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