1. Bipolar magnetic regions (BMRs)

The simplest representation of ARs in models is as BMR instantaneously introduced into dynamo or surface flux transport (SFT) models as a source term. We showed by analytic calculations that the contribution of such a BMR to the Sun’s global dipole shows a Gaussian dependence on latitude. An analytic expression for the half-width of this Gaussian, i.e. the dynamo effectivity range ?R of ARs was given, supported by numerical SFT calculations [1]. As the Gaussian results as the difference between two shifted erf function contributions from the two opposite polarities, the results could later be generalized to BMRs with an asymmetric flux distribution [8].

2. Real solar active regions

Real ARs can have much more complex structure than a simple BMR. We found that the BMR representation is quite often manifestly incorrect for such ARs [4]. We studied in detail how the representation of the AR source term in SFT and dynamo models affects their further evolution and found that the predicted evolution can show high sensitivity to details of the data assimilation process [12,16,17].

3. Nonlinear feedback mechanisms

The deterministic component of solar cycle variations is governed by systematic feedback effects in the source term in models [13]. We explored the contribution of different candidates to this feedback. Latitude quenching (LQ) [5,6], consisting in a positive correlation between cycle amplitude and mean emergence latitude of ARs, is a new candidate showing more promise than tilt quenching (TQ), which may be a weaker effect, although the robustness of TQ was supported by a new analysis [10]. We also found that the relative importance of LQ and TQ scales as c1+c2/?R2 [11]. A third feedback mechanism, inflows towards the activity belts, was also studied [3].

4. Stochastic effects

Large ARs with unusual properties can have a major impact on the further evolution of solar cycles. Such freak events represent a fundamental limitation to solar cycle forecasting. We performed in-depth studies of a number of such events in Solar Cycle 24 [7,18]. To characterize an AR’s potential for this, we further introduced a new quantity we call ARDoR (Active Region Degree of Rogueness) [2]. Further use of ARDoR may be based on studies of the magnetic structures of a large sample of ARs [4].

5. SFT, polar field buildup and early precursors:

The buildup of the Sun’s new global dipole field during a solar cycle is most often described in phenomenological surface flux transport (SFT) models. In an extensive collaborative effort we reviewed the main tenets of SFT models and the constraints on its input paramaters [14]. Reconstructions of the historical evolution of the Sun’s large scale magnetic field have also been given attention [19,20], as they provide potential constraints on SFT models.
As the buildup proceeds in the decay phase of a solar cycle, prediction of the final dipole becomes ever more reliable, opening the possibility to extend the time horizon of precursor-based cycle forecasting backwards. In studies based on empirical data and a variety of dynamo models we indeed found that reasonably reliable prediction of the next cycle may be possible from around or soon after polar reversal [9,15,21].

For numbered references, see Publications.