  Cool giant and supergiant stars are among the largest and most luminous stars
in the Universe and, therefore, dominate the integrated light of their host
galaxies. These stars were extensively studied during last few decades, however
their photometric variability and mass loss are still poorly constrained. The
atmospheres of evolved stars are characterized by complex dynamics due to
different interacting processes, such as convection, pulsation, formation of
molecules and dust, and the development of mass loss. These dynamical processes
impact the formation of spectral lines producing their asymmetries and Doppler
shifts. Thus, by studying the line-profile variations on spatial and temporal
scales it is possible to reconstruct atmospheric motions in stars and link them
to the photometric variability and mass loss. The tomographic method, which is
based on the cross-sectioning through the stellar atmosphere and recovering the
velocity field for each atmospheric slice, is an ideal technique for this
purpose. We present the tomographic method and its application to spectroscopic
and spectro-interferometric observations of giant and supergiant stars as well
as to state-of-the-art three-dimensional numerical simulations to constrain
their atmospheric motions on spatial and temporal scales and better understand
respective mechanisms responsible for their photometric variability and mass
loss.
