Relationship between TIGRE solar S-index and USET Ca <sc>II</sc> K full disk images

Context. Full disk observations of the solar chromosphere in the Ca II K line represent a valuable dataset for studies of solar magnetic activity. The well known S-index is widely used to investigate the magnetic activity of stars, however, its connection to the coverage of stellar magnetic structure is still poorly understood. Aims. We use the archives of full disk Ca II K images taken by the Royal Observatory of Belgium with the Uccle Solar Equatorial Table (USET) to derive the area fraction of the brightest chromospheric structures over the last decade. These data have allowed us to study the end of the solar cycle 24 and the beginning of the solar cycle 25. Our aim is to compare this dataset with the solar S-index from the Telescopio Internacional de Guanajuato Robotico Espectroscopico (TIGRE) lunar spectroscopy to analyze the relationship between a disk coverage index and an integrated spectrum. We also searched for periodic modulations in our two datasets to detect the solar rotation period. Methods. We used more than 2700 days of observations since the beginning of the Ca II K observations with USET in July 2012. We performed a calibration of the images (re-centering and center-to-limb variation correction). The brightest regions of the solar surface (plages and enhanced network) were then segmented using an algorithm based on an intensity threshold. We computed the area fraction over the solar disk and compared it with the S-index from TIGRE. For the detection of periodic modulations, we applied a discrete Fourier power spectrum method to both datasets. Results. A tight linear relationship was found between the USET area fraction and the TIGRE S-index, with an improved correlation obtained in the low-activity regime by considering the enhanced network. In both time series, we detected the modulation caused by the rotation of bright structures on the solar disk. However, this detection is constrained in the case of TIGRE due to its observation strategy. Conclusions. We studied the correlation between the disk coverage with chromospheric structures and the variability of the S-index on an overlapping period of ten years. We concluded that the disk coverage index is a good proxy for the S-index and will be useful in future studies of the magnetic activity of solar-type stars. The USET area fraction dataset is most appropriate for evaluating the solar rotation period and will be used in future works to analyze the impact of the inclination of the stellar rotation axis on the detectability of such periodic modulations in solar-type stars.