We study the implications of averaging methods with different reference depth
scales for 3D hydrodynamical model atmospheres computed with the Stagger-code.
The temporally and spatially averaged (hereafter denoted as ) models are
explored in the light of local thermodynamic equilibrium (LTE) spectral line
formation by comparing spectrum calculations using full 3D atmosphere
structures with those from averages. We explore methods for computing mean
stratifications from the Stagger-grid time-dependent 3D radiative hydro-
dynamical atmosphere models by considering four different reference depth
scales (geometrical depth, column-mass density, and two optical depth scales).
Furthermore, we investigate the influence of alternative averages (logarithmic
or enforced hydrostatic equilibrium, flux-weighted temperatures). For the line
formation we compute curves of growth for Fe i and Fe ii lines in LTE . The
resulting stratifications for the four reference depth scales can be
considerably different. We find typically that in the upper atmosphere and in
the superadiabatic region just below the optical surface, where the temperature
and density fluctuations are highest, the differences become considerable and
increase for higher Teff, lower logg, and lower [Fe/H]. The differential
comparison of spectral line formation shows distinctive differences depending
on which model is applied. The averages over layers of constant
column-mass density yield the best mean representation for LTE line
formation, while the averages on layers at constant geometrical height are the
least appropriate. Unexpectedly, the usually preferred averages over layers of
constant optical depth are prone to the increasing interference of the reversed
granulation towards higher effective temperature, in particular at low
metallicity.Comment: Accepted for publication in A&A, 18 pages, 16 figure