Effects of spatial resolution on inferences of atmospheric quantities from simulations

Context. Small-scale processes are thought to be important for the dynamics of the solar atmosphere. While numerical resolution fundamentally limits their inclusion in magnetohydronamic (MHD) simulations, real observations at the same nominal resolution should still contain imprints of subresolution effects. This means that the synthetic observables from a simulation of a given resolution might not be directly comparable to real observables at the same resolution. It is thus of interest to investigate how inferences based on synthetic spectra from simulations with different numerical resolutions compare, and whether these differences persist after the spectra have been spatially degraded to a common resolution Aims. We aim to compare synthetic spectra obtained from realistic 3D radiative magnetohydrodynamic (rMHD) simulations run at different numerical resolutions from the same initial atmosphere, using very simple methods for inferring line-of-sight velocities and magnetic fields. Additionally we examine how the differing spatial resolution impacts the results retrieved from the STiC inversion code. Methods. We used the RH 1.5D code to synthesize the photospheric Fe I 617.33 line in local thermodynamic equilibrium (LTE), and the chromospheric Ca II 854.209 line in non-LTE from three MHD simulation snapshots of differing spatial resolution. The simulations were produced by the Bifrost code, using horizontal grid spacing of 6 km, 12 km, and 23 km, respectively. They were started from the exact same atmosphere, and the snapshots were taken after the same exact elapsed time. The spectra obtained from the high-resolution snapshots were spatially degraded to match the lowest resolution. Simple methods, such as the center-of-gravity approach and the weak field approximation, were then used to estimate line-of-sight velocities and magnetic fields for the three cases after degradation. Finally, the spectra were input into the STiC inversion code and the retrieved line-of-sight velocities and magnetic field strengths, as well as the temperatures, from the inversions were compared. Results. We find that while the simple inferences for all three simulations reveal the same large-scale tendencies, the higher resolutions yield more fine-grained structures and more extreme line-of-sight velocities and magnetic fields in concentrated spots even after spatial smearing. We also see indications that the imprints of subresolution effects on the degraded spectra result in systematic errors in the inversions, and that these errors increase with the amount of subresolution effects included. Fortunately, however, we find that successively including more subresolution yields smaller additional effects; that is to say, there is a clear trend of diminishing importance for progressively finer subresolution effects.