  The presence of the magnetic field is critical to transport energy through
the solar atmosphere. The new generation of telescopes will provide new insight
into how the magnetic field arrives into the chromosphere and its role in the
energy balance of the solar atmosphere. We have used a 3D radiative MHD
numerical model of the solar atmosphere with high spatial resolution (4~km)
calculated with the Bifrost code. This code solves the full MHD equations with
non-grey and non-LTE radiative transfer and thermal conduction along magnetic
field lines. The model shows how the lower chromosphere in the internetwork, a
region dominated by magneto-acoustic shocks and where plasma beta is greater
than 1, is able to generate magnetic field in-situ Martinez-Sykora et al 2019.
We have synthesized full-polarimetric Stokes profiles from this model for
several spectral lines formed in the photosphere and the chromosphere. These
synthetic profiles illustrate the types of observables expected from DKIST and
IRIS. Our work provides insight into how to interpret observations from these
observatories. We find that in order to discern the chromospheric magnetic
observables it is crucial to compensate for Doppler shift rather than use fix
wavelength range.
