A variational approach to Data Assimilation in the Solar Wind

Variational Data Assimilation (DA) has enabled huge improvements in the skill of operational weather forecasting. In this study, we use a simple solar-wind propagation model to develop the first solar-wind variational DA scheme. This scheme enables solar-wind observations far from the Sun, such as at 1 AU, to update and improve the inner boundary conditions of the solar wind model (at $30$ solar radii). In this way, observational information can be used to improve estimates of the near-Earth solar wind, even when the observations are not directly downstream of the Earth. Using controlled experiments with synthetic observations we demonstrate this method's potential to improve solar wind forecasts, though the best results are achieved in conjunction with accurate initial estimates of the solar wind. The variational DA scheme is also applied to STEREO in-situ observations using initial solar wind conditions supplied by a coronal model of the observed photospheric magnetic field. We consider the period Oct 2010-Oct 2011, when the STEREO spacecraft were approximately $80^{\circ}$ ahead/behind Earth in its orbit. For 12 of 13 Carrington Rotations, assimilation of STEREO data improves the near-Earth solar wind estimate over the non-assimilated state, with a $18.4\%$ reduction in the root-mean-squared-error. The largest gains are made by the DA during times when the steady-state assumption of the coronal models breaks down. While applying this pure variational approach to complex solar-wind models is technically challenging, we discuss hybrid DA approaches which are simpler to implement and may retain many of the advantages demonstrated here.