  Recent precise observations of solar global parameters are used to calibrate
an upgraded solar model which takes into account magnetic fields in the solar
interior. Historical data about sunspot numbers (from 1500 to the present) and
solar radius changes (between 1715 and 1979) are used to compute solar
variability on years to centuries timescales. The results show that although
the 11 year variability of the total irradiance is of the order of 0.1%,
additional, longer lived changes of the order of 0.1% may have occurred in the
past centuries. These could, for example, account for the occurrence of climate
excursions such as little ice ages.
