  We show how magnetic observations of the Sun can be used in conjunction with
an axisymmetric flux-transport solar dynamo model in order to estimate the
large-scale meridional circulation throughout the convection zone. Our
innovative approach rests on variational data assimilation, whereby the
distance between predictions and observations (measured by an objective
function) is iteratively minimized by means of an optimization algorithm
seeking the meridional flow which best accounts for the data. The minimization
is performed using a quasi-Newton technique, which requires the knowledge of
the sensitivity of the objective function to the meridional flow. That
sensitivity is efficiently computed via the integration of the adjoint
flux-transport dynamo model. Closed-loop (also known as twin) experiments using
synthetic data demonstrate the validity and accuracy of this technique, for a
variety of meridional flow configurations, ranging from unicellular and
equatorially symmetric to multicellular and equatorially asymmetric. In this
well-controlled synthetic context, we perform a systematic study of the
behavior of our variational approach under different observational
configurations, by varying their spatial density, temporal density, noise
level, as well as the width of the assimilation window. We find that the method
is remarkably robust, leading in most cases to a recovery of the true
meridional flow to within better than 1%. These encouraging results are a first
step towards using this technique to i) better constrain the physical processes
occurring inside the Sun and ii) better predict solar activity on decadal time
scales.
