Modelling the coronal magnetic field using hinode (and future) data

There is considerable interest in accurate modelling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data, and the nonlinear force-free model is often used. However, recent studies using Hinode data have demonstrated that this modelling fails in basic ways, with the failure attributable to the departure of the inferred photospheric magnetic field from a force free state. The solar boundary data are inconsistent with the model, which leads to inconsistencies in calculated force-free solutions. A method for constructing a self-consistent nonlinear force-free solution is described, which identifies a force free solution that is close to the observed boundary data. Steps towards developing more sophisticated magnetohydrostatic modelling taking into account pressure and gravitational forces at the level of the solar boundary data are also outlined.