  Knowledge of solar irradiance variability is critical to Earth's climate
models and understanding the solar influence on Earth's climate. Direct solar
irradiance measurements are only available since 1978. Reconstructions of past
variability typically rely on sunspot data. These provide only indirect
information on the facular and network regions, which are decisive contributors
to irradiance variability on timescales of the solar cycle and longer. Our
ultimate goal is to reconstruct past solar irradiance variations using
historical full-disc Ca II K observations to describe the facular contribution
independently of sunspot observations. Here, we develop the method and test it
extensively by using modern CCD-based Ca II K observations and carry out
initial tests on two photographic archives. We employ carefully reduced and
calibrated Ca II K images from 13 datasets, such as those from the Meudon, Mt
Wilson, and Rome observatories. We convert them to unsigned magnetograms and
then use them as input to the adapted SATIRE model to reconstruct TSI
variations over the period 1978-2019, for which direct irradiance measurements
are available. The reconstructed TSI from the analysed Ca II K archives agrees
well with direct TSI measurements and existing reconstructions. The model also
returns good results on data taken with different bandpasses and images with
low spatial resolution. Historical Ca II K archives suffer from numerous
inconsistencies, but we show that these archives can still be used to
reconstruct TSI with reasonable accuracy provided the observations are
accurately processed. By using the unsigned magnetograms of the Sun
reconstructed from high-quality Ca II K observations as input into the SATIRE
model, we can reconstruct solar irradiance variations nearly as accurately as
from directly recorded magnetograms.
