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This paper reviews recent advances and current debates in modeling the solar cycle as a hydromagnetic dynamo process. Emphasis is placed on (relatively) simple dynamo models that are nonetheless detailed enough to be comparable to solar cycle observations. After a brief overview of the dynamo problem and of key observational constraints, we begin by reviewing the various magnetic field regeneration mechanisms that have been proposed in the solar context. We move on to a presentation and critical discussion of extant solar cycle models based on these mechanisms. We then turn to the origin and consequences of fluctuations in these models, including amplitude and parity modulation, chaotic behavior, intermittency, and predictability. The paper concludes with a discussion of our current state of ignorance regarding various key questions relating to the explanatory framework offered by dynamo models of the solar cycle.

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Abstract. This paper describes the recommended solar forcing dataset for CMIP6 and highlights changes with respect to CMIP5. The solar forcing is provided for radiative properties, namely total solar irradiance (TSI), solar spectral irradiance (SSI), and the F10.7 index as well as particle forcing, including geomagnetic indices Ap and Kp, and ionization rates to account for effects of solar protons, electrons, and galactic cosmic rays. This is the first time that a recommendation for solar-driven particle forcing has been provided for a CMIP exercise. The solar forcing datasets are provided at daily and monthly resolution separately for the CMIP6 preindustrial control, historical (1850CMIP6 preindustrial control, historical ( -2014, and future (2015-2300) simulations. For the preindustrial control simulation, both constant and time-varying solar forcing components are provided, with the latter including variability on 11-year and shorter timescales but no long-term changes. For the future, we provide a realistic scenario of what solar behavior could be, as well as an additional extreme Maunderminimum-like sensitivity scenario. This paper describes the forcing datasets and also provides detailed recommendations as to their implementation in current climate models.For the historical simulations, the TSI and SSI time series are defined as the average of two solar irradiance models that are adapted to CMIP6 needs: an empirical onePublished by Copernicus Publications on behalf of the European Geosciences Union. A new and lower TSI value is recommended: the contemporary solar-cycle average is now 1361.0 W m −2 . The slight negative trend in TSI over the three most recent solar cycles in the CMIP6 dataset leads to only a small global radiative forcing of −0.04 W m −2 . In the 200-400 nm wavelength range, which is important for ozone photochemistry, the CMIP6 solar forcing dataset shows a larger solar-cycle variability contribution to TSI than in CMIP5 (50 % compared to 35 %).We compare the climatic effects of the CMIP6 solar forcing dataset to its CMIP5 predecessor by using timeslice experiments of two chemistry-climate models and a reference radiative transfer model. The differences in the long-term mean SSI in the CMIP6 dataset, compared to CMIP5, impact on climatological stratospheric conditions (lower shortwave heating rates of −0.35 K day −1 at the stratopause), cooler stratospheric temperatures (−1.5 K in the upper stratosphere), lower ozone abundances in the lower stratosphere (−3 %), and higher ozone abundances (+1.5 % in the upper stratosphere and lower mesosphere). Between the maximum and minimum phases of the 11-year solar cycle, there is an increase in shortwave heating rates (+0.2 K day −1 at the stratopause), temperatures (∼ 1 K at the stratopause), and ozone (+2.5 % in the upper stratosphere) in the tropical upper stratosphere using the CMIP6 forcing dataset. This solar-cycle response is slightly larger, but not statistically significantly different from that for the CMIP5 forcing dataset.CMIP6 models wi...

We report on a global magnetohydrodynamical simulation of the solar convection zone, which succeeds in generating a large-scale axisymmetric magnetic component, antisymmetric about the equatorial plane and undergoing regular polarity reversals on decadal timescales. We focus on a specific simulation run covering 175 yr, during which 5 polarity reversals are observed, with a mean period of 32 yr. Time-latitude slices of the zonally-averaged toroidal magnetic component at the base of the convecting envelope show a well-organized toroidal flux system building up in each solar hemisphere, peaking at mid-latitudes and migrating towards the equator in the course of each cycle, in remarkable agreement with inferences based on the sunspot butterfly diagram. The simulation also produces a large-scale dipole moment, varying in phase with the internal toroidal component, suggesting that the simulation may be operating as what is known in mean-field theory as an αΩ dynamo.

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The Sun's magnetic field is the engine and energy source driving all phenomena collectively defining solar activity, which in turn structures the whole heliosphere and significantly impacts Earth's atmosphere down at least to the stratosphere. The solar magnetic field is believed to originate through the action of a hydromagnetic dynamo process operating in the Sun's interior, where the strongly turbulent environment of the convection zone leads to flow-field interactions taking place on an extremely wide range of spatial and temporal scales. Following a necessarily brief observational overview of the solar magnetic field and its cycle, this review on solar dynamo theory is structured around three areas in which significant advances have been made in recent years: (a) global magnetohydrodynamical simulations of convection and magnetic cycles, (b) the turbulent electromotive force and the dynamo saturation problem, and (c) flux transport dynamos, and their application to model cycle fluctuations and grand minima and to carry out cycle prediction.

We investigate the e †ect of stochastic Ñuctuations on a Ñux transport model of the solar cycle based on the Babcock-Leighton mechanism. SpeciÐcally, we make use of our recent Ñux transport model (Dikpati & Charbonneau) to investigate the consequences of introducing large-amplitude stochastic Ñuc-tuations in either or both the meridional Ñow and poloidal source term in the model. Solar cycleÈlike oscillatory behavior persists even for Ñuctuation amplitudes as high as 300%, thus demonstrating the inherent robustness of this class of solar cycle models. We also Ðnd that high-amplitude Ñuctuations lead to a spread of cycle amplitude and duration showing a statistically signiÐcant anticorrelation, comparable to that observed in sunspot data. This is a feature of the solar cycle that is notoriously difficult to reproduce with dynamo models based on mean Ðeld electrodynamics and relying only on nonlinearities associated with the back-reaction of the Lorentz force to produce amplitude modulation. Another noteworthy aspect of our Ñux transport model is the fact that meridional circulation in the convective envelope acts as a "" clock ÏÏ regulating the tempo of the solar cycle ; shorter-than-average cycles are typically soon followed by longer-than-average cycles. In other words, the oscillation exhibits good phase locking, a property that also characterizes the solar activity cycle. This shows up quite clearly in our model, but we argue that it is in fact a generic property of Ñux transport models based on the BabcockLeighton mechanism, and relies on meridional circulation as the primary magnetic Ðeld transport agent.