Variational Estimation of the Large-scale Time-dependent Meridional Circulation in the Sun: Proofs of Concept with a Solar Mean Field Dynamo Model

Abstract

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 midterm goal is to predict quasi-cyclic solar 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 the 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 through a closed-loop experiment involving 40 years of synthetic, solar-like data. By assimilating the synthetic magnetic proxies, we are able to reconstruct a (stochastic) time-varying meridional circulation that 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 one cycle length.