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We study the implications of averaging methods with different reference depthscales for 3D hydrodynamical model atmospheres computed with the Stagger-code.The temporally and spatially averaged (hereafter denoted as <3D>) models areexplored in the light of local thermodynamic equilibrium (LTE) spectral lineformation by comparing spectrum calculations using full 3D atmospherestructures with those from <3D> averages. We explore methods for computing mean<3D> stratifications from the Stagger-grid time-dependent 3D radiative hydro-dynamical atmosphere models by considering four different reference depthscales (geometrical depth, column-mass density, and two optical depth scales).Furthermore, we investigate the influence of alternative averages (logarithmicor enforced hydrostatic equilibrium, flux-weighted temperatures). For the lineformation we compute curves of growth for Fe i and Fe ii lines in LTE . Theresulting <3D> stratifications for the four reference depth scales can beconsiderably different. We find typically that in the upper atmosphere and inthe superadiabatic region just below the optical surface, where the temperatureand density fluctuations are highest, the differences become considerable andincrease for higher Teff, lower logg, and lower [Fe/H]. The differentialcomparison of spectral line formation shows distinctive differences dependingon which <3D> model is applied. The averages over layers of constantcolumn-mass density yield the best mean <3D> representation for LTE lineformation, while the averages on layers at constant geometrical height are theleast appropriate. Unexpectedly, the usually preferred averages over layers ofconstant optical depth are prone to the increasing interference of the reversedgranulation towards higher effective temperature, in particular at lowmetallicity.

The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - II. Horizontal and Temporal Averaging and Spectral Line Formation