Toward a fast and consistent approach to modeling solar magnetic fields in multiple layers

Aims. We aim to develop a fast and consistent extrapolation method for modeling multiple layers of the solar atmosphere. Methods. The new approach combines the magnetohydrostatic (MHS) extrapolation, which models the solar low atmosphere in a flat box, together with the nonlinear force-free field (NLFFF) extrapolation, which models the solar corona with a chromospheric vector magnetogram deduced from the MHS extrapolation. We tested our code with a snapshot of a radiative magnetohydrodynamic simulation of a solar flare and we conducted quantitative comparisons based on several metrics. Results. Following a number of test runs, we found an optimized configuration for the combination of two extrapolations with a 5.8-Mm-high box for the MHS extrapolation and a magnetogram at a height of 1 Mm for the NLFFF extrapolation. The new approach under this configuration has the capability to reconstruct the magnetic fields in multi-layers accurately and efficiently. Based on figures of merit that are used to assess the performance of different extrapolations (NLFFF extrapolation, MHS extrapolation, and the combined one), we find the combined extrapolation reaches the same level of accuracy as the MHS extrapolation and they are both better than the NLFFF extrapolation. The combined extrapolation is moderately efficient for application to magnetograms with high resolution