In this report, we present our recent effort to understand the cyclic behavior of network magnetic elements based on the unique database from full-disk observations provided by Michelson Doppler Imager on board the Solar and Heliospheric Observatory in the interval including the entire cycle 23. The following results are unclosed. (1) The quiet regions dominate the solar magnetic flux for about 8 years in solar cycle 23, and from the solar minimum to maximum they contribute (0.94-1.44)×1023Mx flux to the solar photosphere. In the entire cycle 23, the magnetic flux of the quiet regions is 1.12 times that of active regions. The occupation ratio of quiet region flux equally characterizes the course of a solar cycle. (2) With the increasing magnetic flux per element, the variations of numbers and total flux of the network elements show three-fold scenario: no-correlation, anti-correlation, and correlation with sunspots, respectively. The anti-correlated elements covering the range of (3-32)×1018Mx occupy 77% of total element number and 37% of quiet Sun flux. (3) The time-latitude distribution of anti-correlated magnetic elements is out of phase with that of sunspots, while the correlated elements display the similar butterfly diagram of sunspots but with wider latitude distribution. These results imply that the correlated elements are the debris of decayed sunspots, and the source of anti-correlated elements is modulated by sunspot magnetic field.

Sunspot data and large-scale solar magnetic field data are used to demonstrate the operation of the Babcock-Leighton mechanism on the Sun. A dynamo model is developed that employs jointly a nonlocal alpha-effect of the Babcock-Leighton type and diamagnetic downward pumping. The pumping concentrates magnetic fields to the base of the convection zone. The magnetic cycle period, equatorial symmetry of the generated fields, their meridional drift, and the polar-to-toroidal field ratio obtained in the model agree with observations.

The tachocline is important in the solar dynamo for the generation and the storage of the magnetic fields. A most plausible explanation for the confinement of the tachocline is given by the fast tachocline model in which the tachocline is confined by the anisotropic momentum transfer by the Maxwell stress of the dynamo generated magnetic fields. We employ a flux transport dynamo model coupled with the simple feedback formula of this fast tachocline model which basically relates the thickness of the tachocline to the Maxwell stress. We find that this nonlinear coupling not only produces a stable solar-like dynamo solution but also a significant latitudinal variation in the tachocline thickness which is in agreement with the observations.

We point out the difficulties in carrying out direct numerical simulation of the solar dynamo problem and argue that kinematic mean-field models are our best theoretical tools at present for explaining various aspects of the solar cycle in detail. The most promising kinematic mean-field model is the flux transport dynamo model, in which the toroidal field is produced by differential rotation in the tachocline, the poloidal field is produced by the Babcock–Leighton mechanism at the solar surface and the meridional circulation plays a crucial role. Depending on whether the diffusivity is high or low, either the diffusivity or the meridional circulation provides the main transport mechanism for the poloidal field to reach the bottom of the convection zone from the top. We point out that the high-diffusivity flux transport dynamo model is consistent with various aspects of observational data. The irregularities of the solar cycle are primarily produced by fluctuations in the Babcock–Leighton mechanism and in the meridional circulation. We summarize recent work on the fluctuations of meridional circulation in the flux transport dynamo, leading to explanations of such things as the Waldmeier effect.