ZZ Ceti stars are variable DA white dwarfs (WDs) with effective
temperatures 
. Their amplitudes range from
to 
. The pulsations are non-radial g
modes with periods of the order of 
. A well-known
property of g modes is that radius variations are negligible because
of the high surface gravity ( 
) of WDs (Robinson et al. 1982;
hereafter RKN). Therefore, one can think of these oscillations as
temperature waves.
Recently, Brassard et al. (1995; hereafter BFW) calculated spectra
semi-analytically for temperature distributions across the surface
expressed as 
where 
is
a sum of spherical harmonics. The aim of this analysis was to
investigate non-linear effects that occur since the specific intensity
I is not a linear function of 
. We have developed a
program that calculates the time-variable spectrum by integrating I
over the visible disk of the WD for a distribution of
across the WD surface. For now, we use for an expression
similar to that of BFW. However, we can adapt our program to
non-linear variations of , which were suggested by
Brickhill (1992) and could be caused by the response of the convective
flux to linear pressure perturbations in deeper layers of these
stars. We interpolate I from a grid containing I as a function of
, 
, , and different
parametrizations of the mixing length theory (MLT). The grid was
calculated with a stellar atmospheres code.