  Context. Solar spectral irradiance (SSI) variability is one of the key inputs
to models of the Earth's climate. Understanding solar irradiance fluctuations
also helps to place the Sun among other stars in terms of their brightness
variability patterns and to set detectability limits for terrestrial
exo-planets.
  Aims. One of the most successful and widely used models of solar irradiance
variability is SATIRE-S. It uses spectra of the magnetic features and
surrounding quiet Sun computed with the ATLAS9 spectral synthesis code under
the assumption of Local Thermodynamic Equilibrium (LTE). SATIRE-S has been at
the forefront of solar variability modelling, but due to the limitations of the
LTE approximation its output SSI has to be empirically corrected below 300 nm,
which reduces the physical consistency of its results. This shortcoming is
addressed in the present paper.
  Methods. We replace the ATLAS9 spectra of all atmospheric components in
SATIRE-S with the spectra calculated using the non-LTE Spectral Synthesis Code
(NESSY). We also use Fontenla et al. (1999) temperature and density
stratification models of the solar atmosphere to compute the spectrum of the
quiet Sun and faculae.
  Results. We compute non-LTE contrasts of spots and faculae and combine them
with the SDO/HMI filling factors of the active regions to calculate the total
and spectral solar irradiance variability during solar cycle 24.
  Conclusions. The non-LTE contrasts result in total and spectral solar
irradiance in good agreement with the empirically corrected output of the LTE
version. This suggests that empirical correction introduced into SATIRE-S
output is well judged and that the corrected total and spectral solar
irradiance obtained from the SATIRE-S model in LTE is fully consistent with the
results of non-LTE computations.
