  Chromospheric umbral oscillations produce periodic brightenings in the core
of some spectral lines, known as umbral flashes. They are also accompanied by
fluctuations in velocity, temperature, and, according to several recent works,
magnetic field. In this study, we aim to ascertain the accuracy of the magnetic
field determined from inversions of the Ca II 8542 \AA\ line. We have developed
numerical simulations of wave propagation in a sunspot umbra. Synthetic Stokes
profiles emerging from the simulated atmosphere were computed and then inverted
using the NICOLE code. The atmospheres inferred from the inversions have been
compared with the original parameters from the simulations. Our results show
that the inferred chromospheric fluctuations in velocity and temperature match
the known oscillations from the numerical simulation. In contrast, the vertical
magnetic field obtained from the inversions exhibits an oscillatory pattern
with a $\sim$300 G peak-to-peak amplitude which is absent in the simulation. We
have assessed the error in the inferred parameters by performing numerous
inversions with slightly different configurations of the same Stokes profiles.
We find that when the atmosphere is approximately at rest, the inversion tends
to favor solutions that underestimate the vertical magnetic field strength. On
the contrary, during umbral flashes, the values inferred from most of the
inversions are concentrated at stronger fields than those from the simulation.
Our analysis provides a quantification of the errors associated with the
inversions of the Ca II 8542 \AA\ line and suggests caution with the
interpretation of the inferred magnetic field fluctuations.
