Towards Estimating the Solar Meridional Flow and Predicting the 11-yr Cycle Using Advanced Variational Data Assimilation Techniques

Abstract : We present in this work the development of a solar data assimilation method based on an axisymmetric mean field dynamo model and magnetic surface data. Our mid-term goal is to predict the solar quasi cyclic activity. We focus on the ability of our variational data assimilation algorithm to constrain the deep meridional circulation of the Sun based on solar magnetic observations. Within a given assimilation window, the assimilation procedure minimizes the differences between data and the forecast from the model, by finding an optimal meridional circulation in the convection zone, and an optimal initial magnetic field, via a quasi-Newton algorithm. We demonstrate the capability of the technique to estimate the meridional flow by a closed-loop experiment involving 40 years of synthetic, solar-like data. We show that the method is robust in estimating a (stochastic) time-varying flow fluctuating 30% about the average, and that the horizon of predictability of the method is ~ 1 cycle length.