  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. Here we focus on
the ability of our algorithm to constrain the deep meridional circulation of
the Sun based on solar magnetic observations. To that end, we develop a
variational data assimilation technique. 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. By assimilating the synthetic magnetic proxies annually, we
are able to reconstruct a (stochastic) time-varying meridional circulation
which is also slightly equatorially asymmetric. We show that the method is
robust in estimating a flow whose level of fluctuation can reach 30% about the
average, and that the horizon of predictive capability of the method is of the
order of 1 cycle length.
