  The apparently unusual behaviour of the TSI during the most recent minimum of
solar activity has been interpreted as evidence against solar surface magnetism
as the main driver of the secular change in the TSI. We test claims that the
evolution of the solar surface magnetic field does not reproduce the observed
TSI in cycle 23. We use sensitive, 60-minute averaged MDI magnetograms and
quasi-simultaneous continuum images as an input to our SATIRE-S model and
calculate the TSI variation over cycle 23, sampled roughly twice-monthly. The
computed TSI is then compared to the PMOD composite of TSI measurements and to
the data from two individual instruments, SORCE/TIM and UARS/ACRIM II, that
monitored the TSI during the declining phase of cycle 23 and over the previous
minimum in 1996, respectively. Excellent agreement is found between the trends
shown by the model and almost all sets of measurements. The only exception is
the early, i.e. 1996 to 1998, PMOD data. Whereas the agreement between the
model and the PMOD composite over the period 1999-2009 is almost perfect, the
modelled TSI shows a steeper increase between 1996 and 1999 than implied by the
PMOD composite. On the other hand, the steeper trend in the model agrees
remarkably well with the ACRIM II data. A closer look at the VIRGO data, that
make the basis of the PMOD composite after 1996, reveals that only one of the
two VIRGO instruments, the PMO6V, shows the shallower trend present in the
composite, whereas the DIARAD measurements indicate a steeper trend. We
conclude that (1) the sensitivity changes of the PMO6V radiometers within VIRGO
during the first two years have very likely not been correctly evaluated, and
that (2) the TSI variations over cycle 23 and the change in the TSI levels
between the minima in 1996 and 2008 are consistent with the solar surface
magnetism mechanism.
