
• Meridional flow in the solar polar caps revealed by magnetic field observation and simulation
• Modeling effects of starspots on stellar magnetic cycles
• Algebraic Quantification of the Contribution of Active Regions to the Sun's Dipole Moment: Applications to Century-scale Polar Field Estimates and Solar Cycle Forecasting
• Surface Flux Transport Modeling using Physics Informed Neural Networks
• Minimal Roles of Solar Subsurface Meridional Flow in the distributed-shear Babcock-Leighton Dynamo
• Observation-Based Iterative Map for Solar Cycles. I. Nature of Solar Cycle Variability
• Active regions and the large-scale magnetic field of solar cycle 24
• Prediction of the Solar Polar Fields in 2026: An Unusually Weak Level Across the Last Five Solar Cycles
• Solar Cycle Prediction: Challenges, Progress, and Future Perspectives
• Effect of Nonlinear Surface Inflows into Activity Belts on Solar Cycle Modulation
• Ultra-fast simulations of the solar dipole and open flux