  One-dimensional, semi-empirical models of the solar atmosphere are widely
employed in numerous contexts within solar physics, ranging from the
determination of element abundances and atomic parameters to studies of the
solar irradiance and from Stokes inversions to coronal extrapolations. These
models provide the physical parameters (i.e. temperature, gas pressure, etc.)
in the solar atmosphere as a function of the continuum optical depth $\tau_{\rm
c}$. The transformation to the geometrical $z$ scale (i.e. vertical coordinate)
is provided via vertical hydrostatic equilibrium. Our aim is to provide
updated, one-dimensional, semi-empirical models of the solar atmosphere as a
function of $z,$ but employing the more general case of three-dimensional
magneto-hydrostatic equilibrium (MHS) instead of vertical hydrostatic
equilibrium (HE). We employed a recently developed Stokes inversion code that,
along with non-local thermodynamic equilibrium effects, considers MHS instead
of HE. This code is applied to spatially and temporally resolved
spectropolarimetric observations of the quiet Sun obtained with the CRISP
instrument attached to the Swedish Solar Telescope. We provide average models
for granules, intergranules, dark magnetic elements, and overall quiet-Sun as a
function of both $\tau_{\rm c}$ and $z$ from the photosphere to the lower
chromosphere. We demonstrate that, in these quiet-Sun models, the effect of
considering MHS instead of HE is negligible. However, employing MHS increases
the consistency of the inversion results before averaging. We surmise that in
regions with stronger magnetic fields (i.e. pores, sunspots, network) the
benefits of employing the magneto-hydrostatic approximation will be much more
palpable.
