Knowledge of solar irradiance variability is critical to Earths climate models and understanding the solar influence on Earths 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.
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