Casting the Coronal Magnetic Field Reconstructions with Magnetic Field Constraints above the Photosphere in 3D Using MHD Bifrost Model

Measuring and modeling coronal magnetic field, especially above active regions (ARs), remains one of the central problems of solar physics given that the solar coronal magnetism is the key driver of all solar activity. Nowadays the coronal magnetic field is often modelled using methods of nonlinear force-free field reconstruction, whose accuracy has not yet been comprehensively assessed. Given that the coronal magnetic probing is routinely unavailable, only morphological tests have been applied to evaluate performance of the reconstruction methods and a few direct tests using available semi-analytical force-free field solution. Here we report a detailed casting of various tools used for the nonlinear force-free field reconstruction, such as disambiguation methods, photospheric field preprocessing methods, and volume reconstruction methods in a 3D domain using a 3D snapshot of the publicly available full-fledged radiative MHD model. We take advantage of the fact that from the realistic MHD model we know the magnetic field vector distribution in the entire 3D domain, which enables us to perform "voxel-by-voxel" comparison of the restored magnetic field and the true magnetic field in the 3D model volume. Our tests show that the available disambiguation methods often fail at the quiet sun areas, where the magnetic structure is dominated by small-scale magnetic elements, while they work really well at the AR photosphere and (even better) chromosphere. The preprocessing of the photospheric magnetic field, although does produce a more force-free boundary condition, also results in some effective `elevation' of the magnetic field components. The effective `elevation' height turns out to be different for the longitudinal and transverse components of the magnetic field, which results in a systematic error in absolute heights in the reconstructed magnetic data cube. The extrapolation performed starting from actual AR photospheric magnetogram (i.e., without preprocessing) are free from this systematic error, while have other metrics either comparable or only marginally worse than those estimated for extrapolations from the preprocessed magnetograms. This finding favors the use of extrapolations from the original photospheric magnetogram without preprocessing.