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The solar cycle is generated by a magnetohydrodynamic dynamo mechanism, whichinvolves the induction and recycling of the toroidal and poloidal components ofthe Sun's magnetic field. Recent observations indicate that theBabcock-Leighton mechanism -- mediated via the emergence and evolution oftilted bipolar active regions -- is the primary contributor to the Sun'slarge-scale dipolar field. Surface flux transport models and dynamo models havebeen employed to simulate this mechanism, which also allows for physics-basedsolar cycle forecasts. Recently, an alternative analytic method has beenproposed to quantify the contribution of individual active regions to the Sun'sdipole moment. Utilizing solar cycle observations spanning a century, here wetest the efficacy of this algebraic approach. Our results demonstrate that thealgebraic quantification approach is reasonably successful in estimating dipolemoments at solar minima over the past century -- providing an independentverification of the Babcock-Leighton mechanism as the primary contributor tothe Sun's dipole field variations. We highlight that this algebraic methodologystands as an independent approach for estimating the dipole moment at theminima of solar cycles, relying on characteristics of the sunspot cycle. Wealso show how this method may be utilized for solar cycle predictions; ourestimate of the Sun's dipole field at the end of cycle 24 using this approachindicates that solar cycle 25 would be a moderately weak cycle, ranging betweensolar cycle 20 and cycle 24.

Algebraic Quantification of the Contribution of Active Regions to the  Sun's Dipole Moment: Applications to Polar Field Estimates and Solar Cycle  Forecasting