Solar magnetic activity and total irradiance since the maunder minimum

We develop a model for estimating solar total irradiance since 1600 AD using the sunspot number record as input, since this is the only intrinsic record of solar activity extending back far enough in time. Sunspot number is strongly correlated, albeit nonlinearly with the 10.7-cm radio flux (F (10.7)), which forms a continuous record back to 1947. This enables the nonlinear relationship to be estimated with usable accuracy and shows that relationship to be consistent over multiple solar activity cycles. From the sunspot number record we estimate F (10.7) values back to 1600 AD. F (10.7) is linearly correlated with the total amount of magnetic flux in active regions, and we use it as input to a simple cascade model for the other magnetic flux components. The irradiance record is estimated by using these magnetic flux components plus a very rudimentary model for the modulation of energy flow to the photosphere by the subphotospheric magnetic flux reservoir feeding the photospheric magnetic structures. Including a Monte Carlo analysis of the consequences of measurement and fitting errors, the model indicates the mean irradiance during the Maunder Minimum was about 1 +/- 0.4 Wm(-2) lower than the mean irradiance over the last solar activity cycle.