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We present in this work the development of a solar data assimilation methodbased on an axisymmetric mean field dynamo model and magnetic surface data, ourmid-term goal is to predict the solar quasi cyclic activity. Here we focus onthe ability of our algorithm to constrain the deep meridional circulation ofthe Sun based on solar magnetic observations. To that end, we develop avariational data assimilation technique. Within a given assimilation window,the assimilation procedure minimizes the differences between data and theforecast from the model, by finding an optimal meridional circulation in theconvection zone, and an optimal initial magnetic field, via a quasi-Newtonalgorithm. We demonstrate the capability of the technique to estimate themeridional flow by a closed-loop experiment involving 40 years of synthetic,solar-like data. By assimilating the synthetic magnetic proxies annually, weare able to reconstruct a (stochastic) time-varying meridional circulationwhich is also slightly equatorially asymmetric. We show that the method isrobust in estimating a flow whose level of fluctuation can reach 30% about theaverage, and that the horizon of predictive capability of the method is of theorder of 1 cycle length.

Variational estimation of the large scale time dependent meridional circulation in the Sun: proofs of concept with a solar mean field dynamo model