We have calculated the models presented in this paper using our
multipurpose model atmosphere code `PHOENIX`, version 10.5. Details of the code and the
general input physics setup are discussed in and and
references therein. The model atmospheres for Cepheids
presented here were calculated with the same general input physics. However,
they use spherical geometry (including spherically symmetric radiative
transfer) rather than plane parallel geometry.
For giant models with low gravities (), this can be
important for the correct calculation of the structure of the model
atmosphere and the synthetic spectrum .

Our combined molecular line list includes about 500 million molecular lines.
These lines are treated with a direct opacity sampling technique where each
line has its individual Voigt (for strong lines) or Gauss (weak lines) line
profile. The lines are selected for every model from the master line list at
the beginning of each model iteration to account for changes in the model
structure .
This procedure selects about 190
million molecular lines for a typical giant model atmosphere with .Accordingly, we generally use the parallelized version of `PHOENIX` to perform calculations efficiently on parallel
supercomputers. Details of the calculations are given in the above references
and are not repeated here.

The parameterization of giant models requires an additional parameter compared
to plane parallel model atmospheres. This complicates the task of relating
theoretical models to observed data, see for a discussion of these
issues. In the models presented here, we set the stellar radius *R* by the
condition , where we define as the
gravitational acceleration at , *G* is the constant of gravity, and
is the optical depth in the continuum at . The luminosity
*L* of the model is then given by . For convenience,
our model grid is based on the set of parameters . The
above formulae and the structures of the model atmospheres can be used to
transform them to any target set of parameters (e.g., for a different
definition of ).

for a discussion of these
issues. In the models presented here, we set the stellar radius *R* by the
condition , where we define as the
gravitational acceleration at , *G* is the constant of gravity, and
is the optical depth in the continuum at . The luminosity
*L* of the model is then given by . For convenience,
our model grid is based on the set of parameters . The
above formulae and the structures of the model atmospheres can be used to
transform them to any target set of parameters (e.g., for a different
definition of ).