  We present a new model of total solar irradiance (TSI) based on magnetograms
simulated with a surface flux transport model (SFTM) and the SATIRE (Spectral
And Total Irradiance REconstructions) model. Our model provides daily maps of
the distribution of the photospheric field and the TSI starting from 1878. We
first calculate the magnetic flux on the solar surface emerging in active and
ephemeral regions. The evolution of the magnetic flux in active regions is
computed using a surface flux transport model fed with the observed record of
sunspot group areas and positions. The magnetic flux in ephemeral regions is
treated separately using the concept of overlapping cycles. To model the
ephemeral region cycles, we assume that their length and amplitude are related
to that of the sunspot cycles. We then use a version of the SATIRE model to
compute the TSI. The area coverage and the distribution of different magnetic
features as a function of time, which are required by SATIRE, are extracted
from the simulated magnetograms and the modelled ephemeral region magnetic
flux. Previously computed intensity spectra of the various types of magnetic
features are employed. Our model reproduces the PMOD composite of TSI
measurements starting from 1978 at daily and rotational timescales more
accurately than the previous version of the SATIRE model computing TSI over
this period of time. The simulated magnetograms provide a more realistic
representation of the evolution of the magnetic field on the photosphere and
also allow us to make use of information on the spatial distribution of the
magnetic fields before the times when observed magnetograms were available. We
find that the secular increase in TSI since 1878 is fairly stable to
modifications of the treatment of the ephemeral region magnetic flux.
