  In this work, we study the accuracy that can be achieved when inferring the
atmospheric information from realistic numerical magneto-hydrodynamic
simulations that reproduce the spatial resolution we will obtain with future
observations made by the 4m class telescopes DKIST and EST. We first study
multiple inversion configurations using the SIR code and the Fe I transitions
at 630 nm until we obtain minor differences between the input and the inferred
atmosphere in a wide range of heights. Also, we examine how the inversion
accuracy depends on the noise level of the Stokes profiles. The results
indicate that when the majority of the inverted pixels come from strongly
magnetised areas, there are almost no restrictions in terms of the noise,
obtaining good results for noise amplitudes up to 1$\times10^{-3}$ of $I_c$. At
the same time, the situation is different for observations where the dominant
magnetic structures are weak, and noise restraints are more demanding.
Moreover, we find that the accuracy of the fits is almost the same as that
obtained without noise when the noise levels are on the order of
1$\times10^{-4}$of $I_c$. We, therefore, advise aiming for noise values on the
order of or lower than 5$\times10^{-4}$ of $I_c$ if observers seek reliable
interpretations of the results for the magnetic field vector reliably. We
expect those noise levels to be achievable by next-generation 4m class
telescopes thanks to an optimised polarisation calibration and the large
collecting area of the primary mirror.
