<p>Solar irradiance is a crucial input to climate models, but its measurements are only available since 1978. The variability of solar irradiance on climate-relevant time-scales is caused by the competition between bright and dark features formed by the magnetic fields emerging on the solar surface. Thus, models have been developed that reconstruct past irradiance variability from proxies of the solar magnetic activity. The longest direct proxy is the sunspot number. The common problem of such reconstructions is, however, that while sunspots adequately describe the evolution of the active regions (ARs) (large bipolar regions hosting sunspots), the evolution of their smaller counterparts, the ephemeral regions (ERs), is not directly featured by sunspots. At the same time, these small regions are much more numerous and are believed to be the main source of the long-term irradiance changes, which are of special interest to climate models. We develop an improved description of the ephemeral region emergence taking different solar observational constraints into account. The model builds on the SATIRE-T model, in which the emergence of ARs is described by the sunspot number and the emergence of the ERs is linearly linked to that of ARs. The latter, however, implies that whenever the sunspot number drops to zero, no magnetic field emerges in the model. In the new model, the emergence of the ERs is no longer linked to sunspots linearly. Instead, ARs and ERs are considered to be parts of a single power-law size distribution of the emerging magnetic regions. This ensures that even in the absence of ARs (e.g., during the grand minima of solar activity), the emergence rate of ERs remains non-zero. In particular, the solar open magnetic flux reconstructed using this approach does not drop to zero during the Maunder minimum, in agreement with independent reconstructions from the cosmogenic isotope data. Such an improved description of the ERs will allow a better constraint on the maximum solar irradiance drop during grand minima events. This, in turn, will allow a better constraint on the potential solar forcing in the future.</p>
A model for grand minima and geomagnetic reversals
