  Realistic atmospheric models that link the properties and the physical
conditions of supernova ejecta to observable spectra are required for the
quantitative interpretation of observational data of type Ia supernovae (SN Ia)
and the assessment of the physical merits of theoretical supernova explosion
models. The numerical treatment of the radiation transport - yielding the
synthetic spectra - in models of SN Ia ejecta in early phases is usually
carried out in analogy to atmospheric models of `normal' hot stars. Applying
this analogy indiscriminately leads to inconsistencies in SN Ia models because
a diffusive lower boundary, while justified for hot stars, is invalid for
hydrogen and helium-deficient supernova ejecta. In type Ia supernovae the
radiation field does not thermalize even at large depths, and large optical
depths are not reached at all wavelengths. We derive an improved description of
the lower boundary that allows a more consistent solution of the radiation
transfer in SN Ia and therefore yields more realistic synthetic spectra. We
analyze the conditions that lead to a breakdown of the conventional diffusion
approximation as the lower boundary in SN Ia. For the radiative transfer, we
use a full non-LTE code originally developed for radiatively driven winds of
hot stars, with adaptations for the physical conditions in SN Ia. In addition
to a well-tested treatment of the underlying microphysical processes, this code
allows a direct comparison of the results for SN Ia and hot stars. We develop a
semi-analytical description that allows us to overcome some of the limiting
assumptions in the conventional treatment of the lower boundary in SN Ia
radiative transfer models. We achieve good agreement in a comparison between
the synthetic spectrum of our test model and an observed spectrum.
