  Standard spectroscopic analyses of variable stars are based on hydrostatic
one-dimensional model atmospheres. This quasi-static approach has theoretically
not been validated. We aim at investigating the validity of the quasi-static
approximation for Cepheid variables. We focus on the spectroscopic
determination of the effective temperature $T_\mathrm{eff}$, surface gravity
$\log \,g$, microturbulent velocity $\xi_\mathrm{t}$, and a generic metal
abundance $\log\,A$ -- here taken as iron. We calculate a grid of 1D
hydrostatic plane-parallel models covering the ranges in effective temperature
and gravity encountered during the evolution of a two-dimensional
time-dependent envelope model of a Cepheid computed with the
radiation-hydrodynamics code CO5BOLD. We perform 1D spectral syntheses for
artificial iron lines in local thermodynamic equilibrium varying the
microturbulent velocity and abundance. We fit the resulting equivalent widths
to corresponding values obtained from our dynamical model. For the
four-parametric case, the stellar parameters are typically underestimated
exhibiting a bias in the iron abundance of $\approx-0.2\,\mbox{dex}$. To avoid
biases of this kind it is favourable to restrict the spectroscopic analysis to
photometric phases $\phi_\mathrm{ph}\approx0.3\ldots 0.65$ using additional
information to fix effective temperature and surface gravity. Hydrostatic 1D
model atmospheres can provide unbiased estimates of stellar parameters and
abundances of Cepheid variables for particular phases of their pulsations. We
identified convective inhomogeneities as the main driver behind potential
biases. For obtaining a complete view on the effects when determining stellar
parameters with 1D models, multi-dimensional Cepheid atmosphere models are
necessary for variables of longer period than investigated here.
