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We aim to compare and contrast the typical shapes of synthetic Ca II 854.2 nmspectra found in Bifrost simulations having different magnetic activity withthe spectral shapes found in a quiet Sun observation from the Swedish 1-m SolarTelescope (SST). We use clustering techniques to extract the typical Ca II854.2 nm profile shapes synthesized from Bifrost simulations with varyingamounts of magnetic activity. We degrade the synthetic profiles toobservational conditions and repeat the clustering, and we compare oursynthetic results with actual observations. While the mean spectra for our highresolution simulations compare reasonably well with the observations, we findthat there are considerable differences between the clusters of observed andsynthetic intensity profiles, even after the synthetic profiles have beendegraded. The typical absorption profiles from the simulations are bothnarrower and display a steeper transition from the inner wings to the linecore. Furthermore, even in our most quiescent simulation we find a far largerfraction of profiles with local emission around the core, or other exoticprofile shapes, than in the observations. Looking into the atmosphericstructure for a selected set of synthetic clusters, we find distinctdifferences in the temperature stratification for the clusters most and leastsimilar to the observations. The narrow and steep profiles are associated witheither weak gradients in temperature, or temperatures rising to a local maximumin the line wing forming region before sinking to a minimum in the line coreforming region. The profiles that display less steep transitions show extendedtemperature gradients that are steeper in the range $-3 \lesssim \log\tau_{5000} \lesssim -1$.

Comparative clustering analysis of Ca II 854.2 nm spectral profiles from simulations and observations