Modelling magneto-hydro-static equilibria in quiet Sun regions

The solar magnetic field is measured routinely only
in the solar photosphere. While reliable measurements
of the photospheric magnetic field vector are only available
in active regions, in the quiet Sun at present only
 the vertical component of the magnetic field can be obtained accurately.
 To derive magnetic field structures throughout the solar atmosphere, from
 the chromosphere to the corona, we extrapolate these photospheric measurements
into the upper photosphere, chromosphere and corona with a magneto-hydro-static
model. We optimize free model parameters by comparing the modelled magnetic
field lines with structures observed in solar images. The comparison is
done automatically with a number of quantitative measurements and
the optimal model parameters are found with the help of
a downhill simplex minimization. This newly developed modelling approach can
provide an accurate and deep understanding of the magnetic field structures
that extend to any height in the solar atmosphere.