Context :

Aims : We investigate the impact of realistic three-dimensional ( 3D ) hydrodynamical model atmospheres of red giant stars at different metallicities on the formation of spectral lines of a number of ions and molecules .

Methods : We carry out realistic , ab initio , 3D , hydrodynamical simulations of surface convection at the surface of red giant stars with varying effective temperatures and metallicities .
We use the convection simulations as time-dependent hydrodynamical model stellar atmospheres to calculate spectral lines for a number of atomic ( Li i , O i , Na i , Mg i , Ca i , Fe i , and Fe ii ) and molecular ( CH , NH , and OH ) lines under the assumption of local thermodynamic equilibrium ( LTE ) .
We carry out a differential comparison of the line strengths computed in 3D with the results of analogous line formation calculations for classical , 1D , hydrostatic , plane-parallel marcs model atmospheres in order to estimate the impact of 3D models on the derivation of elemental abundances .

Results : The temperature and density inhomogeneities and correlated velocity fields in 3D models , as well as the differences between the mean 3D stratifications and corresponding 1D model atmospheres significantly affect the predicted strengths of spectral lines .
Under the assumption of LTE , the low atmospheric temperatures encountered in 3D model atmospheres of very metal-poor giant stars cause spectral lines from neutral species and molecules to appear stronger than within the framework of 1D models .
As a consequence , elemental abundances derived from these lines using 3D models are significantly lower than according to 1D analyses .
In particular , the differences between 3D and 1D abundances of C , N , and O derived from CH , NH , and OH weak low-excitation lines are found to be in the range -0.5 dex to -1.0 dex for the the red giant stars at [ \mathrm { Fe / H } ] = -3 considered here .
At this metallicity , large negative corrections ( about -0.8 dex ) are also found , in LTE , for weak low-excitation Fe i lines .
We caution , however , that the neglected departures from LTE might be significant for these and other elements and comparable to the effects due to stellar granulation .

Conclusions :