Prediction of Sunspot Cycles by Data Assimilation Method

Despite the known general properties of the solar cycles, a reliable forecast of the 11-year sunspot number variations is still a problem. The difficulties are caused by the apparent chaotic behavior of the sunspot numbers from cycle to cycle and by the influence of various turbulent dynamo processes, which are far from understanding. For predicting the solar cycle properties we make an initial attempt to use the Ensemble Kalman Filter (EnKF), a data assimilation method, which takes into account uncertainties of a dynamo model and measurements, and allows to estimate future observational data. We present the results of forecasting of the solar cycles obtained by the EnKF method in application to a low-mode nonlinear dynamical system modeling the solar $\alpha\Omega$-dynamo process with variable magnetic helicity. Calculations of the predictions for the previous sunspot cycles show a reasonable agreement with the actual data. This forecast model predicts that the next sunspot cycle will be significantly weaker (by $\sim 30$) than the previous cycle, continuing the trend of low solar activity.Comment: 10 pages, 3 figure

Mechanism of spontaneous formation of stable magnetic structures on the Sun

One of the puzzling features of solar magnetism is formation of long-living compact magnetic structures; such as sunspots and pores, in the highly turbulent upper layer of the solar convective zone. We use realistic radiative 3D MHD simulations to investigate the interaction between magnetic field and turbulent convection. In the simulations, a weak vertical uniform magnetic field is imposed in a region of fully developed granular convection; and the total magnetic flux through the top and bottom boundaries is kept constant. The simulation results reveal a process of spontaneous formation of stable magnetic structures, which may be a key to understanding of the magnetic self-organization on the Sun and formation of pores and sunspots. This process consists of two basic steps: 1) formation of small-scale filamentary magnetic structures associated with concentrations of vorticity and whirlpool-type motions, and 2) merging of these structures due to the vortex attraction, caused by converging downdrafts around magnetic concentration below the surface. In the resulting large-scale structure maintained by the converging plasma motions, the magnetic field strength reaches ~1.5 kG at the surface and ~6 kG in the interior; and the surface structure resembles solar pores. The magnetic structure remains stable for the whole simulation run of several hours with no sign of decay.Comment: 13 pages, 4 figures, submitted to the Astrophysical Journa

Non-zero phase-shifts of acoustic waves in the lower solar atmosphere measured from realistic simulations and their role in local helioseismology

Previous studies analyzing the evanescent nature of acoustic waves in the lower solar atmosphere, up to 300\,km above the photosphere, have shown an unexpected phase shift of an order of 1\,s between different heights. Those studies investigated the spectral line \ion{Fe}{1} 6173.3\,\AA, commonly used for helioseismic measurements. Such phase-shifts can contribute to a misinterpretation of the measured travel times in local helioseismology, complicating inferences of, e.g., the deep meridional flow. In this study, we carry out phase-shift computations using a simulated, fully radiative, and convective atmosphere from which the \ion{Fe}{1} 6173.3\,\AA\ line is synthesized. The resulting phase-shifts as functions of frequency across multiple heights show non-zero values in evanescent waves, similar to what was found in observational data. Comparing the Doppler-velocities estimated from the synthesized absorption line with the true velocities directly obtained from the simulated plasma motions, we find substantial differences in phase-shifts between the two. This leads us to hypothesize that the non-adiabaticity of the solar atmosphere yields extra phase-shift contributions to Doppler velocities. Finally, computing phase-differences for different viewing angles reveals a systematic center-to-limb variation, similar to what is present in observations. Overall, this study helps to improve our understanding of the physical cause of the helioseismic center-to-limb effect

Data Assimilation and Uncertainties in Early Solar Cycle Predictions

Stochastic nature of solar activity variations together with our limited knowledge of the dynamo mechanism and subsurface dynamics causes uncertainty in predictions of the solar cycle. For improving the physics-based predictions we can take advantage of the mathematical data assimilation approach that allows us to take into account both, observational errors and model uncertainties, and provide estimates of the next solar cycle along with prediction uncertainties. In this study we use the Parker's migratory dynamo model together with the equation of magnetic helicity balance, which reproduces main properties of the sunspot cycles and allow us to minimize discrepancies between the observed global activity variations and the model solution. The test simulation runs show that a reliable prediction can be obtained for two phases of preceding solar cycle: 1) if the polar field reversals shortly after the solar maxima (strong toroidal field and weak poloidal field), and 2) during the solar minima (strongest poloidal and weak toroidal fields). The early estimate of Cycle 25 obtained by this method shows that this cycle will start in 2019 2020, reach the maximum in 2023 2024, and that the mean sunspot number at the maximum will be about 90 (for the v2.0 sunspot number series)

Numerical MHD Simulations of Solar Magnetoconvection and Oscillations in Inclined Magnetic Field Regions

The sunspot penumbra is a transition zone between the strong vertical magnetic field area (sunspot umbra) and the quiet Sun. The penumbra has a fine filamentary structure that is characterized by magnetic field lines inclined toward the surface. Numerical simulations of solar convection in inclined magnetic field regions have provided an explanation of the filamentary structure and the Evershed outflow in the penumbra. In this paper, we use radiative MHD simulations to investigate the influence of the magnetic field inclination on the power spectrum of vertical velocity oscillations. The results reveal a strong shift of the resonance mode peaks to higher frequencies in the case of a highly inclined magnetic field. The frequency shift for the inclined field is significantly greater than that in vertical field regions of similar strength. This is consistent with the behavior of fast MHD waves.Comment: 9 pages, 6 figures, Solar Physics (in press

Solar Activity Modeling: From Subgranular Dynamical Scales to the Solar Cycles

The dynamical effects of solar magnetoconvection span a wide range spatial and temporal scales that extend from the interior to the corona and from fast turbulent motions to global magnetic activity. To study the solar activity on short temporal scales (from minutes to hours), we use 3D radiative MHD simulations that allow us to investigate complex turbulent interactions that drive various phenomena, such as plasma eruptions, spontaneous formation of magnetic structures, funnel-like structures and magnetic loops in the corona, and others. In particular, we focus on multi-scale processes of energy exchange across layers of the solar interior and atmosphere, which contribute to coronal heating and eruptive dynamics. For modeling global-scale activity, we use a data assimilation approach that has demonstrated great potential for building reliable long-term forecasts of solar activity. In particular, it has been shown that the Ensemble Kalman Filter (EnKF) method applied to the Parker-Kleeorin-Ruzmakin dynamo model is capable of predicting solar activity up to one sunspot cycle ahead in time, as well as estimating the properties of the next cycle a few years before it begins. In this presentation, using the available magnetogram data, we discuss development of the methodology and forecast quality criteria (including forecast uncertainties and sources of errors). We demonstrate the influence of observational limitations on prediction accuracy, and we present the EnKF predictions of the upcoming Solar Cycle (25) based on both the sunspot number series and observed magnetic fields and discuss the uncertainties and potential of the data assimilation approach for modeling and forecasting solar activity