  The Ca II H & K lines are strong chromospheric diagnostics that can be used
to determine the temperature stratification and magnetic structure of the solar
atmosphere. The Atacama Large Millimetre/Submillimetre Array (ALMA) offers
complementary information on the thermal structure of stellar atmospheres using
mm continuum radiation. The overall aim is to establish more robust
solar/stellar activity indicators using ALMA observations in comparison with
classical diagnostics, such as the s index and infrared triplet (IRT) index. A
study was conducted using 1.5D radiative transfer codes RH1.5D and advanced
radiative transfer (ART), along with an enhanced network atmosphere model
generated by the state-of-the-art 3D radiation magnetohydrodynamics (rMHD)
Bifrost code, to compute synthetic spectra for both Ca II lines and mm
continua. To account for the limited spatial resolution of ALMA, we simulated
the effect using a Gaussian point spread function (PSF). Additionally, we
analysed the correlations and slopes of scatter plots between the Ca II indices
and mm continuum for the original and degraded resolutions, focusing on the
entire simulation box, quiet Sun regions, and enhanced network patches
separately. The activity indices generated from these lines could further be
used to compare the spectra of Sun-like stars with the solar spectrum. The Ca
II activity indices and mm brightness temperatures are weakly correlated at the
high resolution, with the highest correlation observed at a wavelength of 0.3
mm, corresponding to ALMA band 10. As the resolution decreases, the correlation
consistently increases. Conversely, the slopes exhibit a decreasing trend with
increasing wavelength, while the degradation of resolution does not noticeably
affect the calculated slopes. Consequently, these relationships could be
valuable for calibrating the mm continuum maps obtained through ALMA
observations.
