Context : The study of variations in total solar irradiance ( TSI ) is important for understanding how the Sun affects the Earth ’ s climate .

Aims : Full-disk continuum images and magnetograms are now available for three full solar cycles .
We investigate how modelled TSI compares with direct observations by building a consistent modelled TSI dataset .
The model , based only on changes in the photospheric magnetic flux can then be tested on rotational , cyclical and secular timescales .

Methods : We use Kitt Peak and SoHO/MDI continuum images and magnetograms in the SATIRE-S model to reconstruct TSI over cycles 21-23 .
To maximise independence from TSI composites , SORCE/TIM TSI data are used to fix the one free parameter of the model .
We compare and combine the separate data sources for the model to estimate an uncertainty on the reconstruction and prevent any additional free parameters entering the model .

Results : The reconstruction supports the PMOD composite as being the best historical record of TSI observations , although on timescales of the solar rotation the IRMB composite provides somewhat better agreement .
Further to this , the model is able to account for 92 % of TSI variations from 1978 to 2009 in the PMOD composite and over 96 % during cycle 23 .
The reconstruction also displays an inter-cycle , secular decline of 0.20 ^ { +0.12 } _ { -0.09 } Wm ^ { -2 } between cycle 23 minima , in agreement with the PMOD composite .

Conclusions : SATIRE-S is able to recreate TSI observations on all timescales of a day and longer over 31 years from 1978 .
This is strong evidence that changes in photospheric magnetic flux alone are responsible for almost all solar irradiance variations over the last three solar cycles .